From 33794f2f06a24716da6d7ef348a53bd743cfaabb Mon Sep 17 00:00:00 2001 From: Jeff Hanson Date: Thu, 2 Dec 2021 12:24:02 +1300 Subject: [PATCH] Update vignettes (#216) Update vignettes Rebuild sites Tweak grammar in some docs --- DESCRIPTION | 2 +- NEWS.md | 7 + R/ConservationProblem-proto.R | 4 +- R/Parameter-proto.R | 2 +- R/ScalarParameter-proto.R | 2 +- R/add_absolute_targets.R | 2 +- R/add_binary_decisions.R | 6 +- R/add_boundary_penalties.R | 24 +- R/add_cbc_solver.R | 4 +- R/add_connectivity_penalties.R | 16 +- R/add_contiguity_constraints.R | 16 +- R/add_cplex_solver.R | 6 +- R/add_cuts_portfolio.R | 6 +- R/add_default_decisions.R | 2 +- R/add_default_portfolio.R | 2 +- R/add_default_solver.R | 2 +- R/add_extra_portfolio.R | 4 +- R/add_feature_contiguity_constraints.R | 12 +- R/add_feature_weights.R | 14 +- R/add_gap_portfolio.R | 9 +- R/add_gurobi_solver.R | 12 +- R/add_linear_constraints.R | 14 +- R/add_linear_penalties.R | 14 +- R/add_locked_in_constraints.R | 6 +- 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vignettes/package_overview.Rmd delete mode 100644 vignettes/saltspring.Rmd rename vignettes/{solver_benchmark.Rmd => solver_benchmarks.Rmd} (77%) delete mode 100644 vignettes/tasmania.Rmd diff --git a/DESCRIPTION b/DESCRIPTION index 8f0ff20d9..e279d18da 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,6 +1,6 @@ Package: prioritizr Type: Package -Version: 7.1.1.4 +Version: 7.1.1.5 Title: Systematic Conservation Prioritization in R Description: Systematic conservation prioritization using mixed integer linear diff --git a/NEWS.md b/NEWS.md index 843a54e96..00444d87b 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,3 +1,10 @@ +# prioritizr 7.1.1.5 + +- The _Tasmania tutorial_ has been reworked into the _Getting started_ tutorial. This tutorial now provides short introduction to using the package. +- The _Salt Spring Island tutorial_ has been reworked into the _Connectivity tutorial_. This tutorial now explores different approaches for incorporating connectivity. +- The _prioritizr_ vignette has been renamed to the _Package overview_ vignette. +- New _Calibrating trade-offs tutorial_ showcasing methods for running calibration analyses. It outlines blended and hierarchical approaches for generating a set of different prioritizations based on different parameters. It also covers different approaches for selecting a candidate prioritization based on different trade-offs. + # prioritizr 7.1.1.4 - Update tests to reduce run time and pass given slightly different results diff --git a/R/ConservationProblem-proto.R b/R/ConservationProblem-proto.R index 025cf060f..7f85bb1d0 100644 --- a/R/ConservationProblem-proto.R +++ b/R/ConservationProblem-proto.R @@ -9,13 +9,13 @@ NULL #' #' This class is used to represent conservation planning problems. A #' conservation planning problem has spatially explicit planning units. -#' A prioritization involves making a decision on each planning unit (e.g. is +#' A prioritization involves making a decision on each planning unit (e.g., is #' the planning unit going to be turned into a protected area?). Each #' planning unit is associated with a cost that represents the cost incurred #' by applying the decision to the planning unit. The problem also has a set #' of representation targets for each feature. Further, it also has #' constraints used to ensure that the solution meets additional -#' objectives (e.g. certain areas are locked into the solution). Finally, +#' objectives (e.g., certain areas are locked into the solution). Finally, #' a conservation planning problem---unlike an optimization problem---also #' requires a method to solve the problem. **This class represents a #' planning problem, to actually build and then solve a planning problem, diff --git a/R/Parameter-proto.R b/R/Parameter-proto.R index 74ba78b1a..0ca2204d7 100644 --- a/R/Parameter-proto.R +++ b/R/Parameter-proto.R @@ -22,7 +22,7 @@ NULL #' \item{$default}{`numeric` vector of default values.} #' #' \item{$class}{`character` name of the class that the values inherit -#' from (e.g. `"integer"`.} +#' from (e.g., `"integer"`.} #' #' \item{$lower_limit}{`numeric` vector specifying the minimum #' permitted value for each element in `$value`.} diff --git a/R/ScalarParameter-proto.R b/R/ScalarParameter-proto.R index 5fcefca18..0a6940b8a 100644 --- a/R/ScalarParameter-proto.R +++ b/R/ScalarParameter-proto.R @@ -22,7 +22,7 @@ NULL #' \item{$default}{`numeric` scalar default value.} #' #' \item{$class}{`character` name of the class that `$value` should -#' inherit from (e.g. `integer`).} +#' inherit from (e.g., `integer`).} #' #' \item{$lower_limit}{`numeric` scalar value that is the minimum value #' that `$value` is permitted to be.} diff --git a/R/add_absolute_targets.R b/R/add_absolute_targets.R index 4b0ac7eea..ea5dd9e93 100644 --- a/R/add_absolute_targets.R +++ b/R/add_absolute_targets.R @@ -9,7 +9,7 @@ NULL #' planning units for which their summed feature values are equal to or greater #' than 10. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param targets Object that specifies the targets for each feature. #' See the Targets format section for more information. diff --git a/R/add_binary_decisions.R b/R/add_binary_decisions.R index fb5c193b8..0abf8c693 100644 --- a/R/add_binary_decisions.R +++ b/R/add_binary_decisions.R @@ -9,16 +9,16 @@ NULL #' the planning unit to include in a protected area network. If no decision is #' added to a problem then this decision class will be used by default. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @details Conservation planning problems involve making decisions on planning -#' units. These decisions are then associated with actions (e.g. turning a +#' units. These decisions are then associated with actions (e.g., turning a #' planning unit into a protected area). Only a #' single decision should be added to a `ConservationProblem` object. #' Note that if multiple decisions are added to a problem object, then the #' last one to be added will be used. #' -#' @return Object (i.e. [`ConservationProblem-class`]) with the decisions added +#' @return Object (i.e., [`ConservationProblem-class`]) with the decisions added #' to it. #' #' @seealso diff --git a/R/add_boundary_penalties.R b/R/add_boundary_penalties.R index ed492f3ab..36e651e3e 100644 --- a/R/add_boundary_penalties.R +++ b/R/add_boundary_penalties.R @@ -7,11 +7,11 @@ NULL #' that spatially clump planning units together based on the overall #' boundary length (perimeter). #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param penalty `numeric` penalty that is used to scale the importance #' of selecting planning units that are spatially clumped together compared -#' to the main problem objective (e.g. solution cost when the argument to +#' to the main problem objective (e.g., solution cost when the argument to #' `x` has a minimum set objective per [add_min_set_objective()]). #' Higher `penalty` values prefer solutions with a higher degree of spatial #' clumping, and smaller `penalty` values prefer solutions with a smaller @@ -36,19 +36,19 @@ NULL #' allocated to the same zone. Cell values must range between 1 and -1, where #' negative values favor solutions that spread out planning units. The default #' argument to `zones` is an identity -#' matrix (i.e. a matrix with ones along the matrix diagonal and zeros +#' matrix (i.e., a matrix with ones along the matrix diagonal and zeros #' elsewhere), so that penalties are incurred when neighboring planning units #' are not assigned to the same zone. If the cells along #' the matrix diagonal contain markedly smaller values than those found #' elsewhere in the matrix, then solutions are preferred that surround #' planning units with those allocated to different zones -#' (i.e. greater spatial fragmentation). +#' (i.e., greater spatial fragmentation). #' #' @param data `NULL`, `data.frame`, `matrix`, or `Matrix` #' object containing the boundary data. These data describe the total #' amount of boundary (perimeter) length for each planning unit, #' and the amount of boundary (perimeter) length shared between different -#' planning units (i.e. planning units that are adjacent to each other). +#' planning units (i.e., planning units that are adjacent to each other). #' See the Data format section for more information. #' #' @details @@ -75,14 +75,14 @@ NULL #' Note that the boundary data must be supplied #' using one of the other formats below if the planning unit data #' in the argument to `x` do not explicitly contain spatial information -#' (e.g. planning unit data are a `data.frame` or `numeric` class).} +#' (e.g., planning unit data are a `data.frame` or `numeric` class).} #' #' \item{`data` as a `matrix`/`Matrix` object}{where rows and columns represent #' different planning units and the value of each cell represents the #' amount of shared boundary length between two different planning units. #' Cells that occur along the matrix diagonal represent the amount of #' exposed boundary associated with each planning unit that has -#' no neighbor (e.g. these value might pertain to boundaries along a +#' no neighbor (e.g., these value might pertain to boundaries along a #' coastline).} #' #' \item{`data` as a `data.frame` object}{with the columns `"id1"`, @@ -91,7 +91,7 @@ NULL #' column contains the amount of shared boundary length between these #' two planning units. #' This format follows the the standard *Marxan* format for boundary -#' data (i.e. per the "bound.dat" file).} +#' data (i.e., per the "bound.dat" file).} #' #' } #' @@ -101,11 +101,11 @@ NULL #' (indexed by \eqn{i} or \eqn{j}), \eqn{Z} represent #' the set of management zones (indexed by \eqn{z} or \eqn{y}), and #' \eqn{X_{iz}}{Xiz} represent the decision -#' variable for planning unit \eqn{i} for in zone \eqn{z} (e.g. with binary +#' variable for planning unit \eqn{i} for in zone \eqn{z} (e.g., with binary #' values one indicating if planning unit is allocated or not). Also, let #' \eqn{p} represent the argument to `penalty`, \eqn{E_z}{Ez} represent the #' argument to `edge_factor`, \eqn{B_{ij}}{Bij} represent the matrix argument -#' to `data` (e.g. generated using [boundary_matrix()]), and +#' to `data` (e.g., generated using [boundary_matrix()]), and #' \eqn{W_{zz}}{Wzz} represent the matrix argument to `zones`. #' #' \deqn{ @@ -121,7 +121,7 @@ NULL #' benefit and not minimize some measure of cost, the term \eqn{p} is #' replaced with \eqn{-p}. #' -#' @return Object (i.e. [`ConservationProblem-class`]) with the penalties +#' @return Object (i.e., [`ConservationProblem-class`]) with the penalties #' added to it. #' #' @seealso @@ -214,7 +214,7 @@ NULL #' #' # create zone matrix which favors clumping planning units in zones 1 and 2 #' # together, and favors planning units in zone 3 being spread out -#' # (i.e. negative clumping) +#' # (i.e., negative clumping) #' zm10 <- diag(3) #' zm10[3, 3] <- -1 #' print(zm10) diff --git a/R/add_cbc_solver.R b/R/add_cbc_solver.R index dfa799ea7..6192a4158 100644 --- a/R/add_cbc_solver.R +++ b/R/add_cbc_solver.R @@ -22,7 +22,7 @@ NULL #' Although formal benchmarks examining the performance of this solver for #' conservation planning problems have yet to be completed, preliminary #' analyses suggest that it performs much faster than the other open-source -#' solvers (i.e. [add_rsymphony_solver()], [add_rsymphony_solver()]), and +#' solvers (i.e., [add_rsymphony_solver()], [add_rsymphony_solver()]), and #' so we recommend using this solver if the *Gurobi* and *IBM CPLEX* solvers #' are unavailable. #' @@ -45,7 +45,7 @@ NULL #' #' @inheritSection add_gurobi_solver Start solution format #' -#' @return Object (i.e. [`ConservationProblem-class`]) with the solver +#' @return Object (i.e., [`ConservationProblem-class`]) with the solver #' added to it. #' #' @seealso diff --git a/R/add_connectivity_penalties.R b/R/add_connectivity_penalties.R index ae779e413..da7c90a1a 100644 --- a/R/add_connectivity_penalties.R +++ b/R/add_connectivity_penalties.R @@ -6,11 +6,11 @@ NULL #' Add penalties to a conservation planning [problem()] to favor #' solutions that select planning units with high connectivity between them. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param penalty `numeric` penalty that is used to scale the importance #' of selecting planning units with strong connectivity between them compared -#' to the main problem objective (e.g. solution cost when the argument to +#' to the main problem objective (e.g., solution cost when the argument to #' `x` has a minimum set objective set using #' [add_min_set_objective()]). Higher `penalty` values #' can be used to obtain solutions with a high degree of connectivity, @@ -26,7 +26,7 @@ NULL #' the level of connectivity between planning units allocated to the #' same zone. Cell values must lay between 1 and -1, where negative #' values favor solutions with weak connectivity. The default argument to -#' `zones` is an identity matrix (i.e. a matrix with ones along the +#' `zones` is an identity matrix (i.e., a matrix with ones along the #' matrix diagonal and zeros elsewhere), so that planning units are #' only considered to be connected when they are allocated to the same zone. #' This argument is required when the argument to `data` is a @@ -72,7 +72,7 @@ NULL #' *Marxan* format. The data can be used to denote symmetric or #' asymmetric relationships between planning units. By default, #' input data is assumed to be symmetric unless asymmetric data is -#' also included (e.g. if data is present for planning units 2 and 3, then +#' also included (e.g., if data is present for planning units 2 and 3, then #' the same amount of connectivity is expected for planning units 3 and 2, #' unless connectivity data is also provided for planning units 3 and 2). #' If the argument to `x` contains multiple zones, then the columns @@ -86,7 +86,7 @@ NULL #' containing four-dimensions where cell values #' indicate the strength of connectivity between planning units #' when they are assigned to specific management zones. The first two -#' dimensions (i.e. rows and columns) indicate the strength of +#' dimensions (i.e., rows and columns) indicate the strength of #' connectivity between different planning units and the second two #' dimensions indicate the different management zones. Thus #' the `data[1, 2, 3, 4]` indicates the strength of @@ -101,7 +101,7 @@ NULL #' (indexed by \eqn{i} or \eqn{j}), \eqn{Z} represent the set #' of management zones (indexed by \eqn{z} or \eqn{y}), and \eqn{X_{iz}}{Xiz} #' represent the decision variable for planning unit \eqn{i} for in zone -#' \eqn{z} (e.g. with binary +#' \eqn{z} (e.g., with binary #' values one indicating if planning unit is allocated or not). Also, let #' \eqn{p} represent the argument to `penalty`, \eqn{D} represent the #' argument to `data`, and \eqn{W} represent the argument @@ -177,7 +177,7 @@ NULL #' } #' # create a symmetric connectivity matrix where the connectivity between #' # two planning units corresponds to their spatial proximity -#' # i.e. planning units that are further apart share less connectivity +#' # i.e., planning units that are further apart share less connectivity #' centroids <- rgeos::gCentroid(sim_pu_polygons, byid = TRUE) #' d_matrix <- (1 / (as(dist(centroids@coords), "Matrix") + 1)) #' @@ -220,7 +220,7 @@ NULL #' # find if planning units are adjacent #' if (adjacent_units[i, j]) { #' # find if planning units lay north and south of each other -#' # i.e. they have the same x-coordinate +#' # i.e., they have the same x-coordinate #' if (centroids@coords[i, 1] == centroids@coords[j, 1]) { #' if (centroids@coords[i, 2] > centroids@coords[j, 2]) { #' # if i is north of j add 10 units of connectivity diff --git a/R/add_contiguity_constraints.R b/R/add_contiguity_constraints.R index 435a34175..d31dfee63 100644 --- a/R/add_contiguity_constraints.R +++ b/R/add_contiguity_constraints.R @@ -7,12 +7,12 @@ NULL #' that all selected planning units are spatially connected with each other #' and form a single contiguous unit. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param zones `matrix` or `Matrix` object describing the #' connection scheme for different zones. Each row and column corresponds #' to a different zone in the argument to `x`, and cell values must -#' contain binary `numeric` values (i.e. one or zero) that indicate +#' contain binary `numeric` values (i.e., one or zero) that indicate #' if connected planning units (as specified in the argument to #' `data`) should be still considered connected if they are allocated to #' different zones. The cell values along the diagonal @@ -21,7 +21,7 @@ NULL #' arguments to `zones` must be symmetric, and that a row or column has #' a value of one then the diagonal element for that row or column must also #' have a value of one. The default argument to `zones` is an identity -#' matrix (i.e. a matrix with ones along the matrix diagonal and zeros +#' matrix (i.e., a matrix with ones along the matrix diagonal and zeros #' elsewhere), so that planning units are only considered connected if they #' are both allocated to the same zone. #' @@ -44,16 +44,16 @@ NULL #' #' \item{`data` as a `NULL` value}{indicating that connection data should be #' calculated automatically using the [adjacency_matrix()] function. -#' This is the default argument. +#' This is the default argument. #' Note that the connection data must be manually defined #' using one of the other formats below when the planning unit data -#' in the argument to `x` is not spatially referenced (e.g. +#' in the argument to `x` is not spatially referenced (e.g., #' in `data.frame` or `numeric` format).} #' #' \item{`data` as a `matrix`/`Matrix` object}{where rows and columns represent #' different planning units and the value of each cell indicates if the #' two planning units are connected or not. Cell values should be binary -#' `numeric` values (i.e. one or zero). Cells that occur along the +#' `numeric` values (i.e., one or zero). Cells that occur along the #' matrix diagonal have no effect on the solution at all because each #' planning unit cannot be a connected with itself.} #' @@ -66,7 +66,7 @@ NULL #' or not. This data can be used to describe symmetric or #' asymmetric relationships between planning units. By default, #' input data is assumed to be symmetric unless asymmetric data is -#' also included (e.g. if data is present for planning units 2 and 3, then +#' also included (e.g., if data is present for planning units 2 and 3, then #' the same amount of connectivity is expected for planning units 3 and 2, #' unless connectivity data is also provided for planning units 3 and 2).} #' @@ -76,7 +76,7 @@ NULL #' In early versions, this function was named as the #' `add_connected_constraints()` function. #' -#' @return Object (i.e. [`ConservationProblem-class`]) with the constraints +#' @return Object (i.e., [`ConservationProblem-class`]) with the constraints #' added to it. #' #' @seealso diff --git a/R/add_cplex_solver.R b/R/add_cplex_solver.R index 3331b67cb..1932d317f 100644 --- a/R/add_cplex_solver.R +++ b/R/add_cplex_solver.R @@ -18,12 +18,12 @@ NULL #' @details #' [*IBM CPLEX*](https://www.ibm.com/analytics/cplex-optimizer) is a #' commercial optimization software. It is faster than -#' the available open source solvers (e.g. [add_lpsymphony_solver()] and +#' the available open source solvers (e.g., [add_lpsymphony_solver()] and #' [add_rsymphony_solver()]. #' Although formal benchmarks examining the performance of this solver for #' conservation planning problems have yet to be completed, preliminary #' analyses suggest that it performs slightly slower than the *Gurobi* -#' solver (i.e. [add_gurobi_solver()]). +#' solver (i.e., [add_gurobi_solver()]). #' We recommend using this solver if the *Gurobi* solver is not available. #' Licenses are available for the *IBM CPLEX* software to academics at no cost #' (see ). @@ -39,7 +39,7 @@ NULL #' export CPLEX_BIN="/opt/ibm/ILOG/CPLEX_Studio128/cplex/bin/x86-64_linux/cplex" #' ``` #' Note that you may need to change the version -#' number in the file path (i.e. `"CPLEX_Studio128"`). For more information +#' number in the file path (i.e., `"CPLEX_Studio128"`). For more information #' on installing the pkg{cplexAPI} package, please see the #' [official installation instructions for the package](https://github.com/cran/cplexAPI/blob/master/inst/INSTALL). #' diff --git a/R/add_cuts_portfolio.R b/R/add_cuts_portfolio.R index c79cd99af..6df40d638 100644 --- a/R/add_cuts_portfolio.R +++ b/R/add_cuts_portfolio.R @@ -9,7 +9,7 @@ NULL #' [add_gap_portfolio()] when the *Gurobi* software is not #' available. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param number_solutions `integer` number of attempts to generate #' different solutions. Defaults to 10. @@ -22,11 +22,11 @@ NULL # #' @section Notes: #' In early versions (< 4.0.1), this function was only compatible with -#' *Gurobi* (i.e. [add_gurobi_solver()]). To provide functionality with +#' *Gurobi* (i.e., [add_gurobi_solver()]). To provide functionality with #' exact algorithm solvers, this function now adds constraints to the #' problem formulation to generate multiple solutions. #' -#' @return Object (i.e. [`ConservationProblem-class`]) with the portfolio +#' @return Object (i.e., [`ConservationProblem-class`]) with the portfolio #' added to it. #' #' @seealso diff --git a/R/add_default_decisions.R b/R/add_default_decisions.R index 93cfd0b5c..e31a51973 100644 --- a/R/add_default_decisions.R +++ b/R/add_default_decisions.R @@ -7,7 +7,7 @@ NULL #' [problem()]. The default types are binary and are added using #' the [add_binary_decisions()] function. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @inherit add_binary_decisions return #' diff --git a/R/add_default_portfolio.R b/R/add_default_portfolio.R index 2d83bf234..5f86fecd0 100644 --- a/R/add_default_portfolio.R +++ b/R/add_default_portfolio.R @@ -6,7 +6,7 @@ NULL #' Generate a portfolio for a conservation planning [problem()] #' that contains a single solution. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @seealso #' See [portfolios] for an overview of all functions for adding a portfolio. diff --git a/R/add_default_solver.R b/R/add_default_solver.R index 445c47d28..c46af02ae 100644 --- a/R/add_default_solver.R +++ b/R/add_default_solver.R @@ -10,7 +10,7 @@ NULL #' run time and solution quality of some of the available solvers when applied #' to different sized datasets. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param ... arguments passed to the solver. #' diff --git a/R/add_extra_portfolio.R b/R/add_extra_portfolio.R index f5fa72628..7d105ee76 100644 --- a/R/add_extra_portfolio.R +++ b/R/add_extra_portfolio.R @@ -10,10 +10,10 @@ NULL #' but does not provide any guarantees on the number of solutions, or #' the quality of solutions. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @details This strategy for generating a portfolio requires problems to -#' be solved using the *Gurobi* software suite (i.e. using +#' be solved using the *Gurobi* software suite (i.e., using #' [add_gurobi_solver()]. Specifically, version 8.0.0 (or greater) #' of the \pkg{gurobi} package must be installed. #' diff --git a/R/add_feature_contiguity_constraints.R b/R/add_feature_contiguity_constraints.R index 7a21e79aa..01ec9e52a 100644 --- a/R/add_feature_contiguity_constraints.R +++ b/R/add_feature_contiguity_constraints.R @@ -13,13 +13,13 @@ NULL #' feature to ensure that all features can disperse through out the areas #' designated for their conservation. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param zones `matrix`, `Matrix` or `list` object describing #' the connection scheme for different zones. For `matrix` or #' and `Matrix` arguments, each row and column corresponds #' to a different zone in the argument to `x`, and cell values must -#' contain binary `numeric` values (i.e. one or zero) that indicate +#' contain binary `numeric` values (i.e., one or zero) that indicate #' if connected planning units (as specified in the argument to #' `data`) should be still considered connected if they are allocated to #' different zones. The cell values along the diagonal @@ -32,7 +32,7 @@ NULL #' be a `list` of `matrix` or `Matrix` objects that shows the #' specific scheme for each feature using the conventions described above. #' The default argument to `zones` is an identity -#' matrix (i.e. a matrix with ones along the matrix diagonal and zeros +#' matrix (i.e., a matrix with ones along the matrix diagonal and zeros #' elsewhere), so that planning units are only considered connected if they #' are both allocated to the same zone. #' @@ -73,13 +73,13 @@ NULL #' as potentially dispersible for all features. #' Note that the connection data must be manually defined #' using one of the other formats below when the planning unit data -#' in the argument to `x` is not spatially referenced (e.g. +#' in the argument to `x` is not spatially referenced (e.g., #' in `data.frame` or `numeric` format).} #' #' \item{`data` as a`matrix`/`Matrix` object}{where rows and columns represent #' different planning units and the value of each cell indicates if the #' two planning units are connected or not. Cell values should be binary -#' `numeric` values (i.e. one or zero). Cells that occur along the +#' `numeric` values (i.e., one or zero). Cells that occur along the #' matrix diagonal have no effect on the solution at all because each #' planning unit cannot be a connected with itself. Note that pairs #' of connected planning units are treated as being potentially dispersible @@ -94,7 +94,7 @@ NULL #' or not. This data can be used to describe symmetric or #' asymmetric relationships between planning units. By default, #' input data is assumed to be symmetric unless asymmetric data is -#' also included (e.g. if data is present for planning units 2 and 3, then +#' also included (e.g., if data is present for planning units 2 and 3, then #' the same amount of connectivity is expected for planning units 3 and 2, #' unless connectivity data is also provided for planning units 3 and 2). #' Note that pairs of connected planning units are treated as being diff --git a/R/add_feature_weights.R b/R/add_feature_weights.R index 55c834a94..915507ef7 100644 --- a/R/add_feature_weights.R +++ b/R/add_feature_weights.R @@ -12,14 +12,14 @@ NULL #' representation of some features over other features when making decisions #' about how the budget should be allocated. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param weights `numeric` or `matrix` of weights. #' See the Weights format section for more information. #' #' @details #' Weights can only be applied to problems that have an objective -#' that is budget limited (e.g. [add_max_cover_objective()]). +#' that is budget limited (e.g., [add_max_cover_objective()]). #' They can be applied to problems that aim to maximize phylogenetic #' representation ([add_max_phylo_div_objective()]) to favor the #' representation of specific features over the representation of @@ -54,7 +54,7 @@ NULL #' #' } #' -#' @return Object (i.e. [`ConservationProblem-class`]) with the weights +#' @return Object (i.e., [`ConservationProblem-class`]) with the weights #' added to it. #' #' @seealso @@ -88,7 +88,7 @@ NULL #' #' # create manually specified weights that assign higher importance to #' # certain features. These weights could be based on a pre-calculated index -#' # (e.g. an index measuring extinction risk where higher values +#' # (e.g., an index measuring extinction risk where higher values #' # denote higher extinction risk) #' w3 <- c(0, 0, 0, 100, 200) #' p3 <- p1 %>% add_feature_weights(w3) @@ -130,18 +130,18 @@ NULL #' tip.color = replace(rep("black", nlayers(sim_features)), #' which(r4$met), "red")) #' } -#' # we can see here that the third feature ("layer.3", i.e. +#' # we can see here that the third feature ("layer.3", i.e., #' # sim_features[[3]]) is not represented in the solution. Let us pretend #' # that it is absolutely critical this feature is adequately conserved #' # in the solution. For example, this feature could represent a species #' # that plays important role in the ecosystem, or a species that is -#' # important commercial activities (e.g. eco-tourism). So, to generate +#' # important commercial activities (e.g., eco-tourism). So, to generate #' # a solution that conserves the third feature whilst also aiming to #' # maximize phylogenetic diversity, we will create a set of weights that #' # assign a particularly high weighting to the third feature #' w5 <- c(0, 0, 1000, 0, 0) #' -#' # we can see that this weighting (i.e. w5[3]) has a much higher value than +#' # we can see that this weighting (i.e., w5[3]) has a much higher value than #' # the branch lengths in the phylogeny so solutions that represent this #' # feature be much closer to optimality #' print(sim_phylogeny$edge.length) diff --git a/R/add_gap_portfolio.R b/R/add_gap_portfolio.R index 1359cd596..5216ab499 100644 --- a/R/add_gap_portfolio.R +++ b/R/add_gap_portfolio.R @@ -10,7 +10,7 @@ NULL #' frequencies for moderate and large-sized problems (similar to #' *Marxan*). #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param number_solutions `integer` number of solutions required. #' @@ -18,19 +18,20 @@ NULL #' This relative gap specifies a threshold worst-case performance for #' solutions in the portfolio. For example, value of 0.1 will result in the #' portfolio returning solutions that are within 10% of an optimal solution. -#' Note that the gap specified in the solver (i.e. +#' Note that the gap specified in the solver (i.e., #' [add_gurobi_solver()] must be less than or equal to the gap #' specified to generate the portfolio. Defaults to 0.1. #' #' @details This strategy for generating a portfolio requires problems to -#' be solved using the *Gurobi* software suite (i.e. using +#' be solved using the *Gurobi* software suite (i.e., using #' [add_gurobi_solver()]. Specifically, version 9.0.0 (or greater) #' of the \pkg{gurobi} package must be installed. #' Note that the number of solutions returned may be less than the argument to #' `number_solutions`, if the total number of solutions that #' meet the optimality gap is less than the number of solutions requested. #' Also, note that this portfolio function only works with problems -#' that have binary decisions (i.e. specified using [add_binary_decisions()]). +#' that have binary decisions (i.e., specified using +#' [add_binary_decisions()]). #' #' @inherit add_cuts_portfolio return #' diff --git a/R/add_gurobi_solver.R b/R/add_gurobi_solver.R index 3b89796a3..deee3eb15 100644 --- a/R/add_gurobi_solver.R +++ b/R/add_gurobi_solver.R @@ -10,7 +10,7 @@ NULL #' It requires the \pkg{gurobi} package to be installed #' (see below for installation instructions). #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param gap `numeric` gap to optimality. This gap is relative #' and expresses the acceptable deviance from the optimal objective. @@ -18,12 +18,12 @@ NULL #' it has found a solution within 1% of optimality. #' Additionally, a value of 0 will result in the solver stopping #' when it has found an optimal solution. -#' The default value is 0.1 (i.e. 10% from optimality). +#' The default value is 0.1 (i.e., 10% from optimality). #' #' @param time_limit `numeric` time limit (seconds) for generating solutions. #' The solver will return the current best solution when this time limit is #' exceeded. The default value is the largest integer value -#' (i.e. `.Machine$integer.max`), effectively meaning that solver +#' (i.e., `.Machine$integer.max`), effectively meaning that solver #' will keep running until a solution within the optimality gap is found. #' #' @param presolve `integer` number indicating how intensively the @@ -57,7 +57,7 @@ NULL #' will begin storing this information on disk #' (using the *Gurobi( `NodeFileStart` parameter). #' This functionality is useful if the system has insufficient memory to -#' solve a given problem (e.g. solving the problem with default settings +#' solve a given problem (e.g., solving the problem with default settings #' yields the `OUT OF MEMORY` error message) and a system with more memory is #' not readily available. #' For example, a value of 4 indicates that the solver will start using @@ -69,7 +69,7 @@ NULL #' @param start_solution `NULL` or object containing the starting solution #' for the solver. Defaults to `NULL` such that no starting solution is used. #' To specify a starting solution, the argument to `start_solution` should -#' be in the same format as the planning units (i.e. a `NULL`, `numeric`, +#' be in the same format as the planning units (i.e., a `NULL`, `numeric`, #' `matrix`, `data.frame`, [`Raster-class`], [`Spatial-class`], #' or [sf::sf()] object). #' See the Start solution format section for more information. @@ -106,7 +106,7 @@ NULL #' for each of the different planning unit data formats: #' `r solution_format_documentation("start_solution")` #' -#' @return Object (i.e. [`ConservationProblem-class`]) with the solver +#' @return Object (i.e., [`ConservationProblem-class`]) with the solver #' added to it. #' #' @seealso diff --git a/R/add_linear_constraints.R b/R/add_linear_constraints.R index c2c36c187..96ef7c8d5 100644 --- a/R/add_linear_constraints.R +++ b/R/add_linear_constraints.R @@ -32,12 +32,12 @@ NULL #' (see Examples section below for details). #' For example, these constraints can be used to add multiple budgets. #' They can also be used to ensure that the total number of planning units -#' allocated to a certain administrative area (e.g. country) does not exceed -#' a certain threshold (e.g. 30% of its total area). Furthermore, +#' allocated to a certain administrative area (e.g., country) does not exceed +#' a certain threshold (e.g., 30% of its total area). Furthermore, #' they can also be used to ensure that features have a minimal level -#' of representation (e.g. 30%) when using an objective +#' of representation (e.g., 30%) when using an objective #' function that aims to enhance feature representation given a budget -#' (e.g. [add_min_shortfall_objective()]). +#' (e.g., [add_min_shortfall_objective()]). #' #' @section Mathematical formulation: #' The linear constraints are implemented using the following @@ -45,13 +45,13 @@ NULL #' Let \eqn{I} denote the set of planning units #' (indexed by \eqn{i}), \eqn{Z} the set of management zones (indexed by #' \eqn{z}), and \eqn{X_{iz}}{Xiz} the decision variable for allocating -#' planning unit \eqn{i} to zone \eqn{z} (e.g. with binary +#' planning unit \eqn{i} to zone \eqn{z} (e.g., with binary #' values indicating if each planning unit is allocated or not). Also, let #' \eqn{D_{iz}}{Diz} denote the constraint data associated with #' planning units \eqn{i \in I}{i in I} for zones \eqn{z \in Z}{z in Z} #' (argument to `data`, if supplied as a `matrix` object), #' \eqn{\theta} denote the constraint sense -#' (argument to `sense`, e.g. \eqn{<=}), and \eqn{t} denote the constraint +#' (argument to `sense`, e.g., \eqn{<=}), and \eqn{t} denote the constraint #' threshold (argument to `threshold`). #' #' \deqn{ @@ -149,7 +149,7 @@ NULL #' # third, let's create a modified version of p0 that contains #' # additional constraints to ensure that the solution equitably #' # distributes conservation effort across different administrative areas -#' # (e.g. countries) within the study region +#' # (e.g., countries) within the study region #' #' # to begin with, we will simulate a dataset describing the spatial extent of #' # four different administrative areas across the study region diff --git a/R/add_linear_penalties.R b/R/add_linear_penalties.R index f35bdb0ac..3d872fed9 100644 --- a/R/add_linear_penalties.R +++ b/R/add_linear_penalties.R @@ -5,12 +5,12 @@ NULL #' #' Add penalties to a conservation planning [problem()] to penalize #' solutions that select planning units with higher values from a specific -#' data source (e.g. anthropogenic impact). These penalties assume +#' data source (e.g., anthropogenic impact). These penalties assume #' a linear trade-off between the penalty values and the primary -#' objective of the conservation planning [problem()] (e.g. +#' objective of the conservation planning [problem()] (e.g., #' solution cost for minimum set problems; [add_min_set_objective()]. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param penalty `numeric` penalty value that is used to scale the #' importance not selecting planning units with high `data` values. @@ -88,7 +88,7 @@ NULL #' Let \eqn{I} denote the set of planning units #' (indexed by \eqn{i}), \eqn{Z} the set of management zones (indexed by #' \eqn{z}), and \eqn{X_{iz}}{Xiz} the decision variable for allocating -#' planning unit \eqn{i} to zone \eqn{z} (e.g. with binary +#' planning unit \eqn{i} to zone \eqn{z} (e.g., with binary #' values indicating if each planning unit is allocated or not). Also, let #' \eqn{P_z} represent the penalty scaling value for zones #' \eqn{z \in Z}{z in Z} (argument to `penalty`), and @@ -121,7 +121,7 @@ NULL #' data(sim_pu_polygons, sim_pu_zones_stack, sim_features, sim_features_zones) #' #' # add a column to contain the penalty data for each planning unit -#' # e.g. these values could indicate the level of habitat +#' # e.g., these values could indicate the level of habitat #' sim_pu_polygons$penalty_data <- runif(nrow(sim_pu_polygons)) #' #' # plot the penalty data to visualise its spatial distribution @@ -152,7 +152,7 @@ NULL #' s2 <- solve(p2) #' #' # plot the solutions and compare them, -#' # since we supplied a very high penalty value (i.e. 100), relative +#' # since we supplied a very high penalty value (i.e., 100), relative #' # to the range of values in the penalty data and the objective function, #' # the solution in s2 is very sensitive to values in the penalty data #' spplot(s1, zcol = "solution_1", main = "solution without penalties", @@ -161,7 +161,7 @@ NULL #' axes = FALSE, box = FALSE) #' #' # for real conservation planning exercises, -#' # it would be worth exploring a range of penalty values (e.g. ranging +#' # it would be worth exploring a range of penalty values (e.g., ranging #' # from 1 to 100 increments of 5) to explore the trade-offs #' } #' diff --git a/R/add_locked_in_constraints.R b/R/add_locked_in_constraints.R index 80dcf0e65..32a6e3441 100644 --- a/R/add_locked_in_constraints.R +++ b/R/add_locked_in_constraints.R @@ -10,13 +10,13 @@ NULL #' solution fills in the gaps in the existing reserve network. If specific #' planning units should be locked out of a solution, use #' [add_locked_out_constraints()]. For problems with non-binary -#' planning unit allocations (e.g. proportions), the +#' planning unit allocations (e.g., proportions), the #' [add_manual_locked_constraints()] function can be used to lock #' planning unit allocations to a specific value. #' #' @usage add_locked_in_constraints(x, locked_in) #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param locked_in Object that determines which planning units that should be #' locked in. See the Data format section for more information. @@ -58,7 +58,7 @@ NULL #' compatible if the planning units in the argument to `x` are a #' [`Spatial-class`], [sf::sf()], or #' `data.frame` object. The fields -#' (columns) must have `logical` (i.e. `TRUE` or `FALSE`) +#' (columns) must have `logical` (i.e., `TRUE` or `FALSE`) #' values indicating if the planning unit is to be locked for the solution. #' For problems that contain a single zone, the argument to `data` must #' contain a single field name. Otherwise, for problems that diff --git a/R/add_locked_out_constraints.R b/R/add_locked_out_constraints.R index da4c765da..a52de85ee 100644 --- a/R/add_locked_out_constraints.R +++ b/R/add_locked_out_constraints.R @@ -9,13 +9,13 @@ NULL #' useful to lock out planning units that have been degraded and are not #' suitable for conserving species. If specific planning units should be locked #' in to the solution, use [add_locked_out_constraints()]. For -#' problems with non-binary planning unit allocations (e.g. proportions), the +#' problems with non-binary planning unit allocations (e.g., proportions), the #' [add_manual_locked_constraints()] function can be used to lock #' planning unit allocations to a specific value. #' #' @usage add_locked_out_constraints(x, locked_out) #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param locked_out Object that determines which planning units that should be #' locked out. See the Data format section for more information. diff --git a/R/add_loglinear_targets.R b/R/add_loglinear_targets.R index f735d0ee9..f50abb389 100644 --- a/R/add_loglinear_targets.R +++ b/R/add_loglinear_targets.R @@ -10,7 +10,7 @@ NULL #' distributions from being over-represented #' in solutions (Butchart *et al.* 2015). #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param lower_bound_amount `numeric` threshold. #' @@ -56,7 +56,7 @@ NULL #' #' The target calculations do not account for the #' size of each planning unit. Therefore, the feature data should account for -#' the size of each planning unit if this is important (e.g. pixel values in +#' the size of each planning unit if this is important (e.g., pixel values in #' the argument to `features` in the function [problem()] could #' correspond to amount of land occupied by the feature in \eqn{km^2} units). #' Additionally, the function can only be applied to diff --git a/R/add_mandatory_allocation_constraints.R b/R/add_mandatory_allocation_constraints.R index e4ed7676f..5a42249cf 100644 --- a/R/add_mandatory_allocation_constraints.R +++ b/R/add_mandatory_allocation_constraints.R @@ -7,7 +7,7 @@ NULL #' management zone in the solution. Note that this function can only be used #' with problems that contain multiple zones. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @details For a conservation planning [problem()] with multiple #' management zones, it may sometimes be desirable to obtain a solution that @@ -16,11 +16,11 @@ NULL #' every single parcel of land has been allocated a specific land-use type. #' In other words are no "left over" areas. Although it might seem tempting #' to simply solve the problem and manually assign "left over" planning units -#' to a default zone afterwards (e.g. an "other", "urban", or "grazing" +#' to a default zone afterwards (e.g., an "other", "urban", or "grazing" #' land-use), this could result in highly sub-optimal solutions if there #' penalties for siting the default land-use adjacent to other zones. #' Instead, this function can be used to specify that all planning units in a -#' problem with multiple zones must be allocated to a management zone (i.e. +#' problem with multiple zones must be allocated to a management zone (i.e., #' zone allocation is mandatory). #' #' @inherit add_contiguity_constraints return diff --git a/R/add_manual_bounded_constraints.R b/R/add_manual_bounded_constraints.R index f827ada11..a00358102 100644 --- a/R/add_manual_bounded_constraints.R +++ b/R/add_manual_bounded_constraints.R @@ -4,7 +4,7 @@ NULL #' Add manually specified bound constraints #' #' Add constraints to a conservation planning [problem()] to ensure -#' that the planning unit values (e.g. proportion, binary) in a solution +#' that the planning unit values (e.g., proportion, binary) in a solution #' range between specific lower and upper bounds. This function offers more #' fine-grained control than the [add_manual_locked_constraints()] #' function and is is most useful for problems involving proportion-type @@ -12,7 +12,7 @@ NULL #' #' @usage add_manual_bounded_constraints(x, data) #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param data `data.frame` or [tibble::tibble()] object. #' See the Data format section for more information. @@ -213,7 +213,7 @@ methods::setMethod("add_manual_bounded_constraints", data$zone <- x$zone_names()[1] data$zone <- match(as.character(data$zone), x$zone_names()) # remove rows for raster cells that aren't really planning units - # i.e. contain NA values in all zones + # i.e., contain NA values in all zones pu <- x$get_data("cost") if (inherits(pu, "Raster")) { if (raster::nlayers(pu) == 1) { diff --git a/R/add_manual_locked_constraints.R b/R/add_manual_locked_constraints.R index 4f73c78aa..cd0932582 100644 --- a/R/add_manual_locked_constraints.R +++ b/R/add_manual_locked_constraints.R @@ -11,7 +11,7 @@ NULL #' #' @usage add_manual_locked_constraints(x, data) #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param data `data.frame` or [tibble::tibble()] object. #' See the Data format section for more information. @@ -30,10 +30,10 @@ NULL #' #' \item{status}{`numeric` values indicating how much #' of each planning unit should be allocated to each zone in the solution. -#' For example, the `numeric` values could be binary values (i.e. zero +#' For example, the `numeric` values could be binary values (i.e., zero #' or one) for problems containing binary-type decision variables #' (using the [add_binary_decisions()] function). Alternatively, -#' the `numeric` values could be proportions (e.g. 0.5) for problems +#' the `numeric` values could be proportions (e.g., 0.5) for problems #' containing proportion-type decision variables (using the #' [add_proportion_decisions()]).} #' @@ -224,7 +224,7 @@ methods::setMethod("add_manual_locked_constraints", data$zone <- x$zone_names()[1] data$zone <- match(as.character(data$zone), x$zone_names()) # remove rows for raster cells that aren't really planning units - # i.e. contain NA values in all zones + # i.e., contain NA values in all zones pu <- x$get_data("cost") if (inherits(pu, "Raster")) { if (raster::nlayers(pu) == 1) { diff --git a/R/add_manual_targets.R b/R/add_manual_targets.R index 44dbafa15..1204a8fac 100644 --- a/R/add_manual_targets.R +++ b/R/add_manual_targets.R @@ -11,10 +11,10 @@ NULL #' functions. However, this function can be used to (i) mix absolute and #' relative targets for different features and zones, (ii) set targets that #' pertain to the allocations of planning units in multiple zones, and (iii) -#' set targets that require different senses (e.g. targets which specify the +#' set targets that require different senses (e.g., targets which specify the #' solution should not exceed a certain quantity using `"<="` values). #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param targets `data.frame` or [tibble::tibble()] object. #' See the Target data format section for more information. @@ -49,7 +49,7 @@ NULL #' #' } #' -#' @return Object (i.e. [`ConservationProblem-class`]) with the targets added +#' @return Object (i.e., [`ConservationProblem-class`]) with the targets added #' to it. #' #' @seealso diff --git a/R/add_max_cover_objective.R b/R/add_max_cover_objective.R index b17a562dd..ce9981b5c 100644 --- a/R/add_max_cover_objective.R +++ b/R/add_max_cover_objective.R @@ -9,7 +9,7 @@ NULL #' weights should be used instead to increase the representation of certain #' features by a solution. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param budget `numeric` value specifying the maximum expenditure of #' the prioritization. For problems with multiple zones, the argument @@ -22,10 +22,10 @@ NULL #' maximizes the number of represented features, while keeping cost within a #' fixed budget. Here, features are treated as being represented if #' the reserve system contains at least a single instance of a feature -#' (i.e. an amount greater than 1). This formulation has often been +#' (i.e., an amount greater than 1). This formulation has often been #' used in conservation planning problems dealing with binary biodiversity #' data that indicate the presence/absence of suitable habitat -#' (e.g. Church & Velle 1974). Additionally, weights can be used to favor the +#' (e.g., Church & Velle 1974). Additionally, weights can be used to favor the #' representation of certain features over other features (see #' [add_feature_weights()]). Check out the #' [add_max_features_objective()] for a more @@ -48,7 +48,7 @@ NULL #' sum_i^I (xi * rij) >= (yj * 1) for all j in J & #' sum_i^I (xi * ci) <= B} #' -#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g. +#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g., #' specifying whether planning unit \eqn{i}{i} has been selected (1) or not #' (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning #' unit \eqn{i}{i}, \eqn{y_j}{yj} indicates if the solution has meet diff --git a/R/add_max_features_objective.R b/R/add_max_features_objective.R index f551c8f17..081bd7e0e 100644 --- a/R/add_max_features_objective.R +++ b/R/add_max_features_objective.R @@ -37,7 +37,7 @@ NULL #' sum_i^I (xi * rij) >= (yj tj) for all j in J & #' sum_i^I (xi * ci) <= B} #' -#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g. +#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g., #' specifying whether planning unit \eqn{i}{i} has been selected (1) or not #' (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning #' unit \eqn{i}{i}, \eqn{t_j}{tj} is the representation target for feature diff --git a/R/add_max_phylo_div_objective.R b/R/add_max_phylo_div_objective.R index e91d63b53..b896c1b47 100644 --- a/R/add_max_phylo_div_objective.R +++ b/R/add_max_phylo_div_objective.R @@ -59,7 +59,7 @@ NULL #' (xi * rij) >= (yj * tj) for all j in J & mb <= yj for all j in T(b) & #' sum_i^I (xi * ci) <= B} #' -#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g. +#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g., #' specifying whether planning unit \eqn{i}{i} has been selected (1) or not #' (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning #' unit \eqn{i}{i}, \eqn{t_j}{tj} is the representation target for feature diff --git a/R/add_max_phylo_end_objective.R b/R/add_max_phylo_end_objective.R index 3580dffa0..09cc42f18 100644 --- a/R/add_max_phylo_end_objective.R +++ b/R/add_max_phylo_end_objective.R @@ -56,7 +56,7 @@ NULL #' subject to sum_i^I (xi * rij) >= (yj * tj) for all j in J & #' mb <= yj for all j in T(b) & sum_i^I (xi * ci) <= B} #' -#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g. +#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g., #' specifying whether planning unit \eqn{i}{i} has been selected (1) or not #' (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning #' unit \eqn{i}{i}, \eqn{t_j}{tj} is the representation target for feature diff --git a/R/add_max_utility_objective.R b/R/add_max_utility_objective.R index 0c59e9a2b..bc3407000 100644 --- a/R/add_max_utility_objective.R +++ b/R/add_max_utility_objective.R @@ -12,7 +12,7 @@ NULL #' possible, and so often results in solutions that are heavily biased towards #' just a few features. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param budget `numeric` value specifying the maximum expenditure of #' the prioritization. For problems with multiple zones, the argument @@ -40,7 +40,7 @@ NULL #' Maximize sum_i^I (-s * ci * xi) + sum_j^J (aj * wj) subject to #' aj = sum_i^I (xi * rij) for all j in J & sum_i^I (xi * ci) <= B} #' -#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g. +#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g., #' specifying whether planning unit \eqn{i}{i} has been selected (1) or not #' (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning #' unit \eqn{i}{i}, \eqn{A_j}{Aj} is the amount of feature \eqn{j}{j} diff --git a/R/add_min_largest_shortfall_objective.R b/R/add_min_largest_shortfall_objective.R index 5e5ea6508..83b6c43f9 100644 --- a/R/add_min_largest_shortfall_objective.R +++ b/R/add_min_largest_shortfall_objective.R @@ -7,7 +7,7 @@ NULL #' minimize the largest target shortfall while ensuring that #' the cost of the solution does not exceed a budget. Note that if the #' target shortfall for a single feature cannot be decreased beyond a certain -#' point (e.g. because all remaining planning units occupied by that feature +#' point (e.g., because all remaining planning units occupied by that feature #' are too costly or are locked out), then solutions may only use a small #' proportion of the specified budget. #' @@ -41,7 +41,7 @@ NULL #' l >= (yj / tj) for all j in J & #' sum_i^I (xi * ci) <= B} #' -#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g. +#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g., #' specifying whether planning unit \eqn{i}{i} has been selected (1) or not #' (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning #' unit \eqn{i}{i}, and \eqn{t_j}{tj} is the representation target for feature diff --git a/R/add_min_set_objective.R b/R/add_min_set_objective.R index 2fc40f8f1..f5c4e5246 100644 --- a/R/add_min_set_objective.R +++ b/R/add_min_set_objective.R @@ -8,7 +8,7 @@ NULL #' This objective is similar to that used in #' *Marxan* and is detailed in Rodrigues *et al.* (2000). #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @details #' The minimum set objective -- in the the context of systematic reserve @@ -31,7 +31,7 @@ NULL #' Minimize sum_i^I (xi * ci) subject to sum_i^I (xi * rij) >= Tj for all #' j in J} #' -#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g. +#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g., #' specifying whether planning unit \eqn{i}{i} has been selected (1) or not #' (0)), \eqn{c_i}{ci} is the cost of planning unit \eqn{i}{i}, #' \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning unit @@ -51,7 +51,7 @@ NULL #' #' @family objectives #' -#' @return Object (i.e. [`ConservationProblem-class`]) with the objective +#' @return Object (i.e., [`ConservationProblem-class`]) with the objective #' added to it. #' #' @examples diff --git a/R/add_min_shortfall_objective.R b/R/add_min_shortfall_objective.R index c7817c857..ed9e162da 100644 --- a/R/add_min_shortfall_objective.R +++ b/R/add_min_shortfall_objective.R @@ -33,7 +33,7 @@ NULL #' sum_i^I (xi * rij) + yj >= tj for all j in J & #' sum_i^I (xi * ci) <= B} #' -#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g. +#' Here, \eqn{x_i}{xi} is the [decisions] variable (e.g., #' specifying whether planning unit \eqn{i}{i} has been selected (1) or not #' (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning #' unit \eqn{i}{i}, \eqn{t_j}{tj} is the representation target for feature diff --git a/R/add_neighbor_constraints.R b/R/add_neighbor_constraints.R index bedd37549..67981ae22 100644 --- a/R/add_neighbor_constraints.R +++ b/R/add_neighbor_constraints.R @@ -7,7 +7,7 @@ NULL #' that all selected planning units in the solution have at least a certain #' number of neighbors that are also selected in the solution. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param k `integer` minimum number of neighbors for selected #' planning units in the solution. For problems with multiple zones, @@ -16,13 +16,13 @@ NULL #' @param zones `matrix` or `Matrix` object describing the #' neighborhood scheme for different zones. Each row and column corresponds #' to a different zone in the argument to `x`, and cell values must -#' contain binary `numeric` values (i.e. one or zero) that indicate +#' contain binary `numeric` values (i.e., one or zero) that indicate #' if neighboring planning units (as specified in the argument to #' `data`) should be considered neighbors if they are allocated to #' different zones. The cell values along the diagonal #' of the matrix indicate if planning units that are allocated to the same #' zone should be considered neighbors or not. The default argument to -#' `zones` is an identity matrix (i.e. a matrix with ones along the +#' `zones` is an identity matrix (i.e., a matrix with ones along the #' matrix diagonal and zeros elsewhere), so that planning units are #' only considered neighbors if they are both allocated to the same zone. #' @@ -48,13 +48,13 @@ NULL #' using the [adjacency_matrix()] function. This is the default #' argument. Note that the neighborhood data must be manually defined #' using one of the other formats below when the planning unit data -#' in the argument to `x` is not spatially referenced (e.g. +#' in the argument to `x` is not spatially referenced (e.g., #' in `data.frame` or `numeric` format).} #' #' \item{`data` as a `matrix`/`Matrix` object}{where rows and columns represent #' different planning units and the value of each cell indicates if the #' two planning units are neighbors or not. Cell values should be binary -#' `numeric` values (i.e. one or zero). Cells that occur along the +#' `numeric` values (i.e., one or zero). Cells that occur along the #' matrix diagonal have no effect on the solution at all because each #' planning unit cannot be a neighbor with itself.} #' @@ -67,7 +67,7 @@ NULL #' or not. This data can be used to describe symmetric or #' asymmetric relationships between planning units. By default, #' input data is assumed to be symmetric unless asymmetric data is -#' also included (e.g. if data is present for planning units 2 and 3, then +#' also included (e.g., if data is present for planning units 2 and 3, then #' the same amount of connectivity is expected for planning units 3 and 2, #' unless connectivity data is also provided for planning units 3 and 2). #' If the argument to `x` contains multiple zones, then the columns @@ -81,7 +81,7 @@ NULL #' `numeric` values indicate if planning unit should be treated #' as being neighbors with every other planning unit when they #' are allocated to every combination of management zone. The first two -#' dimensions (i.e. rows and columns) correspond to the planning units, +#' dimensions (i.e., rows and columns) correspond to the planning units, #' and second two dimensions correspond to the management zones. For #' example, if the argument to `data` had a value of 1 at the index #' `data[1, 2, 3, 4]` this would indicate that planning unit 1 and diff --git a/R/add_proportion_decisions.R b/R/add_proportion_decisions.R index 11cd2ca16..5cf51ddb5 100644 --- a/R/add_proportion_decisions.R +++ b/R/add_proportion_decisions.R @@ -11,7 +11,7 @@ NULL #' decisions will solve much faster than problems that use binary-type #' decisions #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @inherit add_binary_decisions details return #' diff --git a/R/add_relative_targets.R b/R/add_relative_targets.R index e8eeb4da9..7c09c7803 100644 --- a/R/add_relative_targets.R +++ b/R/add_relative_targets.R @@ -9,7 +9,7 @@ NULL #' (including any locked out planning units, or planning units with `NA` #' cost data) using the [feature_abundances()] function. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param targets Object that specifies the targets for each feature. #' See the Targets format section for more information. diff --git a/R/add_semicontinuous_decisions.R b/R/add_semicontinuous_decisions.R index 27b60f15b..ca5a7c857 100644 --- a/R/add_semicontinuous_decisions.R +++ b/R/add_semicontinuous_decisions.R @@ -11,14 +11,14 @@ NULL #' function except that it has an upper bound parameter. By default, the #' decision can range from prioritizing none (0%) to all (100%) of a #' planning unit. However, an upper bound can be specified to ensure that at -#' most only a fraction (e.g. 80%) of a planning unit can be preserved. This +#' most only a fraction (e.g., 80%) of a planning unit can be preserved. This #' type of decision may be useful when it is not practical to conserve entire #' planning units. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param upper_limit `numeric` value specifying the maximum proportion -#' of a planning unit that can be reserved (e.g. set to 0.8 for 80%). +#' of a planning unit that can be reserved (e.g., set to 0.8 for 80%). #' #' @inherit add_binary_decisions details return #' diff --git a/R/add_shuffle_portfolio.R b/R/add_shuffle_portfolio.R index 90d012f88..4b4b89b25 100644 --- a/R/add_shuffle_portfolio.R +++ b/R/add_shuffle_portfolio.R @@ -9,7 +9,7 @@ NULL #' [add_top_portfolio()] when the *Gurobi* software is not #' available. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param number_solutions `integer` number of attempts to generate #' different solutions. Defaults to 10. diff --git a/R/add_top_portfolio.R b/R/add_top_portfolio.R index 9d03e6cec..f0d66d58c 100644 --- a/R/add_top_portfolio.R +++ b/R/add_top_portfolio.R @@ -7,12 +7,12 @@ NULL #' [problem()] by finding a pre-specified number of solutions that #' are closest to optimality (i.e the top solutions). #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param number_solutions `integer` number of solutions required. #' #' @details This strategy for generating a portfolio requires problems to -#' be solved using the *Gurobi* software suite (i.e. using +#' be solved using the *Gurobi* software suite (i.e., using #' [add_gurobi_solver()]. Specifically, version 9.0.0 (or greater) #' of the \pkg{gurobi} package must be installed. #' Note that the number of solutions returned may be less than the argument to diff --git a/R/boundary_matrix.R b/R/boundary_matrix.R index 3823d9ab1..59aad27b0 100644 --- a/R/boundary_matrix.R +++ b/R/boundary_matrix.R @@ -20,7 +20,7 @@ NULL #' will be used to pre-compute which planning units are adjacent to #' each other and potentially reduce the processing time required to #' generate the boundary matrices. This argument is only used when -#' the planning unit data are vector-based polygons (i.e. +#' the planning unit data are vector-based polygons (i.e., #' [sp::SpatialPolygonsDataFrame()] objects). **Note that #' using `TRUE` may crash Mac OSX systems.** The default argument #' is `FALSE`. @@ -29,11 +29,11 @@ NULL #' symmetric sparse matrix. Cells on the off-diagonal indicate the length of #' the shared boundary between two different planning units. Cells on the #' diagonal indicate length of a given planning unit's edges that have no -#' neighbors (e.g. for edges of planning units found along the +#' neighbors (e.g., for edges of planning units found along the #' coastline). **This function assumes the data are in a coordinate #' system where Euclidean distances accurately describe the proximity #' between two points on the earth**. Thus spatial data in a longitude/latitude -#' coordinate system (i.e. +#' coordinate system (i.e., #' [WGS84](https://spatialreference.org/ref/epsg/wgs-84/)) #' should be reprojected to another coordinate system before using this #' function. Note that for [`Raster-class`] objects diff --git a/R/compile.R b/R/compile.R index 440a53064..1261bbef6 100644 --- a/R/compile.R +++ b/R/compile.R @@ -6,7 +6,7 @@ NULL #' Compile a conservation planning [problem()] into an #' (potentially mixed) integer linear programming problem. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param compressed_formulation `logical` should the conservation problem #' compiled into a compressed version of a planning problem? diff --git a/R/connectivity_matrix.R b/R/connectivity_matrix.R index 193ed7250..39e8531f2 100644 --- a/R/connectivity_matrix.R +++ b/R/connectivity_matrix.R @@ -26,7 +26,7 @@ NULL #' Also, note that if the argument to `x` is a #' [`Raster-class`] object then #' argument to `y` must have the same spatial properties as it -#' (i.e. coordinate system, extent, resolution). +#' (i.e., coordinate system, extent, resolution). #' #' @param ... additional arguments passed to [fast_extract()] for #' extracting and calculating the conductance values for each planning unit. @@ -94,7 +94,7 @@ NULL #' # create connectivity matrix using habitat suitability data for each feature, #' # this could be useful if prioritisations should spatially clump #' # together adjacent planning units that have suitable habitat -#' # for the same species (e.g. to maintain functional connectivity) +#' # for the same species (e.g., to maintain functional connectivity) #' #' ## let's use the raster data for this example, and we can generate the #' ## connectivity matrix that we would use in the prioritization by @@ -113,7 +113,7 @@ NULL #' #' ## we could take this example one step further, and use weights to indicate #' ## relative importance of maintaining functional connectivity -#' ## for each feature (i.e. use the weighted sum instead of the sum) +#' ## for each feature (i.e., use the weighted sum instead of the sum) #' #' ## let's pretend that the first feature is 20 times more important #' ## than all the other species @@ -133,7 +133,7 @@ NULL #' } #' #' ## since the statistical distribution of the connectivity values -#' ## for each feature (e.g. the mean and standard deviation of the +#' ## for each feature (e.g., the mean and standard deviation of the #' ## connectivity values) are different, it might make sense -- depending #' ## on the goal of the conservation planning exercise and the underlying #' ## data -- to first normalize the conductance values before applying the diff --git a/R/constraints.R b/R/constraints.R index 40986112e..aaa03e196 100644 --- a/R/constraints.R +++ b/R/constraints.R @@ -56,7 +56,7 @@ NULL #' criteria. For example, they can be used to add #' multiple budgets, or limit the number of #' planning units selected in different administrative areas within a study -#' region (e.g. different countries).} +#' region (e.g., different countries).} #' #' \item{[add_mandatory_allocation_constraints()]}{ #' Add constraints to ensure that every planning unit is allocated to a diff --git a/R/decisions.R b/R/decisions.R index 3c5013419..858e3d5fb 100644 --- a/R/decisions.R +++ b/R/decisions.R @@ -39,7 +39,7 @@ NULL #' bound parameter. By default, the decision can range from prioritizing #' none (0%) to all (100%) of a planning unit. However, a upper #' bound can be specified to ensure that at most only a fraction -#' (e.g. 80%) of a planning unit can be preserved. This type of +#' (e.g., 80%) of a planning unit can be preserved. This type of #' decision may be useful when it is not practical to conserve the #' entire area encompassed by any single planning unit.} #' diff --git a/R/deprecated.R b/R/deprecated.R index 942a83d14..9821bd471 100644 --- a/R/deprecated.R +++ b/R/deprecated.R @@ -13,7 +13,7 @@ NULL #' (where applicable). #' If a function is described as being renamed, then this means #' that only the name of the function has changed -#' (i.e. the inputs, outputs, and underlying code remain the same). +#' (i.e., the inputs, outputs, and underlying code remain the same). #' #' @param ... not used. #' diff --git a/R/eval_boundary_summary.R b/R/eval_boundary_summary.R index 786b8eec0..af940e2eb 100644 --- a/R/eval_boundary_summary.R +++ b/R/eval_boundary_summary.R @@ -18,7 +18,7 @@ NULL #' reported by the [*Marxan* software](https://marxansolutions.org) #' (Ball *et al.* 2009). #' It is calculated using the same equations used to penalize solutions -#' according to their total exposed boundary (i.e. [add_boundary_penalties()]). +#' according to their total exposed boundary (i.e., [add_boundary_penalties()]). #' See the Examples section for examples on how differences `zone` arguments #' can be used to calculate boundaries for different combinations of zones. #' diff --git a/R/eval_connectivity_summary.R b/R/eval_connectivity_summary.R index 251ef946f..a7519ad86 100644 --- a/R/eval_connectivity_summary.R +++ b/R/eval_connectivity_summary.R @@ -16,7 +16,7 @@ NULL #' reported by the #' [*Marxan* software](https://marxansolutions.org) (Ball *et al.* 2009). #' It is calculated using the same equations used to penalize solutions -#' with connectivity data (i.e. [add_connectivity_penalties()]). +#' with connectivity data (i.e., [add_connectivity_penalties()]). #' Specifically, it is calculated as the sum of the pair-wise connectivity #' values in the argument to `data`, weighted by the value of the planning #' units in the solution. diff --git a/R/eval_cost_summary.R b/R/eval_cost_summary.R index 9f05e8f14..375e5e460 100644 --- a/R/eval_cost_summary.R +++ b/R/eval_cost_summary.R @@ -9,7 +9,7 @@ NULL #' (USD), then the total cost would be net cost (USD) needed to acquire #' all planning units selected within the solution. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param solution `numeric`, `matrix`, `data.frame`, #' [`Raster-class`], [`Spatial-class`], @@ -23,7 +23,7 @@ NULL #' [*Marxan* software](https://marxansolutions.org) (Ball *et al.* 2009). #' Specifically, the cost of a solution is defined as the sum of the cost #' values, supplied when creating a [problem()] object -#' (e.g. using the `cost_column` argument), +#' (e.g., using the `cost_column` argument), #' weighted by the status of each planning unit in the solution. #' #' @section Solution format: diff --git a/R/eval_feature_representation_summary.R b/R/eval_feature_representation_summary.R index a3be24cbe..46585d4a7 100644 --- a/R/eval_feature_representation_summary.R +++ b/R/eval_feature_representation_summary.R @@ -14,7 +14,7 @@ NULL #' #' @return [tibble::tibble()] object describing feature representation. #' Here, each row describes a specific summary statistic -#' (e.g. different management zone) for a specific feature. +#' (e.g., different management zone) for a specific feature. #' It contains the following columns: #' #' \describe{ @@ -34,13 +34,14 @@ NULL #' (not just planning units selected within the solution). #' It is calculated as the sum of the feature data, #' supplied when creating a [problem()] object -#' (e.g. presence/absence values).} +#' (e.g., presence/absence values).} #' #' \item{absolute_held}{`numeric` total amount of each feature secured within #' the solution. It is calculated as the sum of the feature data, #' supplied when creating a [problem()] object -#' (e.g. presence/absence values), weighted by the status of each -#' planning unit in the solution (e.g. selected or not for prioritization).} +#' (e.g., presence/absence values), weighted by the status of each +#' planning unit in the solution (e.g., selected or not for +#' prioritization).} #' #' \item{relative_held}{`numeric` proportion of #' each feature secured within the solution. It is calculated diff --git a/R/eval_n_summary.R b/R/eval_n_summary.R index 0496c37ec..8309b911f 100644 --- a/R/eval_n_summary.R +++ b/R/eval_n_summary.R @@ -13,8 +13,8 @@ NULL #' @details #' This summary statistic is calculated as the sum of the values in #' the solution. As a consequence, this metric can produce a -#' non-integer value (e.g. 4.3) for solutions containing proportion values -#' (e.g. generated by solving a [problem()] built using the +#' non-integer value (e.g., 4.3) for solutions containing proportion values +#' (e.g., generated by solving a [problem()] built using the #' [`add_proportion_decisions()`] function). #' #' @return [tibble::tibble()] object containing the number of planning diff --git a/R/eval_rare_richness_importance.R b/R/eval_rare_richness_importance.R index 981c9186f..aad0ad082 100644 --- a/R/eval_rare_richness_importance.R +++ b/R/eval_rare_richness_importance.R @@ -6,7 +6,7 @@ NULL #' Calculate importance scores for planning units selected in a solution #' using rarity weighted richness scores (based on Williams *et al.* 1996). #' This method is only recommended for large-scaled conservation -#' planning exercises (i.e. more than 100,000 planning units) where +#' planning exercises (i.e., more than 100,000 planning units) where #' importance scores cannot be calculated using other methods in a feasible #' period of time. This is because rarity weighted richness scores cannot (i) #' account for the cost of different planning units, (ii) account for multiple diff --git a/R/eval_replacement_importance.R b/R/eval_replacement_importance.R index 869bdddc4..07346049d 100644 --- a/R/eval_replacement_importance.R +++ b/R/eval_replacement_importance.R @@ -47,19 +47,19 @@ NULL #' replacement cost scores correspond to the reduction in the utility when #' each planning unit is locked out. Infinite values mean that no feasible #' solution exists when planning units are locked out---they are -#' absolutely essential for obtaining a solution (e.g. they contain rare +#' absolutely essential for obtaining a solution (e.g., they contain rare #' species that are not found in any other planning units or were locked in). #' Zeros values mean that planning units can swapped with other planning units #' and this will have no effect on the performance of the solution at all -#' (e.g. because they were only selected due to spatial fragmentation +#' (e.g., because they were only selected due to spatial fragmentation #' penalties). #' #' These calculations can take a long time to complete for large #' or complex conservation planning problems. As such, we using this #' method for small or moderate-sized conservation planning problems -#' (e.g. < 30,000 planning units). To reduce run time, we -#' recommend calculating these scores without additional penalties (e.g. -#' [add_boundary_penalties()]) or spatial constraints (e.g. +#' (e.g., < 30,000 planning units). To reduce run time, we +#' recommend calculating these scores without additional penalties (e.g., +#' [add_boundary_penalties()]) or spatial constraints (e.g., #' [add_contiguity_constraints()]). To further reduce run time, #' we recommend using proportion-type decisions when calculating the scores #' (see below for an example). diff --git a/R/eval_target_coverage_summary.R b/R/eval_target_coverage_summary.R index da50d27bc..a2fd140ad 100644 --- a/R/eval_target_coverage_summary.R +++ b/R/eval_target_coverage_summary.R @@ -40,16 +40,16 @@ NULL #' #' \item{sense}{`character` sense associated with each target. #' Sense values specify the nature of the target. -#' Typically (e.g. when using the [add_absolute_targets()] or +#' Typically (e.g., when using the [add_absolute_targets()] or #' [add_relative_targets()] functions), targets are specified using sense #' values indicating that the total amount of a feature held within a #' solution (ideally) be greater than or equal to a threshold amount -#' (i.e. a sense value of `">="`). -#' Additionally, targets (i.e. using the [add_manual_targets()] function) +#' (i.e., a sense value of `">="`). +#' Additionally, targets (i.e., using the [add_manual_targets()] function) #' can also be specified using sense values indicating that the total #' amount of a feature held within a solution must be equal to a -#' threshold amount (i.e. a sense value of `"="`) or smaller than or equal -#' to a threshold amount (i.e. a sense value of `"<="`). +#' threshold amount (i.e., a sense value of `"="`) or smaller than or equal +#' to a threshold amount (i.e., a sense value of `"<="`). #' This column is only included if the argument to `include_sense` is #' `TRUE`.} #' @@ -73,44 +73,45 @@ NULL #' `"feature"` and `"zone"` columns, respectively). #' This column is calculated as the sum of the feature data, #' supplied when creating a [problem()] object -#' (e.g. presence/absence values), weighted by the status of each -#' planning unit in the solution (e.g. selected or not for prioritization).} +#' (e.g., presence/absence values), weighted by the status of each +#' planning unit in the solution (e.g., selected or not for +#' prioritization).} #' #' \item{absolute_shortfall}{ `numeric` total amount by which the solution #' fails to meet each target. #' This column is calculated as the difference between the total amount #' held within the solution for the feature and (if relevant) zones -#' associated with the target (i.e. `"absolute_held"` column) and the -#' target total threshold amount (i.e. `"absolute_target"` column), with +#' associated with the target (i.e., `"absolute_held"` column) and the +#' target total threshold amount (i.e., `"absolute_target"` column), with #' values set to zero depending on the sense specified for the target -#' (e.g. if the target sense is `>=` then the difference is +#' (e.g., if the target sense is `>=` then the difference is #' set to zero if the value in the `"absolute_held"` is smaller than #' that in the `"absolute_target"` column).} #' #' \item{relative_target}{`numeric` proportion threshold amount associated #' with each target. #' This column is calculated by dividing the total threshold amount -#' associated with each target (i.e. `"absolute_target"` column) by +#' associated with each target (i.e., `"absolute_target"` column) by #' the total amount associated with each target -#' (i.e. `"total_amount"` column).} +#' (i.e., `"total_amount"` column).} #' #' \item{relative_held}{`numeric` proportion held within the solution for the #' feature and (if relevant) zones associated with each target (per the #' `"feature"` and `"zone"` columns, respectively). #' This column is calculated by dividing the total amount held -#' for each target (i.e. `"absolute_held"` column) by the +#' for each target (i.e., `"absolute_held"` column) by the #' total amount for with each target -#' (i.e. `"total_amount"` column).} +#' (i.e., `"total_amount"` column).} #' #' \item{relative_shortfall}{`numeric` proportion by which the solution fails #' to meet each target. #' This column is calculated by dividing the total shortfall for -#' each target (i.e. `"absolute_shortfall"` column) by the -#' total amount for each target (i.e. `"total_amount"` column).} +#' each target (i.e., `"absolute_shortfall"` column) by the +#' total amount for each target (i.e., `"total_amount"` column).} #' #' \item{met}{`logical` indicating if each target is met by the solution. This #' column is calculated by checking if the total shortfall associated -#' with each target (i.e. `"absolute_shortfall`" column) is equal to +#' with each target (i.e., `"absolute_shortfall`" column) is equal to #' zero.} #' #' } diff --git a/R/feature_abundances.R b/R/feature_abundances.R index e65398119..28c20cf5f 100644 --- a/R/feature_abundances.R +++ b/R/feature_abundances.R @@ -6,17 +6,17 @@ NULL #' Calculate the total abundance of each feature found in the planning units #' of a conservation planning problem. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param na.rm `logical` should planning units with `NA` cost #' data be excluded from the abundance calculations? The default argument #' is `FALSE`. #' #' @details Planning units can have cost data with finite values -#' (e.g. 0.1, 3, 100) and `NA` values. This functionality is provided so +#' (e.g., 0.1, 3, 100) and `NA` values. This functionality is provided so #' that locations which are not available for protected area acquisition can #' be included when calculating targets for conservation features -#' (e.g. when targets are specified using [add_relative_targets()]). +#' (e.g., when targets are specified using [add_relative_targets()]). #' If the total amount of each feature in all the planning units is #' required---including the planning units with `NA` cost data---then the #' the `na.rm` argument should be set to `FALSE`. However, if @@ -129,8 +129,8 @@ NULL #' s5 <- solve(p5) #' #' # plot the solution -#' # this solution contains all the planning units with finite cost data (i.e. -#' # cost data that do not have NA values) +#' # this solution contains all the planning units with finite cost data +#' # (i.e., cost data that do not have NA values) #' plot(s5) #' } #' @export diff --git a/R/feature_names.R b/R/feature_names.R index bbb985f49..afc93e37f 100644 --- a/R/feature_names.R +++ b/R/feature_names.R @@ -5,7 +5,7 @@ NULL #' #' Extract the names of the features in an object. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) or [Zones()] +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) or [Zones()] #' object. #' #' @return `character` feature names. diff --git a/R/importance.R b/R/importance.R index 26f2d10a2..de7d94551 100644 --- a/R/importance.R +++ b/R/importance.R @@ -16,7 +16,7 @@ NULL #' Calculate importance scores using replacement costs (based #' on Cabeza and Moilanen 2006). #' These scores quantify the change in the objective -#' function (e.g. additional costs required to meet feature targets) of the +#' function (e.g., additional costs required to meet feature targets) of the #' optimal solution if a given planning unit in a solution cannot be acquired. #' They can (i) account for the cost of different planning units, (ii) account #' for multiple management zones, (iii) apply to any objective function, and @@ -27,7 +27,7 @@ NULL #' Calculate importance scores following Ferrier *et al.* (2000). #' These scores measure importance based on how critical #' planning units are for meeting targets. They can only be applied to -#' conservation problems with a minimum set objective and a single zone (i.e. +#' conservation problems with a minimum set objective and a single zone (i.e., #' the classic *Marxan*-type problem). Furthermore---unlike the #' replacement cost scores---these scores provide a #' score for each feature within each planning unit, providing insight into @@ -51,8 +51,8 @@ NULL #' zones considered in the problem -- and measure planning unit importance based #' on degradation of the prioritization. #' Although the replacement cost scores can be calculated for small and -#' moderate sized problems (e.g. less than 30,000 planning units), they may not -#' be feasible for particularly large problems (e.g. more than 100,000 planning +#' moderate sized problems (e.g., less than 30,000 planning units), they may not +#' be feasible for particularly large problems (e.g., more than 100,000 planning #' units). In such cases, we recommend calculating importance scores using the #' Ferrier method. This is because the Ferrier method can be #' calculated relatively quickly for large-sized problems and it diff --git a/R/marxan_boundary_data_to_matrix.R b/R/marxan_boundary_data_to_matrix.R index 6e767e1ac..6e931bd7f 100644 --- a/R/marxan_boundary_data_to_matrix.R +++ b/R/marxan_boundary_data_to_matrix.R @@ -11,7 +11,7 @@ NULL #' a single zone, then a matrix object is returned. Otherwise if the boundary #' data contains data for multiple zones, then an array is returned. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object that +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object that #' contains planning unit and zone data to ensure that the argument to #' `data` is converted correctly. This argument can be set to #' `NULL` if checks are not required (not recommended). diff --git a/R/marxan_problem.R b/R/marxan_problem.R index bdc8a960e..4cfba0cb5 100644 --- a/R/marxan_problem.R +++ b/R/marxan_problem.R @@ -6,7 +6,7 @@ NULL #' Create a conservation planning [problem()] following the #' mathematical formulations used in *Marxan* (detailed in Beyer #' *et al.* 2016). Note that these problems are solved using -#' exact algorithms and not simulated annealing (i.e. the *Marxan* software). +#' exact algorithms and not simulated annealing (i.e., the *Marxan* software). #' #' @param x `character` file path for a *Marxan* input file (typically #' called `"input.dat"`), or `data.frame` containing planning unit @@ -108,7 +108,7 @@ NULL #' [official *Marxan* website](https://marxansolutions.org) and Ball #' *et al.* (2009). #' -#' @return [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @return [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @references #' Ball IR, Possingham HP, and Watts M (2009) *Marxan and relatives: diff --git a/R/number_of_features.R b/R/number_of_features.R index 381ab84c6..ebbe8d7c3 100644 --- a/R/number_of_features.R +++ b/R/number_of_features.R @@ -5,7 +5,7 @@ NULL #' #' Extract the number of features in an object. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]), +#' @param x [problem()] (i.e., [`ConservationProblem-class`]), #' [`OptimizationProblem-class`], or [Zones()] object. #' #' @return `integer` number of features. diff --git a/R/number_of_planning_units.R b/R/number_of_planning_units.R index 36c2b9de9..2030e1839 100644 --- a/R/number_of_planning_units.R +++ b/R/number_of_planning_units.R @@ -5,7 +5,7 @@ NULL #' #' Extract the number of planning units in an object. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]), +#' @param x [problem()] (i.e., [`ConservationProblem-class`]), #' [`OptimizationProblem-class`], or [Zones()] object. #' #' @return `integer` number of planning units. diff --git a/R/number_of_total_units.R b/R/number_of_total_units.R index bb31dfc8e..fecf7f48c 100644 --- a/R/number_of_total_units.R +++ b/R/number_of_total_units.R @@ -5,7 +5,7 @@ NULL #' #' Extract the number of total units in an object. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]), +#' @param x [problem()] (i.e., [`ConservationProblem-class`]), #' [`OptimizationProblem-class`], or [Zones()] object. #' #' @return `integer` number of total units. diff --git a/R/number_of_zones.R b/R/number_of_zones.R index 5b80ca1b7..dccab7350 100644 --- a/R/number_of_zones.R +++ b/R/number_of_zones.R @@ -5,7 +5,7 @@ NULL #' #' Extract the number of zones in an object. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]), +#' @param x [problem()] (i.e., [`ConservationProblem-class`]), #' [`OptimizationProblem-class`], or [Zones()] object. #' #' @return `integer` number of zones. diff --git a/R/package.R b/R/package.R index 8870121a6..28d0e592f 100644 --- a/R/package.R +++ b/R/package.R @@ -38,7 +38,7 @@ NULL #' @details This package contains several vignettes that are designed to #' showcase its functionality. To view them, please use the code #' `vignette("name", package = "prioritizr")` where `"name"` is the -#' name of the desired vignette (e.g. `"gurobi_installation"`). +#' name of the desired vignette (e.g., `"gurobi_installation"`). #' #' \describe{ #' diff --git a/R/penalties.R b/R/penalties.R index db277e4bd..f69cc74db 100644 --- a/R/penalties.R +++ b/R/penalties.R @@ -6,7 +6,7 @@ NULL #' A penalty can be applied to a conservation planning [problem()] to #' penalize solutions according to a specific metric. Penalties---unlike #' [constraints]---act as an explicit trade-off with the objective -#' being minimized or maximized (e.g. solution cost when used with +#' being minimized or maximized (e.g., solution cost when used with #' [add_min_set_objective()]). #' #' @details Both penalties and constraints can be used to modify a problem and @@ -31,7 +31,7 @@ NULL #' \item{[add_linear_penalties()]}{Add penalties to a #' conservation problem to favor solutions that avoid selecting #' planning units based on a certain variable -#' (e.g. anthropogenic pressure).} +#' (e.g., anthropogenic pressure).} #' #' } #' diff --git a/R/planning_unit_solution_status.R b/R/planning_unit_solution_status.R index 1112beeb4..7a5b69c4c 100644 --- a/R/planning_unit_solution_status.R +++ b/R/planning_unit_solution_status.R @@ -5,7 +5,7 @@ NULL #' #' Extract planning unit solution status values. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @param solution object with solution data. #' diff --git a/R/portfolios.R b/R/portfolios.R index d60ff242d..96fea9b60 100644 --- a/R/portfolios.R +++ b/R/portfolios.R @@ -6,10 +6,10 @@ NULL #' Conservation planning exercises rarely have access to all the #' data needed to identify the *truly* perfect solution. This is because #' available data may lack important details -#' (e.g. land acquisition costs may be unavailable), contain errors -#' (e.g. species presence/absence data may have false positives), +#' (e.g., land acquisition costs may be unavailable), contain errors +#' (e.g., species presence/absence data may have false positives), #' or key objectives may not be formally incorporated into the -#' prioritization process (e.g. future land use requirements). +#' prioritization process (e.g., future land use requirements). #' As such, conservation planners can help decision makers by providing #' them with a portfolio of solutions to inform their decision. #' diff --git a/R/presolve_check.R b/R/presolve_check.R index 6ab37e02d..ebcd7676f 100644 --- a/R/presolve_check.R +++ b/R/presolve_check.R @@ -12,7 +12,7 @@ NULL #' false positives. Please note that these checks will not be able to #' verify if a problem has a feasible solution or not. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) or +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) or #' [`OptimizationProblem-class`] object. #' #' @details This function checks for issues that are likely to result in @@ -21,7 +21,7 @@ NULL #' planning units have negative cost values (after applying penalties if any #' were specified). Although such conservation planning problems #' are mathematically valid, they are generally the result of a coding mistake -#' when building the problem (e.g. using an absurdly high +#' when building the problem (e.g., using an absurdly high #' penalty value or using the wrong dataset to lock in planning units). #' Thus such issues, if they are indeed issues and not false positives, can #' be fixed by carefully checking the code, data, and parameters used to build @@ -30,15 +30,15 @@ NULL #' This function then checks for values that may lead to numerical instability #' issues when solving the problem. Specifically, it checks if the range of #' values in certain components of the optimization problem are over a -#' certain threshold (i.e. \eqn{1 \times 10 ^9}{1e+9}) or if the values +#' certain threshold (i.e., \eqn{1 \times 10 ^9}{1e+9}) or if the values #' themselves exceed a certain threshold -#' (i.e. \eqn{1 \times 10^{10}}{1e+10}). +#' (i.e., \eqn{1 \times 10^{10}}{1e+10}). #' In most cases, such issues will simply cause an exact #' algorithm solver to take a very long time to generate a solution. In rare #' cases, such issues can cause incorrect calculations which can lead #' to exact algorithm solvers returning infeasible solutions -#' (e.g. a solution to the minimum set problem where not all targets are met) -#' or solutions that exceed the specified optimality gap (e.g. a suboptimal +#' (e.g., a solution to the minimum set problem where not all targets are met) +#' or solutions that exceed the specified optimality gap (e.g., a suboptimal #' solution when a zero optimality gap is specified). #' #' What can you do if a conservation planning problem fails to pass these @@ -56,7 +56,7 @@ NULL #' costs of the planning units in terms of USD then you might have #' some planning units that cost over one billion dollars in large-scale #' planning exercises. This can be fixed by rescaling the values so that they -#' are smaller (e.g. multiplying the values by a number smaller than one, or +#' are smaller (e.g., multiplying the values by a number smaller than one, or #' expressing them as a fraction of the maximum cost). Let's consider another #' common issue, let's pretend that you used habitat suitability models to #' predict the amount of suitable habitat @@ -83,7 +83,7 @@ NULL #' solving the problem, you will need to manually recalculate the cost #' of the solutions but at least now you can be confident that you have the #' optimal solution. Now let's pretend that you are using the maximum features -#' objective (i.e. [add_max_features_objective()]) and assigned some +#' objective (i.e., [add_max_features_objective()]) and assigned some #' really high weights to the targets for some features to ensure that their #' targets were met in the optimal solution. If you set the weights for #' these features to one billion then you will probably run into numerical @@ -91,7 +91,7 @@ NULL #' guarantee that these features will be represented in the optimal solution #' and use this value instead of one billion. This minimum weight value #' can be calculated as the sum of the weight values for the other features -#' and adding a small number to it (e.g. 1). Finally, if you're running out +#' and adding a small number to it (e.g., 1). Finally, if you're running out #' of ideas for addressing numerical stability issues you have one remaining #' option: you can use the `numeric_focus` argument in the #' [add_gurobi_solver()] function to tell the solver to pay extra diff --git a/R/problem.R b/R/problem.R index 8dd0ddc80..ca7e2e129 100644 --- a/R/problem.R +++ b/R/problem.R @@ -6,7 +6,7 @@ NULL #' Create a systematic conservation planning problem. This function is used to #' specify the basic data used in a spatial prioritization problem: the #' spatial distribution of the planning units and their costs, as well as -#' the features (e.g. species, ecosystems) that need to be conserved. After +#' the features (e.g., species, ecosystems) that need to be conserved. After #' constructing this `ConservationProblem-class` object, it can be #' customized to meet specific goals using [objectives], #' [targets], [constraints], and @@ -29,7 +29,7 @@ NULL #' cells to `NA`, or use the `add_locked_out_constraint` function. #' #' @param features The feature data can be specified in a variety of ways. -#' The specific formats that can be used depend on the cost data format (i.e. +#' The specific formats that can be used depend on the cost data format (i.e., #' argument to `x`) and whether the problem should have a single zone or #' multiple zones. If the problem should have a single zone, then the feature #' data can be specified following: @@ -38,7 +38,7 @@ NULL #' [`x = sf::st_sf()`][sf::st_sf()]: #' [`y = Raster-class`][raster::Raster-class] #' object showing the distribution of conservation features. Missing -#' values (i.e. `NA` values) can be used to indicate the absence of +#' values (i.e., `NA` values) can be used to indicate the absence of #' a feature in a particular cell instead of explicitly setting these #' cells to zero. Note that this argument type for `features` can #' only be used to specify data for problems involving a single zone. @@ -77,7 +77,7 @@ NULL #' [`x = sf::st_sf()`][sf::st_sf()]: #' [`y = ZonesRaster`][zones()]: #' object showing the distribution of conservation features in multiple -#' zones. As above, missing values (i.e. `NA` values) can be used to +#' zones. As above, missing values (i.e., `NA` values) can be used to #' indicate the absence of a feature in a particular cell instead of #' explicitly setting these cells to zero. #' * [`x = Spatial-class`][sp::Spatial-class], or @@ -159,34 +159,34 @@ NULL #' on the management action(s), you can compile the following data. #' #' First, you will need to create a set of planning units -#' (i.e. discrete spatial areas) to inform decision making. +#' (i.e., discrete spatial areas) to inform decision making. #' Planning units are often created by subdividing a study region #' into a set square or hexagonal cells. They can also be created using -#' administrative boundaries (e.g. provinces), land management boundaries -#' (e.g. property boundaries derived from cadastral data), or -#' ecological boundaries (e.g. based on ecosystem classification data). -#' The size (i.e. spatial grain) of the planning units is often determined +#' administrative boundaries (e.g., provinces), land management boundaries +#' (e.g., property boundaries derived from cadastral data), or +#' ecological boundaries (e.g., based on ecosystem classification data). +#' The size (i.e., spatial grain) of the planning units is often determined #' based on a compromise between the scale needed to inform decision making, the #' spatial accuracy (resolution) of available datasets, and #' the computational resources available for generating prioritizations -#' (e.g. RAM and number of CPUs on your computer). +#' (e.g., RAM and number of CPUs on your computer). #' #' Second, you will need data to quantify the cost of implementing #' implementing each management action within each planning unit. #' Critically, the cost data should reflect the management action(s) #' considered in the exercise. #' For example, costs are often specified using data that reflect economic -#' expenditure (e.g. land acquisition cost), -#' socioeconomic conditions (e.g. human population density), +#' expenditure (e.g., land acquisition cost), +#' socioeconomic conditions (e.g., human population density), #' opportunity costs of foregone commercial activities -#' (e.g. logging or agriculture), or +#' (e.g., logging or agriculture), or #' opportunity costs of foregone recreational activities -#' (e.g. recreational fishing) activities, +#' (e.g., recreational fishing) activities, #' In some cases -- depending on the management action(s) considered -- #' it can make sense to use a constant cost value -#' (e.g. all planning units are assigned a cost value equal to one) +#' (e.g., all planning units are assigned a cost value equal to one) #' or use a cost value based on spatial extent -#' (e.g. each planning unit is assigned a cost value based on its total area). +#' (e.g., each planning unit is assigned a cost value based on its total area). #' Also, in most cases, you want to avoid negative cost values. #' This because a negative value means that a place is *desirable* #' for implementing a management action, and such places will almost @@ -197,13 +197,13 @@ NULL #' To achieve this, you will need to select a set of conservation features #' that relate to the over-arching goals of the exercise. #' For example, conservation features often include -#' species (e.g. Clouded Leopard), habitats (e.g. mangroves or +#' species (e.g., Clouded Leopard), habitats (e.g., mangroves or #' cloud forest), or ecosystems. #' The benefit that each feature derives from a planning unit -#' can take a variety of forms, but is typically occupancy (i.e. +#' can take a variety of forms, but is typically occupancy (i.e., #' presence or absence), area of occurrence within each planning unit -#' (e.g. based on species' geographic range data), or -#' a measure of habitat suitability (e.g. estimated using a statistical model). +#' (e.g., based on species' geographic range data), or +#' a measure of habitat suitability (e.g., estimated using a statistical model). #' After compiling these data, you have the minimal data need to generate #' a prioritization. #' @@ -256,7 +256,7 @@ NULL #' formulated as mixed integer linear programming problem, you can use #' the [write_problem()] function to save the optimization problem #' to a plain-text file on your computer and then view it using a standard -#' text editor (e.g. Notepad). +#' text editor (e.g., Notepad). #' #' Please note that this function internally computes the amount of each #' feature in each planning unit when this data is not supplied (using the @@ -322,13 +322,13 @@ NULL #' add_default_solver(verbose = FALSE) #' #' # since geo-processing can be slow for large spatial vector datasets -#' # (e.g. polygons, lines, points), it can be worthwhile to pre-process the +#' # (e.g., polygons, lines, points), it can be worthwhile to pre-process the #' # planning unit data so that it contains columns indicating the amount of #' # each feature inside each planning unit -#' # (i.e. each column corresponds to a different feature) +#' # (i.e., each column corresponds to a different feature) #' #' # calculate the amount of each species within each planning unit -#' # (i.e. SpatialPolygonsDataFrame object) +#' # (i.e., SpatialPolygonsDataFrame object) #' pre_proc_data <- rij_matrix(sim_pu_polygons, sim_features) #' #' # add extra columns to the polygon (Spatial) planning unit data @@ -361,7 +361,7 @@ NULL #' #' # in addition to spatially explicit data, pre-processed aspatial data #' # can also be used to create a problem -#' # (e.g. data created using external spreadsheet software) +#' # (e.g., data created using external spreadsheet software) #' costs <- sim_pu_polygons$cost #' features <- data.frame(id = seq_len(nlayers(sim_features)), #' name = names(sim_features)) @@ -1062,7 +1062,7 @@ methods::setMethod( assertthat::assert_that( all(!geometry_classes(x) %in% c("GEOMETRYCOLLECTION", "MULTIPOINT")), msg = paste("argument to x contains invalid geometry types", - "(i.e. GEOMETRYCOLLECTION or MULTIPOINT)")) + "(i.e., GEOMETRYCOLLECTION or MULTIPOINT)")) x2 <- sf::st_drop_geometry(x) assertthat::assert_that( all(unlist(as.list(features), recursive = TRUE, use.names = FALSE) %in% diff --git a/R/rij_matrix.R b/R/rij_matrix.R index e30d6e7ec..87e57dfc1 100644 --- a/R/rij_matrix.R +++ b/R/rij_matrix.R @@ -21,7 +21,7 @@ NULL #' @param ... not used. #' #' @details -#' Generally, processing vector (i.e. [`Spatial-class`] or +#' Generally, processing vector (i.e., [`Spatial-class`] or #' [sf::sf()]) data takes much #' longer to process then [`Raster-class`] data, #' so it is recommended to use [`Raster-class`] data diff --git a/R/run_calculations.R b/R/run_calculations.R index 89748dac2..99061f87e 100644 --- a/R/run_calculations.R +++ b/R/run_calculations.R @@ -6,10 +6,10 @@ NULL #' Execute preliminary calculations in a conservation problem and store the #' results for later use. This function is useful when creating slightly #' different versions of the same conservation planning problem that involve -#' the same pre-processing steps (e.g. calculating boundary data), because +#' the same pre-processing steps (e.g., calculating boundary data), because #' means that the same calculations will not be run multiple times. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) object. +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) object. #' #' @details This function is used for the effect of modifying the input #' [`ConservationProblem-class`] object. As such, it does not return diff --git a/R/solve.R b/R/solve.R index 793ed079c..f3311eb62 100644 --- a/R/solve.R +++ b/R/solve.R @@ -5,7 +5,7 @@ NULL #' #' Solve a conservation planning [problem()]. #' -#' @param a [problem()] (i.e. [`ConservationProblem-class`]) or +#' @param a [problem()] (i.e., [`ConservationProblem-class`]) or #' [`OptimizationProblem-class`] object. #' #' @param b [`Solver-class`] object. Not used if `a` is an @@ -29,15 +29,15 @@ NULL #' then the best available exact algorithm solver will be used by default #' (see [add_default_solver()]. Although these exact algorithm #' solvers will often display a lot of information that isn't really that -#' helpful (e.g. nodes, cutting planes), they do display information -#' about the progress they are making on solving the problem (e.g. the +#' helpful (e.g., nodes, cutting planes), they do display information +#' about the progress they are making on solving the problem (e.g., the #' performance of the best solution found at a given point in time). If #' potential issues were detected during the #' presolve checks (see [presolve_check()]) -#' and the problem is being forcibly solved (i.e. with `force = TRUE`), +#' and the problem is being forcibly solved (i.e., with `force = TRUE`), #' then it is also worth checking for any warnings displayed by the solver #' to see if these potential issues are actually causing issues -#' (e.g. *Gurobi* can display warnings that include +#' (e.g., *Gurobi* can display warnings that include #' `"Warning: Model contains large matrix coefficient range"` and #' `"Warning: Model contains large rhs"`). #' @@ -85,11 +85,11 @@ NULL #' will contain fields (columns) that solution the values. #' Specifically, the field name(s) containing the solution values #' be will named as `"solution_XXX"` where `"XXX"` corresponds to a solution -#' identifier (e.g. `"solution_1"`). +#' identifier (e.g., `"solution_1"`). #' If the argument to `a` contains multiple zones, then the fields #' containing solutions will be named as `"solution_XXX_YYY"` where #' `"XXX"` corresponds to the solution identifier and `"YYY"` is the name -#' of the management zone (e.g. `"solution_1_zone1"`).} +#' of the management zone (e.g., `"solution_1_zone1"`).} #' #' } #' @@ -100,8 +100,8 @@ NULL #' attributes: `"objective"` containing the solution's objective, #' `"runtime"` denoting the number of seconds that elapsed while solving #' the problem, and `"status"` describing the status of the solution -#' (e.g. `"OPTIMAL"` indicates that the optimal solution was found). -#' In most cases, the first solution (e.g. `"solution_1"`) +#' (e.g., `"OPTIMAL"` indicates that the optimal solution was found). +#' In most cases, the first solution (e.g., `"solution_1"`) #' will contain the best solution found by the solver (note that this #' may not be an optimal solution depending on the gap used to solve #' the problem and noting that the default gap is 0.1). @@ -289,7 +289,7 @@ methods::setMethod( # check that solution is valid #nocov start if (is.null(sol) || is.null(sol[[1]]$x)) { - stop("no solution found (e.g. due to problem infeasibility or time ", + stop("no solution found (e.g., due to problem infeasibility or time ", "limits)") } #nocov end diff --git a/R/zone_names.R b/R/zone_names.R index 06451edca..905a7af6e 100644 --- a/R/zone_names.R +++ b/R/zone_names.R @@ -5,7 +5,7 @@ NULL #' #' Extract the names of zones in an object. #' -#' @param x [problem()] (i.e. [`ConservationProblem-class`]) or [Zones()] +#' @param x [problem()] (i.e., [`ConservationProblem-class`]) or [Zones()] # object. #' #' @return `character` zone names. diff --git a/R/zones.R b/R/zones.R index 0ae672db1..de9c8bde8 100644 --- a/R/zones.R +++ b/R/zones.R @@ -17,7 +17,7 @@ NULL #' Specifically, the data should describe the expected amount of each #' feature within each planning unit given each management zone. #' For example, the data could describe the occupancy -#' (e.g. presence/absence), probability of occurrence, or +#' (e.g., presence/absence), probability of occurrence, or #' abundance expected for each feature when each planning unit #' is allocated to a different zone. #' diff --git a/README.Rmd b/README.Rmd index 44b96120d..90aded7f8 100644 --- a/README.Rmd +++ b/README.Rmd @@ -6,7 +6,7 @@ output: -# prioritizr: +# prioritizr: # Systematic Conservation Prioritization in R @@ -242,8 +242,23 @@ spplot(rc, "rc", main = "Irreplaceability", xlim = c(-0.1, 1.1), "#FF0000")) ``` -This short example demonstrates how the _prioritizr R_ package can be used to build a minimal conservation problem, how constraints and penalties can be iteratively added to the problem to obtain a solution, and how importance scores can be calculated for the solution to identify critical places. Although we explored just a few different functions for modifying the a conservation problem, the _prioritizr R_ package provides many functions for specifying objectives, constraints, penalties, and decision variables, so that you can build and custom-tailor a conservation planning problem to suit your exact planning scenario. +This short example demonstrates how the _prioritizr R_ package can be used to build and customize conservation problems, and then solve them to generate solutions. Although we explored just a few different functions for modifying a conservation problem, the package provides many functions for specifying objectives, constraints, penalties, and decision variables, so that you can build and custom-tailor conservation planning problems to suit your planning scenario. + +## Learning resources + +The [package website](https://prioritizr.net/index.html) contains information on the _prioritizr R_ package. Here you can find [documentation for every function and built-in dataset](https://prioritizr.net/reference/index.html), and [news describing the updates in each package version](https://prioritizr.net/news/index.html). It also contains the following articles and tutorials. + +* [**Getting started**](https://prioritizr.net/articles/prioritizr.html): Short tutorial on using the package. +* [**Package overview**](https://prioritizr.net/articles/package_overview.html): Introduction to systematic conservation planning and a comprehensive overview of the package. +* [**Connectivity tutorial**](https://prioritizr.net/articles/connectivity_tutorial.html): Tutorial on incorporating connectivity into prioritizations. +* [**Calibrating trade-offs tutorial**](https://prioritizr.net/articles/calibrating_trade-offs_tutorial.html): Tutorial on running calibration analyses to satisfy multiple criteria. +* [**Management zones tutorial**](https://prioritizr.net/articles/management_zones_tutorial.html): Tutorial on incorporating multiple management zones and actions into prioritizations. +* [**Gurobi installation guide**](https://prioritizr.net/articles/gurobi_installation_guide.html): Instructions for installing the _Gurobi_ optimization suite for generating prioritizations. +* [**Solver benchmarks**](https://prioritizr.net/articles/solver_benchmarks.html): Performance comparison of optimization solvers for generating prioritizations. +* [**Publication record**](https://prioritizr.net/articles/publication_record.html): List of publications that have cited the package. + +Additional resources can also be found in [online repositories under the _prioritizr_ organization](https://github.com/prioritizr). These resources include [slides for talks and seminars about the package](https://github.com/prioritizr/teaching). Additionally, workshop materials are available too (e.g., the [Massey University 2021 workshop](https://prioritizr.github.io/massey-workshop/) and the [PacMara 2019 workshop](https://prioritizr.github.io/PacMara_workshop/)). ## Getting help -Please refer to the [package website](https://prioritizr.net/index.html) for more information on the _prioritizr R_ package. This website contains [a comprehensive tutorial on the package](https://prioritizr.net/articles/prioritizr.html), [instructions for installing the _Gurobi_ software suite to solve large-scale and complex conservation planning problems](https://prioritizr.net/articles/gurobi_installation.html), and [a tutorial on solving problems with multiple management zones](https://prioritizr.net/articles/zones.html). It also provides two worked examples that involve real-world data from [Tasmania, Australia](https://prioritizr.net/articles/tasmania.html) and [Salt Spring Island, Canada](https://prioritizr.net/articles/saltspring.html). Additionally, slides for previous seminars about the package can be found in [teaching repository](https://github.com/prioritizr/teaching). Furthermore, materials accompanying previous workshops are also available online too (i.e. the [CIBIO 2019 workshop](https://prioritizr.github.io/cibio-workshop/) and the [PacMara 2019 workshop](https://prioritizr.github.io/PacMara_workshop/)). If you have any questions about using the _prioritizr R_ package or suggestions for improving it, please [file an issue at the package's online code repository](https://github.com/prioritizr/prioritizr/issues/new). +If you have any questions about the _prioritizr R_ package or suggestions for improving it, please [post an issue on the code repository](https://github.com/prioritizr/prioritizr/issues/new). diff --git a/README.md b/README.md index d14480584..b40b819cc 100644 --- a/README.md +++ b/README.md @@ -1,7 +1,7 @@ -# prioritizr: +# prioritizr: # Systematic Conservation Prioritization in R @@ -69,7 +69,7 @@ Alternatively, to cite the latest development version, please use: > Hanson JO, Schuster R, Morrell N, Strimas-Mackey M, Edwards BPM, Watts > ME, Arcese P, Bennett J, Possingham HP (2021). prioritizr: Systematic -> Conservation Prioritization in R. R package version 7.1.1.4. Available +> Conservation Prioritization in R. R package version 7.1.1.5. Available > at . Additionally, we keep a [record of @@ -249,7 +249,7 @@ s1 <- solve(p1) ## StrongCG: 2 ## Flow cover: 1 ## - ## Explored 145469 nodes (243327 simplex iterations) in 3.74 seconds (2.59 work units) + ## Explored 145469 nodes (243327 simplex iterations) in 3.83 seconds (2.59 work units) ## Thread count was 1 (of 8 available processors) ## ## Solution count 6: 2627.64 2747.38 2761.33 ... 3139.89 @@ -271,7 +271,7 @@ print(attr(s1, "runtime")) ``` ## solution_1 - ## 3.762 + ## 3.836 ``` r # extract state message from the solver @@ -419,7 +419,7 @@ s2 <- solve(p2) ## StrongCG: 1 ## Flow cover: 1 ## - ## Explored 10262 nodes (23307 simplex iterations) in 0.53 seconds (0.54 work units) + ## Explored 10262 nodes (23307 simplex iterations) in 0.62 seconds (0.54 work units) ## Thread count was 1 (of 8 available processors) ## ## Solution count 5: 2838.26 2839.12 3021.28 ... 3027.7 @@ -616,36 +616,64 @@ spplot(rc, "rc", main = "Irreplaceability", xlim = c(-0.1, 1.1), This short example demonstrates how the *prioritizr R* package can be -used to build a minimal conservation problem, how constraints and -penalties can be iteratively added to the problem to obtain a solution, -and how importance scores can be calculated for the solution to identify -critical places. Although we explored just a few different functions for -modifying the a conservation problem, the *prioritizr R* package -provides many functions for specifying objectives, constraints, -penalties, and decision variables, so that you can build and -custom-tailor a conservation planning problem to suit your exact -planning scenario. +used to build and customize conservation problems, and then solve them +to generate solutions. Although we explored just a few different +functions for modifying a conservation problem, the package provides +many functions for specifying objectives, constraints, penalties, and +decision variables, so that you can build and custom-tailor conservation +planning problems to suit your planning scenario. + +## Learning resources + +The [package website](https://prioritizr.net/index.html) contains +information on the *prioritizr R* package. Here you can find +[documentation for every function and built-in +dataset](https://prioritizr.net/reference/index.html), and [news +describing the updates in each package +version](https://prioritizr.net/news/index.html). It also contains the +following articles and tutorials. + +- [**Getting + started**](https://prioritizr.net/articles/prioritizr.html): Short + tutorial on using the package. +- [**Package + overview**](https://prioritizr.net/articles/package_overview.html): + Introduction to systematic conservation planning and a comprehensive + overview of the package. +- [**Connectivity + tutorial**](https://prioritizr.net/articles/connectivity_tutorial.html): + Tutorial on incorporating connectivity into prioritizations. +- [**Calibrating trade-offs + tutorial**](https://prioritizr.net/articles/calibrating_trade-offs_tutorial.html): + Tutorial on running calibration analyses to satisfy multiple + criteria. +- [**Management zones + tutorial**](https://prioritizr.net/articles/management_zones_tutorial.html): + Tutorial on incorporating multiple management zones and actions into + prioritizations. +- [**Gurobi installation + guide**](https://prioritizr.net/articles/gurobi_installation_guide.html): + Instructions for installing the *Gurobi* optimization suite for + generating prioritizations. +- [**Solver + benchmarks**](https://prioritizr.net/articles/solver_benchmarks.html): + Performance comparison of optimization solvers for generating + prioritizations. +- [**Publication + record**](https://prioritizr.net/articles/publication_record.html): + List of publications that have cited the package. + +Additional resources can also be found in [online repositories under the +*prioritizr* organization](https://github.com/prioritizr). These +resources include [slides for talks and seminars about the +package](https://github.com/prioritizr/teaching). Additionally, workshop +materials are available too (e.g., the [Massey University 2021 +workshop](https://prioritizr.github.io/massey-workshop/) and the +[PacMara 2019 +workshop](https://prioritizr.github.io/PacMara_workshop/)). ## Getting help -Please refer to the [package website](https://prioritizr.net/index.html) -for more information on the *prioritizr R* package. This website -contains [a comprehensive tutorial on the -package](https://prioritizr.net/articles/prioritizr.html), [instructions -for installing the *Gurobi* software suite to solve large-scale and -complex conservation planning -problems](https://prioritizr.net/articles/gurobi_installation.html), and -[a tutorial on solving problems with multiple management -zones](https://prioritizr.net/articles/zones.html). It also provides two -worked examples that involve real-world data from [Tasmania, -Australia](https://prioritizr.net/articles/tasmania.html) and [Salt -Spring Island, Canada](https://prioritizr.net/articles/saltspring.html). -Additionally, slides for previous seminars about the package can be -found in [teaching repository](https://github.com/prioritizr/teaching). -Furthermore, materials accompanying previous workshops are also -available online too (i.e. the [CIBIO 2019 -workshop](https://prioritizr.github.io/cibio-workshop/) and the [PacMara -2019 workshop](https://prioritizr.github.io/PacMara_workshop/)). If you -have any questions about using the *prioritizr R* package or suggestions -for improving it, please [file an issue at the package’s online code +If you have any questions about the *prioritizr R* package or +suggestions for improving it, please [post an issue on the code repository](https://github.com/prioritizr/prioritizr/issues/new). diff --git a/_pkgdown.yml b/_pkgdown.yml index 8d59b719d..869805be1 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -1,10 +1,5 @@ url: https://prioritizr.net -home: - links: - - text: Learn about contributing - href: http://prioritizr.net/CONTRIBUTING.html - authors: Jeffrey O Hanson: href: https://jeffrey-hanson.com @@ -26,6 +21,40 @@ template: docsearch: api_key: 486efa122ea6783724263412c5f28ab3 index_name: prioritizr + +home: + sidebar: + structure: [links, citation, license, authors, dev] + links: + - text: Learn about contributing + href: http://prioritizr.net/CONTRIBUTING.html + +navbar: + structure: + left: [home, intro, reference, articles, tutorial, news] + right: [search, github] + components: + articles: + text: Articles + menu: + - text: Package overview + href: articles/package_overview.html + - text: Gurobi installation guide + href: articles/gurobi_installation_guide.html + - text: Solver benchmarks + href: articles/solver_benchmarks.html + - text: Publication record + href: articles/publication_record.html + tutorial: + text: Tutorials + menu: + - text: Connectivity + href: articles/connectivity_tutorial.html + - text: Calibrating trade-offs + href: articles/calibrating_trade-offs_tutorial.html + - text: Management zones + href: articles/management_zones_tutorial.html + reference: - title: Overview desc: Overview of the package diff --git a/docs/404.html b/docs/404.html index de82f7dd1..293d1b862 100644 --- a/docs/404.html +++ b/docs/404.html @@ -25,7 +25,7 @@ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Contributing to development of the prioritizr R package • prioritizr - - - - - - - - - - - - - - +
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Contributing to development of the prioritizr R package

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Contributing to development of the prioritizr R package

We welcome contributions to the prioritizr R package. These contributions could be simple typo fixes, sentence rewrites to improve clarity, enhancing the vignettes to provide a greater understanding this package, or completely new functions to customize conservation planning problems. No contribution is too small.

The aim of this document is to provide a comprehensive guide for making contributions to the prioritizr R package. It also serves to document the internal organization and rationale behind the design of this package. Please note that it is beyond the scope of this document to teach R programming or package development practices. To learn more about these topics, we strongly recommend reading R for Data Science, Advanced R, and R Packages. Additionally, a substantial proportion of the code in this package is written in the C++ programming language using the Rcpp R package. Therefore, individuals wishing to contribute new functionality (e.g. a function to add a new set of constraints to a conservation planning problem) may need to learn C++ programming and the Rcpp R package. To learn more about C++ programming and/or the Rcpp R package, we recommend reading Rcpp for everyone. All of these are books are free, online, and absolutely fantastic resources.

If you have any questions about contributing to prioritizr that are not covered in this document, please post an issue on the GitHub repository.

-
-

-Style guide

+
+

Style guide

This package uses American spelling for all English words. All code should use snake-case (i.e. under-scores and lower-case spelling; e.g. add_relative_targets), except for class names which use camel-case (i.e. no under-scores and upper-case letters; e.g. ConservationProblem). The <- operator should be used for object assignment. Spaces should surround all infix operators (e.g. +, -, etc.) and should be placed after commas. All indenting should use two-spaces. All lines should not exceed 80 characters in length, except for text in vignettes (and @aliases roxygen2 tags because they must be on a single line). All code should escape character objects using double quotes (i.e. " symbols). Where possible, functions from other packages should not be imported and instead should be referred to using the :: function (e.g. Matrix::sparseMatrix to access the sparseMatrix function from the Matrix package). All functions should use the assertthat package to validate arguments. This package uses the testthat package for unit testing. All functions should have at least one unit test that verifies that it works and ideally several tests that verify that invalidate arguments return an error. All private functions that are not exported via the NAMESPACE should be located in the R/internal.R file. Although this package exports the pipe operator (%>%) for ease of use, for clarity, this operator should not be used anywhere in this package’s source code (excepting documentation and unit tests).

This package uses the roxygen2 package for generating documentation. Thus help files should be generated using roxygen2 comments. Software and R package names should be written in italics in markdown documents and enclosed in \pkg tags in Latex files (e.g. ). When referring to parameter names in the documentation, they should be encapsulated by \code tags (e.g. \code{x} in help for problem). When referring to the names of columns in a data.frame object, please use the format \code{"column_name"}, where column_name is the name of the column (e.g. \code{"mpg"} to refer to a column in the mtcars object). All help files for functions should contain the following sections at a minimum: Description, Value, and Examples.

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-Prototype class

+
+

Prototype class

The main class used to represent objects in prioritizr is the pproto class (defined in R/pproto.R). This class is inspired by the ggproto system used in the ggplot2 package and uses environments to manage data (based on the proto class defined in the proto package). It has several desirable properties: pproto objects can be modified in place, specific elements in a pproto object can be modified without R needing to copy all of the data stored in the pproto object (unlike list and S3 objects in R), a pproto object can be copied without physically needing to copy all of raw data stored within it (specifically, when we copy a pproto object R just copies pointers to the data in the original pproto object). These properties are especially desirable when working with large data sets. However, they come at a cost. Notably, these “features” may be unnecessary for small data sets and so pproto objects may incur unnecessary overheads that mean manipulating them may take slightly longer than otherwise expected. Additionally, the raw syntax for working with pproto objects is object-oriented—though perhaps this may be argued as a feature and not a cost—and so some extra experience may be required to understand how to manipulate them.

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-

-Conservation problems

+
+

Conservation problems

The ConservationProblem class (defined in R/ConservationProblem-proto.R) is used to represent conservation planning objects. They are created by the problem function and should contain all the data and parameters needed to generate a mathematical formulation of the problem. They should also contain all the information needed to instantiate an interactive web application to manipulate them (using the shiny package, though the functionality to achieve this is still being developed).

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-Conservation modifiers

+
+

Conservation modifiers

The ConservationModifier class (defined in R/ConservationModifier-proto.R) is used to instantiate objects that systematically alter the mathematical formulation of a conservation planning problem (i.e. a ConservationProblem object). All of the functions used for specifying objectives, constraints, penalties, decisions, solvers, and portfolios involve creating a new ConservationModifier object and appending it to a ConservationProblem object. To help standardize the behavior of different ConservationModifier objects, we have created specializations of the ConservationModifier class: Objective (defined in R/Objective-proto.R), Constraint (defined in R/Constraint-proto.R), Penalty (defined in R/Penalty-proto.R), Decision (defined in R/Decision-proto.R), Solver (defined in R/Solver-proto.R), and Portfolio (defined in R/Portfolio-proto.R). Every single ConservationModifier object contains an apply method that is used to modify an OptimizationProblem object to “apply” the mathematical formulation described by the object.

-
-

-Optimization problems

+
+

Optimization problems

The OptimizationProblem class (defined in R/OptimizationProblem-proto.R) represents the precise mathematical formulation of a conservation planning problem. When a ConservationProblem object is “solved” (using the solve function), the ConservationProblem object is first “compiled” into an OptimizationProblem object (using the compile function) and the OptimizationProblem object is then solved (using the solve function). This distinction is important because if a contributor wants to add a new objective, constraint, penalty, or decision function to prioritizr they will need to write code that adds the mathematical formulation of the function to a OptimizationProblem object. Alas, this is not entirely trivial.

All OptimizationProblem objects are simply a wrapper to an external pointer pointer (XPtr) that points to a C++ OPTIMIZATIONPROBLEM class object (defined in src/optimization_problem.h). We decided to implement the OptimizationProblem class in this manner because (1) storing objects as external pointers reduces memory consumption and (2) the process of adding in constraints requires iteration and loops which are slow in R. We elected not to use the ompr package because (1) benchmarks at the time indicated that this package would take too long to compile problems with many constraints and (2) it uses the R Optimization Infrastructure (ROI) which as yet solve problems using Gurobi (discounting repositories on GitHub which do not appear to be actively maintained). As a consequence, Rcpp code is needed to modify OptimizationProblem objects and users will need to write Rcpp functions to add new objectives, constraints, penalties to prioritizr.

The C++ OPTIMIZATIONPROBLEM class contains the standard data needed to formulate a mixed integer linear programming problem (i.e. model sense, problem objective , constraint matrix, constraint senses, right-hand-side values, variable decision types, and variable bounds). This class also contains additional data that pertain to conservation problems (i.e. number of features, planning units, and zones). If a potential contributor is unfamiliar with the standard representation of a mixed integer linear programming problem, we encourage them to read the documentation for the gurobi R package. The fields A_i, A_j, and A_x correspond the row, column, and cells values for the constraint matrix of the optimization problem (respectively). The other fields follow standard conventions. Note that the constraint matrix is, ultimately, constructed as a Matrix::sparseMatrix so row and column indices do not need to be sequential. Additionally, all Rcpp constraint and penalty functions should be independent. In other words, though it may be computationally efficient to reuse constraints and variables encoded in other functions, each Rcpp constraint and penalty function define its own constraints and variables. All conservation planning problems are defined following one of two standard mathematical formulations: the compressed and the expanded formulation.

@@ -355,30 +268,25 @@

+
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- - - - - - - - - - + diff --git a/docs/articles/calibrating_trade-offs_tutorial.html b/docs/articles/calibrating_trade-offs_tutorial.html new file mode 100644 index 000000000..58fe9f173 --- /dev/null +++ b/docs/articles/calibrating_trade-offs_tutorial.html @@ -0,0 +1,892 @@ + + + + + + + +Calibrating trade-offs tutorial • prioritizr + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+
+
+

Calibrating trade-offs tutorial

+ + + Source: vignettes/calibrating_trade-offs_tutorial.Rmd + + +
+ + + +
+

Introduction +

+

Systematic conservation planning requires making trade-offs (Margules & Pressey 2000; Vane-Wright et al. 1991). Since different criteria may conflict with one another – or not align perfectly – prioritizations need to make trade-offs between different criteria (Klein et al. 2013). Although some criteria can easily be accounted for by using locked constraints or representation targets (e.g., Dorji et al. 2020; Hermoso et al. 2018), this is not always the case (e.g., Beger et al. 2010). For example, prioritizations often need to balance overall cost with the overall level spatial fragmentation among reserves (Hermoso et al. 2011; Stewart & Possingham 2005). Additionally, prioritizations often need to balance the overall level of connectivity among reserves against other criteria (Hermoso et al. 2012). Since the best trade-off depends on a range of factors – such as available budgets, species’ connectivity requirements, and management capacity – finding the best balance can be challenging.

+

The prioritizr R package provides multi-objective optimization methods to help identify the best trade-offs between different criteria. To achieve this, a conservation planning problem can be formulated with a primary objective (e.g., add_min_set_objective()) and penalties (e.g., add_boundary_penalties()) that relate to such criteria. When building the problem, the nature of the trade-offs can be specified using certain parameters (e.g., the penalty parameter of the add_boundary_penalties() function). To identify a prioritization that finds the best balance between different criteria, the trade-off parameters can be tuned using a calibration analysis. These analyses – in the context of systematic conservation planning – typically involve generating a set of candidate prioritizations based on different parameters, measuring their performance according to each of the criteria, and then selecting a prioritization (or set of prioritizations) based on how well they achieve the criteria (Hermoso et al. 2011; Stewart & Possingham 2005; Hermoso et al. 2012). For example, the Marxan decision support tool has a range of parameters (e.g., species penalty factors, boundary length modifier) that are calibrated to balance cost, species’ representation, and spatial fragmentation (Ardron et al. 2010).

+

The aim of this tutorial is to provide guidance on calibrating trade-offs when using the prioritizr R package. Here we will explore a couple of different approaches for generating candidate prioritizations, and methods for finding the best balance between different criteria. Specifically, we will try to generate prioritizations that strike the best balance between total cost and spatial fragmentation (measured as total boundary length). As such, the code used in this vignette will be directly applicable when performing a boundary length calibration analysis.

+
+
+

Data +

+

Let’s load the packages and dataset used in this tutorial. Since this tutorial uses the prioritizrdata R package along with several other R packages (see below), please ensure that they are all installed. This particular dataset comprises two object: tas_pu and tas_features. Although we will briefly discuss this dataset below, please refer to the Tasmania Tutorial vignette for further details.

+
+# load packages
+library(prioritizrdata)
+library(prioritizr)
+library(dplyr)
+library(tibble)
+library(scales)
+library(ggplot2)
+library(topsis)
+library(withr)
+
+# load planning unit data
+data(tas_pu)
+
+# convert planning units to sf format
+tas_pu <- st_as_sf(tas_pu)
+
+# load feature data
+data(tas_features)
+
+# print planning unit data
+print(tas_pu)
+
## Simple feature collection with 1130 features and 5 fields
+## Geometry type: MULTIPOLYGON
+## Dimension:     XY
+## Bounding box:  xmin: 298809.6 ymin: 5167775 xmax: 613818.8 ymax: 5502544
+## Projected CRS: WGS 84 / UTM zone 55S
+## First 10 features:
+##   id      cost status locked_in locked_out                       geometry
+## 0  1 60.246377      0     FALSE      FALSE MULTIPOLYGON (((328497 5497...
+## 1  2 19.863008      0     FALSE      FALSE MULTIPOLYGON (((307121.6 54...
+## 2  3 59.680513      0     FALSE      FALSE MULTIPOLYGON (((321726.1 54...
+## 3  4 32.416138      0     FALSE      FALSE MULTIPOLYGON (((304314.5 54...
+## 4  5 26.177062      0     FALSE      FALSE MULTIPOLYGON (((314958.5 54...
+## 5  6 51.262177      0     FALSE      FALSE MULTIPOLYGON (((327904.3 54...
+## 6  7 32.299112      0     FALSE      FALSE MULTIPOLYGON (((308194.1 54...
+## 7  8 38.404063      0     FALSE      FALSE MULTIPOLYGON (((322792.7 54...
+## 8  9  3.554745      0     FALSE      FALSE MULTIPOLYGON (((334896.6 54...
+## 9 10  1.834921      0     FALSE      FALSE MULTIPOLYGON (((356377.1 54...
+
+# print feature data
+print(tas_features)
+
## class      : RasterStack 
+## dimensions : 398, 359, 142882, 62  (nrow, ncol, ncell, nlayers)
+## resolution : 1000, 1000  (x, y)
+## extent     : 288801.7, 647801.7, 5142976, 5540976  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## names      : tas_features.1, tas_features.2, tas_features.3, tas_features.4, tas_features.5, tas_features.6, tas_features.7, tas_features.8, tas_features.9, tas_features.10, tas_features.11, tas_features.12, tas_features.13, tas_features.14, tas_features.15, ... 
+## min values :              0,              0,              0,              0,              0,              0,              0,              0,              0,               0,               0,               0,               0,               0,               0, ... 
+## max values :              1,              1,              1,              1,              1,              1,              1,              1,              1,               1,               1,               1,               1,               1,               1, ...
+

The tas_pu object contains planning units represented as spatial polygons (i.e., converted to a sf::st_sf() object). This object has three columns that denote the following information for each planning unit: a unique identifier (id), unimproved land value (cost), and current conservation status (locked_in). Specifically, the conservation status column indicates if at least half the area planning unit is covered by existing protected areas (denoted by a value of 1) or not (denoted by a value of zero).

+
+# plot map of planning unit costs
+plot(tas_pu[, "cost"], main = "Planning unit costs")
+

+
+# plot map of planning unit statuses
+plot(tas_pu[, "locked_in"], main = "Planning unit status")
+

+

The tas_features object describes the spatial distribution of different vegetation communities (using presence/absence data). We will use the vegetation communities as the biodiversity features for the prioritization.

+
+# plot map of the first four vegetation classes
+plot(tas_features[[1:4]], main = paste("Feature", 1:4))
+

+

We can use this dataset to generate a prioritization. Specifically, we will use the minimum set objective so that the optimization process minimizes total cost. We will add representation targets to ensure that prioritizations cover 17% of each vegetation community. Additionally, we will add constraints to ensure that planning units covered by existing protected areas are selected (i.e., locked in). Finally, we will specify that the conservation planning exercise involves binary decisions (i.e., selecting or not selecting planning units for protected area establishment).

+
+# define a problem
+p0 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# print problem
+print(p0)
+
## Conservation Problem
+##   planning units: sf (1130 units)
+##   cost:           min: 0.19249, max: 61.92727
+##   features:       tas_features.1, tas_features.2, tas_features.3, ... (62 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
+##   decisions:      Binary decision 
+##   constraints:    <Locked in planning units [257 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+# solve problem
+s0 <- solve(p0)
+
+# print result
+print(s0)
+
+# create column for making a map of the prioritization
+s0$map_1 <- case_when(
+  s0$locked_in > 0.5 ~ "locked in",
+  s0$solution_1 > 0.5 ~ "priority",
+  TRUE ~ "other"
+)
+
+# plot map of prioritization
+plot(
+  s0[, "map_1"], pal = c("purple", "grey90", "darkgreen"),
+  main = NULL, key.pos = 1
+)
+

+

We can see that the priority areas identified by the prioritization are scattered across the study area (shown in green). Indeed, none of the priority areas are connect to existing protected areas (shown in purple), and very of them are connect with other priority areas. As such, the prioritization has a high level of spatial fragmentation. If it is important avoid such levels of spatial fragmentation, then we will need to explicitly account spatial fragmentation in the optimization process.

+
+
+

Preliminary processing +

+

We need to conduct some preliminary processing procedures to prepare the data for subsequent analysis. This is important to help make it easier to find suitable trade-off parameters, and avoid numerical scaling issues that can result in overly long run times (see presolve_check() for further information). These processing steps are akin to data scaling (or normalization) procedures that are applied in statistical analysis to improve model convergence.

+

The first processing procedure involves setting the cost values for all locked in planning units to zero. This is so that the total cost estimates of the prioritization reflects the total cost of establishing new protected areas – not just total land value. In other words, we want the total cost estimate for a prioritization to reflect the cost of implementing conservation actions. This procedure is especially important when using the hierarchical approach described below, so that cost thresholds are based on percentage increases in the cost of establishing new protected areas.

+
+# set costs for planning units covered by existing protected areas to zero
+tas_pu$cost[tas_pu$locked_in > 0.5] <- 0
+
+# plot map of planning unit costs
+plot(tas_pu[, "cost"], main = "Planning unit cost")
+

+

The second procedure involves pre-computing the boundary length data and manually re-scaling the boundary length values. This procedure is important because boundary length values are often very large that, in turn, can cause numerical issues that result in excessive run times (see presolve_check() for further details).

+
+# generate boundary length data for the planning units
+tas_bd <- boundary_matrix(tas_pu)
+
+# manually re-scale the boundary length values
+tas_bd@x <- rescale(tas_bd@x, to = c(0.01, 100))
+

After applying these procedures, our data is ready for subsequent analysis.

+
+
+

Generating candidate prioritizations +

+

Here we will start the calibration analysis by generating a set of candidate prioritizations. Specifically, these prioritizations will be generated using different parameters to specify different trade-offs between the different criteria. Since this tutorial involves navigating trade-offs between the overall cost of a prioritization and the level of spatial fragmentation associated with a prioritization (as measured by total boundary length), we will generate prioritizations using different parameters related to these criteria. We will examine two approaches for generating candidate prioritizations based on multi-objective optimization procedures. Although we’ll be examining both approaches in this tutorial, you would normally only use one of these approaches when conducting your own analysis

+
+

Blended approach +

+

The blended approach for multi-objective optimization involves combining separate criteria (e.g., total cost and total boundary length) into a single joint criterion. To achieve this, a trade-off (or scaling) parameter is used to specify the relative importance of each criterion. This approach is the default approach provided by the prioritizr R package. Specifically, each of the functions for adding a penalty to a problem formulation (e.g., add_boundary_penalties()) contains a parameter to control the relative importance of the penalties (i.e., the penalty parameter). For example, when using the add_boundary_penalties() function, setting a high penalty value will indicate that it is important to reduce the overall exposed boundary (perimeter) of the prioritization.

+

The main challenge with the blended approach is identifying a range of suitable penalty values to generate candidate prioritizations. If we set a penalty value that is too low, then the penalties will have no effect (e.g., boundary length penalties would have no effect on the prioritization). If we set a penalty value too high, then the prioritization will effectively ignore the primary objective. In such cases, the prioritization will be overly spatially clustered – because the planning unit cost values have no effect — and contain a single reserve. Thus we need to find a suitable range of penalty values before we can generate a set of candidate prioritizations.

+

We can find a suitable range of penalty values by generating a set of preliminary prioritizations. These preliminary prioritizations will be based on different penalty values – similar to the process for generating the candidate prioritizations – but solved using customized settings that sacrifice optimality for fast run times (see below for details). This is especially important because specifying a penalty value that is too high will cause the optimization process to take a very long time to generate a solutions (due to the numerical scaling issues mentioned previously). To find a suitable range of penalty values, we need to identify an upper limit for the penalty value (i.e., the highest penalty value that result in a prioritization containing a single reserve). Let’s create some preliminary penalty to identify this upper limit. Please note that you might need to adjust the prelim_upper value to find the upper limit when analyzing different datasets.

+
+# define a range of different penalty values
+## note that we use a power scale to avoid focusing on very high penalty values
+prelim_lower <- -5   # change this for your own data
+prelim_upper <- 2.8  # change this for your own data
+prelim_penalty <- round(10^seq(prelim_lower, prelim_upper, length.out = 9), 5)
+
+# print penalty values
+print(prelim_penalty)
+
## [1]   0.00001   0.00009   0.00089   0.00841   0.07943   0.74989   7.07946
+## [8]  66.83439 630.95734
+

Next, let’s use the preliminary penalty values to generate preliminary prioritizations. As mentioned earlier, we will generate these preliminary prioritizations using customized settings to reduce runtime. Specifically, we will set a time limit of 10 minutes per run, and relax the optimality gap to 20%. Although we would not normally use such settings – because the resulting prioritizations are not guaranteed to be near-optimal (the default gap is 10%) – this is fine because our goal here is to tune the preliminary penalty values. Indeed, none of these preliminary prioritizations will be considered as candidate prioritizations. Please note that you might need to set a higher time limit, or relax the optimality gap even further (e.g., 40%) when analyzing larger datasets.

+
+# define a problem without boundary penalties
+p0 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# generate preliminary prioritizations based on each penalty
+## note that we specify a relaxed gap and time limit for the solver
+prelim_blended_results <- lapply(prelim_penalty, function(x) {
+  s <-
+    p0 %>%
+    add_boundary_penalties(penalty = x, data = tas_bd) %>%
+    add_default_solver(gap = 0.2, time_limit = 10 * 60) %>%
+    solve()
+  s <- data.frame(s = s$solution_1)
+  names(s) <- with_options(list(scipen = 30), paste0("penalty_", x))
+  s
+})
+
+# format results as a single spatial object
+prelim_blended_results <- cbind(
+  tas_pu, do.call(bind_cols, prelim_blended_results)
+)
+
+# preview results
+print(prelim_blended_results)
+

After generating the preliminary prioritizations, let’s create some maps to visualize them. In particular, we want to understand how different penalty values influence the spatial fragmentation of the prioritizations.

+
+# plot maps of prioritizations
+plot(
+  x =
+    prelim_blended_results %>%
+    dplyr::select(starts_with("penalty_")) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        prelim_blended_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
+

+

We can see that as the penalty value used to generate the prioritizations increases, the spatial fragmentation of the prioritizations decreases. In particular, we can see that a penalty value of 66.83439 results in a single reserve – meaning this is our best guess of the upper limit. Using this penalty value as an upper limit, we will now generate a second series of prioritizations that will be the candidate prioritizations. Critically, these candidate prioritizations will not be generated using with time limit and be generated using a more suitable gap (i.e., default gap of 10%).

+
+# define a new set of penalty values
+## note that we use a linear scale to explore both low and high penalty values
+penalty <- round(seq(1e-5, prelim_penalty[8], length.out = 9), 5)
+
+# generate prioritizations based on each penalty
+blended_results <- lapply(penalty, function(x) {
+  ## generate solution
+  s <-
+    p0 %>%
+    add_boundary_penalties(penalty = x, data = tas_bd) %>%
+    solve()
+  ## return data frame with solution
+  s <- data.frame(s = s$solution_1)
+  names(s) <- with_options(list(scipen = 30), paste0("penalty_", x))
+  s
+})
+
+# format results as a single spatial object
+blended_results <- cbind(tas_pu, do.call(bind_cols, blended_results))
+
+# plot maps of prioritizations
+plot(
+  x =
+    blended_results %>%
+    dplyr::select(starts_with("penalty_")) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        blended_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
+

+

We now have a set of candidate prioritizations generated using the blended approach. The main advantages of this approach is that it is similar calibration analyses used by other decision support tools for conservation (i.e., Marxan) and it is relatively straightforward to implement. However, this approach also has a key disadvantage. Because the penalty parameter is a unitless trade-off parameter – meaning that we can’t leverage existing knowledge to specify a suitable range of penalty values – we first have to conduct a preliminary analysis to identify an upper limit. Although finding an upper limit was fairly simple for the example datset, it can be difficult to find for more realistic data. In the next section, we will show how to generate a set of candidate prioritzations using the hierachical approach – which does not have this disadvantage.

+
+
+

Hierarchical approach +

+

The hierarchical approach for multi-objective optimization involves generating a series of incremental prioritizations – using a different objective at each increment to refine the previous solution – until the final solution achieves all of the objectives. The advantage with this approach is that we can specify trade-off parameters for each objective based on a percentage from optimality. This means that we can leverage our own knowledge – or that of decision maker – when to generate a range of suitable trade-off parameters. As such, this approach does not require us to generate a series of preliminary prioritizations.

+

This approach is slightly more complicated to implement within the prioritizr R package then the blended approach. To start off, we generate an initial prioritization based on a problem formulation that does not consider any penalties. Critically, we will generate this prioritization by solving the problem to optimality (using the gap parameter of the add_default_solver() function).

+
+# define a problem without boundary penalties
+p1 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0)
+
+# solve problem
+s1 <- solve(p1)
+
+# add column for making a map of the prioritization
+s1$map_1 <- case_when(
+  s1$locked_in > 0.5 ~ "locked in",
+  s1$solution_1 > 0.5 ~ "priority",
+  TRUE ~ "other"
+)
+
+# plot map of prioritization
+plot(
+  s0[, "map_1"], pal = c("purple", "grey90", "darkgreen"),
+  main = NULL, key.pos = 1
+)
+

+

Next, we will calculate the total cost of the initial prioritization.

+
+# calculate cost
+s1_cost <- eval_cost_summary(p1, s1[, "solution_1"])$cost
+
+# print cost
+print(s1_cost)
+
## [1] 904.5156
+

Now we will calculate a series of cost thresholds. These cost thresholds will be calculated by inflating the cost of the initial prioritization by a range of percentage values. Since these values are percentages – and not unitless values unlike those used in the blended approach – we can use domain knowledge to specify a suitable range of cost thresholds. For this tutorial, let’s assume that it would be impractical – per our domain knowledge – to expend more than four times the total cost of the initial prioritization to reduce spatial fragmentation.

+
+# calculate cost threshold values
+threshold <- s1_cost + (s1_cost * seq(1e-5, 4, length.out = 9))
+threshold <- ceiling(threshold)
+
+# print cost thresholds
+print(threshold)
+
## [1]  905 1357 1810 2262 2714 3166 3619 4071 4523
+

After generating the cost thresholds, we can use them to generate prioritizations. Specifically, we will generate prioritizations that aim to minimize total boundary length as much as possible – ignoring the total cost of the prioritizations – whilst ensuring that the total cost of the prioritization does not exceed a given cost threshold and the other considerations (e.g., locked in constraints). To achieve this, we create a new column in the tas_pu object that contains only zero values (called zeros) and use this new column to specify the cost data for the prioritizations. Although we normally recommend against cost data that contain zero values – because planning units with zero costs are often selected in prioritizations even if they are not needed – here we use zero cost values so that the prioritization will focus exclusively on spatial fragmentation. Additionally, when it comes to generating the prioritization, we will add linear constraints to ensure that the total cost of the prioritization does not exceed a given cost threshold (using the add_linear_constraints() function).

+
+# add a column with zeros
+tas_pu$zeros <- 0
+
+# define a problem with zero cost values and boundary penalties
+## note that because all the costs are all zero, it doesn't actually
+## matter what penalty value is used (as long as the value is > 0)
+## and so we just use a value of 1
+p2 <- problem(tas_pu, tas_features, cost_column = "zeros") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 1, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# generate prioritizations based on each cost threshold
+## note that the prioritizations are solved to within 10% of optimality
+## (the default gap) because the gap is not specified
+hierarchical_results <- lapply(threshold, function(x) {
+  ## generate solution by adding a constraint based on the threshold and
+  ## using the "real" cost values (i.e., not zeros)
+  s <-
+    p2 %>%
+    add_linear_constraints(threshold = x, sense = "<=", data = "cost") %>%
+    solve()
+  ## return data frame with solution
+  s <- data.frame(s = s$solution_1)
+  names(s) <- paste0("threshold_", x)
+  s
+})
+
+# format results as a single spatial object
+hierarchical_results <- cbind(tas_pu, do.call(bind_cols, hierarchical_results))
+
+# plot maps of prioritizations
+plot(
+  x =
+    hierarchical_results %>%
+    dplyr::select(starts_with("threshold_")) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        hierarchical_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
+

+

We now have a set of candidate prioritizations generated using the hierarchical approach. This approach can be much faster than the blended approach because it does not require generating a set of prioritizations to identify an upper limit for the penalty trade-off parameter. After generating a set of candidate prioritizations, we can then calculate performance metrics to compare the prioritizations.

+
+
+
+

Calculating performance metrics +

+

Here we will calculate performance metrics to compare the prioritizations. Since we aim to navigate trade-offs between the total cost of a prioritization and the overall level of spatial fragmentation associated with a prioritization (as measured by total boundary length), we will calculate metrics to assess these criteria. Although we generated two sets of candidate prioritizations in the previous section; for brevity, here we will consider the candidate prioritizations generated using the hierarchical approach. Please note that you could also apply the following procedures to candidate prioritizations generated using the blended approach.

+
+# calculate metrics for prioritizations
+## note that we use p0 and not p1 so that cost calculations are based
+## on the cost values and not zeros
+hierarchical_metrics <- lapply(
+  grep("threshold_", names(hierarchical_results)), function(x) {
+    x <- hierarchical_results[, x]
+    data.frame(
+      total_cost = eval_cost_summary(p0, x)$cost,
+      total_boundary_length = eval_boundary_summary(p0, x)$boundary
+    )
+  }
+)
+hierarchical_metrics <- do.call(bind_rows, hierarchical_metrics)
+hierarchical_metrics$threshold <- threshold
+hierarchical_metrics <- as_tibble(hierarchical_metrics)
+
+# preview metrics
+print(hierarchical_metrics)
+
## # A tibble: 9 × 3
+##   total_cost total_boundary_length threshold
+##        <dbl>                 <dbl>     <dbl>
+## 1       905.              2919388.       905
+## 2      1357.              2407733.      1357
+## 3      1807.              2205799.      1810
+## 4      2256.              2049117.      2262
+## 5      2712.              1945849.      2714
+## 6      3164.              1862288.      3166
+## 7      3608.              1809343.      3619
+## 8      4071.              1755416.      4071
+## 9      4521.              1737961.      4523
+

After calculating the metrics, let’s we can use them to help select a prioritization.

+
+
+

Selecting a prioritization +

+

Now we need to decide on which candidate prioritization achieves the best trade-off. There are a range of qualitative and quantitative methods that are available to select a candidate prioritization (Ardron et al. 2010). Here we will consider three different methods. Since some of these methods a set of candidate prioritizations, we will use the candidate prioritizations using the hierarchical approach for these methods. To keep track of the prioritizations selected by different methods, let’s create a results_data table.

+
+# create data for plotting
+result_data <-
+  hierarchical_metrics %>%
+  ## rename threshold column to value column
+  rename(value = "threshold") %>%
+  ## add column with column names that contain candidate prioritizations
+  mutate(name = grep(
+    "threshold_", names(hierarchical_results), value = TRUE, fixed = TRUE
+  )) %>%
+  ## add column with labels for plotting
+  mutate(label = paste("Threshold =", value)) %>%
+  ## add column to keep track prioritizations selected by different methods
+  mutate(method = "none")
+
+# print table
+print(result_data)
+
## # A tibble: 9 × 6
+##   total_cost total_boundary_length value name           label            method
+##        <dbl>                 <dbl> <dbl> <chr>          <chr>            <chr> 
+## 1       905.              2919388.   905 threshold_905  Threshold = 905  none  
+## 2      1357.              2407733.  1357 threshold_1357 Threshold = 1357 none  
+## 3      1807.              2205799.  1810 threshold_1810 Threshold = 1810 none  
+## 4      2256.              2049117.  2262 threshold_2262 Threshold = 2262 none  
+## 5      2712.              1945849.  2714 threshold_2714 Threshold = 2714 none  
+## 6      3164.              1862288.  3166 threshold_3166 Threshold = 3166 none  
+## 7      3608.              1809343.  3619 threshold_3619 Threshold = 3619 none  
+## 8      4071.              1755416.  4071 threshold_4071 Threshold = 4071 none  
+## 9      4521.              1737961.  4523 threshold_4523 Threshold = 4523 none
+

Next, let’s examine some different methods for selecting prioritizations.

+
+

Visual method +

+

One qualitative method involves plotting the relationship between the different criteria, and using the plot to visually select a candidate prioritization. This visual method is often used to help calibrate trade-offs among prioritizations generated using the Marxan decision support tool (e.g., Hermoso et al. 2011; Stewart & Possingham 2005). So, let’s create a plot to select a prioritization.

+
+# create plot to visualize trade-offs and show selected candidate prioritization
+result_plot <-
+  ggplot(
+    data = result_data,
+    aes(x = total_boundary_length, y = total_cost, label = label)
+  ) +
+  geom_line() +
+  geom_point(size = 3) +
+  geom_text(hjust = -0.15) +
+  scale_color_manual(
+    values = c("visual" = "blue", "not selected" ="black")
+  ) +
+  xlab("Total boundary length of prioritization") +
+  ylab("Total cost of prioritization") +
+  scale_x_continuous(expand = expansion(mult = c(0.05, 0.4))) +
+  theme(legend.title = element_blank())
+
+# render plot
+print(result_plot)
+

+

We can see that there is a clear relationship between total cost and total boundary length. It would seem that in order to achieve a lower total boundary length – and thus lower spatial fragmentation – the prioritization must have a greater cost. Although we might expect the results to show a smoother curve – in other words, only Pareto dominant solutions – this result is expected because we generated candidate prioritizations using the default optimality gap of 10%. Typically, the visual method involves selecting a prioritization near the elbow of the plot. So, let’s select the prioritization generated using a threshold value of 1810. To keep of the prioritizations selected based on different methods, let’s create a method column in the result_data table.

+
+# specify prioritization selected by visual method
+result_data$method[3] <- "visual"
+

Next, let’s consider a quantitative approach.

+
+
+

TOPSIS method +

+

Multiple-criteria decision analysis is a disciple that uses analytical methods to evaluate trade-offs between multiple criteria (MCDA; reviewed in Greene et al. 2011). Although this discipline contains many different methods, here we will use the the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method (Hwang & Yoon 1981). This method requires (i) data describing the performance of each prioritization according the different criteria, (ii) weights to encode the relative importance of each criteria, and (iii) details on whether each criteria should ideally be minimized or maximized. Let’s run the analysis, assuming that we equal weighting for total cost and total boundary length.

+
+# calculate TOPSIS scores
+topsis_results <- topsis(
+  decision =
+    hierarchical_metrics %>%
+    dplyr::select(total_cost, total_boundary_length) %>%
+    as.matrix(),
+  weights = c(1, 1),
+  impacts = c("-", "-")
+)
+
+# print results
+print(topsis_results)
+
##   alt.row     score rank
+## 1       1 0.6861663    3
+## 2       2 0.7570982    1
+## 3       3 0.7218541    2
+## 4       4 0.6442282    4
+## 5       5 0.5530166    5
+## 6       6 0.4697259    6
+## 7       7 0.3999050    7
+## 8       8 0.3480699    8
+## 9       9 0.3138337    9
+

The candidate prioritization with the greatest TOPSIS score is considered to represent the best trade-off between total cost and total boundary length. So, based on this method, we would select the prioritization generated using a threshold value of 1357. Let’s update the result_data with this information.

+
+# add column indicating prioritization selected by TOPSIS method
+result_data$method[which.max(topsis_results$score)] <- "TOPSIS"
+

Next, let’s consider another quantitative method.

+
+
+

Cohon et al. (1979) method +

+

This method is based on an algorithm that was originally developed by Cohon et al. (Cohon et al. 1979), and was later adapted for use in systematic conservation planning (Fischer & Church 2005). Specifically, it involves generating two ideal prioritizations – with each prioritization representing the ideal prioritization for each criteria – and then using the performance metrics calculated for these prioritizations to automatically derive a trade-off penalty value (Ardron et al. 2010; Cohon et al. 1979). Thus, unlike the two other methods, this method does not require a set of candidate prioritizations. As such, this method can be used to find a prioritization that meets multiple criteria in a much shorter period of time than the other methods. To implement this method, we first need to generate the ideal prioritizations (note that we specify an gap of 0% to ensure optimality).

+
+# generate ideal prioritization based on cost criteria
+## note that this is simply the same as the s1 prioritization we generated
+## for the hierarchical approach
+p3 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0)
+
+# solve problem
+s3 <- solve(p3)
+
+# generate ideal prioritization based on spatial fragmentation criteria
+## note that any non-zero penalty value would here,
+## so we just use a penalty  of 1
+p4 <- problem(tas_pu, tas_features, cost_column = "zeros") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 1, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0)
+
+# solve problem
+s4 <- solve(p4)
+

Next, let’s calculate the performance metrics for these prioritizations.

+
+# generate problem formulation with costs and boundary penalties for
+# calculating performance metrics
+p5 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 1, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# calculate performance metrics for ideal cost prioritization
+s3_metrics <- tibble(
+  total_cost = eval_cost_summary(p5, s3[, "solution_1"])$cost,
+  total_boundary_length =
+    eval_boundary_summary(p5, s3[, "solution_1"])$boundary
+)
+
+# calculate performance metrics for ideal boundary length prioritization
+s4_metrics <- tibble(
+  total_cost = eval_cost_summary(p5, s4[, "solution_1"])$cost,
+  total_boundary_length =
+    eval_boundary_summary(p5, s4[, "solution_1"])$boundary
+)
+

After calculating these performance metrics, we can use them to automatically calculate a penalty value.

+
+# calculate penalty value based on Cohon et al. 1979
+cohon_penalty <- abs(
+  (s3_metrics$total_cost - s4_metrics$total_cost) /
+  (s3_metrics$total_boundary_length - s4_metrics$total_boundary_length)
+)
+
+# round to 5 decimal places to avoid numerical issues during optimization
+cohon_penalty <- round(cohon_penalty, 5)
+
+# print penalty value
+print(cohon_penalty)
+
## [1] 0.00945
+

Now that we have calculated a penalty value using this method, we can use it to generate a prioritization.

+
+# generate prioritization using penalty value calculated using Cohon et al. 1979
+p6 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = cohon_penalty, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# solve problem
+s6 <- solve(p6)
+

Let’s update the results_data table with results about the prioritization.

+
+# add new row with data for prioritization generated following Cohon et al. 1979
+result_data <- bind_rows(
+  result_data,
+  tibble(
+    total_cost = eval_cost_summary(p6, s6[, "solution_1"])$cost,
+    total_boundary_length =
+      eval_boundary_summary(p6, s6[, "solution_1"])$boundary,
+    value = cohon_penalty,
+    name = paste0("penalty_", cohon_penalty),
+    label = paste0("Penalty = ",  cohon_penalty),
+    method = "Cohon"
+  )
+)
+

Next, let’s compare the prioritizations selected by different methods.

+
+
+

Method comparison +

+

Let’s create a plot to visualize the results from the different methods.

+
+# create plot to visualize trade-offs and show selected candidate prioritization
+result_plot <-
+  ggplot(
+    data =
+      result_data %>%
+      mutate(vjust = if_else(method == "Cohon", -1, 0.5)),
+    aes(x = total_boundary_length, y = total_cost, label = label)
+  ) +
+  geom_line() +
+  geom_point(aes(color = method), size = 3) +
+  geom_text(aes(vjust = vjust, color = method), hjust = -0.1) +
+  scale_color_manual(
+    name = "Method",
+    values = c(
+      "visual" = "#984ea3",
+      "none" = "#000000",
+      "TOPSIS" = "#e41a1c",
+      "Cohon" = "#377eb8"
+    )
+  ) +
+  xlab("Total boundary length of prioritization") +
+  ylab("Total cost of prioritization") +
+  scale_x_continuous(expand = expansion(mult = c(0.05, 0.4)))
+
+# render plot
+print(result_plot)
+

+

We can see that the different method selected different prioritizations. To further compare the results from the different methods, let’s create some maps showing the selected prioritizations.

+
+# extract column names for creating the prioritizations
+visual_name <- result_data$name[[which(result_data$method == "visual")]]
+topsis_name <- result_data$name[[which(result_data$method == "TOPSIS")]]
+
+# create object with selected prioritizations
+solutions  <- bind_cols(
+  tas_pu,
+  hierarchical_results %>%
+    st_drop_geometry() %>%
+    dplyr::select(all_of(c(visual_name, topsis_name))) %>%
+    setNames(c("Visual", "TOPSIS")),
+  s6 %>%
+    st_drop_geometry() %>%
+    dplyr::select(solution_1) %>%
+    rename(Cohon = "solution_1")
+)
+
+# plot maps of selected prioritizations
+plot(
+  x =
+    solutions %>%
+    dplyr::select(Visual, TOPSIS, Cohon) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        hierarchical_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
+

+

How do we determine which one is best? This is difficult to say. Ideally, additional information could be used to help select a prioritization, such as knowledge on available resources, species’ connectivity requirements, and impacts of neighboring land use. However, from a practical perspective, prioritizations generated for academic contexts might find the quantitative approaches more useful because they have greater transparency and reproducibility. Ultimately, all of these methods are designed to support decision making. This means that they are intended to assist the decision making process, not serve as a replacement.

+
+
+
+

Conclusion +

+

Hopefully, this vignette has provided a useful introduction for resolving trade-offs in prioritizations. Although we only explored trade-offs between total cost and spatial fragmentation in this tutorial, this analysis could be adapted to explore trade-offs between a wide range of different criteria. For instance, instead of considering total cost as the primary objective, future analyses could explore trade-offs with feature representation (using the add_min_shortfall_objective() function). Additionally, instead of spatial fragmentation, future analyses could explore trade-offs that directly relate to connectivity (using the add_connectivity_penalties() function) or specific variables of interest – such as ecosystem intactness or inverse human footprint index (Williams et al. 2020; Beyer et al. 2019) – to inform decision making (using the add_linear_penalties() function). Furthermore, after identifying the best penalty or threshold values to strike a balance between multiple criteria, you could generate a portfolio of prioritizations (e.g., using the add_gap_portfolio_function()) to find multiple options for achieving a similar balance. This might be helpful when you need to generate a set of prioritizations that have comparable performance – in terms of how well they achieve different criteria – but select different planning units.

+
+
+

References +

+
+
+Ardron, J.A., Possingham, H.P. & Klein, C.J. (2010). Marxan Good Practices Handbook. Pacific Marine Analysis; Research Association, Vancouver, Victoria, BC. +
+
+Beger, M., Linke, S., Watts, M., Game, E., Treml, E., Ball, I. & Possingham, H.P. (2010). Incorporating asymmetric connectivity into spatial decision making for conservation. Conservation Letters, 3, 359–368. +
+
+Beyer, H.L., Venter, O., Grantham, H.S. & Watson, J.E.M. (2019). Substantial losses in ecoregion intactness highlight urgency of globally coordinated action. Conservation Letters, 13. +
+
+Cohon, J.L., Church, R.L. & Sheer, D.P. (1979). Generating multiobjective trade-offs: An algorithm for bicriterion problems. Water Resources Research, 15, 1001–1010. +
+
+Dorji, T., Linke, S. & Sheldon, F. (2020). Freshwater conservation planning in the context of nature needs half and protected area dynamism in bhutan. Biological Conservation, 251, 108785. +
+
+Fischer, D.T. & Church, R.L. (2005). The SITES reserve selection system: A critical review. Environmental Modeling and Assessment, 10, 215–228. +
+
+Greene, R., Devillers, R., Luther, J.E. & Eddy, B.G. (2011). GIS-based multiple-criteria decision analysis. Geography Compass, 5, 412–432. +
+
+Hermoso, V., Cattarino, L., Linke, S. & Kennard, M.J. (2018). Catchment zoning to enhance co-benefits and minimize trade-offs between ecosystem services and freshwater biodiversity conservation. Aquatic Conservation: Marine and Freshwater Ecosystems, 28, 1004–1014. +
+
+Hermoso, V., Kennard, M.J. & Linke, S. (2012). Integrating multidirectional connectivity requirements in systematic conservation planning for freshwater systems. Diversity and Distributions, 18, 448–458. +
+
+Hermoso, V., Linke, S., Prenda, J. & Possingham, H.P. (2011). Addressing longitudinal connectivity in the systematic conservation planning of fresh waters. Freshwater Biology, 56, 57–70. +
+
+Hwang, C.L. & Yoon, K.G. (1981). Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag, New York, NY. +
+
+Klein, C.J., Tulloch, V.J., Halpern, B.S., Selkoe, K.A., Watts, M.E., Steinback, C., Scholz, A. & Possingham, H.P. (2013). Tradeoffs in marine reserve design: Habitat condition, representation, and socioeconomic costs. Conservation Letters, 324–332. +
+
+Margules, C.R. & Pressey, R.L. (2000). Systematic conservation planning. Nature, 405, 243–253. +
+
+Stewart, R.R. & Possingham, H.P. (2005). Efficiency, costs and trade-offs in marine reserve system design. Environmental Modeling and Assessment, 10, 203–213. +
+
+Vane-Wright, R.I., Humphries, C.J. & Williams, P.H. (1991). What to protect? — Systematics and the agony of choice. Biological Conservation, 55, 235–254. +
+
+Williams, B.A., Venter, O., Allan, J.R., Atkinson, S.C., Rehbein, J.A., Ward, M., Marco, M.D., Grantham, H.S., Ervin, J., Goetz, S.J., Hansen, A.J., Jantz, P., Pillay, R., Rodrı́guez-Buriticá, S., Supples, C., Virnig, A.L.S. & Watson, J.E.M. (2020). Change in terrestrial human footprint drives continued loss of intact ecosystems. One Earth, 3, 371–382. +
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- - - - - - - - - - - -Articles • prioritizr - - - - - - - - - - - - - - +

    -
    -

    Articles

    @@ -181,42 +99,39 @@

    Articles

    All vignettes

    -
    -
    Gurobi Installation Guide
    -
    -
    prioritizr: Systematic Conservation Prioritization in R
    -
    -
    Publication Record
    -
    -
    Salt Spring Island Tutorial
    -
    -
    Solver Benchmarks
    -
    -
    Tasmania Tutorial
    -
    -
    Management Zones
    -
    -
    -
    +
    Calibrating trade-offs tutorial
    +
    +
    Connectivity tutorial
    +
    +
    Gurobi installation guide
    +
    +
    Management zones tutorial
    +
    +
    Package overview
    +
    +
    Getting started
    +
    +
    Publication record
    +
    +
    Solver benchmarks
    +
    +
    -
    +
    + + + + +
    +
    +
    +

    Connectivity tutorial

    + + + Source: vignettes/connectivity_tutorial.Rmd + + +
    + + + +
    +

    Introduction +

    +

    Connectivity is a key consideration in systematic conservation planning (Margules & Pressey 2000; Briers 2002). This is because isolated and fragmented populations are often more vulnerable to extinction (Dixo et al. 2009; Olds et al. 2012; Hodgson et al. 2009). To promote connectivity in prioritizations, a range of different approaches are available (reviewed in Balbar & Metaxas 2019). These approaches can solely on the spatial configuration of a prioritization to enhance structural connectivity (e.g, reducing the spatial fragmentation of a prioritization; Watts et al. 2009). They can also leverage data – such as environmental, river flow, and telemetry data – to generate prioritizations that promote functional connectivity (e.g., Hermoso et al. 2012; Dwyer et al. 2019; Leonard et al. 2017).

    +

    The aim of this tutorial is to show how connectivity can be incorporated into prioritizations using the prioritizr R package. Here we will explore various approaches for incorporating connectivity, and see how they alter the spatial configuration of prioritizations. As you will discover, many of these approaches involve setting threshold or penalty values to specify the relative importance of connectivity compared to other criteria (e.g., overall cost). For more information on calibrating these values, please see the Calibrating trade-offs tutorial.

    +
    +
    +

    Data +

    +

    The dataset used in this tutorial was created for the Coastal Douglas-fir Conservation Partnership (CDFCP; Morrell et al. 2017). Although the original dataset covers a much larger area; for brevity, here we focus only on Salt Spring Island, British Columbia. Briefly, Salt Spring Island supports a diverse and globally unique mix of dry forest and savanna habitats. Today, these habitats are critically threatened due to land conversion, invasive species, and altered disturbance regimes. For more information on the data, please refer to the Marxan tool portal and the tool tutorial.

    +
    +
    +

    Extent of Coastal Douglas-fir Conservation Partnership Tool area and location of Salt Spring Island

    +
    +
    +

    Let’s begin by loading the packages and data for this tutorial. Since this tutorial requires the prioritizrdata R package, please ensure that it is installed. Specifically, two objects underpin the data for this tutorial. The salt_pu object specifies the planning unit data as a raster layer (i.e., RasterLayer object), and the salt_features object contains biodiversity data represented as a multi-band raster stack (i.e., a RasterStack object).

    +
    +# load packages
+library(prioritizr)
+library(prioritizrdata)
+library(scales)
+
+# load planning unit data
+data(salt_pu)
+
+# load ecological data
+data(salt_features)
    +

    Now we will conduct some preliminary processing. Specifically, we will aggregate from the 100 m resolution to the 300 m resolution. This is to reduce the time needed to generate prioritizations in this tutorial. In practice, we generally recommend consider other criteria too – such as the spatial scale that is relevant for decision making and the resolution of available datasets – when deciding on an appropriate scale for planning units.

    +
    +# aggregate data to coarser resolution
+salt_pu <- aggregate(salt_pu, fact = 3)
+salt_features <- aggregate(salt_features, fact = 3)
    +

    Next, let’s have a look at the salt_pu object. Here each grid cell represents a planning unit, and the grid cell values denote acquisition costs (BC Assessment 2015). To aid with visualization, we will log-transform the values when plotting them on a map.

    +
    +# print planning unit data
+print(salt_pu)
    +
    ## class      : RasterLayer 
+## dimensions : 94, 67, 6298  (nrow, ncol, ncell)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : salt_pu 
+## values     : 0.02552, 8290.383  (min, max)
    +
    +# plot map showing the planning units costs on a log-scale
+plot(log(salt_pu), main = "Planning unit costs (log)", axes = FALSE)
    +

    +

    Let’s also look at the salt_features object. This object is a stack of raster layers, with each layer corresponding to a different variable that describes a particular aspect of biodiversity. The first four layers correspond to different ecological communities (i.e., Old Forest, Savannah, Wetland, and Shrub communities), and their cell values indicate the probability of encountering a bird species associated a given community. The fifth layer describes the inverse probability of occurrence of human commensal species. In this tutorial, we will use the first four layers as biodiversity features, and the fifth layer to help parameterize connectivity (wherein higher values denote greater connectivity). So, let’s extract the data and visualize them.

    +
    +# print original data
+print(salt_features)
    +
    ## class      : RasterBrick 
+## dimensions : 94, 67, 6298, 5  (nrow, ncol, ncell, nlayers)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : salt_features.1, salt_features.2, salt_features.3, salt_features.4, salt_features.5 
+## min values :       0.3596232,       0.3340984,       0.1420134,       0.4415211,       0.4060181 
+## max values :       0.8951858,       0.6440319,       0.5926431,       0.8065580,       0.8969550
    +
    +# extract connectivity data
+salt_con <- salt_features[[nlayers(salt_features)]]
+
+# print connectivity data
+print(salt_con)
    +
    ## class      : RasterLayer 
+## dimensions : 94, 67, 6298  (nrow, ncol, ncell)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : salt_features.5 
+## values     : 0.4060181, 0.896955  (min, max)
    +
    +# plot map showing the connectivity data
+plot(salt_con, main = "Connectivity data", axes = FALSE)
    +

    +
    +# extract ecological communities and use these as features
+salt_features <- salt_features[[seq_len(4)]]
+
+# assign names to features
+names(salt_features) <- c("Old_Forest", "Savannah", "Wetland", "Shrub")
+
+# print features
+print(salt_features)
    +
    ## class      : RasterBrick 
+## dimensions : 94, 67, 6298, 4  (nrow, ncol, ncell, nlayers)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : Old_Forest,  Savannah,   Wetland,     Shrub 
+## min values :  0.3596232, 0.3340984, 0.1420134, 0.4415211 
+## max values :  0.8951858, 0.6440319, 0.5926431, 0.8065580
    +
    +# plot map showing the distribution of the features
+plot(salt_features, main = names(salt_features), axes = FALSE)
    +

    +
    +
    +

    Baseline problem +

    +

    In this tutorial, we will explore a few different ways of incorporating connectivity into prioritizations. To enable comparisons among prioritizations based on different approaches, we will first create a baseline problem formulation that we will subsequently customize to incorporate connectivity. Specifically, we will formulate the baseline problem using the minimum set objective. We will use representation targets of 17% – based on Aichi Biodiversity Target 11 – to provide adequate coverage of each ecological community. Additionally, because land properties on Salt Spring Island can either be acquired in their entirety or not at all, we will use binary decision types. This means that planning units are either selected in the solution or not selected in the solution—planning units cannot be partially acquired. Given all these details, let’s formulate the baseline problem.

    +
    +# create problem
+p0 <- problem(salt_pu, salt_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_binary_decisions() %>%
+      add_default_solver()
+
+# print problem
+print(p0)
    +
    ## Conservation Problem
+##   planning units: RasterLayer (2389 units)
+##   cost:           min: 0.02552, max: 8290.38315
+##   features:       Old_Forest, Savannah, Wetland, Shrub (4 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (1)]
    +

    After formulating the baseline problem, we can solve it to generate a prioritization.

    +
    +# solve problem
+s0 <- solve(p0)
    +
    +# print solution
+print(s0)
    +
    ## class      : RasterLayer 
+## dimensions : 94, 67, 6298  (nrow, ncol, ncell)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : salt_pu 
+## values     : 0, 1  (min, max)
    +
    +# plot solution
+plot(
+  s0, main = "Baseline prioritization", axes = FALSE,
+  breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    Next, let’s explore some options for incorporating connectivity.

    +
    +
    +

    Adding constraints +

    +

    Let’s explore approaches for promoting connectivity in prioritizations by adding constraints to the baseline problem formulation. These approaches ensure that prioritizations exhibit certain characteristics (e.g., ensure prioritizations form a contiguous reserve; Önal & Briers 2006). This means that, regardless of the optimality gap used to generate a prioritization, the prioritization will always exhibit these characteristics.

    +
    +

    Neighbor constraints +

    +

    Neighbor constraints can be added to ensure that each selected planning unit has a certain number of neighbors surrounding it (using the add_neighbor_constraints() function) (based on Billionnet 2013). The k parameter can be used to specify the required number of neighbors for each selected planning unit. Let’s generate a prioritization by specifying that each planning unit requires at least two neighbors.

    +
    +# create problem with added neighbor constraints and solve it
+s1 <- p0 %>%
+      add_neighbor_constraints(k = 2) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s1), main = c("baseline", "neighbors constraints"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +
    +
    +

    Contiguity constraints +

    +

    Contiguity constraints can be added to ensure that all planning units form a single contiguous reserve (using the add_contiguity_constraints() function) (similar to Önal & Briers 2006). These constraints are extremely complex. As such, they can only be applied to small conservation planning problems and the Gurobi solver is required to solve them in a feasible period of time. Since it would take a long time to generate a near-optimal prioritization for this dataset with contiguity constraints, we will also tell the solver to simply return the first solution that it finds which meets the representation targets and the contiguity constraints.

    +
    +# create problem with added contiguity constraints and solve it
+s2 <- p0 %>%
+      add_contiguity_constraints() %>%
+      add_gurobi_solver(first_feasible = TRUE) %>%
+      solve()
    +
    ## Warning in res(x, ...): overwriting previously defined solver
    +
    +# plot solutions
+plot(
+  stack(s0, s2), main = c("baseline", "contiguity constraints"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    There is also an even more complex version of the contiguity constraints that is available. These constraints – termed feature contiguity constraints (similar to Cerdeira et al. 2010) – can be added to ensure that all of the selected planning units used to the reach representation targets within a prioritization form a contiguous network for each feature (using the add_feature_contiguity_constraints() function). In other words, they ensure that each feature can disperse through the prioritization to access a target threshold amount of habitat. However, these constraints are extraordinarily complex, only feasible for small problems, and require preprocessing routines to identify initial solutions. As such, we will not consider them in this tutorial.

    +
    +
    +

    Linear constraints +

    +

    Linear constraints can be used to specify that the prioritizations must meet an arbitrary set of criteria. As such, they can be used to ensure that prioritizations provide adequate coverage of planning units that have facilitate a high level of connectivity. Recall that the salt_con data are used to describe connectivity across the study area. Since higher values denote planning units with greater connectivity, we could use linear constraints to ensure that the total sum of connectivity values – based on this dataset – meets a particular threshold (e.g. cover at least 30% of the total amount). This would effectively be treating connectivity as an additional feature (similar to Daigle et al. 2020).

    +
    +# compute threshold for constraints
+## here we use a threshold of 30% of the total connectivity values
+threshold <- cellStats(salt_con, "sum") * 0.3
+
+# print threshold
+print(threshold)
    +
    ## [1] 520.7628
    +
    +# create problem with added linear constraints and solve it
+s3 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s3), main = c("baseline", "linear constraints"),
+   axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    Although using continuous values has the advantage that the prioritization process can explicitly account for differences in the relative amount of connectivity facilitated by different planning units, the disadvantage is that the prioritization could potentially focus on selecting lots of planning units with low connectivity values. To avoid this result, one strategy is to convert the continuous values into binary values using a threshold limit (similar to Carroll 2021). By applying such a threshold limit, linear constraints can then be used to ensure that the prioritization selects a minimum amount of planning units with high connectivity values (i.e., those with connectivity values that are equal to or greater than the threshold limit).

    +
    +# calculate threshold limit
+## here we set a threshold limit based on the median
+threshold_limit <- quantile(salt_con, probs = 0.5)
+
+# convert continuous values to binary values
+salt_con_binary <- round(salt_con <= threshold_limit)
+
+# plot binary values
+plot(salt_con_binary, main = "salt_con_binary", axes = FALSE)
    +

    +
    +# create problem with added linear constraints and solve it
+## note that we use the original threshold computed before,
+## to ensure the prioritization covers at least 30% of the total amount
+## connectivity values
+s4 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con_binary, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s4), main = c("baseline", "linear constraints (binary)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    Another strategy is to clamp the continuous values below a threshold limit are assigned a value of zero (similar to Hanson et al. 2020). This strategy has the advantage that (i) the prioritization won’t focus on selecting lots of planning units with low connectivity values to meet the constraint threshold, and (ii) the optimization process can use semi-continuous values to distinguish between places that can facilitate a moderate amount and a high amount of connectivity.

    +
    +# clamp continuous values using the threshold limit we computed before
+salt_con_clamp <- salt_con
+salt_con_clamp[Which(salt_con <= threshold_limit)] <- 0
+
+# plot clamped values
+plot(salt_con_clamp, main = "salt_con_clamp", axes = FALSE)
    +

    +
    +# create problem with added linear constraints and solve it
+## note that we use the original threshold computed before,
+## to ensure the prioritization covers at least 30% of the total amount
+## connectivity values
+s5 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con_clamp, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s5), main = c("baseline", "linear constraints (clamped)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    If we were concerned that the prioritization did not facilitate a high enough level of connectivity, we could increase the threshold value or the threshold_limit value. For example, let’s increase the threshold_limit value used to clamp the continuous connectivity values.

    +
    +# compute threshold limit
+threshold_limit2 <- quantile(salt_con, probs = 0.7)
+
+# clamp continuous values using the threshold limit we computed before
+salt_con_clamp2 <- salt_con
+salt_con_clamp2[Which(salt_con <= threshold_limit2)] <- 0
+
+# plot clamped values
+plot(salt_con_clamp2, main = "salt_con_clamp", axes = FALSE)
    +

    +
    +# create problem with added linear constraints and solve it
+## note that we use the original threshold computed before,
+## to ensure the prioritization covers at least 30% of the total amount
+## connectivity values
+s6 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con_clamp2, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s6), main = c("baseline", "linear constraints (clamped 2)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    Despite the advantages of clamping the connectivity values, we can see that the prioritization has a relatively high level of spatial fragmentation. In fact, all prioritizations generated using the linear constraints can potentially have this issue. This is because linear constraints do not explicitly account for the spatial arrangement of the planning units. As such, we recommend combining the linear constraints approach with another approach [e.g., the boundary penalties approach discussed below; Carroll (2021)].

    +
    +
    +
    +

    Adding penalties +

    +

    Now let’s explore approaches for promoting connectivity in prioritizations by adding penalties to the baseline problem formulation. These approaches involve penalizing solutions according to exhibit certain (e.g., penalize spatial fragmentation of prioritizations; Watts et al. 2009). Unlike constraint-based methods for incorporating connectivity – if the optimality gap used to generate a prioritization is too high – they may not necessarily produce prioritizations that exhibit desirable characteristics.

    +
    +

    Boundary penalties +

    +

    Boundary penalties can be added to used to reduce the spatial fragmentation of prioritizations (using the add_boundary_penalties() function). Specifically, these penalties update the problem formulation to penalize solutions that have a high total amount of exposed boundary length (Ball et al. 2009). Since boundary data often have large values which can degrade solver performance and result in excessive run times (see the Calibrating trade-offs tutorial for details), we will first precompute rescale the boundry data.

    +
    +# precompute the boundary data
+salt_boundary_data <- boundary_matrix(salt_pu)
+
+# rescale boundary data
+salt_boundary_data@x <- rescale(salt_boundary_data@x, to = c(0.01, 100))
    +

    Next, let’s generate a prioritization using boundary penalties. To specify the relative importance reducing spatial fragmentation – compared with the primary objective of a problem (e.g. minimizing cost) – we need to a value for the penalty parameter is used. Setting a higher value for penalty indicates that it is more important to avoid highly fragmented solutions. Let’s generate a prioritization with a penalty value of 0.001.

    +
    +# create problem with added boundary penalties
+s7 <- p0 %>%
+      add_boundary_penalties(penalty = 0.001, data = salt_boundary_data) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s7), main = c("baseline", "boundary penalties (0.001)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    We can see that the resulting prioritization is still relatively fragmented, so let’s try generating another prioritization with a higher penalty value.

    +
    +# create problem with increased boundary penalties
+s8 <- p0 %>%
+      add_boundary_penalties(penalty = 10, data = salt_boundary_data) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s8), main = c("baseline", "boundary penalties (10)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    Although the prioritization is now less fragmented, it has also selected a greater number of planning units. Let’s calculate the cost of the prioritizations to see how they vary in overall cost.

    +
    +# calculate cost of baseline prioritization
+eval_cost_summary(p0, s0)
    +
    ## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall  46.0
    +
    +# calculate cost of prioritization with low boundary penalties (i.e., 0.001)
+eval_cost_summary(p0, s7)
    +
    ## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall  46.0
    +
    +# calculate cost of prioritization high low boundary penalties (i.e., 0.1)
+eval_cost_summary(p0, s8)
    +
    ## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall  52.3
    +

    We can see that the cost of the prioritizations increase with when we use higher penalty values. This is because there is a trade-off between the cost of a prioritization and the level of spatial fragmentation. Although it can be challenging to find the best balance, there are qualitative and quantitative methods available to help navigate such trade-offs. Please see the Calibrating trade-offs tutorial for a details on these methods.

    +
    +
    +

    Connectivity penalties +

    +

    Connectivity penalties can be used to promote connectivity in prioritizations (using the add_connectivity_penalties() function). These penalties use connectivity scores to parametrize the strength of connectivity between pairs of planning units (Beger et al. 2010). Thus higher scores denote a greater level of connectivity between different planning units. For example, previous studies have parametrized connectivity scores using habitat quality, environmental, and river flow data (e.g. Leonard et al. 2017; Alagador et al. 2012; Hermoso et al. 2012). Although there are many approaches to calculate connectivity scores, one approach involves using conductance data – data that describe how much each planning unit facilitates movement (opposite of landscape resistance data) – and calculating scores for each pair of planning units by averaging their conductance values (implemented using the connectivity_matrix() function).

    +

    Let’s compute connectivity scores by treating the salt_con object as conductance data. This means that we assume that neighboring planning units with higher values in the salt_con object are capable of facilitating a greater amount of connectivity. Note that the data used to compute connectivity scores must conform to the same spatial properties as the planning unit data (e.g., resolution, spatial extent, coordinate reference system). Also, although we are using raster data here, these scores can also be computed for vector data too (e.g., sf::st_sf() objects). Similar to the boundary data, we will also rescale the connectivity scores to avoid numerical issues during optimization.

    +
    +# compute connectivity scores
+salt_con_scores <- connectivity_matrix(salt_pu, salt_con)
+
+# rescale scores
+salt_con_scores@x <- rescale(salt_con_scores@x, to = c(0.01, 100))
    +

    After computing the connectivity scores, we can use them to generate prioritizations using connectivity penalties. Similar to the boundary penalties, we use the penalty parameter to specify the relative importance of promoting connectivity relative to the primary objective of a problem (i.e., minimizing overall cost). Let’s generate a prioritization with a penalty value of 0.001.

    +
    +# create problem with added connectivity penalties
+s9 <- p0 %>%
+      add_connectivity_penalties(penalty = 0.001, data = salt_con_scores) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s9), main = c("baseline", "connectivity penalties (0.001)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    Now let’s try generating another prioritization with a higher penalty value.

    +
    +# create problem with increased connectivity penalties
+s10 <- p0 %>%
+      add_connectivity_penalties(penalty = 0.002, data = salt_con_scores) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s10), main = c("baseline", "connectivity penalties (0.002)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
    +

    +

    We can see that increasing the penalty parameter causes the prioritizations to select planning units in regions with greater connectivity values (i.e., per the salt_con object). As discussed with the boundary penalties, increasing the penalty value tells the optimization process to focus more on promoting connectivity—meaning that it won’t focus as much on the primary objective (i.e., because the primary objective is to minimize overall costs). For details on calibrating these trade-offs please see the Calibrating trade-offs tutorial. Note that you will need to the use eval_connectivity_summary() function – instead of the eval_boundary_summary() function – when adapting the tutorial code for connectivity penalties.

    +
    +
    +
    +

    Conclusion +

    +

    Hopefully, this tutorial has provided a helpful introduction for incorporating connectivity into prioritizations. Broadly speaking, we recommend using the boundary penalties or the connectivity penalties to ensure that prioritizations explicitly account for the spatial configuration of selected planning units. Additionally, though not fully explored here, the connectivity penalties are a very flexible approach for promoting connectivity. For instance, in addition to parameterizing pair-wise connectivity scores for neighboring planning units, they can also be used to parametrize pair-wise connectivity scores between more distant planning units. Thus connectivity penalties could be used to parametrize connectivity across both small scales and large spatial scales (e.g., using a scaling procedure wherein connectivity scores between pairs of planning units decline with the distance between them).

    +
    +
    +

    References +

    +
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    +
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    + + + +
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- - - - - - - - - - + diff --git a/docs/articles/management_zones_tutorial.html b/docs/articles/management_zones_tutorial.html new file mode 100644 index 000000000..b1d8c3edc --- /dev/null +++ b/docs/articles/management_zones_tutorial.html @@ -0,0 +1,1010 @@ + + + + + + + +Management zones tutorial • prioritizr + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+
+
+

Management zones tutorial

+ + + Source: vignettes/management_zones_tutorial.Rmd + + +
+ + + +
+

Introduction +

+

One of the main aims in conservation planning is to identify the most cost-effective set of areas to manage biodiversity (Margules & Pressey 2000). To achieve this, prioritizations are generally created to identify areas for expanding protected area systems. However, many real-world conservation problems do not simply involve deciding if an area should be protected or not (e.g., Klein et al. 2009; Stigner et al. 2016). Instead, many problems involve a range of different management categories and the goal is to determine which areas should be allocated to which management category. For example, a manager might have a range of different methods (e.g., baiting or trapping at various intensities) for controlling invasive pests in a set of different areas (e.g., Cattarino et al. 2018). They would need a prioritization that shows which control methods should be implemented in which areas. In this particular case, a binary prioritization showing which areas contain the most biodiversity is simply not helpful. Furthermore, many real-world problems require decisions that meet multiple, and sometimes conflicting, objectives from different stakeholders. For example, a manager might need to implement a set of no-take and partial-take areas to prevent overfishing, but also ensure that there still remain plenty of areas for fishing activities (e.g., Wilson et al. 2010; Klein et al. 2013). Popularized by the Marxan with Zones decision support tool (Watts et al. 2009), this concept has become known as “zones” and is becoming increasingly important in conservation planning.

+

The aim of this tutorial is to showcase the zones functionality of the prioritizr R package. It will assume a certain level of familiarity with conservation planning terminology and the package. If you don’t have much experience in either of these topics, we recommend first reading the Package overview vignette.

+
+
+

Usage +

+
+

Simple minimum set problem +

+

In the prioritizr R package, all conservation planning problems – including those which contain multiple management zones or actions – are initialized using the problem function. To refresh our memory on how we can construct problems, let us quickly construct a simple conservation planning problem. This problem will use the simulated built-in planning unit and feature data distributed with the package. It will have a minimum set objective, targets which require that solution secure to 10 % of the habitat in the study area for each feature, and binary decision variables indicating that planning units are selected or not selected for protection.

+
+# load prioritizr package
+library(prioritizr)
+
## Loading required package: raster
+
## Loading required package: sp
+
## Loading required package: sf
+
## Linking to GEOS 3.9.0, GDAL 3.2.2, PROJ 7.2.1
+
## Loading required package: proto
+
+# load data
+data(sim_pu_raster, sim_features)
+
+# create targets for each of the five features
+t1 <- rep(0.1, 5)
+
+# build single-zone problem
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(t1) %>%
+      add_binary_decisions()
+
+# print problem
+print(p1)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+# solve problem
+s1 <- solve(p1)
+
## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 5 rows, 90 columns and 450 nonzeros
+## Model fingerprint: 0x6442bf6e
+## Variable types: 0 continuous, 90 integer (90 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-01, 9e-01]
+##   Objective range  [2e+02, 2e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [3e+00, 8e+00]
+## Found heuristic solution: objective 2337.9617505
+## Presolve time: 0.00s
+## Presolved: 5 rows, 90 columns, 450 nonzeros
+## Variable types: 0 continuous, 90 integer (90 binary)
+## Found heuristic solution: objective 2332.1003790
+## Root relaxation presolved: 5 rows, 90 columns, 450 nonzeros
+## 
+## 
+## Root relaxation: objective 1.931582e+03, 12 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 1931.58191    0    4 2332.10038 1931.58191  17.2%     -    0s
+## H    0     0                    1987.3985265 1931.58191  2.81%     -    0s
+## 
+## Explored 1 nodes (12 simplex iterations) in 0.00 seconds (0.00 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 3: 1987.4 2332.1 2337.96 
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 1.987398526526e+03, best bound 1.931581908865e+03, gap 2.8085%
+
+# calculate feature representation
+r1 <- eval_feature_representation_summary(p1, s1)
+print(r1)
+
## # A tibble: 5 × 5
+##   summary feature total_amount absolute_held relative_held
+##   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+## 1 overall layer.1         83.3          8.91         0.107
+## 2 overall layer.2         31.2          3.13         0.100
+## 3 overall layer.3         72.0          7.34         0.102
+## 4 overall layer.4         42.7          4.35         0.102
+## 5 overall layer.5         56.7          6.01         0.106
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+

+
+
+

Adding management zones +

+

Now let us imagine that instead of having a single management zone (e.g., protected area), we have two management zones. Similar to the example above, we require a solution that secures 10 % of the habitat in the study area for each feature in the first management zone. But we also require a solution that secures 5 % of the habitat in the study area for each feature in the second management zone. Each planning unit must be allocated to either zone or not selected for management at all. In this example, each planning unit costs the same when it is allocated to either of the two zones. We can formulate and solve this problem using the following code.

+
+# create a matrix with the targets
+# here each column corresponds to a different zone,
+# each row corresponds to a different feature, and
+# each cell value corresponds to the target
+t2 <- matrix(NA, ncol = 2, nrow = 5)
+t2[, 1] <- 0.1
+t2[, 2] <- 0.05
+
+# print targets
+print(t2)
+
##      [,1] [,2]
+## [1,]  0.1 0.05
+## [2,]  0.1 0.05
+## [3,]  0.1 0.05
+## [4,]  0.1 0.05
+## [5,]  0.1 0.05
+
+# create a zones object that contains the amount of each feature
+# in each planning unit when it is allocated to each zone
+# since our zones pertain to the same habitat data, we will
+# to specify the same habitat data for each zone
+z2 <- zones("zone 1" = sim_features, "zone 2" = sim_features)
+
+# print zones
+print(z2)
+
## Zones
+##   zones: zone 1, zone 2 (2 zones)
+##   features: 1, 2, 3, ... (5 features)
+##   data type: RasterStack
+
+# create a raster stack with the planning unit data
+# since our planning unit costs are the same for each zone,
+# we will create a stack with two replicates of the cost data
+pu2 <- stack(sim_pu_raster, sim_pu_raster)
+
+# print stack
+print(pu2)
+
## class      : RasterStack 
+## dimensions : 10, 10, 100, 2  (nrow, ncol, ncell, nlayers)
+## resolution : 0.1, 0.1  (x, y)
+## extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+## crs        : NA 
+## names      :  layer.1,  layer.2 
+## min values : 190.1328, 190.1328 
+## max values : 215.8638, 215.8638
+
+# build two-zone problem
+p2 <- problem(pu2, z2) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(t2) %>%
+      add_binary_decisions()
+
+# print problem
+print(p2)
+
## Conservation Problem
+##   zones:          zone 1, zone 2 (2 zones)
+##   planning units: RasterStack (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       1, 2, 3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.05, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+# solve problem
+s2 <- solve(p2)
+
## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 100 rows, 180 columns and 1080 nonzeros
+## Model fingerprint: 0xbdab1647
+## Variable types: 0 continuous, 180 integer (180 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-01, 1e+00]
+##   Objective range  [2e+02, 2e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [1e+00, 8e+00]
+## Found heuristic solution: objective 3568.4931394
+## Presolve time: 0.00s
+## Presolved: 100 rows, 180 columns, 1080 nonzeros
+## Variable types: 0 continuous, 180 integer (180 binary)
+## Found heuristic solution: objective 3440.6550560
+## Root relaxation presolved: 100 rows, 180 columns, 1080 nonzeros
+## 
+## 
+## Root relaxation: objective 2.911333e+03, 80 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 2911.33335    0   10 3440.65506 2911.33335  15.4%     -    0s
+## H    0     0                    3003.8743974 2911.33335  3.08%     -    0s
+## 
+## Explored 1 nodes (83 simplex iterations) in 0.00 seconds (0.00 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 3: 3003.87 3440.66 3568.49 
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 3.003874397435e+03, best bound 2.911333350606e+03, gap 3.0807%
+
+# calculate feature representation
+r2 <- eval_feature_representation_summary(p2, s2)
+print(r2)
+
## # A tibble: 15 × 5
+##    summary feature total_amount absolute_held relative_held
+##    <chr>   <chr>          <dbl>         <dbl>         <dbl>
+##  1 overall 1              167.          13.3         0.0799
+##  2 overall 2               62.4          4.75        0.0761
+##  3 overall 3              144.          10.9         0.0760
+##  4 overall 4               85.3          6.44        0.0755
+##  5 overall 5              113.           9.03        0.0796
+##  6 zone 1  1               83.3          8.87        0.106 
+##  7 zone 1  2               31.2          3.18        0.102 
+##  8 zone 1  3               72.0          7.22        0.100 
+##  9 zone 1  4               42.7          4.27        0.100 
+## 10 zone 1  5               56.7          6.07        0.107 
+## 11 zone 2  1               83.3          4.44        0.0533
+## 12 zone 2  2               31.2          1.57        0.0504
+## 13 zone 2  3               72.0          3.72        0.0517
+## 14 zone 2  4               42.7          2.17        0.0508
+## 15 zone 2  5               56.7          2.96        0.0521
+
+# plot solution
+# here we use the category layer function to generate raster showing the zone
+# that each planning unit was allocated. Specifically, pixels with the
+# value 1 are allocated to "zone 1" and pixels with the value 2 are allocated
+# to "zone 2". Thus units depicted in gray are not allocated
+# to any zone, units depicted in yellow are allocated to zone 1, and units
+# depicted in green are allocated to zone 2
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+

+
+
+

Multiple zones with varying costs +

+

Real-world problems often have different costs for managing planning units under different zones. These problems also tend to have different expected amounts of each feature when planning units are managed differently. So let us consider a slightly more complex example. Similar to before we will have two management zones. But this time, the cost of managing each planning unit is different depending on which management zone it is assigned to in the solution. Furthermore, when we assign a planning unit to the second zone, we only expect to end up with half of the habitat we would get if we managed the unit in the first zone (e.g., because the second zone is a partial-take zone and the first zone is a no-take zone). We will use the same target data as in the previous example.

+
+# create new planning unit and cost data
+data(sim_pu_zones_stack)
+pu3 <- sim_pu_zones_stack[[1:2]]
+
+# plot cost data
+plot(pu3, main = c("zone 1", "zone 2"), axes = FALSE, box = FALSE)
+

+
+# create problem
+p3 <- problem(pu3, zones(sim_features, sim_features * 0.5)) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(t2) %>%
+      add_binary_decisions()
+
+# print problem
+print(p3)
+
## Conservation Problem
+##   zones:          1, 2 (2 zones)
+##   planning units: RasterStack (90 units)
+##   cost:           min: 182.60173, max: 221.36296
+##   features:       1, 2, 3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.05, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+# solve problem
+s3 <- solve(p3)
+
## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 100 rows, 180 columns and 1080 nonzeros
+## Model fingerprint: 0x07455a48
+## Variable types: 0 continuous, 180 integer (180 binary)
+## Coefficient statistics:
+##   Matrix range     [1e-01, 1e+00]
+##   Objective range  [2e+02, 2e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [8e-01, 8e+00]
+## Found heuristic solution: objective 3667.7708672
+## Presolve time: 0.01s
+## Presolved: 100 rows, 180 columns, 1080 nonzeros
+## Variable types: 0 continuous, 180 integer (180 binary)
+## Found heuristic solution: objective 3388.0248890
+## Root relaxation presolved: 100 rows, 180 columns, 1080 nonzeros
+## 
+## 
+## Root relaxation: objective 2.884872e+03, 38 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 2884.87200    0    8 3388.02489 2884.87200  14.9%     -    0s
+## H    0     0                    2958.1201508 2884.87200  2.48%     -    0s
+## 
+## Explored 1 nodes (38 simplex iterations) in 0.01 seconds (0.00 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 3: 2958.12 3388.02 3667.77 
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 2.958120150795e+03, best bound 2.884871999973e+03, gap 2.4762%
+
+# calculate feature representation
+r3 <- eval_feature_representation_summary(p3, s3)
+print(r3)
+
## # A tibble: 15 × 5
+##    summary feature total_amount absolute_held relative_held
+##    <chr>   <chr>          <dbl>         <dbl>         <dbl>
+##  1 overall 1              125.         11.1          0.0891
+##  2 overall 2               46.8         3.92         0.0838
+##  3 overall 3              108.          9.28         0.0860
+##  4 overall 4               64.0         5.37         0.0839
+##  5 overall 5               85.1         7.46         0.0877
+##  6 1       1               83.3         8.94         0.107 
+##  7 1       2               31.2         3.13         0.100 
+##  8 1       3               72.0         7.42         0.103 
+##  9 1       4               42.7         4.29         0.101 
+## 10 1       5               56.7         6.01         0.106 
+## 11 2       1               41.6         2.19         0.0527
+## 12 2       2               15.6         0.794        0.0509
+## 13 2       3               36.0         1.87         0.0519
+## 14 2       4               21.3         1.08         0.0505
+## 15 2       5               28.4         1.44         0.0509
+
+# plot solution
+plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
+

+
+
+

Multiple zones with complex targets +

+

So far, we have dealt with problems where each feature has a target that pertains to a single zone. But sometimes we have targets that pertain to multiple zones. For example, what if we were in charge of managing pest control in a set of areas and we had three different pest control methods we could implement in any given planning unit. We could (i) set up a few traps in a given planning unit and make 10 % of the habitat in the unit pest-free, (ii) set up a lot of traps and make 50 % of the habitat in the unit pest-free, or (iii) drop baits over a given planning unit and make 80 % of the planning unit pest-free. Each of these different actions has a different cost, with a few low intensity trapping costing $100 per planning unit, a high intensity trapping costing $300, and baiting costing $200 (please note these costs aren’t meant to be realistic). After defining our management actions and costs, we require a solution that will yield 8 units of pest free habitat per feature. It’s important to note that unlike the previous examples, here we don’t have targets for each feature in each zone, but rather our targets are for each feature and across multiple zones. In other words, we don’t really care which management actions we implement, we just want the set of actions that will meet our targets for minimum expenditure. We can formulate and solve this problem using the following code.

+
+# create planning unit data with costs
+pu4 <- stack(Which(!is.na(sim_pu_raster)) * 100,
+             Which(!is.na(sim_pu_raster)) * 300,
+             Which(!is.na(sim_pu_raster)) * 200)
+names(pu4) <- c("few.traps", "many.traps", "baiting")
+
+# plot planning unit data
+plot(pu4, nr = 1, axes = FALSE, box = FALSE)
+

+
+# create targets
+t4 <- tibble::tibble(feature = names(sim_features),
+                     zone = list(names(pu4))[rep(1, 5)],
+                     target = rep(8, 5),
+                     type = rep("absolute", 5))
+
+# print targets
+print(t4)
+
## # A tibble: 5 × 4
+##   feature zone      target type    
+##   <chr>   <list>     <dbl> <chr>   
+## 1 layer.1 <chr [3]>      8 absolute
+## 2 layer.2 <chr [3]>      8 absolute
+## 3 layer.3 <chr [3]>      8 absolute
+## 4 layer.4 <chr [3]>      8 absolute
+## 5 layer.5 <chr [3]>      8 absolute
+
+# create problem
+p4 <- problem(pu4, zones(few.traps = sim_features * 0.1,
+                         many.traps = sim_features * 0.5,
+                         baiting = sim_features * 0.8,
+                         feature_names = names(sim_features))) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(t4) %>%
+      add_binary_decisions()
+
+# print problem
+print(p4)
+
## Conservation Problem
+##   zones:          few.traps, many.traps, baiting (3 zones)
+##   planning units: RasterStack (100 units)
+##   cost:           min: 0, max: 300
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Absolute targets [targets (min: 8, max: 8)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+# solve problem
+s4 <- solve(p4)
+
## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 105 rows, 300 columns and 1800 nonzeros
+## Model fingerprint: 0xd67e7fdc
+## Variable types: 0 continuous, 300 integer (300 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-02, 1e+00]
+##   Objective range  [1e+02, 3e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [1e+00, 8e+00]
+## Found heuristic solution: objective 9400.0000000
+## Presolve removed 14 rows and 120 columns
+## Presolve time: 0.00s
+## Presolved: 91 rows, 180 columns, 360 nonzeros
+## Found heuristic solution: objective 4800.0000000
+## Variable types: 0 continuous, 180 integer (180 binary)
+## Root relaxation presolved: 91 rows, 180 columns, 360 nonzeros
+## 
+## 
+## Root relaxation: objective 3.663237e+03, 1 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 3663.23657    0    1 4800.00000 3663.23657  23.7%     -    0s
+## H    0     0                    3800.0000000 3663.23657  3.60%     -    0s
+## 
+## Explored 1 nodes (1 simplex iterations) in 0.00 seconds (0.00 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 3: 3800 4800 9400 
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 3.800000000000e+03, best bound 3.700000000000e+03, gap 2.6316%
+
+# calculate feature representation
+r4 <- eval_feature_representation_summary(p4, s4)
+print(r4)
+
## # A tibble: 20 × 5
+##    summary    feature total_amount absolute_held relative_held
+##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
+##  1 overall    layer.1       117.           18.3          0.157
+##  2 overall    layer.2        43.7           8.19         0.187
+##  3 overall    layer.3       101.           15.2          0.151
+##  4 overall    layer.4        59.7          11.6          0.194
+##  5 overall    layer.5        79.4          12.7          0.161
+##  6 few.traps  layer.1         8.33          0            0    
+##  7 few.traps  layer.2         3.12          0            0    
+##  8 few.traps  layer.3         7.20          0            0    
+##  9 few.traps  layer.4         4.27          0            0    
+## 10 few.traps  layer.5         5.67          0            0    
+## 11 many.traps layer.1        41.6           0            0    
+## 12 many.traps layer.2        15.6           0            0    
+## 13 many.traps layer.3        36.0           0            0    
+## 14 many.traps layer.4        21.3           0            0    
+## 15 many.traps layer.5        28.4           0            0    
+## 16 baiting    layer.1        66.6          18.3          0.275
+## 17 baiting    layer.2        25.0           8.19         0.328
+## 18 baiting    layer.3        57.6          15.2          0.264
+## 19 baiting    layer.4        34.1          11.6          0.340
+## 20 baiting    layer.5        45.4          12.7          0.281
+
+# plot solution
+plot(category_layer(s4), main = "solution", axes = FALSE, box = FALSE)
+

+
+
+

Multiple zones with extra constraints +

+

So it looks like baiting is the way to go! Except that we might recall that we can’t use baits in most of the planning units because they contain native species that are susceptible to baits. So now we need to specify that which of our planning units cannot be assigned to the third zone (baiting) to obtain a more useful solution.

+
+# create data.frame to specify that we cannot bait in the first 40 units
+l5 <- data.frame(pu = seq(1, 80),
+                 zone = "baiting",
+                 status = 0)
+
+# preview locked data
+head(l5)
+
##   pu    zone status
+## 1  1 baiting      0
+## 2  2 baiting      0
+## 3  3 baiting      0
+## 4  4 baiting      0
+## 5  5 baiting      0
+## 6  6 baiting      0
+
+# create problem
+p5 <- problem(pu4, zones(few.traps = sim_features * 0.1,
+                         many.traps = sim_features * 0.5,
+                         baiting = sim_features * 0.8,
+                         feature_names = names(sim_features))) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(t4) %>%
+      add_manual_locked_constraints(l5) %>%
+      add_binary_decisions()
+
+# print problem
+print(p5)
+
## Conservation Problem
+##   zones:          few.traps, many.traps, baiting (3 zones)
+##   planning units: RasterStack (100 units)
+##   cost:           min: 0, max: 300
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Absolute targets [targets (min: 8, max: 8)]
+##   decisions:      Binary decision 
+##   constraints:    <Manually locked planning units [80 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+# solve problem
+s5 <- solve(p5)
+
## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 105 rows, 300 columns and 1800 nonzeros
+## Model fingerprint: 0x4ad99e4b
+## Variable types: 0 continuous, 300 integer (300 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-02, 1e+00]
+##   Objective range  [1e+02, 3e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [1e+00, 8e+00]
+## Found heuristic solution: objective 13600.000000
+## Presolve removed 14 rows and 120 columns
+## Presolve time: 0.00s
+## Presolved: 91 rows, 180 columns, 360 nonzeros
+## Found heuristic solution: objective 9600.0000000
+## Variable types: 0 continuous, 180 integer (180 binary)
+## Root relaxation presolved: 91 rows, 180 columns, 360 nonzeros
+## 
+## 
+## Root relaxation: objective 6.938068e+03, 1 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 6938.06818    0    1 9600.00000 6938.06818  27.7%     -    0s
+## H    0     0                    7000.0000000 6938.06818  0.88%     -    0s
+##      0     0 6938.06818    0    1 7000.00000 6938.06818  0.88%     -    0s
+## 
+## Explored 1 nodes (1 simplex iterations) in 0.00 seconds (0.00 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 3: 7000 9600 13600 
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 7.000000000000e+03, best bound 7.000000000000e+03, gap 0.0000%
+
+# calculate feature representation
+r5 <- eval_feature_representation_summary(p5, s5)
+print(r5)
+
## # A tibble: 20 × 5
+##    summary    feature total_amount absolute_held relative_held
+##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
+##  1 overall    layer.1       117.           21.8          0.187
+##  2 overall    layer.2        43.7           8.04         0.184
+##  3 overall    layer.3       101.           17.7          0.176
+##  4 overall    layer.4        59.7          10.9          0.182
+##  5 overall    layer.5        79.4          15.2          0.192
+##  6 few.traps  layer.1         8.33          0            0    
+##  7 few.traps  layer.2         3.12          0            0    
+##  8 few.traps  layer.3         7.20          0            0    
+##  9 few.traps  layer.4         4.27          0            0    
+## 10 few.traps  layer.5         5.67          0            0    
+## 11 many.traps layer.1        41.6           7.40         0.178
+## 12 many.traps layer.2        15.6           3.42         0.219
+## 13 many.traps layer.3        36.0           6.00         0.167
+## 14 many.traps layer.4        21.3           4.84         0.227
+## 15 many.traps layer.5        28.4           5.26         0.186
+## 16 baiting    layer.1        66.6          14.4          0.217
+## 17 baiting    layer.2        25.0           4.62         0.185
+## 18 baiting    layer.3        57.6          11.7          0.203
+## 19 baiting    layer.4        34.1           6.05         0.177
+## 20 baiting    layer.5        45.4           9.98         0.220
+
+# plot solution
+plot(category_layer(s5), main = "solution", axes = FALSE, box = FALSE)
+

+
+
+

Multiple zones with fragmentation penalties +

+

So now the best strategy seems to be a combination of high intensity trapping and baiting. But we can also see that this solution is fairly fragmented, so we can add penalties to cluster managed planning units together. Here we will add penalties that will cluster the planning units allocated to the two trapping zones together, and penalties that will cluster the planning units allocated to the baiting zone together. We will also set an overall penalty factor to 640 to strongly penalize fragmented solutions.

+
+# create matrix that describe boundary penalties between planning units
+# allocated to different zones
+z6 <- diag(3)
+z6[1, 2] <- 1
+z6[2, 1] <- 1
+colnames(z6) <- c("few.traps", "many.traps", "baiting")
+rownames(z6) <- colnames(z6)
+
+# print matrix
+print(z6)
+
##            few.traps many.traps baiting
+## few.traps          1          1       0
+## many.traps         1          1       0
+## baiting            0          0       1
+
+# create problem
+p6 <- problem(pu4, zones("few.traps" = sim_features * 0.1,
+                         "many.traps" = sim_features * 0.5,
+                         "baiting" = sim_features * 0.8,
+                         feature_names = names(sim_features))) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(t4) %>%
+      add_manual_locked_constraints(l5) %>%
+      add_boundary_penalties(penalty = 640, zones = z6) %>%
+      add_binary_decisions()
+
+# print problem
+print(p6)
+
## Conservation Problem
+##   zones:          few.traps, many.traps, baiting (3 zones)
+##   planning units: RasterStack (100 units)
+##   cost:           min: 0, max: 300
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Absolute targets [targets (min: 8, max: 8)]
+##   decisions:      Binary decision 
+##   constraints:    <Manually locked planning units [80 locked units]>
+##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (640), zones]>
+##   portfolio:      default
+##   solver:         default
+
+# solve problem
+s6 <- solve(p6)
+
## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 1905 rows, 1200 columns and 5400 nonzeros
+## Model fingerprint: 0xb44cc86f
+## Variable types: 0 continuous, 1200 integer (1200 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-02, 1e+00]
+##   Objective range  [1e+02, 6e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [1e+00, 8e+00]
+## Found heuristic solution: objective 20096.000000
+## Presolve removed 1028 rows and 232 columns
+## Presolve time: 0.01s
+## Presolved: 877 rows, 968 columns, 2712 nonzeros
+## Variable types: 0 continuous, 968 integer (968 binary)
+## Found heuristic solution: objective 19632.000000
+## Root relaxation presolved: 877 rows, 968 columns, 2712 nonzeros
+## 
+## 
+## Root relaxation: objective 1.005410e+04, 569 iterations, 0.01 seconds (0.01 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 10054.0986    0   57 19632.0000 10054.0986  48.8%     -    0s
+## H    0     0                    11300.000000 10054.0986  11.0%     -    0s
+## H    0     0                    10588.000000 10054.0986  5.04%     -    0s
+## 
+## Explored 1 nodes (819 simplex iterations) in 0.02 seconds (0.03 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 4: 10588 11300 19632 20096 
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 1.058800000000e+04, best bound 1.005600000000e+04, gap 5.0246%
+
+# calculate feature representation
+r6 <- eval_feature_representation_summary(p6, s6)
+print(r6)
+
## # A tibble: 20 × 5
+##    summary    feature total_amount absolute_held relative_held
+##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
+##  1 overall    layer.1       117.           22.5          0.193
+##  2 overall    layer.2        43.7           8.06         0.184
+##  3 overall    layer.3       101.           18.0          0.179
+##  4 overall    layer.4        59.7          11.6          0.193
+##  5 overall    layer.5        79.4          15.6          0.197
+##  6 few.traps  layer.1         8.33          0            0    
+##  7 few.traps  layer.2         3.12          0            0    
+##  8 few.traps  layer.3         7.20          0            0    
+##  9 few.traps  layer.4         4.27          0            0    
+## 10 few.traps  layer.5         5.67          0            0    
+## 11 many.traps layer.1        41.6           8.01         0.192
+## 12 many.traps layer.2        15.6           3.44         0.221
+## 13 many.traps layer.3        36.0           6.31         0.175
+## 14 many.traps layer.4        21.3           5.50         0.258
+## 15 many.traps layer.5        28.4           5.62         0.198
+## 16 baiting    layer.1        66.6          14.4          0.217
+## 17 baiting    layer.2        25.0           4.62         0.185
+## 18 baiting    layer.3        57.6          11.7          0.203
+## 19 baiting    layer.4        34.1           6.05         0.177
+## 20 baiting    layer.5        45.4           9.98         0.220
+
+# plot solution
+plot(category_layer(s6), main = "solution", axes = FALSE, box = FALSE)
+

+

Finally, it appears we might have a viable solution for this made-up conservation problem.

+
+
+

Multiple zones with fragmentation penalties and mandatory allocations +

+

Finally, we might be interested in conservation planning scenarios where every single planning unit must be allocated to a management zone. This is often the case when developing land-use plans where every single planning unit needs to be allocated to a specific management zone. Though it makes less sense here, let’s see what happens to the solution if we needed to do at least one form of control in every single planning unit.

+
+# create matrix that describe boundary penalties between planning units
+# allocated to different zones
+p7 <- problem(pu4, zones("few.traps" = sim_features * 0.1,
+                         "many.traps" = sim_features * 0.5,
+                         "baiting" = sim_features * 0.8,
+                         feature_names = names(sim_features))) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(t4) %>%
+      add_mandatory_allocation_constraints() %>%
+      add_manual_locked_constraints(l5) %>%
+      add_boundary_penalties(penalty = 640, zones = z6) %>%
+      add_binary_decisions()
+
+# print problem
+print(p7)
+
## Conservation Problem
+##   zones:          few.traps, many.traps, baiting (3 zones)
+##   planning units: RasterStack (100 units)
+##   cost:           min: 0, max: 300
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Absolute targets [targets (min: 8, max: 8)]
+##   decisions:      Binary decision 
+##   constraints:    <Manually locked planning units [80 locked units]
+##                    Mandatory allocation constraints [apply constraints? (1)]>
+##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (640), zones]>
+##   portfolio:      default
+##   solver:         default
+
+# solve problem
+s7 <- solve(p7)
+
## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 1905 rows, 1200 columns and 5400 nonzeros
+## Model fingerprint: 0x89a9dafb
+## Variable types: 0 continuous, 1200 integer (1200 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-02, 1e+00]
+##   Objective range  [1e+02, 6e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [1e+00, 8e+00]
+## Found heuristic solution: objective 19600.000000
+## Presolve removed 1120 rows and 324 columns
+## Presolve time: 0.01s
+## Presolved: 785 rows, 876 columns, 2448 nonzeros
+## Variable types: 0 continuous, 876 integer (876 binary)
+## Found heuristic solution: objective 18988.000000
+## Root relaxation presolved: 785 rows, 876 columns, 2448 nonzeros
+## 
+## 
+## Root relaxation: objective 1.323093e+04, 274 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 13230.9255    0   95 18988.0000 13230.9255  30.3%     -    0s
+## H    0     0                    13260.000000 13230.9255  0.22%     -    0s
+## 
+## Explored 1 nodes (412 simplex iterations) in 0.02 seconds (0.03 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 3: 13260 18988 19600 
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 1.326000000000e+04, best bound 1.323200000000e+04, gap 0.2112%
+
+# calculate feature representation
+r7 <- eval_feature_representation_summary(p7, s7)
+print(r7)
+
## # A tibble: 20 × 5
+##    summary    feature total_amount absolute_held relative_held
+##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
+##  1 overall    layer.1       117.           23.4         0.201 
+##  2 overall    layer.2        43.7           8.04        0.184 
+##  3 overall    layer.3       101.           19.4         0.192 
+##  4 overall    layer.4        59.7          10.9         0.182 
+##  5 overall    layer.5        79.4          16.1         0.203 
+##  6 few.traps  layer.1         8.33          5.92        0.711 
+##  7 few.traps  layer.2         3.12          2.33        0.745 
+##  8 few.traps  layer.3         7.20          5.25        0.730 
+##  9 few.traps  layer.4         4.27          3.18        0.745 
+## 10 few.traps  layer.5         5.67          4.00        0.706 
+## 11 many.traps layer.1        41.6           3.02        0.0725
+## 12 many.traps layer.2        15.6           1.09        0.0700
+## 13 many.traps layer.3        36.0           2.41        0.0670
+## 14 many.traps layer.4        21.3           1.66        0.0779
+## 15 many.traps layer.5        28.4           2.11        0.0743
+## 16 baiting    layer.1        66.6          14.4         0.217 
+## 17 baiting    layer.2        25.0           4.62        0.185 
+## 18 baiting    layer.3        57.6          11.7         0.203 
+## 19 baiting    layer.4        34.1           6.05        0.177 
+## 20 baiting    layer.5        45.4           9.98        0.220
+
+# plot solution
+plot(category_layer(s7), main = "solution", axes = FALSE, box = FALSE)
+

+
+
+
+

Conclusion +

+

Hopefully, this vignette has provided an informative introduction to building and solving problems with multiple zones. Although we have examined only a few different functions here, almost every single function for modifying conservation planning problems is compatible with problems that contain zones. It’s worth noting that working with multiple zones is a lot trickier than working with a single zone, so we would recommend playing around with the code in the Examples sections of the package documentation to help understand how functions work when applied to multiple zones.

+
+
+

References +

+
+
+Cattarino, L., Hermoso, V., Carwardine, J., Adams, V.M., Kennard, M.J. & Linke, S. (2018). Information uncertainty influences conservation outcomes when prioritizing multi-action management efforts. Journal of Applied Ecology, Available at: https://doi.org/10.1111/1365–2664.13147. +
+
+Klein, C.J., Tulloch, V.J., Halpern, B.S., Selkoe, K.A., Watts, M.E., Steinback, C., Scholz, A. & Possingham, H.P. (2013). Tradeoffs in marine reserve design: Habitat condition, representation, and socioeconomic costs. Conservation Letters, 6, 324–332. +
+
+Klein, C., Wilson, K., Watts, M., Stein, J., Berry, S., Carwardine, J., Smith, M.S., Mackey, B. & Possingham, H. (2009). Incorporating ecological and evolutionary processes into continental-scale conservation planning. Ecological Applications, 19, 206–217. +
+
+Margules, C.R. & Pressey, R.L. (2000). Systematic conservation planning. Nature, 405, 243–253. +
+
+Stigner, M.G., Beyer, H.L., Klein, C.J. & Fuller, R.A. (2016). Reconciling recreational use and conservation values in a coastal protected area. Journal of Applied Ecology, 53, 1206–1214. +
+
+Watts, M.E., Ball, I.R., Stewart, R.S., Klein, C.J., Wilson, K., Steinback, C., Lourival, R., Kircher, L. & Possingham, H.P. (2009). Marxan with Zones: Software for optimal conservation based land- and sea-use zoning. Environmental Modelling & Software, 24, 1513–1521. +
+
+Wilson, K.A., Meijaard, E., Drummond, S., Grantham, H.S., Boitani, L., Catullo, G., Christie, L., Dennis, R., Dutton, I., Falcucci, A. & others. (2010). Conserving biodiversity in production landscapes. Ecological Applications, 20, 1721–1732. +
+
+
+
+ + + +
+ + + + +
+ + + + + diff --git a/docs/articles/zones_files/figure-html/unnamed-chunk-9-1.png b/docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-10-1.png similarity index 100% rename from docs/articles/zones_files/figure-html/unnamed-chunk-9-1.png rename to docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-10-1.png diff --git a/docs/articles/zones_files/figure-html/unnamed-chunk-10-1.png b/docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-11-1.png similarity index 100% rename from docs/articles/zones_files/figure-html/unnamed-chunk-10-1.png rename to docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-11-1.png diff --git a/docs/articles/zones_files/figure-html/unnamed-chunk-2-1.png b/docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-3-1.png similarity index 100% rename from docs/articles/zones_files/figure-html/unnamed-chunk-2-1.png rename to docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-3-1.png diff --git a/docs/articles/zones_files/figure-html/unnamed-chunk-3-1.png b/docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-4-1.png similarity index 100% rename from docs/articles/zones_files/figure-html/unnamed-chunk-3-1.png rename to docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-4-1.png diff --git a/docs/articles/zones_files/figure-html/unnamed-chunk-4-1.png b/docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-5-1.png similarity index 100% rename from docs/articles/zones_files/figure-html/unnamed-chunk-4-1.png rename to docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-5-1.png diff --git a/docs/articles/zones_files/figure-html/unnamed-chunk-5-1.png b/docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-6-1.png similarity index 100% rename from docs/articles/zones_files/figure-html/unnamed-chunk-5-1.png rename to docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-6-1.png diff --git a/docs/articles/zones_files/figure-html/unnamed-chunk-6-1.png b/docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-7-1.png similarity index 100% rename from docs/articles/zones_files/figure-html/unnamed-chunk-6-1.png rename to docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-7-1.png diff --git a/docs/articles/zones_files/figure-html/unnamed-chunk-7-1.png b/docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-8-1.png similarity index 100% rename from docs/articles/zones_files/figure-html/unnamed-chunk-7-1.png rename to docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-8-1.png diff --git a/docs/articles/zones_files/figure-html/unnamed-chunk-8-1.png b/docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-9-1.png similarity index 100% rename from docs/articles/zones_files/figure-html/unnamed-chunk-8-1.png rename to docs/articles/management_zones_tutorial_files/figure-html/unnamed-chunk-9-1.png diff --git a/docs/articles/package_overview.html b/docs/articles/package_overview.html new file mode 100644 index 000000000..31eb09c52 --- /dev/null +++ b/docs/articles/package_overview.html @@ -0,0 +1,1814 @@ + + + + + + + +Package overview • prioritizr + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+
+
+

Package overview

+ + + Source: vignettes/package_overview.Rmd + + +
+ + + +
+

Summary +

+

The prioritizr R package uses integer linear programming (ILP) techniques to provide a flexible interface for building and solving conservation planning problems (Rodrigues et al. 2000; Billionnet 2013). It supports a broad range of objectives, constraints, and penalties that can be used to custom-tailor conservation planning problems to the specific needs of a conservation planning exercise. Once built, conservation planning problems can be solved using a variety of commercial and open-source exact algorithm solvers. In contrast to the algorithms conventionally used to solve conservation problems, such as heuristics or simulated annealing (Ball et al. 2009), the exact algorithms used here are guaranteed to find optimal solutions. Furthermore, conservation problems can be constructed to optimize the spatial allocation of different management zone (or actions), meaning that conservation practitioners can identify solutions that benefit multiple stakeholders. Finally, this package has the functionality to read input data formatted for the Marxan conservation planning program (Ball et al. 2009), and find much cheaper solutions in a much shorter period of time than Marxan (Beyer et al. 2016).

+
+
+

Introduction +

+

Systematic conservation planning is a rigorous, repeatable, and structured approach to designing new protected areas that efficiently meet conservation objectives (Margules & Pressey 2000). Historically, conservation decision-making has often evaluated parcels opportunistically as they became available for purchase, donation, or under threat. Although purchasing such areas may improve the status quo, such decisions may not substantially enhance the long-term persistence of target species or communities. Faced with this realization, conservation planners began using decision support tools to help simulate alternative reserve designs over a range of different biodiversity and management goals and, ultimately, guide protected area acquisitions and management actions. Due to the systematic, evidence-based nature of these tools, conservation prioritization can help contribute to a transparent, inclusive, and more defensible decision making process.

+

A conservation planning exercise typically starts by defining a study area. This study area should encompass all the areas relevant to the decision maker or the hypothesis being tested. The extent of a study area could encompass a few important localities (e.g., Stigner et al. 2016), a single state (e.g., Kirkpatrick 1983), an entire country (Fuller et al. 2010), or the entire planet (Butchart et al. 2015). Next, the study area is divided into a set of discrete areas termed planning units. Each planning unit represents a discrete locality in the study area that can be managed independently of other areas. The general idea is that some combination of the planning units can be selected for conservation actions (e.g., protected area establishment, habitat restoration). Planning units are often created as square or hexagon cells that are sized according to the scale of the conservation actions, and the resolution of the data that underpin the planning exercise (but see Klein et al. 2009).

+

Cost data (or a surrogate thereof) are needed to inform the prioritization process. Specifically, these cost data describe the relative expenditure associated with managing each planning unit for conservation. For example, if the goal of the conservation planning exercise is to identify priority areas for expanding a local protected area system, then the cost data could represent the physical cost of purchasing the land. Alternatively, if such data are not available, then surrogate data could are often used instead (e.g., human population density, opportunity cost of foregone commercial activities, or planning unit size).

+

Conservation planning exercises also require data on the biodiversity elements that are of conservation interest (termed conservation features). These features could be species (e.g., Neofelis nebulosa, the Clouded Leopard), populations, or habitats (e.g., mangroves or cloud forest). After identifying the set of relevant conservation features for a conservation planning exercise, spatially explicit data need to be obtained for each and every feature to describe their spatial distribution (e.g., habitat suitability data, probability of occurrence data, presence/absence data). This is important to ensure that conservation features are adequately covered (represented) by prioritizations. After assembling all the data, the next step is to define the conservation planning problem.

+

The prioritizr R package is designed to help you build and solve conservation planning problems. Specifically, prioritizations are generated by using formulating a mathematical optimization problem and then solving it to generate a solution. These mathematical optimization problems are formulated using the planning unit data, cost data, and feature data, and with information related to the overarching aim of the prioritization process. In general, the goal of an optimization problem is to minimize (or maximize) an objective function that is calculated using a set of decision variables, subject to a series of constraints to ensure that solution exhibits specific properties. The objective function describes the quantity which we are trying to minimize (e.g., cost of the solution) or maximize (e.g., number of features conserved). The decision variables describe the entities that we can control, and indicate which planning units are selected for conservation management and which of those are not. The constraints can be thought of as rules that the need decision variables need to follow. For example, a commonly used constraint is specifying that the solution must not exceed a certain budget.

+

A wide variety of approaches have been developed for solving optimization problems. Reserve design problems are frequently solved using simulated annealing (Kirkpatrick et al. 1983) or heuristics (Nicholls & Margules 1993; Moilanen 2007). These methods are conceptually simple and can be applied to a wide variety of optimization problems. However, they do not scale well for large or complex problems (Beyer et al. 2016). Additionally, these methods cannot tell you how close any given solution is to the optimal solution. The package uses exact algorithms to efficiently solve conservation planning problems to within a pre-specified a optimality gap. In other words, you can specify that you need the optimal solution (i.e., a gap of 0%) and the algorithms will, given enough time, find a solution that meets this criteria. In the past, exact algorithms have been too slow for conservation planning exercises (Pressey et al. 1996). However, improvements over the last decade mean that they are now much faster (Achterberg & Wunderling 2013; Beyer et al. 2016).

+

In this package, optimization problems are expressed using integer linear programming (ILP) so that they can be solved using (linear) exact algorithm solvers. The general form of an integer programming problem can be expressed in matrix notation using the following equation.

+

\[\text{Minimize} \space \boldsymbol{c}^\text{T} \boldsymbol{x} \space +\space \text{subject to} \space A\boldsymbol{x} +\space \Box \space \boldsymbol{b}\]

+

Here, where \(x\) is a vector of decision variables, \(c\) and \(b\) are vectors of known coefficients, and \(A\) is the constraint matrix. The final term specifies a series of structural constants and the \(\Box\) symbol is used to indicate that the relational operators for the constraints can be either \(\geq\), \(=\), or \(\leq\). In the context of a conservation planning problem, \(c\) could be used to represent the planning unit costs, \(A\) could be used to store the data showing the presence / absence (or amount) of each feature in each planning unit, \(b\) could be used to represent minimum amount of habitat required for each species in the solution, the \(\Box\) could be set to \(\geq\) symbols to indicate that the total amount of each feature in the solution must exceed the quantities in \(b\). But there are many other ways of formulating the reserve selection problem (Rodrigues et al. 2000).

+
+
+

A grammar for conservation planning +

+

The prioritizr R package uses a grammar to describe elements of conservation planning. This means that functions are organized into verbs that relate to specific concepts. For example, all of the functions used to specify the primary objective for optimization end with the _objective suffix (e.g., add_min_set_objective() and add_min_shortfall_objective()). By combining multiple functions together, they can be used to formulate a complete conservation planning problem. Specifically, the verbs for formulating problems are described below.

+
    +
  • Create a new conservation planning problem by specifying the planning units, features, and management zones of conservation interest.
    • +
  • Add a primary objective to a conservation planning problem (e.g., minimize overall cost).
    • +
  • Add penalties to a conservation planning problem to penalize solutions according to specific metric (e.g., connectivity).
    • +
  • Add targets to a conservation planning problem to specify how much of each feature should ideally be represented solutions.
    • +
  • Add constraints to a conservation planning problem to ensure that solutions exhibit specific properties (e.g., select specific planning units for protection).
    • +
  • Add decisions to a conservation planning problem to specify the nature of the decisions in the problem (e.g., binary decisions indicate the planning units should be selected or not selected for management).
    • +
  • Add a portfolio to a conservation planning problem to specify a methodological approach for generating multiple solutions (e.g. generate multiple solutions by finding 100 solutions within 10% of optimality).
    • +
  • Add a solver to a conservation problem to specify the optimization software (e.g. Gurobi) for generating solutions and customize the optimization settings (e.g. generate an optimal solution).
    • +
+

After building a conservation planning problem, it can be solved to generate a prioritization (using the solve() function). There are also verbs available to help evaluate and interpret solutions. These verbs are described below.

+
    +
  • Evaluate performance by computing summary statistics (e.g. overall cost, feature representation, or total boundary length).
    • +
  • Evaluate the relative importance of planning units selected by a solution (e.g. based on irreplaceability).
    • +
+
+
+

Workflow +

+

The general workflow when using the prioritizr R package starts with creating a new conservation planning problem() object using data. Specifically, the problem() object should be constructed using data that specify the planning units, biodiversity features, management zones (if applicable), and costs. After creating a new problem() object, it can be customized—by adding objectives, penalties, constraints, and other information—to build a precise representation of the conservation planning problem required, and then solved to obtain a solutions.

+

All conservation planning problems require an objective. An objective specifies the property which is used to compare different feasible solutions. Simply put, the objective is the property of the solution which should be maximized or minimized during the optimization process. For instance, with the minimum set objective (specified using add_min_set_objective()), we are seeking to minimize the cost of the solution (similar to Marxan). On the other hand, with the minimum shortfall objective (specified using add_min_shortfall_objective()), we are seeking to minimize the average target shortfall for all features represented in the solution, subject to a budget.

+

Many objectives require representation targets (e.g., the minimum set objective). These targets are a specialized set of constraints that relate to the total quantity of each feature secured in the solution (e.g., amount of suitable habitat or number of individuals). In the case of the minimum set objective ( add_min_set_objective()), they are used to ensure that solutions secure a sufficient quantity of each feature, and in other objectives, such as the maximum features objective ( add_max_features_objective()) they are used to assess whether a feature has been adequately conserved by a candidate solution. Targets can be expressed numerically as the total amount required for a given feature (using add_absolute_targets()), or as a proportion of the total amount found in the planning units (using add_relative_targets()). Note that not all objectives require targets, and a warning will be thrown if an attempt is made to add targets to a problem with an objective that does not use them.

+

Constraints and penalties can be added to a conservation planning problem to ensure that solutions exhibit a specific property or penalize solutions which don’t exhibit a specific property (respectively). The difference between constraints and penalties, strictly speaking, is constraints are used to rule out potential solutions that don’t exhibit a specific property. For instance, constraints can be used to ensure that specific planning units are selected in the solution for prioritization (using add_locked_in_constraints()) or not selected in the solution for prioritization (using add_locked_out_constraints()). On the other hand, penalties are combined with the objective of a problem, with a penalty factor, and the overall objective of the problem then becomes to minimize (or maximize) the primary objective function and the penalty function. For example, penalties can be added to a problem to penalize solutions that are excessively fragmented (using add_boundary_penalties()). These penalties have a penalty argument that specifies the relative importance of having spatially clustered solutions. When the argument to penalty is high, then solutions which are less fragmented are valued more highly – even if they cost more – and when the argument to penalty is low, then the solutions which are more fragmented are valued less highly.

+

After building a conservation problem, it can then be solved to obtain a solution (or portfolio of solutions if desired). The solution is returned in the same format as the planning unit data used to construct the problem. For instance, this means that if raster data was used to initialize the problem, then the solution will also be output in raster format. This can be very helpful when it comes to interpreting and visualizing solutions because it means that the solution data does not first have to be merged with spatial data before they can be plotted on a map.

+
+
+

Usage +

+

Here we will provide an introduction to using the prioritizr R package to build and solve a conservation planning problem. Please note that we will not discuss conservation planning with multiple zones in this vignette, for more information on working with multiple management zones please see the zones vignette.

+

First, we will load the prioritizr package.

+
+# load package
+library(prioritizr)
+
+# set default options for printing tabular data
+options(tibble.width = Inf)
+
+

Data +

+

Now we will load some built-in data sets that are distributed with the prioritizr R package. This package contains several different planning unit data sets. To provide a comprehensive overview of the different ways that we can initialize a conservation planning problem, we will load each of them.

+

First, we will load the raster planning unit data (sim_pu_raster). Here, the planning units are represented as a raster (i.e., a RasterLayer object) and each pixel corresponds to the spatial extent of each panning unit. The pixel values correspond to the acquisition costs of each planning unit.

+
+# load raster planning unit data
+data(sim_pu_raster)
+
+# print description of the data
+print(sim_pu_raster)
+
## class      : RasterLayer 
+## dimensions : 10, 10, 100  (nrow, ncol, ncell)
+## resolution : 0.1, 0.1  (x, y)
+## extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+## crs        : NA 
+## source     : memory
+## names      : layer 
+## values     : 190.1328, 215.8638  (min, max)
+
+# plot the data
+plot(sim_pu_raster)
+

+

Secondly, we will load one of the spatial vector planning unit data sets (sim_pu_polygons). Here, each polygon (i.e., feature using ArcGIS terminology) corresponds to a different planning unit. This data set has an attribute table that contains additional information about each polygon. Namely, the cost field (column) in the attribute table contains the acquisition cost for each planning unit.

+
+# load polygon planning unit data
+data(sim_pu_polygons)
+
+# print first six rows of attribute table
+head(sim_pu_polygons@data)
+
##       cost locked_in locked_out
+## 1 215.8638     FALSE      FALSE
+## 2 212.7823     FALSE      FALSE
+## 3 207.4962     FALSE      FALSE
+## 4 208.9322     FALSE       TRUE
+## 5 214.0419     FALSE      FALSE
+## 6 213.7636     FALSE      FALSE
+
+# plot the planning units
+spplot(sim_pu_polygons, zcol = "cost")
+

+

Thirdly, we will load some planning unit data stored in tabular format (i.e., data.frame format). For those familiar with Marxan or dealing with very large conservation planning problems (> 10 million planning units), it may be useful to work with data in this format because it does not contain any spatial information which will reduce computational burden. When using tabular data to initialize conservation planning problems, the data must follow the conventions used by Marxan. Specifically, each row in the planning unit table must correspond to a different planning unit. The table must also have an “id” column to provide a unique integer identifier for each planning unit, and it must also have a column that indicates the cost of each planning unit. For more information, please see the official Marxan documentation.

+
+# specify file path for planning unit data
+pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr")
+
+# load in the tabular planning unit data
+# note that we use the data.table::fread function, as opposed to the read.csv
+# function, because it is much faster
+pu_dat <- data.table::fread(pu_path, data.table = FALSE)
+
+# preview first six rows of the tabular planning unit data
+# note that it has some extra columns other than id and cost as per the
+# Marxan format
+head(pu_dat)
+
##   id       cost status    xloc     yloc
+## 1  3        0.0      0 1116623 -4493479
+## 2 30   752727.5      3 1110623 -4496943
+## 3 56  3734907.5      0 1092623 -4500408
+## 4 58  1695902.1      0 1116623 -4500408
+## 5 84  3422025.6      0 1098623 -4503872
+## 6 85 17890758.4      0 1110623 -4503872
+

Finally, we will load data showing the spatial distribution of the conservation features. Our conservation features (sim_features) are represented as a stack of raster objects (i.e., a RasterStack object) where each layer corresponds to a different feature (e.g., a multi-band GeoTIFF where each band corresponds to a different feature). The pixel values in each layer correspond to the amount of suitable habitat available in a given planning unit. Note that our planning unit raster layer and our conservation feature stack have exactly the same spatial properties (i.e., resolution, extent, coordinate reference system) so their pixels line up perfectly.

+
+# load feature data
+data(sim_features)
+
+# plot the distribution of suitable habitat for each feature
+plot(sim_features, main = paste("Feature", seq_len(nlayers(sim_features))),
+     nr = 2, box = FALSE, axes = FALSE)
+

+
+
+

Initialize a problem +

+

After having loaded our planning unit and feature data, we will now try initializing the some conservation planning problems. There are a lot of different ways to initialize a conservation planning problem, so here we will just showcase a few of the more commonly used methods. For an exhaustive description of all the ways you can initialize a conservation problem, see the help file for the problem() function. First off, we will initialize a conservation planning problem using the raster data.

+
+# create problem
+p1 <- problem(sim_pu_raster, sim_features)
+
+# print problem
+print(p1)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      none
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+# print number of planning units
+number_of_planning_units(p1)
+
## [1] 90
+
+# print number of features
+number_of_features(p1)
+
## [1] 5
+

Generally, we recommend initializing problems using raster data where possible. This is because the problem() function needs to calculate the amount of each feature in each planning unit, and by providing both the planning unit and feature data in raster format with the same spatial resolution, extents, and coordinate systems, this means that the problem() function does not need to do any geoprocessing behind the scenes. But sometimes we can’t use raster planning unit data because our planning units aren’t equal-sized grid cells. So, below is an example showing how we can initialize a conservation planning problem using planning units that are formatted as spatial vector data. Note that if we had precomputed the amount of each feature in each planning unit and stored the data in the attribute table, we could pass in the names of the columns as an argument to the problem() function.

+
+# create problem with spatial vector data
+# note that we have to specify which column in the attribute table contains
+# the cost data
+p2 <- problem(sim_pu_polygons, sim_features, cost_column = "cost")
+
+# print problem
+print(p2)
+
## Conservation Problem
+##   planning units: SpatialPolygonsDataFrame (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      none
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+

We can also initialize a conservation planning problem using tabular planning unit data (i.e., data.frame format). Since the tabular planning unit data does not contain any spatial information, we also have to provide the feature data in tabular format (i.e., data.frame format) and data showing the amount of each feature in each planning unit in tabular format (i.e., data.frame format). The feature data must have an “id” column containing a unique integer identifier for each feature, and the planning unit by feature data must contain the following three columns: pu corresponding to the planning unit identifiers, species corresponding to the feature identifiers, and amount showing the amount of a given feature in a given planning unit.

+
+# set file path for feature data
+spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr")
+
+# load in feature data
+spec_dat <- data.table::fread(spec_path, data.table = FALSE)
+
+# print first six rows of the data
+# note that it contains extra columns
+head(spec_dat)
+
##   id prop spf   name
+## 1 10  0.3   1  bird1
+## 2 11  0.3   1  nvis2
+## 3 12  0.3   1  nvis8
+## 4 13  0.3   1  nvis9
+## 5 14  0.3   1 nvis14
+## 6 15  0.3   1 nvis20
+
+# set file path for planning unit vs. feature data
+puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr")
+
+# load in planning unit vs feature data
+puvspr_dat <- data.table::fread(puvspr_path, data.table = FALSE)
+
+# print first six rows of the data
+head(puvspr_dat)
+
##   species  pu     amount
+## 1      26  56 1203448.84
+## 2      26  58  451670.10
+## 3      26  84  680473.75
+## 4      26  85   97356.24
+## 5      26  86   78034.76
+## 6      26 111 4783274.17
+
+# create problem
+p3 <- problem(pu_dat, spec_dat, cost_column = "cost", rij = puvspr_dat)
+
+# print problem
+print(p3)
+
## Conservation Problem
+##   planning units: data.frame (1751 units)
+##   cost:           min: 0, max: 41569219.38232
+##   features:       bird1, nvis2, nvis8, ... (17 features)
+##   objective:      none
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+

For more information on initializing problems, please see the help page for the problem() function (which you can open by entering the code: ?problem). Now that we have initialized a conservation planning problem, we will show you how you can customize it to suit the exact needs of your conservation planning scenario. Although we initialized the conservation planning problems using several different methods, moving forward, we will only use raster-based planning unit data to keep things simple.

+
+
+

Add an objective +

+

The next step is to add a primary objective to the problem. A problem objective is used to specify the primary goal of the problem (i.e., the quantity that is to be maximized or minimized). All conservation planning problems involve minimizing or maximizing some kind of objective. For instance, we might require a solution that conserves enough habitat for each species while minimizing the overall cost of the reserve network. Alternatively, we might require a solution that maximizes the number of conserved species while ensuring that the cost of the reserve network does not exceed the budget. Please note that objectives are added in the same way regardless of the type of data used to initialize the problem. The following objectives are available.

+
    +
  • +Minimum set objective: Minimize the cost of the solution whilst ensuring that all targets are met (Rodrigues et al. 2000). This objective is similar to that used in Marxan (Ball et al. 2009). For example, we can add a minimum set objective to a problem using the following code.
    • +
+
+# create a new problem that has the minimum set objective
+p3 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective()
+
+# print the problem
+print(p3)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Maximum cover objective: Represent at least one instance of as many features as possible within a given budget (Church et al. 1996).
    • +
+
+# create a new problem that has the maximum coverage objective and a budget
+# of 5000
+p4 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_cover_objective(5000)
+
+# print the problem
+print(p4)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Maximum coverage objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Maximum features objective: Fulfill as many targets as possible while ensuring that the cost of the solution does not exceed a budget (inspired by Cabeza & Moilanen 2001). This object is similar to the maximum cover objective except that we have the option of later specifying targets for each feature. In practice, this objective is more useful than the maximum cover objective because features often require a certain amount of area for them to persist and simply capturing a single instance of habitat for each feature is generally unlikely to enhance their long-term persistence.
    • +
+
+# create a new problem that has the maximum features objective and a budget
+# of 5000
+p5 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_features_objective(budget = 5000)
+
+# print the problem
+print(p5)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Maximum representation objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Minimum shortfall objective: Minimize the overall (weighted sum) shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when there is a large amount of left-over budget when using the maximum feature representation objective and the remaining funds need to be allocated to places that will enhance the representation of features with unmet targets.
    • +
+
+# create a new problem that has the minimum shortfall objective and a budget
+# of 5000
+p6 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_shortfall_objective(budget = 5000)
+
+# print the problem
+print(p6)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum shortfall objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Minimum largest shortfall objective: Minimize the largest (maximum) shortfall while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when the minimum shortfall objective returns solutions that focus too much on representing a small number of features (e.g., because they occur in much cheaper planning units), and solutions are needed to spread conservation effort out more evenly among all features—even if it means that all features will have (relatively) poor representation.
    • +
+
+# create a new problem that has the minimum largest shortfall objective and a
+# budget of 5000
+p7 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_largest_shortfall_objective(budget = 5000)
+
+# print the problem
+print(p7)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum largest shortfall objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Maximum phylogenetic diversity objective: Maximize the phylogenetic diversity of the features represented in the solution subject to a budget (inspired by Faith 1992; Rodrigues & Gaston 2002). This objective is similar to the maximum features objective except that emphasis is placed on protecting features which are associated with a diverse range of evolutionary histories. The package contains a simulated phylogeny that can be used with the simulated feature data (sim_phylogny).
    • +
+
+# load simulated phylogeny data
+data(sim_phylogeny)
+
+# create a new problem that has the maximum phylogenetic diversity
+# objective and a budget of 5000
+p8 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_phylo_div_objective(budget = 5000, tree = sim_phylogeny)
+
## Loading required namespace: ape
+
+# print the problem
+print(p8)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Phylogenetic diversity objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Maximum phylogenetic endemism objective: Maximize the phylogenetic endemism of the features represented in the solution subject to a budget (inspired by Faith 1992; Rodrigues & Gaston 2002; Rosauer et al. 2009). This objective is similar to the maximum phylogenetic diversity except that emphasis is placed conserving features that are associated with geographically restricted periods of evolutionary history rather than a diverse range of evolutionary histories.
    • +
+
+# load simulated phylogeny data
+data(sim_phylogeny)
+
+# create a new problem that has the maximum phylogenetic diversity
+# objective and a budget of 5000
+p9 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_phylo_end_objective(budget = 5000, tree = sim_phylogeny)
+
+# print the problem
+print(p9)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Phylogenetic endemism objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Maximum utility objective: Secure as much of the features as possible without exceeding a budget. This objective is functionally equivalent to selecting the planning units with the greatest amounts of each feature (e.g., species richness). Generally, we don’t encourage the use of this objective because it will only rarely identify complementary solutions–solutions which adequately conserve a range of different features—except perhaps to explore trade-offs or provide a baseline solution with which to compare other solutions.
    • +
+
+# create a new problem that has the maximum utility objective and a budget
+# of 5000
+p10 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_utility_objective(budget = 5000)
+
+# print the problem
+print(p10)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Maximum utility objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+
+

Add targets +

+

Most conservation planning problems require targets. Targets are used to specify the minimum amount or proportion of a feature’s distribution that needs to be protected in the solution. For example, we may want to develop a reserve network that will secure 20% of the distribution for each feature for minimal cost. The following methods are available for specifying targets.

+
    +
  • +Absolute targets: Targets are expressed as the total amount of each feature in the study area that need to be secured. For example, if we had binary feature data that showed the absence or presence of suitable habitat across the study area, we could set an absolute target as 5 to mean that we require 5 planning units with suitable habitat in the solution.
    • +
+
+# create a problem with targets which specify that the solution must conserve
+# a need a sum total of 3 units of suitable habitat for each feature
+p11 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_absolute_targets(3)
+
+# print problem
+print(p11)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Absolute targets [targets (min: 3, max: 3)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Relative targets: Targets are set as a proportion (between 0 and 1) of the total amount of each feature in the study area. For example, if we had binary feature data and the feature occupied a total of 20 planning units in the study area, we could set a relative target of 50 % to specify that the solution must secure 10 planning units for the feature. We could alternatively specify an absolute target of 10 to achieve the same result, but sometimes proportions are easier to work with.
    • +
+
+# create a problem with the minimum set objective and relative targets of 10 %
+# for each feature
+p12 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1)
+
+# print problem
+print(p12)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+# create a problem with targets which specify that we need 10 % of the habitat
+# for the first feature, 15 % for the second feature, 20 % for the third feature
+# 25 % for the fourth feature and 30 % of the habitat for the fifth feature
+targets <- c(0.1, 0.15, 0.2, 0.25, 0.3)
+p13 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(targets)
+
+# print problem
+print(p13)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.3)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Log-linear targets: Targets are expressed using scaling factors and log-linear interpolation. This method for specifying targets is commonly used for global prioritization analyses (Rodrigues et al. 2004).
    • +
+
+# create problem with added log-linear targets
+p14 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_loglinear_targets(10, 0.9, 100, 0.2)
+
+# print problem
+print(p14)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Absolute targets [targets (min: 17.290505409161, max: 21.5906174426385)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Manual targets: Targets are manually specified. This is only really recommended for advanced users or problems that involve multiple management zones. See the zones vignette for more information on these targets.
    • +
+

As with the functions for specifying the objective of a problem, if we try adding multiple targets to a problem, only the most recently added set of targets are used.

+
+
+

Add constraints +

+

A constraint can be added to a conservation planning problem to ensure that all solutions exhibit a specific property. For example, they can be used to make sure that all solutions select a specific planning unit or that all selected planning units in the solution follow a certain configuration. The following constraints are available.

+
    +
  • +Locked in constraints: Add constraints to ensure that certain planning units are prioritized in the solution. For example, it may be desirable to lock in planning units that are inside existing protected areas so that the solution fills in the gaps in the existing reserve network.
    • +
+
+# create problem with constraints which specify that the first planning unit
+# must be selected in the solution
+p15 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints(1)
+
+# print problem
+print(p15)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked in planning units [1 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Locked out constraints: Add constraints to ensure that certain planning units are not prioritized in the solution. For example, it may be useful to lock out planning units that have been degraded and are not suitable for conserving species.
    • +
+
+# create problem with constraints which specify that the second planning unit
+# must not be selected in the solution
+p16 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_out_constraints(2)
+
+# print problem
+print(p16)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked out planning units [1 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Neighbor constraints: Add constraints to a conservation problem to ensure that all selected planning units have at least a certain number of neighbors.
    • +
+
+# create problem with constraints which specify that all selected planning units
+# in the solution must have at least 1 neighbor
+p17 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_neighbor_constraints(1)
+
+# print problem
+print(p17)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Neighbor constraint [number of neighbors (1), zones]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Contiguity constraints: Add constraints to a conservation problem to ensure that all selected planning units are spatially connected to each other and form spatially contiguous unit.
    • +
+
+# create problem with constraints which specify that all selected planning units
+# in the solution must form a single contiguous unit
+p18 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_contiguity_constraints()
+
+# print problem
+print(p18)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Contiguity constraints [apply constraints? (1), zones]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Feature contiguity constraints: Add constraints to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of those implemented in the add_contiguity_constraints function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit.
    • +
+
+# create problem with constraints which specify that the planning units used
+# to conserve each feature must form a contiguous unit
+p19 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_feature_contiguity_constraints()
+
+# print problem
+print(p19)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Feature contiguity constraints [apply constraints? (1), layer.1 zones, layer.2 zones, layer.3 zones, layer.4 zones, layer.5 zones]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Linear constraints: Add constraints to ensure that all selected planning units meet certain criteria. For example, they can be used to add multiple budgets, or limit the number of planning units selected in different administrative areas within a study region (e.g., different countries).
    • +
+
+# create problem with constraints which specify that the sum of
+# values in sim_features[[1]] among selected planning units must not exceed a
+#' threshold value of 190.
+p20 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_shortfall_objective(budget = 1800) %>%
+       add_relative_targets(0.1) %>%
+       add_linear_constraints(190, "<=", sim_features[[1]])
+
+# print problem
+print(p20)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum shortfall objective [budget (1800)]
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Linear constraints [threshold (190)]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Mandatory allocation constraints: Add constraints to ensure that every planning unit is allocated to a management zone in the solution. Please note that this function can only be used with problems that contain multiple zones. For more information on problems with multiple zones and an example using this function, see the Management Zones vignette.
    • +
+

In particular, The add_locked_in_constraints and add_locked_out_constraints functions are incredibly useful for real-world conservation planning exercises, so it’s worth pointing out that there are several ways we can specify which planning units should be locked in or out of the solutions. If we use raster planning unit data, we can also use raster data to specify which planning units should be locked in our locked out.

+
+# load data to lock in or lock out planning units
+data(sim_locked_in_raster)
+data(sim_locked_out_raster)
+
+# plot the locked data
+plot(stack(sim_locked_in_raster, sim_locked_out_raster),
+     main = c("Locked In", "Locked Out"))
+

+
+# create a problem using raster planning unit data and use the locked raster
+# data to lock in some planning units and lock out some other planning units
+p21 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints(sim_locked_in_raster) %>%
+       add_locked_out_constraints(sim_locked_out_raster)
+
+# print problem
+print(p21)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked out planning units [10 locked units]
+##                    Locked in planning units [10 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+

If our planning unit data are in a spatial vector format (similar to the sim_pu_polygons data) or a tabular format (similar to pu_dat), we can use the field names in the data to refer to which planning units should be locked in and / or out. For example, the sim_pu_polygons object has TRUE / FALSE values in the “locked_in” field which indicate which planning units should be selected in the solution. We could use the data in this field to specify that those planning units with TRUE values should be locked in using the following methods.

+
+# preview first six rows of the attribute table for sim_pu_polygons
+head(sim_pu_polygons@data)
+
##       cost locked_in locked_out
+## 1 215.8638     FALSE      FALSE
+## 2 212.7823     FALSE      FALSE
+## 3 207.4962     FALSE      FALSE
+## 4 208.9322     FALSE       TRUE
+## 5 214.0419     FALSE      FALSE
+## 6 213.7636     FALSE      FALSE
+
+# specify locked in data using the field name
+p22 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints("locked_in")
+
+# print problem
+print(p22)
+
## Conservation Problem
+##   planning units: SpatialPolygonsDataFrame (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked in planning units [10 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+# specify locked in data using the values in the field
+p23 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints(which(sim_pu_polygons$locked_in))
+
+# print problem
+print(p23)
+
## Conservation Problem
+##   planning units: SpatialPolygonsDataFrame (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked in planning units [10 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+
+

Add penalties +

+

We can also add penalties to a problem to favor or penalize solutions according to a secondary objective. Unlike the constraint functions, these functions will add extra information to the objective function of the optimization function to penalize solutions that do not exhibit specific characteristics. For example, penalties can be added to a problem to avoid highly fragmented solutions at the expense of accepting slightly more expensive solutions. All penalty functions have a penalty argument that controls the relative importance of the secondary penalty function compared to the primary objective function. It is worth noting that incredibly low or incredibly high penalty values – relative to the main objective function – can cause problems to take a very long time to solve, so when trying out a range of different penalty values it can be helpful to limit the solver to run for a set period of time. The following penalties are available.

+
    +
  • +Boundary penalties: Add penalties to penalize solutions that are excessively fragmented. These penalties are similar to those used in Marxan (Ball et al. 2009; Beyer et al. 2016).
    • +
+
+# create problem with penalties that penalize fragmented solutions with a
+# penalty factor of 0.01
+p24 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_boundary_penalties(penalty = 0.01)
+
+# print problem
+print(p24)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (0.01), zones]>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Connectivity penalties: Add penalties to favor solutions that select combinations of planning units with high connectivity between them. These penalties are similar to those used in Marxan with Zones (Watts et al. 2009; Beyer et al. 2016). This function supports both symmetric and asymmetric connectivities among planning units.
    • +
+
+# create problem with penalties that favor combinations of planning units with
+# high connectivity, here we will use only the first four layers in
+# sim_features for the features and we will use the fifth layer in sim_features
+# to represent the connectivity data, where the connectivity_matrix function
+# will create a matrix showing the average strength of connectivity between
+# adjacent planning units using the data in the fifth layer of sim_features
+p25 <- problem(sim_pu_raster, sim_features[[1:4]]) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_boundary_penalties(
+         penalty = 5,
+         data = connectivity_matrix(sim_pu_raster, sim_features[[5]]))
+
+# print problem
+print(p25)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, layer.4 (4 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (5), zones]>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Linear penalties: Add penalties to penalize solutions that select planning units according to a certain variable (e.g., anthropogenic pressure).
    • +
+
+# create data for penalizing planning units
+# (note this requires the RandomFields package to be installed)
+pen_raster <- simulate_cost(sim_pu_raster)
+
+# create problem with penalties that penalize solutions that select
+# planning units with high values in the pen_raster object,
+# here we will use a penalty value of 5 to indicate the trade-off (scaling)
+# between the penalty values (in the sim_pu_raster) and the main objective
+# (i.e., the cost of the solution)
+p26 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_linear_penalties(penalty = 5, data = pen_raster)
+
+# print problem
+print(p26)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <Linear penalties [penalty (5)]>
+##   portfolio:      default
+##   solver:         default
+
+
+

Add the decision types +

+

Conservation planning problems involve making decisions on how planning units will be managed. These decisions are then associated with management actions (e.g., turning a planning unit into a protected area). The type of decision describes how the action is applied to planning units. For instance, the default decision-type is a binary decision type, meaning that we are either selecting or not selecting planning units for management. The following decision types are available.

+
    +
  • +Binary decisions: Add a binary decision to a conservation planning problem. This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem object, then this decision class will be used by default.
    • +
+
+# add binary decisions to a problem
+p27 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions()
+
+# print problem
+print(p27)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Proportion decisions: Add a proportion decision to a problem. This is a relaxed decision where a part of a planning unit can be prioritized, as opposed to the default of the entire planning unit. Typically, this decision has the assumed action of buying a fraction of a planning unit to include in a protected area network. Generally, problems can be solved much faster with proportion-type decisions than binary-type decisions, so they can be very useful when commercial solvers are not available.
    • +
+
+# add proportion decisions to a problem
+p28 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_proportion_decisions()
+
+# print problem
+print(p28)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Proportion decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
    +
  • +Semi-continuous decisions: Add a semi-continuous decision to a problem. This decision is similar to proportion decisions except that it has an upper bound parameter. By default, the decision can range from prioritizing none (0%) to all (100%) of a planning unit. However, a upper bound can be specified to ensure that at most only a fraction (e.g., 80%) of a planning unit can be purchased. This type of decision may be useful when it is not practical to conserve the entire area indicated by a planning unit.
    • +
+
+# add semi-continuous decisions to a problem, where we can only manage at most
+# 50 % of the area encompassed by a planning unit
+p29 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_semicontinuous_decisions(0.5)
+
+# print problem
+print(p29)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Semicontinuous decision [upper limit (0.5)]
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
+
+
+

Add a solver +

+

Next, after specifying the mathematical formulation that underpins your conservation planning problem, you can specify how the problem should be solved. If you do not specify this information, the prioritizr R package will automatically use the best solver currently installed on your system with some reasonable defaults. We strongly recommend installing the Gurobi software suite and the gurobi R package to solve problems, and for more information on this topic please refer to the Gurobi Installation Guide. The following solvers are available.

+
    +
  • +Gurobi solver: Gurobi is a state of the art commercial optimization software. It is by far the fastest of the solvers that can be used to solve conservation problems. However, it is not freely available. That said, special licenses are available to academics at no cost.
    • +
+
+# create a problem and specify that Gurobi should be used to solve the problem
+# and specify an optimality gap of zero to obtain the optimal solution
+p30 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_gurobi_solver(gap = 0)
+
+# print problem
+print(p30)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         Gurobi [first_feasible (0), gap (0), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (1)]
+
    +
  • +IBM CPLEX solver: IBM CPLEX is a commercial optimization software. It is faster than the open source solvers available for generating prioritizations (see below), however, it is not freely available. Similar to the Gurobi software, special licenses are available to academics at no cost.
    • +
+
+# create a problem and specify that IBM CPLEX should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p31 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_cplex_solver(gap = 0)
+
+# print problem
+print(p31)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         CPLEX [gap (0), presolve (1), threads (1), time_limit (2147483647), verbose (1)]
+
    +
  • +CBC solver: CBC is an open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. Although formal benchmarks have yet to be completed, preliminary analyses suggest that it is the fastest open-source solver available for generating prioritizations. It requires the rcbc R package, which is currently only available on GitHub.
    • +
+
+# create a problem and specify that CBC should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p32 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_cbc_solver(gap = 0)
+
+# print problem
+print(p32)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         CBC [first_feasible (0), gap (0), presolve (1), threads (1), time_limit (2147483647), verbose (1)]
+
    +
  • +lpsymphony solver: SYMPHONY is an open-source integer programming solver that is also part of the COIN-OR project. This solver uses the lpsymphony R package (available on Bioconductor) to interface with the SYMPHONY software.
    • +
+
+# create a problem and specify that lpsymphony should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p33 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_lpsymphony_solver(gap = 0)
+
+# print problem
+print(p33)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         Lpsymphony [first_feasible (0), gap (0), time_limit (2147483647), verbose (1)]
+
    +
  • +Rsymphony solver: This solver provides a different interface to the SYMPHONY software. It uses the Rsymphony R package which is available on The Comprehensive R Archive Network (CRAN). This solver is generally slower than the other solvers, because it cannot use parallel processing.
    • +
+
+# create a problem and specify that Rsymphony should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p34 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_rsymphony_solver(gap = 0)
+
+# print problem
+print(p34)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         Rsymphony [first_feasible (0), gap (0), time_limit (2147483647), verbose (1)]
+
+
+

Add a portfolio +

+

Many conservation planning exercises require a portfolio of solutions. For example, real-world exercises can involve presenting decision makers with a range of near-optimal decisions. Additionally, the number of times that different planning units are selected in different solutions can provide insight into their relative importance. The following portfolio methods are available.

+
    +
  • +Gap portfolio: Generate a portfolio of solutions by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is especially useful for generating multiple solutions that can used be to calculate selection frequencies (similar to Marxan). Note that this method requires that the Gurobi optimization software is used to generate solutions.
    • +
+
+# create a problem and specify that a portfolio should be created by
+# finding five solutions within 10% of optimality
+p35 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_gap_portfolio(number_solutions = 5, pool_gap = 0.2)
+
+# print problem
+print(p35)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Gap portfolio [number_solutions (5), pool_gap (0.2)]
+##   solver:         default
+
    +
  • +Top portfolio: Generate a portfolio of solutions by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions). Note that this method requires that the Gurobi optimization software is used to generate solutions.
    • +
+
+# create a problem and specify that a portfolio should be created using
+# the top five solutions
+p36 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_top_portfolio(number_solutions = 5)
+
+# print problem
+print(p36)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Top portfolio [number_solutions (5)]
+##   solver:         default
+
    +
  • +Extra portfolio: Generate a portfolio of solutions by storing feasible solutions found during the optimization process. Note that this method requires that the Gurobi optimization software is used to generate solutions.
    • +
+
+# create a problem and specify that a portfolio should be created using
+# extra solutions found while solving the problem
+p37 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_extra_portfolio()
+
+# print problem
+print(p37)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Extra portfolio
+##   solver:         default
+
    +
  • +Cuts portfolio: Generate a portfolio of distinct solutions within a pre-specified optimality gap. This method is only recommended if the Gurobi optimization solver is not available.
    • +
+
+# create a problem and specify that a portfolio containing 10 solutions
+# should be created using using Bender's cuts
+p38 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_cuts_portfolio(number_solutions = 10)
+
+# print problem
+print(p38)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Cuts portfolio [number_solutions (10)]
+##   solver:         default
+
    +
  • +Shuffle portfolio: Generate a portfolio of solutions by randomly reordering the data prior to attempting to solve the problem. If the Gurobi optimization solver is not available, this method is the fastest method for generating a set number of solutions within a specified distance from optimality.
    • +
+
+# create a problem and specify a portfolio should be created that contains
+# 10 solutions and that any duplicate solutions should not be removed
+p39 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_shuffle_portfolio(number_solutions = 10, remove_duplicates = FALSE)
+
+# print problem
+print(p39)
+
## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Shuffle portfolio [number_solutions (10), remove_duplicates (0), threads (1)]
+##   solver:         default
+
+
+

Solve the problem +

+

After formulating our conservation planning problem and specifying how the problem should be solved, we can use the solve function to obtain a solution. Note that the solver will typically print out some information describing the size of the problem and report its progress when searching for a suitable solution.

+
+# formulate the problem
+p40 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_boundary_penalties(penalty = 500, edge_factor = 0.5) %>%
+       add_binary_decisions()
+
+# solve the problem (using the default solver)
+s40 <- solve(p40)
+
## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 293 rows, 234 columns and 1026 nonzeros
+## Model fingerprint: 0xbd38144b
+## Variable types: 0 continuous, 234 integer (234 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-01, 1e+00]
+##   Objective range  [1e+02, 4e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [3e+00, 8e+00]
+## Found heuristic solution: objective 20287.196992
+## Found heuristic solution: objective 3087.9617505
+## Presolve time: 0.00s
+## Presolved: 293 rows, 234 columns, 1026 nonzeros
+## Variable types: 0 continuous, 234 integer (234 binary)
+## Root relaxation presolved: 293 rows, 234 columns, 1026 nonzeros
+## 
+## 
+## Root relaxation: objective 2.265862e+03, 220 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 2265.86242    0  234 3087.96175 2265.86242  26.6%     -    0s
+##      0     0 2325.53449    0  232 3087.96175 2325.53449  24.7%     -    0s
+##      0     0 2361.03063    0  223 3087.96175 2361.03063  23.5%     -    0s
+##      0     0 2371.27288    0  222 3087.96175 2371.27288  23.2%     -    0s
+##      0     0 2371.27288    0  222 3087.96175 2371.27288  23.2%     -    0s
+## H    0     0                    2790.8740409 2371.27288  15.0%     -    0s
+## H    0     0                    2730.9524342 2371.27288  13.2%     -    0s
+##      0     2 2372.02804    0  222 2730.95243 2372.02804  13.1%     -    0s
+## H    6     6                    2604.7426048 2375.46233  8.80%  21.0    0s
+## 
+## Cutting planes:
+##   Gomory: 3
+## 
+## Explored 7 nodes (489 simplex iterations) in 0.09 seconds (0.10 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 5: 2604.74 2730.95 2790.87 ... 20287.2
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 2.604742604847e+03, best bound 2.375462328932e+03, gap 8.8024%
+
+# plot solution
+plot(s40, col = c("grey90", "darkgreen"), main = "Solution",
+     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
+

+

We can plot this solution because the planning unit input data are spatially referenced in a raster format. The output format will always match the planning unit data used to initialize the problem. For example, the solution to a problem with planning units in a spatial vector (shapefile) format would also be in a spatial vector format. Similarly, if the planning units were in a tabular format (i.e., data.frame), the solution would also be returned in a tabular format.

+

We can also extract attributes from the solution that describe the quality of the solution and the optimization process.

+
+# extract the objective (numerical value being minimized or maximized)
+print(attr(s40, "objective"))
+
## solution_1 
+##   2604.743
+
+# extract time spent solving solution
+print(attr(s40, "runtime"))
+
## solution_1 
+##      0.092
+
+# extract state message from the solver that describes why this specific
+# solution was returned
+print(attr(s40, "status"))
+
## solution_1 
+##  "OPTIMAL"
+
+
+
+

Evaluate the solution +

+

Conservation planning involves making trade-offs between different criteria (e.g. overall cost, feature representation, connectivity). After obtaining a solution to a conservation planning problem, it is important to evaluate it to help understand the trade-offs made by the prioritization. This is also useful to compare different solutions with each other.

+
+

Evaluating performance +

+

Summary statistics can be computed to evaluate the overall performance of a solution based on certain criteria. The following summaries can be computed.

+

The following functions are available to summarize a solution:

+
    +
  • +Number summary: Calculate the number of planning units selected by a solution.
    • +
+
+# calculate statistic
+eval_n_summary(p40, s40)
+
## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall    10
+
    +
  • +Cost summary: Calculate the total cost of a solution.
    • +
+
+# calculate statistic
+eval_cost_summary(p40, s40)
+
## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall 2005.
+
    +
  • +Feature representation summary: Calculate how well features are represented by a solution. This function can be used for any type of problem.
    • +
+
+# calculate statistics
+eval_feature_representation_summary(p40, s40)
+
## # A tibble: 5 × 5
+##   summary feature total_amount absolute_held relative_held
+##   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+## 1 overall layer.1         83.3          8.95         0.107
+## 2 overall layer.2         31.2          3.22         0.103
+## 3 overall layer.3         72.0          7.59         0.106
+## 4 overall layer.4         42.7          4.34         0.102
+## 5 overall layer.5         56.7          5.89         0.104
+
    +
  • +Target coverage summary: Calculate how well representation targets are met by a solution. This function can only be used with problems contain targets.
    • +
+
+# calculate statistics
+eval_target_coverage_summary(p40, s40)
+
## # A tibble: 5 × 9
+##   feature met   total_amount absolute_target absolute_held absolute_shortfall
+##   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
+## 1 layer.1 TRUE          83.3            8.33          8.95                  0
+## 2 layer.2 TRUE          31.2            3.12          3.22                  0
+## 3 layer.3 TRUE          72.0            7.20          7.59                  0
+## 4 layer.4 TRUE          42.7            4.27          4.34                  0
+## 5 layer.5 TRUE          56.7            5.67          5.89                  0
+##   relative_target relative_held relative_shortfall
+##             <dbl>         <dbl>              <dbl>
+## 1             0.1         0.107                  0
+## 2             0.1         0.103                  0
+## 3             0.1         0.106                  0
+## 4             0.1         0.102                  0
+## 5             0.1         0.104                  0
+
    +
  • +Boundary summary: Calculate the total exposed boundary length (perimeter) associated with a solution.
    • +
+
+# calculate statistic
+eval_boundary_summary(p40, s40)
+
## # A tibble: 1 × 2
+##   summary boundary
+##   <chr>      <dbl>
+## 1 overall      1.2
+
    +
  • +Connectivity summary: Calculate the connectivity facilitated within a solution.
    • +
+
+# calculate statistic
+# here we use the raster data for the first feature as an example
+# to parametrize pair-wise connectivity between different planning units
+eval_connectivity_summary(
+  p40, s40, data = connectivity_matrix(sim_pu_raster, sim_features[[1]]))
+
## # A tibble: 1 × 2
+##   summary connectivity
+##   <chr>          <dbl>
+## 1 overall         1.97
+
+
+

Evaluating relative importance +

+

Conservation plans can take a long time to implement. Since funding availability and habitat quality can decline over time, it is critical that the most important places in a prioritization are scheduled for management as early as possible. For instance, some planning units in a solution might contain many rare species which do not occur in any other planning units. Alternatively, some planning units might offer an especially high return on investment that reduces costs considerably. As a consequence, conservation planners often need information on which planning units selected in a prioritization are most important to the overall success of the prioritization. To achieve this, conservation planners can use importance scores for each planning unit selected by a solution.

+

Let’s generate a prioritization so that can compare the different importance methods.

+
+# formulate the problem
+p41 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions()
+
+# solve the problem
+s41 <- solve(p41)
+
## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 5 rows, 90 columns and 450 nonzeros
+## Model fingerprint: 0x6442bf6e
+## Variable types: 0 continuous, 90 integer (90 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-01, 9e-01]
+##   Objective range  [2e+02, 2e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [3e+00, 8e+00]
+## Found heuristic solution: objective 2337.9617505
+## Presolve time: 0.00s
+## Presolved: 5 rows, 90 columns, 450 nonzeros
+## Variable types: 0 continuous, 90 integer (90 binary)
+## Found heuristic solution: objective 2332.1003790
+## Root relaxation presolved: 5 rows, 90 columns, 450 nonzeros
+## 
+## 
+## Root relaxation: objective 1.931582e+03, 12 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 1931.58191    0    4 2332.10038 1931.58191  17.2%     -    0s
+## H    0     0                    1987.3985265 1931.58191  2.81%     -    0s
+## 
+## Explored 1 nodes (12 simplex iterations) in 0.00 seconds (0.00 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 3: 1987.4 2332.1 2337.96 
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 1.987398526526e+03, best bound 1.931581908865e+03, gap 2.8085%
+
+# plot solution
+plot(s41, col = c("grey90", "darkgreen"), main = "Solution",
+     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
+

+

The following methods are available for computing importance scores.

+
    +
  • +Replacement cost: Evaluate importance using the replacement cost method (Cabeza & Moilanen 2006). This method quantifies the importance of a given planning unit as the decrease in the performance of the solution (based on the objective function) if the planning unit cannot be acquired (e.g., in terms of the additional costs required to meet feature targets). The advantages of this method are that it (i) accounts for the costs of the planning units, (ii) can be applied to multiple management zones, (iii) can be applied to any objective function, and (iv) can identify truly irreplaceable planning units (denoted with infinite values). However, the key disadvantage of this method, is that can take an infeasible amount of time to complete for large and complex problems.
    • +
+
+# calculate replacement cost scores and make the solver quiet
+rc41 <- p41 %>%
+        add_default_solver(gap = 0, verbose = FALSE) %>%
+        eval_replacement_importance(s41)
+
+# plot replacement cost scores
+plot(rc41, main = "Replacement cost scores")
+

* Ferrier method: Evaluate importance by computing irreplaceability scores following Ferrier et al. (r-34?). The advantages of this method are that it (i) can be computed relatively quickly for moderate and large-sized problems, and (ii) calculates a score for each feature within each planning unit to provide insight into why certain planning units are more important than others. The disadvatange with this method is that it can only be applied to conservation problems with a minimum set objective and a single zone (i.e., similar to Marxan-type problems).

+
+# calculate Ferrier scores and extract total score
+fs41 <- eval_ferrier_importance(p40, s40)[["total"]]
+
+# plot Ferrier scores
+plot(fs41, main = "Ferrier scores")
+

* Rarity weighted richness: Evaluate importance by computing rarity weighted richness scores (Williams et al. 1996). The only advantage with this method is that it can be computed very quickly for very large problems. The key disadvantage with this approach is that it merely describes the spatial patterns of biodiversity, and does not consider any of the goals that underpin conservation planning exercise. For instance, it does not account for planning costs, management zones, objective functions, or feature representation targets.

+
+# calculate rarity weighted richness scores
+rwr41 <- eval_rare_richness_importance(p40, s40)
+
+# plot rarity weighted richness scores
+plot(rwr41, main = "Rarity weighted richness")
+

+

In general, we recommend using replacement cost scores for small and moderate sized problems (e.g., less than 30,000 planning units) when it is feasible to do so. It can take a very long time to compute replacement cost scores, and so it is simply not feasible to compute these scores for particularly large problems. For moderate and large sized problems (e.g., more than 30,000 planning units), we recommend using the Ferrier method. This is because it explicitly accounts for representation targets, unlike the rarity weighted richness scores. We almost never recommend using the rarity weighted richness scores. This is because they do not consider criteria needed to inform conservation decision making (Brown et al. 2015).

+
+
+
+

+Marxan problems +

+

Although we encourage users to build and tailor conservation planning problems to suit their own needs, sometimes it just simply easier to use something you’re already familiar with. The marxan_problem() function is provided as a convenient wrapper for building and solving Marxan-style conservation problems. If users already have their conservation planning data formatted for use with Marxan, this function can also read Marxan data files and solve the Marxan-style problems using exact algorithm solvers. Please note that problems built using the marxan_problem() function are still solved the same way as a problem initialized using the problem() function, and therefore still require the installation of one of the solver packages.

+

Here is a short example showing how the marxan_problem() function can be used to read Marxan input files and the solve function can be used to solve the problem.

+
+# set file path for Marxan input file
+minput <- system.file("extdata/input.dat", package = "prioritizr")
+
+# read Marxan input file
+mp <- marxan_problem(minput)
+
+# print problem
+print(mp)
+
## Conservation Problem
+##   planning units: data.frame (1751 units)
+##   cost:           min: 0, max: 41569219.38232
+##   features:       bird1, nvis2, nvis8, ... (17 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.3, max: 0.3)]
+##   decisions:      default
+##   constraints:    <Locked in planning units [317 locked units]
+##                    Locked out planning units [1 locked units]>
+##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (1), zones]>
+##   portfolio:      default
+##   solver:         default
+
+# solve the problem
+ms <- solve(mp)
+
+# since the Marxan data was in a tabular format, the solution is also returned
+# in a tabular format, so we will print the first six rows of the table
+# containing the solution
+head(ms)
+

Alternatively, rather then using a Marxan input file to construct the problem, we can manually read in the Marxan data files and input these to the marxan_problem() function.

+
+# load data
+pu <- system.file("extdata/input/pu.dat", package = "prioritizr") %>%
+      read.table(sep = ",", header = TRUE)
+features <- system.file("extdata/input/spec.dat", package = "prioritizr") %>%
+            read.table(sep = ",", header = TRUE)
+bound <- system.file("extdata/input/bound.dat", package = "prioritizr") %>%
+         read.table(sep = "\t", header = TRUE)
+rij <- system.file("extdata/input/puvspr.dat", package = "prioritizr") %>%
+       read.table(sep = ",", header = TRUE)
+
+# build Marxan problem using data.frame objects
+mp2 <- marxan_problem(x = pu, spec = features, puvspr = rij, bound = bound,
+                      blm = 0)
+
+# print problem
+print(mp2)
+
## Conservation Problem
+##   planning units: data.frame (1751 units)
+##   cost:           min: 0, max: 41569219.38232
+##   features:       bird1, nvis2, nvis8, ... (17 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.3, max: 0.3)]
+##   decisions:      default
+##   constraints:    <Locked in planning units [317 locked units]
+##                    Locked out planning units [1 locked units]>
+##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (0), zones]>
+##   portfolio:      default
+##   solver:         default
+

Conservation planning problems that are built using the marxan_problem() function can also be customized. For example, we could change the decision type for mp2 to involve selecting a proportion of each planing unit (using the add_proportion_decisions() function).

+
+
+

Conclusion +

+

Hopefully, this vignette has provided an informative overview of the prioritizr R package. For more examples using the package, please see the other vignettes. Perhaps, one of the best ways to learn a new piece of software is to just try it out. Test it, try breaking it, make mistakes, and learn from them. We would recommend trying to build conservation planning problems that resemble those you face in your own work—but using the built-in example data sets. This way you can quickly verify that the problems you build actually mean what you think they mean. For instance, you can try playing around with the targets and see what effect they have on the solutions, or try playing around with penalties and see what effect they have on the solutions. Finally, if you have any questions about using the package or suggestions for it, please post an issue on the package’s online coding repository.

+
+
+

References +

+
+
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+
+Ball, I.R., Possingham, H. & Watts, M.E. (2009). Marxan and relatives: Software for spatial conservation prioritisation. Spatial Conservation Prioritisation: Quantitative Methods & Computational Tools (eds A. Moilanen, K.A. Wilson & H. Possingham), pp. 185–189. Oxford University Press, Oxford, UK. +
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+
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+Williams, P., Gibbons, D., Margules, C., Rebelo, A., Humphries, C. & Pressey, R. (1996). A comparison of richness hotspots, rarity hotspots, and complementary areas for conserving diversity of British birds. Conservation Biology, 10, 155–174. +
+
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+
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ze|rehp&<(;cFp-DOE9D;^WT&ITmL74|DOb2)?TT^3HwNI=SwgV;MY?vL(NKc+lc=M DS|D&F literal 0 HcmV?d00001 diff --git a/docs/articles/prioritizr_files/header-attrs-2.11/header-attrs.js b/docs/articles/prioritizr_files/header-attrs-2.11/header-attrs.js deleted file mode 100644 index dd57d92e0..000000000 --- a/docs/articles/prioritizr_files/header-attrs-2.11/header-attrs.js +++ /dev/null @@ -1,12 +0,0 @@ -// Pandoc 2.9 adds attributes on both header and div. We remove the former (to -// be compatible with the behavior of Pandoc < 2.8). -document.addEventListener('DOMContentLoaded', function(e) { - var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); - var i, h, a; - for (i = 0; i < hs.length; i++) { - h = hs[i]; - if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 - a = h.attributes; - while (a.length > 0) h.removeAttribute(a[0].name); - } -}); diff --git a/docs/articles/publication_record.html b/docs/articles/publication_record.html index 09de752d5..2077566eb 100644 --- a/docs/articles/publication_record.html +++ b/docs/articles/publication_record.html @@ -5,7 +5,7 @@ -Publication Record • prioritizr +Publication record • prioritizr @@ -20,7 +20,7 @@ - + - - - - - -Salt Spring Island Tutorial • prioritizr - - - - - - - - - - - - - - - - - - - - - - -

-
- - - - -
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-

Salt Spring Island Tutorial

- - - Source: vignettes/saltspring.Rmd - - -
- - - -
-

-Introduction

-

This aim of this tutorial is to show how raster data can used to build conservation problems with the prioritizr R package. The data used here is a subset of a much larger dataset for the Georgia Basin obtained as part of an online Marxan-based planning tool created for the Coastal Douglas-fir Conservation Partnership [CDFCP; Morrell et al. (2017)]. For simplicity, we focus only on Salt Spring Island, British Columbia. Salt Spring Island is central to the region and supports a diverse and globally unique mix of dry forest and savanna habitats. Today, these habitats are critically threatened due to land conversion, invasive species, and altered disturbance regimes. Known broadly as the Georgia Depression-Puget Lowlands, this region includes threatened Coastal Douglas-fir forest and Oak-Savannah habitats, also referred to as Garry oak ecosystems. Please note that this tutorial uses data from the prioritizrdata R package, so ensure that it is installed before trying out the code yourself. For more information on the dataset refer to the Marxan tool portal and the tool tutorial.

-
-
-

Extent of Coastal Douglas-fir Conservation Partnership Tool area and location of Salt Spring Island

-
-
-
-
-

-Exploring the data

-

This dataset contains two items. First, a single-band raster planning unit layer where each one hectare pixel represents a planning unit and contains its corresponding cost (BC Assessment 2015). Second, a raster stack containing ecological community feature data. Field and remote sensed data were used to calculate the probability of occurrence of five key ecological communities found on Salt Spring island. Each layer in the stack represents a different community type. In order these are; Old Forest, Savannah, Wetland, Shrub, and a layer representing the inverse probability of occurrence of human commensal species. For a given layer, the cell value indicates the composite probability of encountering the suite of bird species most commonly associated with that community type.

-

First, load the required packages and the data.

-
-# load packages
-library(prioritizrdata)
-library(prioritizr)
-
-# load planning unit data
-data(salt_pu)
-
-# load conservation feature data
-data(salt_features)
-

Let’s have a look at the planning unit data. Note that we log-transformed the raster to better visualize the variation in planning unit cost.

-
-# print planning unit data
-print(salt_pu)
-
## class      : RasterLayer 
-## dimensions : 280, 200, 56000  (nrow, ncol, ncell)
-## resolution : 100, 100  (x, y)
-## extent     : 454589.9, 474589.9, 5394614, 5422614  (xmin, xmax, ymin, ymax)
-## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
-## source     : memory
-## names      : salt_pu 
-## values     : 0.02552, 10000  (min, max)
-
-# plot histogram of the planning unit costs
-hist(values(salt_pu), main = "Distribution of costs",
-     xlab = "Planning unit costs")
-

-
-# plot map showing the planning units costs on a log-scale
-plot(log(salt_pu), main = "Planning unit costs (log)")
-

-

Next, let’s look at the feature data.

-
-# print features
-print(salt_features)
-
## class      : RasterStack 
-## dimensions : 280, 200, 56000, 5  (nrow, ncol, ncell, nlayers)
-## resolution : 100, 100  (x, y)
-## extent     : 454589.9, 474589.9, 5394614, 5422614  (xmin, xmax, ymin, ymax)
-## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
-## names      : salt_features.1, salt_features.2, salt_features.3, salt_features.4, salt_features.5 
-## min values :       0.3595050,       0.2979212,       0.1132785,       0.4013101,       0.3703639 
-## max values :       0.9312289,       0.6608167,       0.6434712,       0.8249719,       0.9032656
-
-# plot map showing the distribution of the features
-plot(salt_features, main = names(salt_features))
-

-
-
-

-Formulating the Problem

-

In this tutorial, we will only cover a few of the different ways that conservation planning problems can be formulated. The examples used here are provided to highlight how different parameters can substantially—or only slightly—alter solutions. Here, we use the minimum set objective to fulfill all targets and constraints for the smallest cost. This objective is similar to that used in the Marxan decision support tool. To keep this simple, we will set biodiversity targets at 17 % to reflect the Aichi Biodiversity Target 11. Because properties on Salt Spring Island can either be acquired in their entirety or not at all, we leave the decision framework as the default; binary decision making. This means that planning units are either selected in the solution or not selected in the solution—planning units cannot be partially acquired.

-

Now we will formulate the conservation planning problem.

-
-# create problem
-p1 <- problem(salt_pu, salt_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_binary_decisions() %>%
-      add_default_solver()
-
-# print problem
-print(p1)
-
## Conservation Problem
-##   planning units: RasterLayer (19794 units)
-##   cost:           min: 0.02552, max: 10000
-##   features:       salt_features.1, salt_features.2, salt_features.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (1)]
-

Note that the %>% notation is used to attach the objectives, targets, and decisions to the problem. Since binary-type decisions are the default decision-type, we don’t have to explicitly specify the decision-type, but we specify it here for clarity.

-
-
-

-Solving the problem

-

The prioritizr R package supports three different integer linear programming solvers: gurobi (via the gurobi package), IBM CPLEX (via the cplexAPI package), SYMPHONY (via the Rsymphony and lpsymphony packages) and CBC (via the rcbc package). There are costs and benefits associated with each of these solvers, but the solver itself should have little impact on the actual solution returned (though certain solvers may take longer to return solutions than others).

-

First, remember that the solvers must be installed. You can check if these packages are installed by running the code below. Some of these solvers are a bit complicated to install. For instance, the gurobi package is distributed with the Gurobi commercial software suite and is not available on the Comprehensive R Archive Network (CRAN). For more information on installing the gurobi package, please refer to the Gurobi Installation Guide for more information on installing the gurobi R package. Additionally, the rcbc package is not available on CRAN, and must be installed from GitHub (please refer to its documentation for installation instructions. Furthermore, although the Rcplex package is available on CRAN, it cannot be successfully installed unless the IBM CPLEX software has already installed on your system.

- -

Now we will try solving the problem using the different solvers (see ?solve for more information). We will also experiment with limiting the maximum amount of time that can be spent looking for each solution when solving the problem (using the time_limit parameter), and see how this alters the solutions.

-
-titles <- c() # create vector to store plot titles
-s1 <- stack()  # create empty stack to store solutions
-
-# create new problem object with added solver
-if (require("Rsymphony")) {
-  titles <- c(titles, "Rsymphony (5s)")
-  p2 <- p1 %>% add_rsymphony_solver(time_limit = 5)
-  s1 <- addLayer(s1, solve(p2))
-}
-
## Warning in res(x, ...): overwriting previously defined solver
-
-if (require("Rsymphony")) {
-  titles <- c(titles, "Rsymphony (10s)")
-  p3 <- p1 %>% add_rsymphony_solver(time_limit = 10)
-  s1 <- addLayer(s1, solve(p3))
-}
-
## Warning in res(x, ...): overwriting previously defined solver
-
-if (require("gurobi")) {
-  titles <- c(titles, "Gurobi (5s)")
-  p4 <- p1 %>% add_gurobi_solver(time_limit = 5)
-  s1 <- addLayer(s1, solve(p4))
-}
-
## Warning in res(x, ...): overwriting previously defined solver
-
-if (require("cplexAPI")) {
-  titles <- c(titles, "IBM CPLEX (5s)")
-  p5 <- p1 %>% add_cplex_solver(time_limit = 5)
-  s1 <- addLayer(s1, solve(p5))
-}
-
## Warning in res(x, ...): overwriting previously defined solver
-
-if (require("lpsymphony")) {
-  titles <- c(titles, "lpsymphony (10s)")
-  p6 <- p1 %>% add_lpsymphony_solver(time_limit = 10)
-  s1 <- addLayer(s1, solve(p6))
-}
-
## Warning in res(x, ...): overwriting previously defined solver
-
-if (require("rcbc")) {
-  titles <- c(titles, "CBC (10s)")
-  p7 <- p1 %>% add_cbc_solver(time_limit = 10)
-  s1 <- addLayer(s1, solve(p7))
-}
-
## Warning in res(x, ...): overwriting previously defined solver
-

Now let’s visualize the solutions.

-
-plot(s1, main = titles, breaks = c(0, 0.5, 1),  col = c("grey70", "darkgreen"))
-

-

We can see that all of the solutions are very similar. Therefore it would appear that for this particular problem, the solution is not highly sensitive to solver choice. For larger and more complex problems, however, we would expect the solution from Gurobi to be far superior when setting time limits. At a glance, it also appears that the time limit settings did not largely impact the solutions (5 seconds vs. 10 seconds), but a more rigorous analysis is needed to investigate this.

-
-
-

-Adding connectivity

-

Isolated and fragmented populations are often more vulnerable to extinction. As a consequence, landscape connectivity is a key focus of many conservation planning exercises. There are a number of methods that can be used to increase connectivity in prioritizations. These methods typically involve adding constraints to a problem to ensure that solutions exhibit a specific property (e.g. selected planning units that form a contiguous reserve), or adding penalties to a problem to penalize solutions that exhibit specific properties (e.g. high levels of fragmentation). Here we will explore a couple different strategies for increasing connectivity in solutions. For brevity, we will use default solver which is automatically added to a problem if a solver is not manually specified.

-
-# basic problem formulation
-p6 <- problem(salt_pu, salt_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_binary_decisions() %>%
-      add_default_solver()
-
-# print problem
-print(p6)
-
## Conservation Problem
-##   planning units: RasterLayer (19794 units)
-##   cost:           min: 0.02552, max: 10000
-##   features:       salt_features.1, salt_features.2, salt_features.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (1)]
-
-titles2 <- c() # create vector to store plot titles
-s2 <- stack()  # create empty stack to store solutions
-
-# no connectivity requirement
-titles2 <- c(titles2, "No connectivity")
-s2 <- addLayer(s2, solve(p6))
-
-# require at least two for each selected planning unit
-titles2 <- c(titles2, "Neighbor constraints (two)")
-p7 <- p6 %>% add_neighbor_constraints(2)
-s2 <- addLayer(s2, solve(p7))
-
-# impose small penalty for fragmented solutions
-titles2 <- c(titles2, "Boundary penalty (low)")
-p8 <- p6 %>% add_boundary_penalties(0.0005, 0.5)
-s2 <- addLayer(s2, solve(p8))
-
-# impose high penalty for fragmented solutions
-titles2 <- c(titles2, "Boundary penalty (high)")
-p9 <- p6 %>% add_boundary_penalties(0.05, 0.5)
-s2 <- addLayer(s2, solve(p9))
-
-# plot solutions
-plot(s2, main = titles2, breaks = c(0, 0.5, 1),  col = c("grey70", "darkgreen"))
-

-

Here we can see that adding the constraints and penalties to the problem has a small, but noticeable effect on the solutions. We would expect to see larger difference between the solutions for problems that contain more than five conservation features. You may also wish to explore the add_connectivity_penalties and add_feature_contiguity_constraints functions. These functions use additional data on landscape resistance to provide a more accurate parametrization of connectivity and, in turn, deliver more effective solutions.

-
-
-

-References

-
-
-BC Assessment. (2015). Property Information Services. URL https://info.bcassessment.ca/ [accessed 13 June 2016]. -
-
-Morrell, N., Schuster, R., Crombie, M. & Arcese, P. (2017). A Prioritization Tool for the Conservation of Coastal Douglas-fir Forest and Savannah Habitats of the Georgia Basin. The Nature Trust of British Colombia, Coastal Douglas Fir Conservation Partnership, and the Department of Forest and Conservation Sciences, University of British Colombia, URL https://peter-arcese-lab.sites.olt.ubc.ca/files/2016/09/CDFCP_tutorial_2017_05.pdf [accessed 9 October 2017]. -
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a/docs/articles/zones.html +++ /dev/null @@ -1,998 +0,0 @@ - - - - - - - -Management Zones • prioritizr - - - - - - - - - - - - - - - - - - - - - - -

- - - - - diff --git a/docs/articles/zones_files/header-attrs-2.11/header-attrs.js b/docs/articles/zones_files/header-attrs-2.11/header-attrs.js deleted file mode 100644 index dd57d92e0..000000000 --- a/docs/articles/zones_files/header-attrs-2.11/header-attrs.js +++ /dev/null @@ -1,12 +0,0 @@ -// Pandoc 2.9 adds attributes on both header and div. We remove the former (to -// be compatible with the behavior of Pandoc < 2.8). -document.addEventListener('DOMContentLoaded', function(e) { - var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); - var i, h, a; - for (i = 0; i < hs.length; i++) { - h = hs[i]; - if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 - a = h.attributes; - while (a.length > 0) h.removeAttribute(a[0].name); - } -}); diff --git a/docs/authors.html b/docs/authors.html index 28bb0784b..a4a728e0e 100644 --- a/docs/authors.html +++ b/docs/authors.html @@ -1,100 +1,18 @@ - - - - - - - -Authors • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Authors and Citation • prioritizr - - - - - - - - - - - - - - + -
-
-
-
-

Authors

+
+
+

Authors

+
+ + +
+
+
+

Citation

+ Source: DESCRIPTION +
- - - + +

Hanson JO, Schuster R, Morrell N, Strimas-Mackey M, Edwards BPM, Watts ME, Arcese P, Bennett J, Possingham HP (2021). +prioritizr: Systematic Conservation Prioritization in R. +https://prioritizr.net, +https://github.com/prioritizr/prioritizr. +

+ 
@Manual{,
+  title = {prioritizr: Systematic Conservation Prioritization in R},
+  author = {Jeffrey O Hanson and Richard Schuster and Nina Morrell and Matthew Strimas-Mackey and Brandon P M Edwards and Matthew E Watts and Peter Arcese and Joseph Bennett and Hugh P Possingham},
+  year = {2021},
+  note = {https://prioritizr.net,
+https://github.com/prioritizr/prioritizr},
+}
+
-
- - - - - - - - - - + diff --git a/docs/extra.css b/docs/extra.css index 68e9213f2..d4c532b04 100644 --- a/docs/extra.css +++ b/docs/extra.css @@ -2,14 +2,20 @@ background: #FFFFFF; } -[id='prioritizr-'] .page-header { - margin-bottom: 0px; - padding-bottom: 0px; +.template-home .contents .section.level1 .page-header { + padding-top: 60px; + padding-bottom: 0px !important; + margin-bottom: 15px !important; } -[id='systematic-conservation-prioritization-in-r'] h1 { - margin-top: 0px; - padding-top: 0px; +[id='prioritizr-'] { + margin-bottom: 0px !important; + padding-bottom: 0px !important; +} + +[id='systematic-conservation-prioritization-in-r'] { + margin-top: 0px !important; + padding-top: 0px !important; font-size: 35px; padding-bottom: 10px; } diff --git a/docs/index.html b/docs/index.html index 587083782..e3822cdef 100644 --- a/docs/index.html +++ b/docs/index.html @@ -65,7 +65,7 @@ prioritizr - 7.1.1.4 + 7.1.1.5
@@ -85,22 +85,34 @@ + +
  • + +
    • @@ -110,7 +122,7 @@
    • - + @@ -134,20 +146,19 @@
      -
      -

      -prioritizr: +
      +

      prioritizr:

      -
      -

      -Systematic Conservation Prioritization in R

      +
      +

      Systematic Conservation Prioritization in R +

      The prioritizr R package uses integer linear programming (ILP) techniques to provide a flexible interface for building and solving conservation planning problems. It supports a broad range of objectives, constraints, and penalties that can be used to custom-tailor conservation planning problems to the specific needs of a conservation planning exercise. Once built, conservation planning problems can be solved using a variety of commercial and open-source exact algorithm solvers. In contrast to the algorithms conventionally used to solve conservation problems, such as heuristics or simulated annealing, the exact algorithms used here are guaranteed to find optimal solutions. Furthermore, conservation problems can be constructed to optimize the spatial allocation of different management actions or zones, meaning that conservation practitioners can identify solutions that benefit multiple stakeholders. Finally, this package has the functionality to read input data formatted for the Marxan conservation planning program, and find much cheaper solutions in a much shorter period of time than Marxan.

      -
      -

      -Installation

      +
      +

      Installation +

      The latest official version of the prioritizr R package can be installed from the Comprehensive R Archive Network (CRAN) using the following R code.

       install.packages("prioritizr", repos = "https://cran.rstudio.com/")
      @@ -156,22 +167,22 @@

      if (!require(remotes)) install.packages("remotes") remotes::install_github("prioritizr/prioritizr")

      -
      -

      -Citation

      +
      +

      Citation +

      Please cite the prioritizr R package when using it in publications. To cite the latest official version, please use:

      Hanson JO, Schuster R, Morrell N, Strimas-Mackey M, Edwards BPM, Watts ME, Arcese P, Bennett J, Possingham HP (2021). prioritizr: Systematic Conservation Prioritization in R. R package version 7.1.1. Available at https://CRAN.R-project.org/package=prioritizr.

      Alternatively, to cite the latest development version, please use:

      -

      Hanson JO, Schuster R, Morrell N, Strimas-Mackey M, Edwards BPM, Watts ME, Arcese P, Bennett J, Possingham HP (2021). prioritizr: Systematic Conservation Prioritization in R. R package version 7.1.1.4. Available at https://github.com/prioritizr/prioritizr.

      +

      Hanson JO, Schuster R, Morrell N, Strimas-Mackey M, Edwards BPM, Watts ME, Arcese P, Bennett J, Possingham HP (2021). prioritizr: Systematic Conservation Prioritization in R. R package version 7.1.1.5. Available at https://github.com/prioritizr/prioritizr.

      Additionally, we keep a record of publications that use the prioritizr R package. If you use this package in any reports or publications, please file an issue on GitHub so we can add it to the record.

      -
      -

      -Usage

      +
      +

      Usage +

      Here we will provide a short example showing how the prioritizr R package can be used to build and solve conservation problems. For brevity, we will use one of the built-in simulated datasets that is distributed with the package. First, we will load the prioritizr R package.

       # load package
@@ -271,7 +282,7 @@ 
      
 ##   StrongCG: 2
 ##   Flow cover: 1
 ## 
-## Explored 145469 nodes (243327 simplex iterations) in 3.74 seconds (2.59 work units)
+## Explored 145469 nodes (243327 simplex iterations) in 3.83 seconds (2.59 work units)
 ## Thread count was 1 (of 8 available processors)
 ## 
 ## Solution count 6: 2627.64 2747.38 2761.33 ... 3139.89
@@ -287,7 +298,7 @@ 
      
 # extract time spent solving the problem
 print(attr(s1, "runtime"))
      ## solution_1 
-##      3.762
      +## 3.836
       # extract state message from the solver
 print(attr(s1, "status"))
      @@ -411,7 +422,7 @@

      ## StrongCG: 1 ## Flow cover: 1 ## -## Explored 10262 nodes (23307 simplex iterations) in 0.53 seconds (0.54 work units) +## Explored 10262 nodes (23307 simplex iterations) in 0.62 seconds (0.54 work units) ## Thread count was 1 (of 8 available processors) ## ## Solution count 5: 2838.26 2839.12 3021.28 ... 3027.7 @@ -558,12 +569,36 @@

      "#1F9E89", "#35B779", "#6DCD59", "#B4DE2C", "#FDE725", "#FF0000"))

      -

      This short example demonstrates how the prioritizr R package can be used to build a minimal conservation problem, how constraints and penalties can be iteratively added to the problem to obtain a solution, and how importance scores can be calculated for the solution to identify critical places. Although we explored just a few different functions for modifying the a conservation problem, the prioritizr R package provides many functions for specifying objectives, constraints, penalties, and decision variables, so that you can build and custom-tailor a conservation planning problem to suit your exact planning scenario.

      +

      This short example demonstrates how the prioritizr R package can be used to build and customize conservation problems, and then solve them to generate solutions. Although we explored just a few different functions for modifying a conservation problem, the package provides many functions for specifying objectives, constraints, penalties, and decision variables, so that you can build and custom-tailor conservation planning problems to suit your planning scenario.

      +
      +
      +

      Learning resources +

      +

      The package website contains information on the prioritizr R package. Here you can find documentation for every function and built-in dataset, and news describing the updates in each package version. It also contains the following articles and tutorials.

      + +

      Additional resources can also be found in online repositories under the prioritizr organization. These resources include slides for talks and seminars about the package. Additionally, workshop materials are available too (e.g., the Massey University 2021 workshop and the PacMara 2019 workshop).

      -
      -

      -Getting help

      -

      Please refer to the package website for more information on the prioritizr R package. This website contains a comprehensive tutorial on the package, instructions for installing the Gurobi software suite to solve large-scale and complex conservation planning problems, and a tutorial on solving problems with multiple management zones. It also provides two worked examples that involve real-world data from Tasmania, Australia and Salt Spring Island, Canada. Additionally, slides for previous seminars about the package can be found in teaching repository. Furthermore, materials accompanying previous workshops are also available online too (i.e. the CIBIO 2019 workshop and the PacMara 2019 workshop). If you have any questions about using the prioritizr R package or suggestions for improving it, please file an issue at the package’s online code repository.

      +
      +

      Getting help +

      +

      If you have any questions about the prioritizr R package or suggestions for improving it, please post an issue on the code repository.

      @@ -573,28 +608,24 @@

      Links

      -
      -

      License

      +
      +

      Citation

      -
      -

      Community

      +
      +

      License

      @@ -602,20 +633,20 @@

      Community

      Developers

      @@ -642,7 +673,7 @@

      Dev status

      -

      Site built with pkgdown 1.6.1.9001.

      +

      Site built with pkgdown 2.0.0.9000.

      diff --git a/docs/news/index.html b/docs/news/index.html index f8c573a68..21edfb2bf 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -1,100 +1,18 @@ - - - - - - - -Changelog • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Changelog • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Changelog

      - Source: NEWS.md + Source: NEWS.md
      -
      -

      -prioritizr 7.1.1.4 Unreleased

      +
      +

      prioritizr 7.1.1.5

      +
      • The Tasmania tutorial has been reworked into the Getting started tutorial. This tutorial now provides short introduction to using the package.
        • +
      • The Salt Spring Island tutorial has been reworked into the Connectivity tutorial. This tutorial now explores different approaches for incorporating connectivity.
        • +
      • The prioritizr vignette has been renamed to the Package overview vignette.
        • +
      • New Calibrating trade-offs tutorial showcasing methods for running calibration analyses. It outlines blended and hierarchical approaches for generating a set of different prioritizations based on different parameters. It also covers different approaches for selecting a candidate prioritization based on different trade-offs.
        • +
      +
      +

      prioritizr 7.1.1.4

      • Update tests to reduce run time and pass given slightly different results with new Gurobi version (9.5.0).
      • Update built-in sim_pu_sf and sim_pu_zones_sf data given class updates to the sf package (compatible with version 1.0.3+).
      • Update example for write_problem function.
      -
      -

      -prioritizr 7.1.1.3 Unreleased

      +
      +

      prioritizr 7.1.1.3

      • Update publication record.
      -
      -

      -prioritizr 7.1.1.2 Unreleased

      +
      +

      prioritizr 7.1.1.2

      • Update publication record.
      -
      -

      -prioritizr 7.1.1.1 Unreleased

      +
      +

      prioritizr 7.1.1.1

      • Fix URL in vignette.
      -
      -

      -prioritizr 7.1.1 2021-10-29

      +
      +

      prioritizr 7.1.12021-10-29

      • Release candidate for CRAN.
      -
      -

      -prioritizr 7.1.0.4 Unreleased

      +
      +

      prioritizr 7.1.0.4

      • Update eval_ferrier_importance function with verified code.
      • Update documentation with information about Ferrier importance scores.
      • Brandon Edwards added to package author list.
        • @@ -215,117 +134,97 @@

      • Update benchmark vignette.
      • Update presolve_check function to throw warning when really high values specified in add_neighbor_constraints.

      -
      -

      -prioritizr 7.1.0.3 Unreleased

      +
      +

      prioritizr 7.1.0.3

      Update add_cbc_solver function so that it can use a starting solution to reduce run time (via the start_solution parameter).

      -
      -

      -prioritizr 7.1.0.2 Unreleased

      +
      +

      prioritizr 7.1.0.2

      • Fix examples that fail package checks.
      • Remove xtable R package from Suggests because it is no longer used.
      -
      -

      -prioritizr 7.1.0.1 Unreleased

      +
      +

      prioritizr 7.1.0.1

      • Update publication vignette.
      -
      -

      -prioritizr 7.1.0.0 Unreleased

      +
      +

      prioritizr 7.1.0.0

      • New add_linear_constraint function to add arbitrary constraints.
      • Update add_min_shortfall_objective and add_min_largest_shortfall_objective functions to handle targets with a target threshold value of zero.
      • Minor improvements to the documentation. These include moving mathematical details to dedicated sections, providing more links in the See also sections, fixing text formatting for the eval_connectivity_summary function, and tweaking the header in the README.
      • Update publication vignette.
      -
      -

      -prioritizr 7.0.1.5 Unreleased

      +
      +

      prioritizr 7.0.1.5

      • Update publication vignette.
      -
      -

      -prioritizr 7.0.1.4 Unreleased

      +
      +

      prioritizr 7.0.1.4

      • Update documentation and examples for problem function.
      • Update publication vignette.
      -
      -

      -prioritizr 7.0.1.3 Unreleased

      +
      +

      prioritizr 7.0.1.3

      • New solver benchmark vignette.
      -
      -

      -prioritizr 7.0.1.2 Unreleased

      +
      +

      prioritizr 7.0.1.2

      • Update add_gurobi_solver function so that it doesn’t print excess debugging information (accidentally introduced in previous version 7.0.1.1).
      -
      -

      -prioritizr 7.0.1.1 Unreleased

      -
      • Update add_gurobi_solver function to support the node_file_start parameter for the Gurobi software. This functionality is useful solving large problems on systems with limited memory (#139).
        • +
        +

        prioritizr 7.0.1.1

        +
        • Update add_gurobi_solver function to support the node_file_start parameter for the Gurobi software. This functionality is useful solving large problems on systems with limited memory (#139).
        -
        -

        -prioritizr 7.0.1 2021-03-31

        +
        +

        prioritizr 7.0.12021-03-31

        • Release candidate for CRAN.
        • Update DESCRIPTION with more information on the package usage.
        • Update DESCRIPTION with details on rcbc R package installation.
        -
        -

        -prioritizr 7.0.0.8 Unreleased

        +
        +

        prioritizr 7.0.0.8

        • New write_problem function to save the mixed integer programming representation of a conservation planning problem to a file. This function is useful for manually executing optimization solvers.
        -
        -

        -prioritizr 7.0.0.7 Unreleased

        -
        • Fix typo in rij_matrix function documentation (#189).
          • +
          +

          prioritizr 7.0.0.7

          +
          • Fix typo in rij_matrix function documentation (#189).
          • Update publication vignette.
          -
          -

          -prioritizr 7.0.0.6 Unreleased

          -
          • Update add_gurobi_solver to allow specification of a starting solution (#187). This functionality is useful for conducting a boundary penalty parameter calibration exercise. Specifically, users can specify the starting solution for a given penalty value based on the solution obtained using a smaller penalty value.
            • +
            +

            prioritizr 7.0.0.6

            +
            • Update add_gurobi_solver to allow specification of a starting solution (#187). This functionality is useful for conducting a boundary penalty parameter calibration exercise. Specifically, users can specify the starting solution for a given penalty value based on the solution obtained using a smaller penalty value.
            • Bug fix: solve now assigns layer names based on zone names for solutions in format.
            -
            -

            -prioritizr 7.0.0.5 Unreleased

            +
            +

            prioritizr 7.0.0.5

            • Update methods for calculating solver runtime.
            -
            -

            -prioritizr 7.0.0.4 Unreleased

            +
            +

            prioritizr 7.0.0.4

            • Update publication record.
            • Bug fix: time_limit and verbose parameters for add_cbc_solver now work as expected.
            -
            -

            -prioritizr 7.0.0.3 Unreleased

            +
            +

            prioritizr 7.0.0.3

            • Update add_gurobi_solver to report timings following the same methods as the other solvers.
            -
            -

            -prioritizr 7.0.0.2 Unreleased

            -
            • Update add_lpsymphony_solver to be more memory efficient (#183).
              • -
            • Added slam R package to dependencies to enable more memory efficient usage of the lpsymphony R package (#183).
              • +
              +

              prioritizr 7.0.0.2

              +
              • Update add_lpsymphony_solver to be more memory efficient (#183).
                • +
              • Added slam R package to dependencies to enable more memory efficient usage of the lpsymphony R package (#183).
              -
              -

              -prioritizr 7.0.0.1 Unreleased

              -
              • Update unit tests to solve a greater proportion of them using continuous integration services (#181).
                • +
                +

                prioritizr 7.0.0.1

                +
                • Update unit tests to solve a greater proportion of them using continuous integration services (#181).
                • Bug fix: add_cbc_solver is now preferred over all other open source solvers.
                • Bug fix: add_cbc_solver would sometimes return incorrect solutions to problems with equality constraints.
                -
                -

                -prioritizr 7.0.0.0 Unreleased

                -
                • Remove unused shiny R package integration and dependencies (#141).
                  • +
                  +

                  prioritizr 7.0.0.0

                  +
                  • Remove unused shiny R package integration and dependencies (#141).
                  -
                  -

                  -prioritizr 6.0.0.2 Unreleased

                  +
                  +

                  prioritizr 6.0.0.2

                  • New add_cbc_solver function to generate solutions using the open source CBC solver via the rcbc R package (https://github.com/dirkschumacher/rcbc).
                  • Update add_rsymphony_solver and add_lpsymphony_solver functions to have a default time_limit argument set as the maximum machine integer for consistency.
                  • Update add_rsymphony_solver, add_lpsymphony_solver, and add_gurobi_solver functions to require logical (TRUE/FALSE) arguments for the first_feasible parameter.
                    • @@ -334,20 +233,18 @@

                  • Update add_default_solver function so that it prefers add_lpsymphony_solver over add_rsymphony_solver, and add_cbc_solver over all open source solvers.
                  • Bug fix: previous versions of the package reported that the gap parameter for the add_rsymphony_solver and add_lpsymphony_solver corresponded to the maximum absolute difference from the optimal objective value. This was an error due to misunderstanding the SYMPHONY documentation. Under previous versions of the package, the gap parameter actually corresponded to a relative optimality gap expressed as a percentage (such thatgap = 10 indicates that solutions must be at least 10% from optimality). We have now fixed this error and the documentation described for the gap parameter is correct. We apologize for any inconvenience this may have caused.

                  -
                  -

                  -prioritizr 6.0.0.1 Unreleased

                  -
                  • Update Solution format section documentation for evaluation functions (i.e. all functions starting with eval_) to mention that the argument to solution should only contain columns that correspond to the solution (#176).
                    • -
                  • Add examples using sf data to documentation for importance evaluation functions (#176).
                    • -
                  • Add more helpful error messages when invalid solution arguments are supplied to the evaluation functions (#176).
                    • +
                    +

                    prioritizr 6.0.0.1

                    +
                    • Update Solution format section documentation for evaluation functions (i.e. all functions starting with eval_) to mention that the argument to solution should only contain columns that correspond to the solution (#176).
                      • +
                    • Add examples using sf data to documentation for importance evaluation functions (#176).
                      • +
                    • Add more helpful error messages when invalid solution arguments are supplied to the evaluation functions (#176).
                    • Add functionality to calculate importance scores using the Ferrier method with sf planning unit data.
                    • Fix broken link in add_manual_targets documentation.
                    • Fix typo in equation for rarity weighted richness documentation.
                    • New add_min_largest_shortfall objective function.
                    -
                    -

                    -prioritizr 6.0.0.0 Unreleased

                    +
                    +

                    prioritizr 6.0.0.0

                    • New eval_cost function to calculate the cost of a solution.
                    • New eval_boundary function to calculate the exposed boundary length associated with a solution.
                    • New eval_connectivity function to calculate the connectivity associated with a solution.
                      • @@ -357,259 +254,218 @@

                    • Rename ferrier_score function as eval_ferrier_importance function for consistency.
                    • Rename replacement_cost function as eval_replacement_importance function for consistency.
                    • Rename rarity_weighted_richness function as eval_rare_richness_importance function for consistency.
                      • -
                    • Fix comparability issues with Matrix R package (version 1.3-0) (#172).
                      • -
                    • Add NEWS to build process (#173).
                      • +
                    • Fix comparability issues with Matrix R package (version 1.3-0) (#172).
                      • +
                    • Add NEWS to build process (#173).
                    • Update publication vignette.

                    -
                    -

                    -prioritizr 5.0.3.2 Unreleased

                    -
                    • Add Schuster et al. 2020 to documentation to provide information on solver benchmarks (#170).
                      • +
                      +

                      prioritizr 5.0.3.2

                      +
                      • Add Schuster et al. 2020 to documentation to provide information on solver benchmarks (#170).
                      -
                      -

                      -prioritizr 5.0.3.1 Unreleased

                      +
                      +

                      prioritizr 5.0.3.1

                      • Fix add_locked_out_constraints function to enable a single planning unit from being locked out of multiple zones (when data are specified in raster format).
                      -
                      -

                      -prioritizr 5.0.3 2020-11-24

                      +
                      +

                      prioritizr 5.0.32020-11-24

                      • Release candidate for CRAN.
                      -
                      -

                      -prioritizr 5.0.2.7 Unreleased

                      +
                      +

                      prioritizr 5.0.2.7

                      • Update publication record vignette.
                      • Fix URLs for CRAN checks.
                      -
                      -

                      -prioritizr 5.0.2.6 Unreleased

                      +
                      +

                      prioritizr 5.0.2.6

                      • Implement GitHub Actions continuous integration (i.e. update tests and README).
                        • -
                      • Update problem function to reduce memory consumption for sparse matrix arguments (#164).
                        • -
                      • Update Tasmania vignette to remove superfluous warnings (#168).
                        • +
                      • Update problem function to reduce memory consumption for sparse matrix arguments (#164).
                        • +
                      • Update Tasmania vignette to remove superfluous warnings (#168).
                      • Update publication record vignette.
                      • Fix compatibility issues between the testthat R package and the gurobi R package in package tests.
                      -
                      -

                      -prioritizr 5.0.2.5 Unreleased

                      +
                      +

                      prioritizr 5.0.2.5

                      • New add_cplex_solver function to generate solutions using IBM CPLEX (via the cplexAPI package).
                      -
                      -

                      -prioritizr 5.0.2.4 Unreleased

                      +
                      +

                      prioritizr 5.0.2.4

                      • Update publication record vignette.
                        • -
                      • Update add_gap_portfolio documentation to note that it only works for problems with binary decisions (#159).
                        • +
                      • Update add_gap_portfolio documentation to note that it only works for problems with binary decisions (#159).
                      • Fix target calculations in add_loglinear_targets and loglinear_interpolation functions. Previously they used a natural logarithm for log-linear interpolation. To follow target setting approaches outlined by Rodrigues et al. (2004), they now use the decadic logarithm (i.e. log10).
                      -
                      -

                      -prioritizr 5.0.2.3 Unreleased

                      +
                      +

                      prioritizr 5.0.2.3

                      • Update publication record vignette.
                      -
                      -

                      -prioritizr 5.0.2.2 Unreleased

                      +
                      +

                      prioritizr 5.0.2.2

                      • Update publication record vignette.
                      -
                      -

                      -prioritizr 5.0.2.1 Unreleased

                      +
                      +

                      prioritizr 5.0.2.1

                      • Update documentation for ferrier_score function. It no longer incorrectly states that these scores can be calculated using CLUZ and now states that this functionality is experimental until the formulation can be double checked.
                      -
                      -

                      -prioritizr 5.0.2 2020-07-30

                      +
                      +

                      prioritizr 5.0.22020-07-30

                      • Release candidate for CRAN.
                      -
                      -

                      -prioritizr 5.0.1.7 Unreleased

                      +
                      +

                      prioritizr 5.0.1.7

                      • Fix tests for updated datasets in the prioritizrdata R package.
                      • Fix small typos in documentation.
                      • Update citation for Scriven et al. (2020) in the Publication Record vignette.
                      • Update Salt Spring Island vignette with Ferrier method for calculating irreplaceability scores and adjust for changes in cost data.
                      • Update examples to run with CRAN checks (i.e. --run-donttest).
                      -
                      -

                      -prioritizr 5.0.1.6 Unreleased

                      +
                      +

                      prioritizr 5.0.1.6

                      • Fix feature_representation bug incorrectly throwing error with vector planning unit data (e.g. sf-class data).
                      -
                      -

                      -prioritizr 5.0.1.5 Unreleased

                      -
                      • Fix typo causing rij_matrix to throw an error for large raster data (#151).
                        • +
                        +

                        prioritizr 5.0.1.5

                        +
                        • Fix typo causing rij_matrix to throw an error for large raster data (#151).
                        • Fix “Non-file package-anchored link(s) in documentation object” warnings in R-devel checks.
                        -
                        -

                        -prioritizr 5.0.1.4 Unreleased

                        +
                        +

                        prioritizr 5.0.1.4

                        • New add_linear_penalties to add penalties that penalize planning units according to a linear metric.
                        • Update connectivity_matrix documentation to provide an example of how to generate connectivity matrices that account for functional connectivity.
                        • Add more information to the documentation for the solve function.
                        • Add links to the documentation for the solve function to the Salt Spring Island and Tasmania vignettes.
                        -
                        -

                        -prioritizr 5.0.1.3 Unreleased

                        +
                        +

                        prioritizr 5.0.1.3

                        • Update compile to throw warning when compiling problems that include feature weights and an objective function that does not use feature weights.
                        -
                        -

                        -prioritizr 5.0.1.2 Unreleased

                        +
                        +

                        prioritizr 5.0.1.2

                        • Add Schuster et al. (2020) to publication record.
                        • Update Hanson et al. (2020) in publication record.
                        • Update Flower et al. (2020) in publication record.
                        -
                        -

                        -prioritizr 5.0.1.1 Unreleased

                        +
                        +

                        prioritizr 5.0.1.1

                        • Update add_gurobi_solver function to provide more options for controlling the pre-solve step when solving a problem.
                        -
                        -

                        -prioritizr 5.0.1 2020-05-15

                        +
                        +

                        prioritizr 5.0.12020-05-15

                        • Release candidate for CRAN.
                        -
                        -

                        -prioritizr 5.0.0.1 Unreleased

                        +
                        +

                        prioritizr 5.0.0.1

                        • New ferrier_score function to compute irreplaceability scores following Ferrier et al (2000).
                        -
                        -

                        -prioritizr 5.0.0.0 Unreleased

                        -
                        • Add full support for sf R package (#6).
                          • -
                        • Add Flower et al. (2020), Hanson et al. (2020), and Visalli et al. (2020) to publication record (#131).
                          • -
                        • New proximity_matrix function to generate matrices indicating which planning units are within a certain distance of each other (#6).
                          • -
                        • Rename connected_matrix function to adjacency_matrix function to follow the naming conventions of other spatial association functions (#6).
                          • -
                        • New add_extra_portfolio, add_top_portfolio, add_gap_portfolio functions to provide specific options for generating portfolios (#134).
                          • -
                        • Enhance intersecting_units and fast_extract functions to use the exactextractr and fasterize R packages to speed up raster data extraction (#130).
                          • +
                          +

                          prioritizr 5.0.0.0

                          +
                          • Add full support for sf R package (#6).
                            • +
                          • Add Flower et al. (2020), Hanson et al. (2020), and Visalli et al. (2020) to publication record (#131).
                            • +
                          • New proximity_matrix function to generate matrices indicating which planning units are within a certain distance of each other (#6).
                            • +
                          • Rename connected_matrix function to adjacency_matrix function to follow the naming conventions of other spatial association functions (#6).
                            • +
                          • New add_extra_portfolio, add_top_portfolio, add_gap_portfolio functions to provide specific options for generating portfolios (#134).
                            • +
                          • Enhance intersecting_units and fast_extract functions to use the exactextractr and fasterize R packages to speed up raster data extraction (#130).
                          • Fix compatibility issues with upcoming version of tibble (3.0.0).
                            • -
                          • Fix bug in boundary_matrix function when handling SpatialPolygon planning unit data that contain multiple polygons (e.g. a single planning unit contains to two separate islands) (#132).
                            • -
                          • Remove velox dependency since it may be archived on CRAN (#130).
                            • +
                          • Fix bug in boundary_matrix function when handling SpatialPolygon planning unit data that contain multiple polygons (e.g. a single planning unit contains to two separate islands) (#132).
                            • +
                          • Remove velox dependency since it may be archived on CRAN (#130).
                          • Deprecate set_number_of_threads, get_number_of_threads, and is.parallel functions since they are no longer used with new data extraction methods.
                            • -
                          • Deprecate add_pool_portfolio function because the new add_extra_portfolio and add_top_portfolio functions provide this functionality (#134).
                            • +
                          • Deprecate add_pool_portfolio function because the new add_extra_portfolio and add_top_portfolio functions provide this functionality (#134).
                          • Built-in datasets are now saved with latest workspace version (i.e. version 3).
                          -
                          -

                          -prioritizr 4.1.5.2 Unreleased

                          +
                          +

                          prioritizr 4.1.5.2

                          • Fix bug in add_rsymphony_solver and add_lpsymphony_solver throwing an an infeasible error message for feasible problems containing continuous or semi-continuous variables.
                          -
                          -

                          -prioritizr 4.1.5.1 Unreleased

                          +
                          +

                          prioritizr 4.1.5.1

                          • Add Lin et al. (in press) to publication record.
                          -
                          -

                          -prioritizr 4.1.5 2020-02-06

                          +
                          +

                          prioritizr 4.1.52020-02-06

                          • Release candidate for CRAN.
                          -
                          -

                          -prioritizr 4.1.4.4 Unreleased

                          +
                          +

                          prioritizr 4.1.4.4

                          • Fix warnings in R-devel CRAN checks related to documentation.
                          -
                          -

                          -prioritizr 4.1.4.3 Unreleased

                          +
                          +

                          prioritizr 4.1.4.3

                          • Add Williams et al. (in press) to publication record.
                          -
                          -

                          -prioritizr 4.1.4.2 Unreleased

                          +
                          +

                          prioritizr 4.1.4.2

                          • Add Rodewald et al. (2019) to publication record.
                          • Update in press version of Rodewald et al. (2019).
                            • -
                          • Make error message for presolve_check function more informative (#124).
                            • +
                          • Make error message for presolve_check function more informative (#124).
                          -
                          -

                          -prioritizr 4.1.4.1 Unreleased

                          +
                          +

                          prioritizr 4.1.4.1

                          • Add Scriven et al. (in press) to publication record.
                          -
                          -

                          -prioritizr 4.1.4 2019-10-03

                          +
                          +

                          prioritizr 4.1.42019-10-03

                          • Release candidate for CRAN.
                          -
                          -

                          -prioritizr 4.1.3.3 Unreleased

                          +
                          +

                          prioritizr 4.1.3.3

                          • Fix rij_matrix so that amounts are calculated correctly for vector-based planning unit data.
                          • Fix documentation for fast_extract.
                          -
                          -

                          -prioritizr 4.1.3.2 Unreleased

                          +
                          +

                          prioritizr 4.1.3.2

                          • Add Rodewald et al. (in press) to publication record.
                          • Update reference for Bombi et al. (2019) in publication record.
                          -
                          -

                          -prioritizr 4.1.3.1 Unreleased

                          +
                          +

                          prioritizr 4.1.3.1

                          • Fix typo in README.
                          -
                          -

                          -prioritizr 4.1.3 2019-09-06

                          +
                          +

                          prioritizr 4.1.32019-09-06

                          • Release candidate for CRAN.
                          -
                          -

                          -prioritizr 4.1.2.8 Unreleased

                          +
                          +

                          prioritizr 4.1.2.8

                          • Update add_locked_in_constraints and add_locked_out_constraints functions so that they no longer throw an unnecessary warning when when they are added to multi-zone problems using raster data with NA values.
                          • Update documentation for add_locked_in_constraints and add_locked_out_constraints functions to provide recommended practices for raster data.
                          • Update documentation for constraints missing “See also” and “Value” sections.
                          -
                          -

                          -prioritizr 4.1.2.7 Unreleased

                          -
                          • Fix issue with rarity_weighted_richness returning incorrect scores when the feature data contains one feature that has zeros amounts in all planning units (e.g. the tas_features object in the prioritizrdata R package; #120).
                            • -
                          • Fix issue with add_gurobi_solver returning solution statuses that are slightly larger than one (e.g. 1+1.0e-10) when solving problems with proportion-type decisions (#118).
                            • -
                          -
                          -

                          -prioritizr 4.1.2.6 Unreleased

                          -
                          • Update replacement_cost function to use parallel processing to speed up calculations (#119).
                            • -
                          • New add_manual_bounded_constraints function to apply lower and upper bounds on planning units statuses in a solution (#118).
                            • -
                          -
                          -

                          -prioritizr 4.1.2.5 Unreleased

                          -
                          • Update add_gurobi_solver, add_lpsymphony_solver, and add_rsymphony_solver functions so that they will not return solutions with values less than zero or greater than one when solving problems with proportion-type decisions. This issue is the result of inconsistent precision when performing floating point arithmetic (#117).
                            • -
                          • Update add_locked_in_constraints and add_locked_out_constraints functions to provide a more helpful error message the locked_in/locked_out argument refers to a column with data that are not logical (i.e. TRUE/FALSE; #118).
                            • -
                          -
                          -

                          -prioritizr 4.1.2.4 Unreleased

                          +
                          +

                          prioritizr 4.1.2.7

                          +
                          • Fix issue with rarity_weighted_richness returning incorrect scores when the feature data contains one feature that has zeros amounts in all planning units (e.g. the tas_features object in the prioritizrdata R package; #120).
                            • +
                          • Fix issue with add_gurobi_solver returning solution statuses that are slightly larger than one (e.g. 1+1.0e-10) when solving problems with proportion-type decisions (#118).
                            • +
                          +
                          +

                          prioritizr 4.1.2.6

                          +
                          • Update replacement_cost function to use parallel processing to speed up calculations (#119).
                            • +
                          • New add_manual_bounded_constraints function to apply lower and upper bounds on planning units statuses in a solution (#118).
                            • +
                          +
                          +

                          prioritizr 4.1.2.5

                          +
                          • Update add_gurobi_solver, add_lpsymphony_solver, and add_rsymphony_solver functions so that they will not return solutions with values less than zero or greater than one when solving problems with proportion-type decisions. This issue is the result of inconsistent precision when performing floating point arithmetic (#117).
                            • +
                          • Update add_locked_in_constraints and add_locked_out_constraints functions to provide a more helpful error message the locked_in/locked_out argument refers to a column with data that are not logical (i.e. TRUE/FALSE; #118).
                            • +
                          +
                          +

                          prioritizr 4.1.2.4

                          • Update solve function to throw a more accurate and helpful error message when no solutions are found (e.g. due to problem infeasibility or solver time limits).
                          • Standardize error messages so that none of them end in a full stop.
                          -
                          -

                          -prioritizr 4.1.2.3 Unreleased

                          +
                          +

                          prioritizr 4.1.2.3

                          • Rename add_max_phylo_objective function to add_max_phylo_div_objective.
                            • -
                          • New add_max_phylo_end_objective function to maximize the phylogenetic endemism of species adequately represented in a prioritization (#113).
                            • +
                          • New add_max_phylo_end_objective function to maximize the phylogenetic endemism of species adequately represented in a prioritization (#113).
                          • Add add_max_phylo_end_objective, replacement_cost, and rarity_weighted_richness functions to the Prioritizr vignette.
                          • Update simulated phylogeny dataset (sim_phylogeny).
                          • Update examples for add_max_phylo_div_objective function.
                          • Prettify equations in the documentation for objective functions.
                          -
                          -

                          -prioritizr 4.1.2.2 Unreleased

                          +
                          +

                          prioritizr 4.1.2.2

                          • New irreplaceability manual entry to document functions for calculating irreproducibility scores.
                            • -
                          • New replacement_cost function to calculate irreproducibility scores for each planning unit in a solution using the replacement cost method (#26).
                            • -
                          • New rarity_weighted_richness function to calculate irreproducibility scores for each planning unit in a solution using rarity weighted richness scores (#26).
                            • +
                          • New replacement_cost function to calculate irreproducibility scores for each planning unit in a solution using the replacement cost method (#26).
                            • +
                          • New rarity_weighted_richness function to calculate irreproducibility scores for each planning unit in a solution using rarity weighted richness scores (#26).
                          • Updated Salt Spring Island vignette with a section on calculating and interpreting irreplaceability scores.
                          -
                          -

                          -prioritizr 4.1.2.1 Unreleased

                          +
                          +

                          prioritizr 4.1.2.1

                          • Fix typo.
                          • Fix broken links to Gurobi academic licenses.
                          • Fix compiler warnings thrown during package installation.
                            • @@ -617,271 +473,223 @@

                          • Skip plotting data in examples during testing to reduce CRAN check times.
                          • Throw warning message if both the prioritizr and oppr R packages are loaded at the same time.

                          -
                          -

                          -prioritizr 4.1.2 Unreleased

                          +
                          +

                          prioritizr 4.1.2

                          • Release candidate for CRAN (rejected).
                          -
                          -

                          -prioritizr 4.1.1.2 Unreleased

                          +
                          +

                          prioritizr 4.1.1.2

                          • Fix example throwing an error during CRAN checks.
                          -
                          -

                          -prioritizr 4.1.1.1 Unreleased

                          +
                          +

                          prioritizr 4.1.1.1

                          • Add Bombi et al. (in press) to publication record.
                          -
                          -

                          -prioritizr 4.1.1.0 Unreleased

                          +
                          +

                          prioritizr 4.1.1.0

                          • Fix broken link in main vignette.
                          -
                          -

                          -prioritizr 4.1.1 2019-06-06

                          +
                          +

                          prioritizr 4.1.12019-06-06

                          • Release candidate for CRAN.
                          -
                          -

                          -prioritizr 4.1.0.1 Unreleased

                          +
                          +

                          prioritizr 4.1.0.1

                          • New add_min_shortfall_objective function to find solutions that minimize target shortfalls.
                          • Add new add_min_shortfall_objective function to main vignette.
                          • Fix problem tests so that they work when no solvers are installed.
                          -
                          -

                          -prioritizr 4.1.0.0 Unreleased

                          +
                          +

                          prioritizr 4.1.0.0

                          • The feature_representation function now requires missing (NA) values for planning unit statuses in a solution for planning units that have missing (NA) cost data.
                          -
                          -

                          -prioritizr 4.0.4.1 Unreleased

                          +
                          +

                          prioritizr 4.0.4.1

                          • New presolve_check function to investigate potential sources of numerical instability before trying to solve a problem. The manual entry for this function discusses common sources of numerical instability and approaches for fixing them.
                          • The solve function will now use the presolve_check function to verify that problems do not have obvious sources of numerical instability before trying to solve them. If a problem is likely to have numerical instability issues then this function will now throw an error (unless the solve(x, force = TRUE)).
                          • The add_rsymphony_solver function now uses sparse matrix formats so that attempts can be made to solve large problems with SYMPHONY—though it is unlikely that SYMPHONY will be able to solve such problems in a feasible period of time.
                          • Fix warnings thrown by the tibble R package when calling tibble::as.tibble instead of tibble::as_tibble.
                            • -
                          • Add example for calculating feature representation a solution in tabular format output by solve (#110).
                            • +
                          • Add example for calculating feature representation a solution in tabular format output by solve (#110).
                          • Fix several typos in documentation.
                          • Thrown warnings are now immediately visible.
                          • Update references in the publication record vignette.
                          • Specify English (US) in the DESCRIPTION file.
                          -
                          -

                          -prioritizr 4.0.4 2019-04-12

                          +
                          +

                          prioritizr 4.0.42019-04-12

                          • Release candidate for CRAN.
                          -
                          -

                          -prioritizr 4.0.3.1 Unreleased

                          +
                          +

                          prioritizr 4.0.3.1

                          • Retain debugging symbols to conform with CRAN policies.
                          -
                          -

                          -prioritizr 4.0.3 2019-04-08

                          +
                          +

                          prioritizr 4.0.32019-04-08

                          • Release candidate for CRAN.
                          -
                          -

                          -prioritizr 4.0.2.16 Unreleased

                          +
                          +

                          prioritizr 4.0.2.16

                          • Add new citations.
                          -
                          -

                          -prioritizr 4.0.2.15 Unreleased

                          -
                          • Fix typos in documentation for add_boundary_penalties and add_connectivity_penalties function (#106).
                            • +
                            +

                            prioritizr 4.0.2.15

                            +
                            • Fix typos in documentation for add_boundary_penalties and add_connectivity_penalties function (#106).
                            -
                            -

                            -prioritizr 4.0.2.14 Unreleased

                            -
                            • Fix issue where Rsymphony (and potentially lpsymphony) return infeasible solutions when subjected to a time limit (#105).
                              • +
                              +

                              prioritizr 4.0.2.14

                              +
                              • Fix issue where Rsymphony (and potentially lpsymphony) return infeasible solutions when subjected to a time limit (#105).
                              -
                              -

                              -prioritizr 4.0.2.13 Unreleased

                              +
                              +

                              prioritizr 4.0.2.13

                              • Fix assorted bugs in the render, setter, and getter parameter functions for ConservationProblem-class objects. These methods were implemented to be used in future interactive applications and are not currently used in the package. As a consequence, these bugs do not affect the correctness of any results.
                              -
                              -

                              -prioritizr 4.0.2.12 Unreleased

                              -
                              • Fix bad error message error being thrown when input rasters are not comparable (i.e. same coordinate reference system, extent, resolutions, and dimensionality) (#104).
                                • +
                                +

                                prioritizr 4.0.2.12

                                +
                                • Fix bad error message error being thrown when input rasters are not comparable (i.e. same coordinate reference system, extent, resolutions, and dimensionality) (#104).
                                • Add Domisch et al. (2019) to publication record vignette.
                                -
                                -

                                -prioritizr 4.0.2.11 Unreleased

                                -
                                • Fix issue solve printing annoying text about tbl_df (#75).
                                  • +
                                  +

                                  prioritizr 4.0.2.11

                                  +
                                  • Fix issue solve printing annoying text about tbl_df (#75).
                                  -
                                  -

                                  -prioritizr 4.0.2.10 Unreleased

                                  +
                                  +

                                  prioritizr 4.0.2.10

                                  • Tweak add_max_features_objective example code.
                                  -
                                  -

                                  -prioritizr 4.0.2.9 Unreleased

                                  +
                                  +

                                  prioritizr 4.0.2.9

                                  • Update publication record vignette.
                                  -
                                  -

                                  -prioritizr 4.0.2.8 Unreleased

                                  -
                                  • Fix bug where the add_neighbor_constraints and add_contiguity_constraints functions used more memory than they actually needed (#102). This is because the argument validation code converted sparse matrix objects (i.e. dgCMatrix) to base objects (i.e. matrix) class temporarily. This bug only meant inefficient utilization of computer resources—it did not affect the correctness of any results.
                                    • +
                                    +

                                    prioritizr 4.0.2.8

                                    +
                                    • Fix bug where the add_neighbor_constraints and add_contiguity_constraints functions used more memory than they actually needed (#102). This is because the argument validation code converted sparse matrix objects (i.e. dgCMatrix) to base objects (i.e. matrix) class temporarily. This bug only meant inefficient utilization of computer resources—it did not affect the correctness of any results.
                                    -
                                    -

                                    -prioritizr 4.0.2.7 Unreleased

                                    +
                                    +

                                    prioritizr 4.0.2.7

                                    • New add_mandatory_allocation_constraints function. This function can be used to ensure that every planning unit is allocated to a management zone in the solution. It is useful when developing land-use plans where every single parcel of land must be assigned to a specific land-use zone.
                                    • Add the add_mandatory_allocation_constraints to the Management Zones and Prioritizr vignettes.
                                    • Fix bug in the $find(x) method for Collection prototypes that caused it to throw an error incorrectly. This method was not used in earlier versions of this package.
                                    -
                                    -

                                    -prioritizr 4.0.2.6 Unreleased

                                    +
                                    +

                                    prioritizr 4.0.2.6

                                    • Fix bug the feature_representation function that caused the “amount_held” column to have NA values instead of the correct values. This bug only affected problems with multiple zones.
                                    -
                                    -

                                    -prioritizr 4.0.2.5 Unreleased

                                    +
                                    +

                                    prioritizr 4.0.2.5

                                    • Fix bug in argument validation code for the category_layer function that it this function to incorrectly throw an error claiming that the input argument to x was invalid when it was in fact valid. This bug is encountered when different layers the argument to x have non-NA values in different cells.
                                    -
                                    -

                                    -prioritizr 4.0.2.4 Unreleased

                                    -
                                    • Update instructions for activating Gurobi licenses on remote machines (#98).
                                      • +
                                      +

                                      prioritizr 4.0.2.4

                                      +
                                      • Update instructions for activating Gurobi licenses on remote machines (#98).
                                      -
                                      -

                                      -prioritizr 4.0.2.3 Unreleased

                                      +
                                      +

                                      prioritizr 4.0.2.3

                                      • The add_contiguity_constraints function now uses sparse matrix formats internally for single-zone problems. This means that the constraints can be applied to single-zoned problem with many more planning units.
                                      -
                                      -

                                      -prioritizr 4.0.2.2 Unreleased

                                      +
                                      +

                                      prioritizr 4.0.2.2

                                      • The add_connectivity_penalties function now uses sparse matrix formats internally for single-zone problems. This means that connectivity penalties can be applied to single-zoned problem with many more planning units.
                                      -
                                      -

                                      -prioritizr 4.0.2.1 Unreleased

                                      -
                                      • Update warning text when compiling problems that contain (i) objective functions that do not use targets and (ii) targets (#93).
                                        • -
                                      • Update documentation for the add_max_utility_objective and add_max_cover_objective functions to make it clearer that they do not use targets (#94).
                                        • +
                                        +

                                        prioritizr 4.0.2.1

                                        +
                                        • Update warning text when compiling problems that contain (i) objective functions that do not use targets and (ii) targets (#93).
                                          • +
                                        • Update documentation for the add_max_utility_objective and add_max_cover_objective functions to make it clearer that they do not use targets (#94).
                                        -
                                        -

                                        -prioritizr 4.0.2 2018-06-28

                                        +
                                        +

                                        prioritizr 4.0.22018-06-28

                                        • Release candidate for CRAN.
                                        -
                                        -

                                        -prioritizr 4.0.1.6 Unreleased

                                        +
                                        +

                                        prioritizr 4.0.1.6

                                        • Fix bug in add_locked_in_constraints and add_locked_out_constraints that incorrectly threw an error when using logical locked data (i.e. TRUE/FALSE) because it incorrectly thought that valid inputs were invalid.
                                          • -
                                        • Fix bug in add_locked_in_constraints, add_locked_out_constraints, and add_manual_locked_constraints where solving the same problem object twice resulted in incorrect planning units being locked in or out of the solution (#92).
                                          • +
                                        • Fix bug in add_locked_in_constraints, add_locked_out_constraints, and add_manual_locked_constraints where solving the same problem object twice resulted in incorrect planning units being locked in or out of the solution (#92).
                                        • Added unit tests for objectives, constraints, decisions, targets, and penalties to ensure that solving problems twice does not result in different solutions.
                                        -
                                        -

                                        -prioritizr 4.0.1.5 Unreleased

                                        +
                                        +

                                        prioritizr 4.0.1.5

                                        • Fix bug in feature_abundances that caused the solve function to throw an error when attempting to solve problems with a single feature.
                                        • Fix bug in add_cuts_portfolio that caused the portfolio to return solutions that were not within the specified optimality gap when using the Gurobi solver.
                                        • Add the ability to specify the search pool method and number of solutions to the add_pool_portfolio function.
                                        -
                                        -

                                        -prioritizr 4.0.1.4 Unreleased

                                        -
                                        • The feature_representation function now allows numeric solutions with attributes (e.g. when output by the solve function) when calculating representation statistics for problems with numeric planning unit data (#91).
                                          • +
                                          +

                                          prioritizr 4.0.1.4

                                          +
                                          • The feature_representation function now allows numeric solutions with attributes (e.g. when output by the solve function) when calculating representation statistics for problems with numeric planning unit data (#91).
                                          • The add_manual_targets function threw a warning when some features had targets equal to zero. This resulted in an excessive amount of warnings. Now, warnings are thrown for targets that are less then zero.
                                          • The problem function sometimes incorrectly threw a warning that feature data had negative values when the data actually did not contain negative values. This has now been addressed.
                                          -
                                          -

                                          -prioritizr 4.0.1.3 Unreleased

                                          +
                                          +

                                          prioritizr 4.0.1.3

                                          • The problem function now allows negative values in the cost and feature data (and throws a warning if such data are detected).
                                          • The add_absolute_targets and add_manual_targets functions now allow negative targets (but throw a warning if such targets are specified).
                                          • The compile function throws an error if a problem is compiled using the expanded formulation with negative feature data.
                                          • The add_absolute_targets function now throws an warning—instead of an error—if the specified targets are greater than the feature abundances in planning units to accommodate negative values in feature data.
                                          -
                                          -

                                          -prioritizr 4.0.1.2 Unreleased

                                          -
                                          • Fix add_max_cover_objective in prioritizr vignette (#90).
                                            • +
                                            +

                                            prioritizr 4.0.1.2

                                            +
                                            • Fix add_max_cover_objective in prioritizr vignette (#90).
                                            -
                                            -

                                            -prioritizr 4.0.1.1 Unreleased

                                            -
                                            • The add_relative_targets documentation now makes it clear that locked out planning units are included in the calculations for setting targets (#89).
                                              • -
                                            • The add_loglinear_targets function now includes a feature_abundances parameter for specifying the total amount of each feature to use when calculating the targets (#89).
                                              • +
                                              +

                                              prioritizr 4.0.1.1

                                              +
                                              • The add_relative_targets documentation now makes it clear that locked out planning units are included in the calculations for setting targets (#89).
                                                • +
                                              • The add_loglinear_targets function now includes a feature_abundances parameter for specifying the total amount of each feature to use when calculating the targets (#89).
                                              -
                                              -

                                              -prioritizr 4.0.1 2018-05-26

                                              +
                                              +

                                              prioritizr 4.0.12018-05-26

                                              • Release candidate for CRAN.
                                              -
                                              -

                                              -prioritizr 4.0.0.12 Unreleased

                                              -
                                              • New feature_abundances function to calculate the total amount of each feature in the planning units (#86).
                                                • +
                                                +

                                                prioritizr 4.0.0.12

                                                +
                                                • New feature_abundances function to calculate the total amount of each feature in the planning units (#86).
                                                -
                                                -

                                                -prioritizr 4.0.0.11 Unreleased

                                                -
                                                • Fix some equations in the documentation (#83).
                                                  • +
                                                  +

                                                  prioritizr 4.0.0.11

                                                  +
                                                  • Fix some equations in the documentation (#83).
                                                  -
                                                  -

                                                  -prioritizr 4.0.0.10 Unreleased

                                                  -
                                                  • Add version requirements for assertthat and tibble (#82).
                                                    • +
                                                    +

                                                    prioritizr 4.0.0.10

                                                    +
                                                    • Add version requirements for assertthat and tibble (#82).
                                                    -
                                                    -

                                                    -prioritizr 4.0.0.9 Unreleased

                                                    +
                                                    +

                                                    prioritizr 4.0.0.9

                                                    • Fix minor typos in the Gurobi Installation Guide and update the Management Zones tutorial.
                                                    -
                                                    -

                                                    -prioritizr 4.0.0.8 Unreleased

                                                    -
                                                    • Add instructions for setting up the Gurobi Academic license on a computer that it is not connected to a university computer network using a computer that is on an academic network (#81). For example, these instructions could be used to set up Gurobi on a cloud-based system using a laptop computer that is connected a university’s wireless network.
                                                      • -
                                                    -
                                                    -

                                                    -prioritizr 4.0.0.7 Unreleased

                                                    -
                                                    • The add_cuts_portfolio function uses the Gurobi solution pool to generate unique solutions within a specified gap of optimality when tasked with solving problems with Gurobi (version 8.0.0+; #80).
                                                      • -
                                                    -
                                                    -

                                                    -prioritizr 4.0.0.6 Unreleased

                                                    -
                                                    • New add_pool_portfolio function to generate a portfolio of solutions using the Gurobi solution pool (#77).
                                                      • -
                                                    -
                                                    -

                                                    -prioritizr 4.0.0.5 Unreleased

                                                    -
                                                    • The boundary_matrix function now has the experimental functionality to use GEOS STR trees to speed up processing (#74).
                                                      • -
                                                    • Solutions obtained from Gurobi that contain binary-type decisions are explicitly rounded to the nearest integer. This is because Gurobi can output solutions to binary problems that contain values which not exactly zero or one (e.g. 0.9999997 using default settings; #78).
                                                      • -
                                                    -
                                                    -

                                                    -prioritizr 4.0.0.4 Unreleased

                                                    -
                                                    • New feature_representation function to how well features are represented in solutions (#73).
                                                      • -
                                                    -
                                                    -

                                                    -prioritizr 4.0.0.3 Unreleased

                                                    +
                                                    +

                                                    prioritizr 4.0.0.8

                                                    +
                                                    • Add instructions for setting up the Gurobi Academic license on a computer that it is not connected to a university computer network using a computer that is on an academic network (#81). For example, these instructions could be used to set up Gurobi on a cloud-based system using a laptop computer that is connected a university’s wireless network.
                                                      • +
                                                    +
                                                    +

                                                    prioritizr 4.0.0.7

                                                    +
                                                    • The add_cuts_portfolio function uses the Gurobi solution pool to generate unique solutions within a specified gap of optimality when tasked with solving problems with Gurobi (version 8.0.0+; #80).
                                                      • +
                                                    +
                                                    +

                                                    prioritizr 4.0.0.6

                                                    +
                                                    • New add_pool_portfolio function to generate a portfolio of solutions using the Gurobi solution pool (#77).
                                                      • +
                                                    +
                                                    +

                                                    prioritizr 4.0.0.5

                                                    +
                                                    • The boundary_matrix function now has the experimental functionality to use GEOS STR trees to speed up processing (#74).
                                                      • +
                                                    • Solutions obtained from Gurobi that contain binary-type decisions are explicitly rounded to the nearest integer. This is because Gurobi can output solutions to binary problems that contain values which not exactly zero or one (e.g. 0.9999997 using default settings; #78).
                                                      • +
                                                    +
                                                    +

                                                    prioritizr 4.0.0.4

                                                    +
                                                    • New feature_representation function to how well features are represented in solutions (#73).
                                                      • +
                                                    +
                                                    +

                                                    prioritizr 4.0.0.3

                                                    • The prioritizrdata package has been listed under Suggests.
                                                    • The vignettes in the prioritizrdata package have been moved to this package to make them easier to find.
                                                    -
                                                    -

                                                    -prioritizr 4.0.0.2 Unreleased

                                                    -
                                                    • Fix issue with the solve function printing superfluous text (#75).
                                                      • +
                                                      +

                                                      prioritizr 4.0.0.2

                                                      +
                                                      • Fix issue with the solve function printing superfluous text (#75).
                                                      -
                                                      -

                                                      -prioritizr 4.0.0.1 Unreleased

                                                      +
                                                      +

                                                      prioritizr 4.0.0.1

                                                      • Minor improvements to the documentation for the problem function.
                                                      -
                                                      -

                                                      -prioritizr 4.0.0.0 Unreleased

                                                      -
                                                      • Added functionality to build and solve problems with multiple management zones (#14).
                                                        • +
                                                        +

                                                        prioritizr 4.0.0.0

                                                        +
                                                        • Added functionality to build and solve problems with multiple management zones (#14).
                                                        • New built-in datasets sim_pu_zones_stack, sim_pu_zones_polygons, and sim_features_zones for exploring conservation problems with multiple management zones.
                                                        • New zones function and Zones class to organize data with multiple zones.
                                                        • The problem function now accepts Zone objects as arguments for feature to create problems with multiple zones.
                                                          • @@ -898,148 +706,122 @@

                                                        • The Quick Start Guide and Prioritizr Basics vignettes have been consolidated into the prioritizr vignette.
                                                        • The marxan_problem has been updated with more comprehensive documentation and to provide more helpful error messages. For clarity, it will now only work with tabular data in the standard Marxan format.

                                                        -
                                                        -

                                                        -prioritizr 3.0.3.6 Unreleased

                                                        -
                                                        • Fix typo in README and update documentation for add_boundary_penalties (#62).
                                                          • +
                                                          +

                                                          prioritizr 3.0.3.6

                                                          +
                                                          • Fix typo in README and update documentation for add_boundary_penalties (#62).
                                                          -
                                                          -

                                                          -prioritizr 3.0.3.5 Unreleased

                                                          -
                                                          • Fix bug where add_locked_in_constraints and add_locked_out_constraints throw an exception when used with semi-continuous-type decisions (#59).
                                                            • +
                                                            +

                                                            prioritizr 3.0.3.5

                                                            +
                                                            • Fix bug where add_locked_in_constraints and add_locked_out_constraints throw an exception when used with semi-continuous-type decisions (#59).
                                                            • Exception in compile thrown when the same planning unit is locked in and locked out now prints the planning unit indices in a readable format.
                                                            -
                                                            -

                                                            -prioritizr 3.0.3.4 Unreleased

                                                            -
                                                            • Fix bug where add_locked_in_constraints and add_locked_out_constraints are ignored when using proportion-type decisions (#58).
                                                              • +
                                                              +

                                                              prioritizr 3.0.3.4

                                                              +
                                                              • Fix bug where add_locked_in_constraints and add_locked_out_constraints are ignored when using proportion-type decisions (#58).
                                                              -
                                                              -

                                                              -prioritizr 3.0.3.3 Unreleased

                                                              +
                                                              +

                                                              prioritizr 3.0.3.3

                                                              • Fix bug in predefined_optimization_problem which incorrectly recognized some inputs as invalid when they were in fact valid.
                                                              • Addressed NOTE in R CMD check related to proto in Depends.
                                                              -
                                                              -

                                                              -prioritizr 3.0.3.2 Unreleased

                                                              +
                                                              +

                                                              prioritizr 3.0.3.2

                                                              • Moved proto package from Imports to Depends in DESCRIPTION
                                                              -
                                                              -

                                                              -prioritizr 3.0.3.1 Unreleased

                                                              +
                                                              +

                                                              prioritizr 3.0.3.1

                                                              • Depends on R version 3.4.0 (avoids ‘patchlevel 0’ NOTE/WARNING in checks)
                                                              -
                                                              -

                                                              -prioritizr 3.0.3 2017-11-22

                                                              +
                                                              +

                                                              prioritizr 3.0.32017-11-22

                                                              • Release candidate for CRAN.
                                                              -
                                                              -

                                                              -prioritizr 3.0.2.3 Unreleased

                                                              -
                                                              • Unit tests that fail when using lpsymphony due to a bug in lpsymphony are now skipped (partially addressing #40).
                                                                • +
                                                                +

                                                                prioritizr 3.0.2.3

                                                                +
                                                                • Unit tests that fail when using lpsymphony due to a bug in lpsymphony are now skipped (partially addressing #40).
                                                                -
                                                                -

                                                                -prioritizr 3.0.2.2 Unreleased

                                                                +
                                                                +

                                                                prioritizr 3.0.2.2

                                                                • -add_lpsymphony_solver now throws warnings to alert users to potentially incorrect solutions (partially addressing #40).
                                                                  • +add_lpsymphony_solver now throws warnings to alert users to potentially incorrect solutions (partially addressing #40).
                                                                -
                                                                -

                                                                -prioritizr 3.0.2.1 Unreleased

                                                                +
                                                                +

                                                                prioritizr 3.0.2.1

                                                                • Vignette sizes have been reduced.
                                                                -
                                                                -

                                                                -prioritizr 3.0.2 Unreleased

                                                                +
                                                                +

                                                                prioritizr 3.0.2

                                                                • Release candidate for CRAN. Release postponed due issues on Travis CI.
                                                                -
                                                                -

                                                                -prioritizr 3.0.1.1 Unreleased

                                                                -
                                                                • Unit tests for add_*_objectives now pass when executed with slow solvers (partially addressing #40).
                                                                  • +
                                                                  +

                                                                  prioritizr 3.0.1.1

                                                                  +
                                                                  • Unit tests for add_*_objectives now pass when executed with slow solvers (partially addressing #40).
                                                                  • -compile now works when no solvers are installed (#41).
                                                                    • -
                                                                  • Gap arguments in add_*_solvers are now unbounded and can accept values larger than 1 (#44).
                                                                    • +compile now works when no solvers are installed (#41). +
                                                                  • Gap arguments in add_*_solvers are now unbounded and can accept values larger than 1 (#44).
                                                                  -
                                                                  -

                                                                  -prioritizr 3.0.1 2017-11-08

                                                                  +
                                                                  +

                                                                  prioritizr 3.0.12017-11-08

                                                                  • Release candidate for CRAN.
                                                                  -
                                                                  -

                                                                  -prioritizr 3.0.0.0 Unreleased

                                                                  -
                                                                  • The add_max_cover_objective function has been renamed to the add_max_utility_objective, because the formulation does not follow the historical formulation of the maximum coverage reserve selection problem (#38).
                                                                    • -
                                                                  • The add_max_cover_objective function now follows the historical maximum coverage objective. This fundamentally changes add_max_cover_objective function and breaks compatibility with previous version of prioritizr (#38).
                                                                    • +
                                                                    +

                                                                    prioritizr 3.0.0.0

                                                                    +
                                                                    • The add_max_cover_objective function has been renamed to the add_max_utility_objective, because the formulation does not follow the historical formulation of the maximum coverage reserve selection problem (#38).
                                                                      • +
                                                                    • The add_max_cover_objective function now follows the historical maximum coverage objective. This fundamentally changes add_max_cover_objective function and breaks compatibility with previous version of prioritizr (#38).
                                                                    • Modify lpsymphony examples and tests to skip on Linux operating systems.
                                                                    • Add tests to unit tests that were being skipped in new version of testthat.
                                                                    -
                                                                    -

                                                                    -prioritizr 2.0.4.1 Unreleased

                                                                    +
                                                                    +

                                                                    prioritizr 2.0.4.1

                                                                    • Fix bug with add_lpsymphony_solver causing error when attempting to solve problems.
                                                                    -
                                                                    -

                                                                    -prioritizr 2.0.4 Unreleased

                                                                    +
                                                                    +

                                                                    prioritizr 2.0.4

                                                                    • Release candidate for CRAN. Release postponed due to bug report.
                                                                    -
                                                                    -

                                                                    -prioritizr 2.0.3.1 Unreleased

                                                                    +
                                                                    +

                                                                    prioritizr 2.0.3.1

                                                                    • Fix bug when solving problems with numeric vector data that caused an error.
                                                                    • Fix bug in compiling problems with numeric vector input with rij data containing NA values.
                                                                    • Added unit tests for solving problems with various input formats.
                                                                    • Updated package sizes reported in cran-comments.
                                                                    -
                                                                    -

                                                                    -prioritizr 2.0.3 Unreleased

                                                                    +
                                                                    +

                                                                    prioritizr 2.0.3

                                                                    • Initial release candidate for CRAN. Release postponed due to bug report.
                                                                    -
                                                                    -

                                                                    -prioritizr 2.0.2.9 Unreleased

                                                                    -
                                                                    • Added vignette to record publications that use prioritizr (#35).
                                                                      • +
                                                                      +

                                                                      prioritizr 2.0.2.9

                                                                      +
                                                                      • Added vignette to record publications that use prioritizr (#35).
                                                                      -
                                                                      -

                                                                      -prioritizr 2.0.2.8 Unreleased

                                                                      -
                                                                      • Unit tests now compatible with development version of testthat (#34).
                                                                        • +
                                                                        +

                                                                        prioritizr 2.0.2.8

                                                                        +
                                                                        • Unit tests now compatible with development version of testthat (#34).
                                                                        -
                                                                        -

                                                                        -prioritizr 2.0.2.7 Unreleased

                                                                        +
                                                                        +

                                                                        prioritizr 2.0.2.7

                                                                        • Fix bug in apply_boundary_penalties and add_connectivity_penalties causing the function to throw an error when the number of boundaries/edges is less than the number of planning units.
                                                                        -
                                                                        -

                                                                        -prioritizr 2.0.2.6 Unreleased

                                                                        -
                                                                        • Makevars now compatible with Mac OSX Sierra (#33).
                                                                          • +
                                                                          +

                                                                          prioritizr 2.0.2.6

                                                                          +
                                                                          • Makevars now compatible with Mac OSX Sierra (#33).
                                                                          -
                                                                          -

                                                                          -prioritizr 2.0.2.5 Unreleased

                                                                          -
                                                                          • Fix bug in boundary_matrix calculations (#30).
                                                                            • +
                                                                            +

                                                                            prioritizr 2.0.2.5

                                                                            +
                                                                            • Fix bug in boundary_matrix calculations (#30).
                                                                            -
                                                                            -

                                                                            -prioritizr 2.0.2.4 Unreleased

                                                                            +
                                                                            +

                                                                            prioritizr 2.0.2.4

                                                                            • Minor tweaks to vignettes.
                                                                            -
                                                                            -

                                                                            -prioritizr 2.0.2.3 Unreleased

                                                                            -
                                                                            • Add logo to README files and package website (#31).
                                                                              • +
                                                                              +

                                                                              prioritizr 2.0.2.3

                                                                              +
                                                                              • Add logo to README files and package website (#31).
                                                                              -
                                                                              -

                                                                              -prioritizr 2.0.2.2 Unreleased

                                                                              +
                                                                              +

                                                                              prioritizr 2.0.2.2

                                                                              • Broad-scale improvements to documentation.
                                                                                • -
                                                                              • Fix documentation for add_max_phylo_objective (#24).
                                                                                • +
                                                                              • Fix documentation for add_max_phylo_objective (#24).
                                                                              • Update Gurobi Installation vignette.
                                                                              • Remove prioritizrdata from package Suggests.
                                                                              • Add shiny and xtable to Suggests for rendering parameters.
                                                                                • @@ -1049,71 +831,60 @@

                                                                              • Fix bug when numeric planning unit data and portfolios that caused the solve to throw an error.
                                                                              • Remove R-devel from AppVeyor testing because it fails for unknown reasons.

                                                                              -
                                                                              -

                                                                              -prioritizr 2.0.2.1 Unreleased

                                                                              +
                                                                              +

                                                                              prioritizr 2.0.2.1

                                                                              • Removed shiny functions for now to prep for CRAN release.
                                                                              • Rebuilt website and documentation.
                                                                              -
                                                                              -

                                                                              -prioritizr 2.0.2.0 Unreleased

                                                                              +
                                                                              +

                                                                              prioritizr 2.0.2.0

                                                                              • Included vignette on Gurobi solver installation and testing.
                                                                              -
                                                                              -

                                                                              -prioritizr 2.0.1.0 Unreleased

                                                                              +
                                                                              +

                                                                              prioritizr 2.0.1.0

                                                                              • Fixed bug where Spatial*DataFrame input to marxan_problem would always use the first column in the attribute table for the cost data. This bug is serious so analysis that used Spatial*DataFrame inputs in marxan_problem should be rerun.
                                                                              • Added functionality to use feature abundance/occurrence data stored as columns in the planning unit data when constructing problem objects.
                                                                              -
                                                                              -

                                                                              -prioritizr 2.0.0.2 Unreleased

                                                                              +
                                                                              +

                                                                              prioritizr 2.0.0.2

                                                                              • Skip add_cuts_portfolio on Travis.
                                                                              -
                                                                              -

                                                                              -prioritizr 2.0.0.1 Unreleased

                                                                              +
                                                                              +

                                                                              prioritizr 2.0.0.1

                                                                              • Skip add_cuts_portfolio and add_shuffle_portfolio tests on CRAN.
                                                                              -
                                                                              -

                                                                              -prioritizr 2.0.0.0 Unreleased

                                                                              +
                                                                              +

                                                                              prioritizr 2.0.0.0

                                                                              • This version breaks compatibility with previous releases because solutions in data.frame and Spatial*DataFrame objects are now stored in columns named "solution_*" (e.g. “solution_1”) to store multiple solutions.
                                                                                • -
                                                                              • Added support for multiple solutions (#23).
                                                                                • -
                                                                              • Solutions now contain additional information in stored in the object’s attributes (#24). See README.Rmd for examples on accessing this information.
                                                                                • +
                                                                              • Added support for multiple solutions (#23).
                                                                                • +
                                                                              • Solutions now contain additional information in stored in the object’s attributes (#24). See README.Rmd for examples on accessing this information.
                                                                              • Tidy examples in add_gurobi_solver.R, add_lpsymphony_solver.R, add_rsymphony_solver.R, and solvers.R.
                                                                              • Add logical verbose argument to all solvers. This replaces the verbosity argument in add_lpsymphony_solver and add_rsymphony_solver.
                                                                              • The verbosity of information presented when solving problems using add_lpsymphony_solver and add_rsymphony_solver is reduced.
                                                                              • Assorted spelling mistakes have been fixed.
                                                                              -
                                                                              -

                                                                              -prioritizr 1.0.2.3 Unreleased

                                                                              +
                                                                              +

                                                                              prioritizr 1.0.2.3

                                                                              • ConservationProblem$print() now only prints the first three species names and a count of the total number of features. This update means that ConservationProblem objects with lots of features can now safely be printed without polluting the R console.
                                                                              • Attempt to make equations in help files prettier.
                                                                              • Fix bug where lpsymphony and Rsymphony solvers would return solutions containing NA values if they did not find a feasible solution within the argument to time_limit.
                                                                              -
                                                                              -

                                                                              -prioritizr 1.0.2.2 Unreleased

                                                                              -
                                                                              -
                                                                              - - - - - - - - - - + diff --git a/docs/reference/Parameter-class.html b/docs/reference/Parameter-class.html index cb23db46c..5ea1af63e 100644 --- a/docs/reference/Parameter-class.html +++ b/docs/reference/Parameter-class.html @@ -1,103 +1,20 @@ - - - - - - - -Parameter class — Parameter-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Parameter class — Parameter-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
                                                                              -
                                                                              -

                                                                              Parameter class

                                                                              - Source: R/Parameter-proto.R + Source: R/Parameter-proto.R
                                                                              @@ -188,81 +105,93 @@

                                                                              Parameter class

                                                                              should interact directly with this class.

                                                                              +
                                                                              Usage,NULL
                                                                              +
                                                                              +

                                                                              Fields

                                                                              + -

                                                                              Fields

                                                                              +
                                                                              $id
                                                                              +

                                                                              Id identifier for parameter.

                                                                              - -
                                                                              +
                                                                              $name
                                                                              +

                                                                              character name of parameter.

                                                                              -
                                                                              $id

                                                                              Id identifier for parameter.

                                                                              -
                                                                              $name

                                                                              character name of parameter.

                                                                              +
                                                                              $value
                                                                              +

                                                                              numeric vector of values.

                                                                              -
                                                                              $value

                                                                              numeric vector of values.

                                                                              -
                                                                              $default

                                                                              numeric vector of default values.

                                                                              +
                                                                              $default
                                                                              +

                                                                              numeric vector of default values.

                                                                              -
                                                                              $class

                                                                              character name of the class that the values inherit -from (e.g. "integer".

                                                                              -
                                                                              $lower_limit

                                                                              numeric vector specifying the minimum -permitted value for each element in $value.

                                                                              +
                                                                              $class
                                                                              +

                                                                              character name of the class that the values inherit +from (e.g., "integer".

                                                                              -
                                                                              $upper_limit

                                                                              numeric vector specifying the maximum + +

                                                                              $lower_limit
                                                                              +

                                                                              numeric vector specifying the minimum permitted value for each element in $value.

                                                                              -
                                                                              +
                                                                              $upper_limit
                                                                              +

                                                                              numeric vector specifying the maximum +permitted value for each element in $value.

                                                                              + -

                                                                              Usage

                                                                              +
                                                                              +
                                                                              +

                                                                              Usage

                                                                              x$print()

                                                                              x$show()

                                                                              x$reset()

                                                                              -

                                                                              Details

                                                                              - +
                                                                              +
                                                                              +

                                                                              Details

                                                                              -
                                                                              -
                                                                              print

                                                                              print the object.

                                                                              -
                                                                              show

                                                                              show the object.

                                                                              -
                                                                              reset

                                                                              change the parameter values to be the default values.

                                                                              +
                                                                              print
                                                                              +

                                                                              print the object.

                                                                              + +
                                                                              show
                                                                              +

                                                                              show the object.

                                                                              -
                                                                              +
                                                                              reset
                                                                              +

                                                                              change the parameter values to be the default values.

                                                                              -

                                                                              See also

                                                                              -

                                                                              ScalarParameter.

                                                                              +
                                                                              +
                                                                              +

                                                                              See also

                                                                              +

                                                                              ScalarParameter.

                                                                              +
                                                                              +
                                                                              -
                                                                              - - - - - - - - - - + diff --git a/docs/reference/Parameters-class.html b/docs/reference/Parameters-class.html index 28574f562..8d75fcd48 100644 --- a/docs/reference/Parameters-class.html +++ b/docs/reference/Parameters-class.html @@ -1,103 +1,20 @@ - - - - - - - -Parameters class — Parameters-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Parameters class — Parameters-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
                                                                              -
                                                                              -

                                                                              Parameters class

                                                                              - Source: R/Parameters-proto.R + Source: R/Parameters-proto.R
                                                                              -

                                                                              This class represents a collection of Parameter objects. +

                                                                              This class represents a collection of Parameter objects. It provides methods for accessing and updating the parameters stored inside it.

                                                                              +
                                                                              Usage,NULL
                                                                              - -

                                                                              Fields

                                                                              - +
                                                                              +

                                                                              Fields

                                                                              -
                                                                              - -
                                                                              $parameters

                                                                              list object containing -Parameter objects.

                                                                              +
                                                                              $parameters
                                                                              +

                                                                              list object containing +Parameter objects.

                                                                              -
                                                                              - -

                                                                              Usage

                                                                              +
                                                                              +
                                                                              +

                                                                              Usage

                                                                              @@ -216,72 +132,85 @@

                                                                              Usage

                                                                              x$get(id)

                                                                              x$set(id, value)

                                                                              x$add(p)

                                                                              -

                                                                              Arguments

                                                                              - +
                                                                              +
                                                                              +

                                                                              Arguments

                                                                              -
                                                                              -
                                                                              id

                                                                              Id object.

                                                                              +
                                                                              id
                                                                              +

                                                                              Id object.

                                                                              + -
                                                                              p

                                                                              Parameter object.

                                                                              +
                                                                              p
                                                                              +

                                                                              Parameter object.

                                                                              -
                                                                              value

                                                                              any object.

                                                                              +
                                                                              value
                                                                              +

                                                                              any object.

                                                                              -
                                                                              -

                                                                              Details

                                                                              +
                                                                              +
                                                                              +

                                                                              Details

                                                                              -
                                                                              +
                                                                              print
                                                                              +

                                                                              print the object.

                                                                              + + +
                                                                              show
                                                                              +

                                                                              show the object.

                                                                              -
                                                                              print

                                                                              print the object.

                                                                              -
                                                                              show

                                                                              show the object.

                                                                              +
                                                                              repr
                                                                              +

                                                                              character representation of object.

                                                                              -
                                                                              repr

                                                                              character representation of object.

                                                                              -
                                                                              names

                                                                              return character names of parameters.

                                                                              +
                                                                              names
                                                                              +

                                                                              return character names of parameters.

                                                                              -
                                                                              ids

                                                                              return character parameter unique identifiers.

                                                                              -
                                                                              length

                                                                              return integer number of parameters in object.

                                                                              -
                                                                              get

                                                                              retrieve the value of a parameter in the object +

                                                                              ids
                                                                              +

                                                                              return character parameter unique identifiers.

                                                                              + + +
                                                                              length
                                                                              +

                                                                              return integer number of parameters in object.

                                                                              + +
                                                                              get
                                                                              +

                                                                              retrieve the value of a parameter in the object using an Id object.

                                                                              -
                                                                              set

                                                                              change the value of a parameter in the object + +

                                                                              set
                                                                              +

                                                                              change the value of a parameter in the object to a new object.

                                                                              -
                                                                              +
                                                                              +
                                                                              -
                                                                              - - - - - - - - - - + diff --git a/docs/reference/Penalty-class.html b/docs/reference/Penalty-class.html index 30f646667..170c7a901 100644 --- a/docs/reference/Penalty-class.html +++ b/docs/reference/Penalty-class.html @@ -1,106 +1,23 @@ - - - - - - - -Penalty prototype — Penalty-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Penalty prototype — Penalty-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
                                                                              -
                                                                              -

                                                                              Penalty prototype

                                                                              - Source: R/Penalty-proto.R + Source: R/Penalty-proto.R
                                                                              @@ -190,40 +107,36 @@

                                                                              Penalty prototype

                                                                              objective function when making a conservation problem. This prototype represents a recipe, to actually add penalties to a planning problem, see the help page on -penalties. Only experts should use this class directly. This -prototype inherits from the ConservationModifier.

                                                                              +penalties. Only experts should use this class directly. This +prototype inherits from the ConservationModifier.

                                                                              +
                                                                              Usage,NULL
                                                                              - -

                                                                              See also

                                                                              - -

                                                                              ConservationModifier.

                                                                              +
                                                                              +

                                                                              See also

                                                                              +

                                                                              ConservationModifier.

                                                                              +
                                                                              +
                                                                              -
                                                                              - - - - - - - - - - + diff --git a/docs/reference/Portfolio-class.html b/docs/reference/Portfolio-class.html index 9ae3d8466..6de200a05 100644 --- a/docs/reference/Portfolio-class.html +++ b/docs/reference/Portfolio-class.html @@ -1,105 +1,22 @@ - - - - - - - -Portfolio prototype — Portfolio-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Portfolio prototype — Portfolio-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
                                                                              -
                                                                              -

                                                                              Portfolio prototype

                                                                              - Source: R/Portfolio-proto.R + Source: R/Portfolio-proto.R
                                                                              @@ -189,29 +106,32 @@

                                                                              Portfolio prototype

                                                                              optimization problems. This class represents a recipe to create portfolio generating method and is only recommended for use by expert users. To customize the method used to generate portfolios, please see the -help page on portfolios.

                                                                              +help page on portfolios.

                                                                              +
                                                                              Usage,NULL
                                                                              - -

                                                                              Fields

                                                                              - +
                                                                              +

                                                                              Fields

                                                                              -
                                                                              +
                                                                              $name
                                                                              +

                                                                              character name of portfolio method.

                                                                              -
                                                                              $name

                                                                              character name of portfolio method.

                                                                              -
                                                                              $parameters

                                                                              Parameters object with parameters used to customize +

                                                                              $parameters
                                                                              +

                                                                              Parameters object with parameters used to customize the the portfolio.

                                                                              -
                                                                              $run

                                                                              function used to generate a portfolio.

                                                                              -
                                                                              +
                                                                              $run
                                                                              +

                                                                              function used to generate a portfolio.

                                                                              -

                                                                              Usage

                                                                              +
                                                                              +
                                                                              +

                                                                              Usage

                                                                              @@ -219,62 +139,65 @@

                                                                              Usage

                                                                              x$show()

                                                                              x$repr()

                                                                              x$run(op, sol)

                                                                              -

                                                                              Arguments

                                                                              - +
                                                                              +
                                                                              +

                                                                              Arguments

                                                                              -
                                                                              - -
                                                                              x

                                                                              Solver object.

                                                                              +
                                                                              x
                                                                              +

                                                                              Solver object.

                                                                              -
                                                                              op

                                                                              OptimizationProblem object.

                                                                              +
                                                                              op
                                                                              +

                                                                              OptimizationProblem object.

                                                                              -
                                                                              -

                                                                              Details

                                                                              +
                                                                              +
                                                                              +

                                                                              Details

                                                                              -
                                                                              -
                                                                              print

                                                                              print the object.

                                                                              +
                                                                              print
                                                                              +

                                                                              print the object.

                                                                              + + +
                                                                              show
                                                                              +

                                                                              show the object.

                                                                              + -
                                                                              show

                                                                              show the object.

                                                                              +
                                                                              repr
                                                                              +

                                                                              character representation of object.

                                                                              -
                                                                              repr

                                                                              character representation of object.

                                                                              -
                                                                              run

                                                                              solve an OptimizationProblem object using this -object and a Solver object.

                                                                              +
                                                                              run
                                                                              +

                                                                              solve an OptimizationProblem object using this +object and a Solver object.

                                                                              -
                                                                              +
                                                                              +
                                                                              -
                                                                              - - - - - - - - - - + diff --git a/docs/reference/Rplot002.png b/docs/reference/Rplot002.png index aef6fa30925a6f3c0688e910ab075dcaed9ce689..a41ce8468a6a9e3712c1a06740b7ae58f5828b74 100644 GIT binary patch literal 7406 zcmc(k2UJt(x`tCENFPCPBJC(BqckPdfZ(VI8KfwJp-34@q=SS`LQsSmiYN+*NM{5@ zic*ypEP(XhArXYo2`C8=67G(A&a6A@-dWC^bJt~&wX?!rdvE^#{hs&zzWi!pq{qj7 zkQ)R7@uBq3T>^o?WcF(>4EO}sU!MpZU_Tq^odb@*&(_(RFyO%Dt#9EA0`Um4U*O&e z{0;~tb{lo>$IF3_mM6mQjBnsbYZO*>Usi^G%l8p`8y@%b{z|;P`0(daLpO+r%u0Ww z%Vy3SQ{&8(3#pMv#4$wLJT*#2+D~&?{aKp2AJRdvUHTYT`kOen=KJI~=$k)OKahkK z$Up`2?qPMXRW&3@rbDu~eobK_EoL%9xU0Fn14j=b;YbFgiMr%^Qr#E_Dna_2elhVF zf@yrD37gpW;$dtKsXB${Ow>55jBVLgV#Tui$&}ALhy(W-k zFEDBKs?2IpgF{DUb4IVkk=F=p{G*a3rd1N51Vo8{4wXhB`xJ7mBIIA@;WGA!5YDeI z?pDw@lEXRYMVz^6-8y2Yc>?PLf;_-gA&Y}x9bLM{q+sCw&BN62Lm$s~-072_iyCSV zyxuQ<2-TZ{Rhh^Rj#%-10a^^nP@~sZUZ_$BdoC4)T5g_Dqx#eUFKGd1 z!!aA&7N8{w~c^qr@PD*odMiotab*ap7gi%}EH8hAE 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z(fv|%bbl%^jFW;2I;lOSFEs>F$nf_vLnH9Z#gywy5Dsx>S)R$Yl7)W3s>2T2R;Dr* z9A5JbFP81o$b*yW1r6F>PR`f(vQ;_=ENGYf>6YyO95VmbCPTeDmI;7D zQLdU*7%%*X7aIc~W7~BKt53;F9eE(q0d(x6bwm`u<)^7XbI#Sm4Sdn{nUUL^*I>a9 Ob{KP;6J^J-fB7$}&ShW# diff --git a/docs/reference/ScalarParameter-class.html b/docs/reference/ScalarParameter-class.html index 50191c630..633bbc068 100644 --- a/docs/reference/ScalarParameter-class.html +++ b/docs/reference/ScalarParameter-class.html @@ -1,102 +1,19 @@ - - - - - - - -Scalar parameter prototype — ScalarParameter-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Scalar parameter prototype — ScalarParameter-class • prioritizr - - - - - - - - - - - - - - +
                                                                              -
                                                                              -

                                                                              Scalar parameter prototype

                                                                              - Source: R/ScalarParameter-proto.R + Source: R/ScalarParameter-proto.R
                                                                              @@ -186,36 +103,47 @@

                                                                              Scalar parameter prototype

                                                                              Only experts should interact directly with this prototype.

                                                                              +
                                                                              Usage,NULL
                                                                              +
                                                                              +

                                                                              Fields

                                                                              + -

                                                                              Fields

                                                                              +
                                                                              $id
                                                                              +

                                                                              character identifier for parameter.

                                                                              - -
                                                                              +
                                                                              $name
                                                                              +

                                                                              character name of parameter.

                                                                              -
                                                                              $id

                                                                              character identifier for parameter.

                                                                              -
                                                                              $name

                                                                              character name of parameter.

                                                                              +
                                                                              $value
                                                                              +

                                                                              numeric scalar value.

                                                                              -
                                                                              $value

                                                                              numeric scalar value.

                                                                              -
                                                                              $default

                                                                              numeric scalar default value.

                                                                              +
                                                                              $default
                                                                              +

                                                                              numeric scalar default value.

                                                                              -
                                                                              $class

                                                                              character name of the class that $value should -inherit from (e.g. integer).

                                                                              -
                                                                              $lower_limit

                                                                              numeric scalar value that is the minimum value -that $value is permitted to be.

                                                                              +
                                                                              $class
                                                                              +

                                                                              character name of the class that $value should +inherit from (e.g., integer).

                                                                              + -
                                                                              $upper_limit

                                                                              numeric scalar value that is the maximum value +

                                                                              $lower_limit
                                                                              +

                                                                              numeric scalar value that is the minimum value that $value is permitted to be.

                                                                              -
                                                                              +
                                                                              $upper_limit
                                                                              +

                                                                              numeric scalar value that is the maximum value +that $value is permitted to be.

                                                                              + -

                                                                              Usage

                                                                              +
                                                                              +
                                                                              +

                                                                              Usage

                                                                              @@ -225,67 +153,72 @@

                                                                              Usage

                                                                              x$get()

                                                                              x$set(x)

                                                                              x$reset()

                                                                              -

                                                                              Arguments

                                                                              - +
                                                                              +
                                                                              +

                                                                              Arguments

                                                                              -
                                                                              +
                                                                              x
                                                                              +

                                                                              object used to set a new parameter value.

                                                                              -
                                                                              x

                                                                              object used to set a new parameter value.

                                                                              -
                                                                              +
                                                                              +
                                                                              +

                                                                              Details

                                                                              + -

                                                                              Details

                                                                              +
                                                                              print
                                                                              +

                                                                              print the object.

                                                                              - -
                                                                              +
                                                                              show
                                                                              +

                                                                              show the object.

                                                                              -
                                                                              print

                                                                              print the object.

                                                                              -
                                                                              show

                                                                              show the object.

                                                                              +
                                                                              validate
                                                                              +

                                                                              check if a proposed new set of parameters are valid.

                                                                              -
                                                                              validate

                                                                              check if a proposed new set of parameters are valid.

                                                                              -
                                                                              get

                                                                              extract the parameter value.

                                                                              +
                                                                              get
                                                                              +

                                                                              extract the parameter value.

                                                                              -
                                                                              set

                                                                              update the parameter value.

                                                                              -
                                                                              reset

                                                                              update the parameter value to be the default value.

                                                                              +
                                                                              set
                                                                              +

                                                                              update the parameter value.

                                                                              -
                                                                              +
                                                                              reset
                                                                              +

                                                                              update the parameter value to be the default value.

                                                                              -

                                                                              See also

                                                                              -

                                                                              Parameter, ArrayParameter.

                                                                              + +
                                                                              +
                                                                              +

                                                                              See also

                                                                              +

                                                                              Parameter, ArrayParameter.

                                                                              +
                                                                              +
                                                                            -
                                                                            - - - - - - - - - - + diff --git a/docs/reference/Solver-class.html b/docs/reference/Solver-class.html index 4de0e19ed..73949ee7d 100644 --- a/docs/reference/Solver-class.html +++ b/docs/reference/Solver-class.html @@ -1,105 +1,22 @@ - - - - - - - -Solver prototype — Solver-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Solver prototype — Solver-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
                                                                            -
                                                                            -

                                                                            Solver prototype

                                                                            - Source: R/Solver-proto.R + Source: R/Solver-proto.R
                                                                            @@ -189,32 +106,37 @@

                                                                            Solver prototype

                                                                            optimization problems. This class represents a recipe to create solver and and is only recommended for use by expert users. To customize the method used to solve optimization problems, please see the -help page on solvers.

                                                                            +help page on solvers.

                                                                            +
                                                                            Usage,NULL
                                                                            - -

                                                                            Fields

                                                                            - +
                                                                            +

                                                                            Fields

                                                                            -
                                                                            +
                                                                            $name
                                                                            +

                                                                            character name of solver.

                                                                            -
                                                                            $name

                                                                            character name of solver.

                                                                            -
                                                                            $data

                                                                            list object optimization problem data.

                                                                            +
                                                                            $data
                                                                            +

                                                                            list object optimization problem data.

                                                                            -
                                                                            $parameters

                                                                            Parameters object with parameters used to customize + +

                                                                            $parameters
                                                                            +

                                                                            Parameters object with parameters used to customize the the solver.

                                                                            -
                                                                            $solve

                                                                            function used to solve a -OptimizationProblem object.

                                                                            -
                                                                            +
                                                                            $solve
                                                                            +

                                                                            function used to solve a +OptimizationProblem object.

                                                                            -

                                                                            Usage

                                                                            +
                                                                            +
                                                                            +

                                                                            Usage

                                                                            @@ -228,80 +150,95 @@

                                                                            Usage

                                                                            x$calculate(op)

                                                                            x$run()

                                                                            x$solve(op)

                                                                            -

                                                                            Arguments

                                                                            - +
                                                                            +
                                                                            +

                                                                            Arguments

                                                                            -
                                                                            - -
                                                                            x

                                                                            Solver object.

                                                                            +
                                                                            x
                                                                            +

                                                                            Solver object.

                                                                            -
                                                                            op

                                                                            OptimizationProblem object.

                                                                            +
                                                                            op
                                                                            +

                                                                            OptimizationProblem object.

                                                                            -
                                                                            -

                                                                            Details

                                                                            +
                                                                            +
                                                                            +

                                                                            Details

                                                                            -
                                                                            -
                                                                            print

                                                                            print the object.

                                                                            +
                                                                            print
                                                                            +

                                                                            print the object.

                                                                            -
                                                                            show

                                                                            show the object.

                                                                            -
                                                                            repr

                                                                            character representation of object.

                                                                            +
                                                                            show
                                                                            +

                                                                            show the object.

                                                                            -
                                                                            get_data

                                                                            return an object stored in the data field with + +

                                                                            repr
                                                                            +

                                                                            character representation of object.

                                                                            + + +
                                                                            get_data
                                                                            +

                                                                            return an object stored in the data field with the corresponding name. If the object is not present in the data field, a waiver object is returned.

                                                                            -
                                                                            set_data

                                                                            store an object stored in the data field with + +

                                                                            set_data
                                                                            +

                                                                            store an object stored in the data field with the corresponding name. If an object with that name already exists then the object is overwritten.

                                                                            -
                                                                            set_variable_ub

                                                                            set the upper bounds on decision variables in + +

                                                                            set_variable_ub
                                                                            +

                                                                            set the upper bounds on decision variables in a pre-calculated optimization problem stored in the solver.

                                                                            -
                                                                            set_variable_lb

                                                                            set the lower bounds on decision variables in + +

                                                                            set_variable_lb
                                                                            +

                                                                            set the lower bounds on decision variables in a pre-calculated optimization problem stored in the solver.

                                                                            -
                                                                            calculate

                                                                            ingest a general purpose -OptimizationProblem object and convert it to the + +

                                                                            calculate
                                                                            +

                                                                            ingest a general purpose +OptimizationProblem object and convert it to the correct format for the solver.

                                                                            -
                                                                            run

                                                                            run the solver and output a solution

                                                                            -
                                                                            solve

                                                                            solve an OptimizationProblem using this +

                                                                            run
                                                                            +

                                                                            run the solver and output a solution

                                                                            + + +
                                                                            solve
                                                                            +

                                                                            solve an OptimizationProblem using this object.

                                                                            -
                                                                            +
                                                                            +
                                                                          -
                                                                        - - - - - - - - - - + diff --git a/docs/reference/Target-class.html b/docs/reference/Target-class.html index 2cfff2e6b..cd9a20a55 100644 --- a/docs/reference/Target-class.html +++ b/docs/reference/Target-class.html @@ -1,105 +1,22 @@ - - - - - - - -Target prototype — Target-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Target prototype — Target-class • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
                                                                        -
                                                                        -

                                                                        Target prototype

                                                                        - Source: R/Target-proto.R + Source: R/Target-proto.R

                                                                        This prototype is used to represent the targets used when making a prioritization. This prototype inherits from the -ConservationModifier. This class represents a +ConservationModifier. This class represents a recipe, to actually add targets to a planning problem, see the help page on -targets. Only experts should use this class directly.

                                                                        +targets. Only experts should use this class directly.

                                                                        +
                                                                        Usage,NULL
                                                                        - -

                                                                        See also

                                                                        - -

                                                                        ConservationModifier.

                                                                        +
                                                                        +

                                                                        See also

                                                                        +

                                                                        ConservationModifier.

                                                                        +
                                                                        +
                                                                        -
                                                                        - - - - - - - - - - + diff --git a/docs/reference/add_absolute_targets.html b/docs/reference/add_absolute_targets.html index 6831c003f..06e98f64a 100644 --- a/docs/reference/add_absolute_targets.html +++ b/docs/reference/add_absolute_targets.html @@ -1,105 +1,22 @@ - - - - - - - -Add absolute targets — add_absolute_targets • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add absolute targets — add_absolute_targets • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
                                                                        -
                                                                        -

                                                                        Add absolute targets

                                                                        - Source: R/add_absolute_targets.R + Source: R/add_absolute_targets.R
                                                                        @@ -192,48 +109,43 @@

                                                                        Add absolute targets

                                                                        than 10.

                                                                        - 
                                                                        add_absolute_targets(x, targets)
-
-# S4 method for ConservationProblem,numeric
-add_absolute_targets(x, targets)
+    
                                                                        Usage,
                                                                        add_absolute_targets(x, targets)
 
-# S4 method for ConservationProblem,matrix
-add_absolute_targets(x, targets)
+# S4 method for ConservationProblem,numeric
+add_absolute_targets(x, targets)
 
-# S4 method for ConservationProblem,character
-add_absolute_targets(x, targets)
                                                                        
+# S4 method for ConservationProblem,matrix
+add_absolute_targets(x, targets)
 
-    
                                                                        Arguments
                                                                        
-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
                                                                        x
                                                                        problem() (i.e. ConservationProblem) object.
                                                                        targets
                                                                        Object that specifies the targets for each feature.
-See the Targets format section for more information.
                                                                        
+# S4 method for ConservationProblem,character
+add_absolute_targets(x, targets)
                                                                        -

                                                                        Value

                                                                        - -

                                                                        Object (i.e. ConservationProblem) with the targets added +

                                                                        +

                                                                        Arguments

                                                                        +
                                                                        x
                                                                        +

                                                                        problem() (i.e., ConservationProblem) object.

                                                                        +
                                                                        targets
                                                                        +

                                                                        Object that specifies the targets for each feature. +See the Targets format section for more information.

                                                                        +
                                                                        +
                                                                        +

                                                                        Value

                                                                        +

                                                                        Object (i.e., ConservationProblem) with the targets added to it.

                                                                        -

                                                                        Details

                                                                        - +
                                                                        +
                                                                        +

                                                                        Details

                                                                        Targets are used to specify the minimum amount or proportion of a feature's distribution that needs to be protected. Most conservation planning problems require targets with the exception of the maximum cover -(see add_max_cover_objective()) and maximum utility -(see add_max_utility_objective()) problems. Attempting to solve +(see add_max_cover_objective()) and maximum utility +(see add_max_utility_objective()) problems. Attempting to solve problems with objectives that require targets without specifying targets will throw an error.

                                                                        For problems associated with multiple management zones, this function can be used to set targets that each pertain to a single feature and a single zone. To set targets which can be met through allocating different -planning units to multiple zones, see the add_manual_targets() +planning units to multiple zones, see the add_manual_targets() function. An example of a target that could be met through allocations to multiple zones might be where each management zone is expected to result in a different amount of a feature and the target requires that @@ -244,154 +156,156 @@

                                                                        Details potentially, be met through allocating all planning units to any specific management zone, or through allocating the planning units to different combinations of management zones.

                                                                        -

                                                                        Targets format

                                                                        - +
                                                                        +
                                                                        +

                                                                        Targets format

                                                                        The targets for a problem can be specified using the following formats.

                                                                        -
                                                                        - -
                                                                        targets as a numeric vector

                                                                        containing target values for each +

                                                                        targets as a numeric vector
                                                                        +

                                                                        containing target values for each feature. Additionally, for convenience, this format can be a single value to assign the same target to each feature. Note that this format cannot be used to specify targets for problems with multiple zones.

                                                                        -
                                                                        targets as a matrix object

                                                                        containing a target for each feature + +

                                                                        targets as a matrix object
                                                                        +

                                                                        containing a target for each feature in each zone. Here, each row corresponds to a different feature in argument to x, each column corresponds to a different zone in argument to x, and each cell contains the target value for a given feature that the solution needs to secure in a given zone.

                                                                        -
                                                                        targets as a character vector

                                                                        containing the names of fields + +

                                                                        targets as a character vector
                                                                        +

                                                                        containing the names of fields (columns) in the feature data associated with the argument to x that contain targets. This format can only be used when the feature data associated with x is a data.frame. This argument must contain a field (column) name for each zone.

                                                                        -
                                                                        - -

                                                                        See also

                                                                        -

                                                                        See targets for an overview of all functions for adding targets.

                                                                        +
                                                                        +
                                                                        +

                                                                        See also

                                                                        +

                                                                        See targets for an overview of all functions for adding targets.

                                                                        Other targets: -add_loglinear_targets(), -add_manual_targets(), -add_relative_targets()

                                                                        +add_loglinear_targets(), +add_manual_targets(), +add_relative_targets()

                                                                        +
                                                                        -

                                                                        Examples

                                                                        - 
                                                                        # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create simple problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_binary_decisions() %>%
-     add_default_solver(verbose = FALSE)
-
-# create problem with targets to secure 3 amounts for each feature
-p1 <- p %>% add_absolute_targets(3)
-
-# create problem with varying targets for each feature
-targets <- c(1, 2, 3, 2, 1)
-p2 <- p %>% add_absolute_targets(targets)
-# \dontrun{
-# solve problem
-s <- stack(solve(p1), solve(p2))
-
-# plot solution
-plot(s, main = c("equal targets", "varying targets"), axes = FALSE,
-     box = FALSE)
-
-# }
-
-# create a problem with multiple management zones
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create a problem with targets that specify an equal amount of each feature
-# to be represented in each zone
-p4_targets <- matrix(2, nrow = number_of_features(sim_features_zones),
-                     ncol = number_of_zones(sim_features_zones),
-                     dimnames = list(feature_names(sim_features_zones),
-                                     zone_names(sim_features_zones)))
-print(p4_targets)
-#>           zone_1 zone_2 zone_3
-#> feature_1      2      2      2
-#> feature_2      2      2      2
-#> feature_3      2      2      2
-#> feature_4      2      2      2
-#> feature_5      2      2      2
-
-p4 <- p3 %>% add_absolute_targets(p4_targets)
-
-# solve problem
-# \dontrun{
-# solve problem
-s4 <- solve(p4)
-
-# plot solution (pixel values correspond to zone identifiers)
-plot(category_layer(s4), main = c("equal targets"))
-
-# }
-# create a problem with targets that require a varying amount of each
-# feature to be represented in each zone
-p5_targets <- matrix(rpois(15, 1),
-                     nrow = number_of_features(sim_features_zones),
-                     ncol = number_of_zones(sim_features_zones),
-                     dimnames = list(feature_names(sim_features_zones),
-                                     zone_names(sim_features_zones)))
-print(p5_targets)
-#>           zone_1 zone_2 zone_3
-#> feature_1      2      0      0
-#> feature_2      1      1      2
-#> feature_3      3      3      2
-#> feature_4      1      2      0
-#> feature_5      2      1      1
-
-p5 <- p3 %>% add_absolute_targets(p4_targets)
-# solve problem
-# \dontrun{
-# solve problem
-s5 <- solve(p5)
-
-# plot solution (pixel values correspond to zone identifiers)
-plot(category_layer(s5), main = c("varying targets"))
-
-# }
-
+    
                                                                        
+    
                                                                        Examples
                                                                        
+    
                                                                        # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create simple problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_binary_decisions() %>%
+     add_default_solver(verbose = FALSE)
+
+# create problem with targets to secure 3 amounts for each feature
+p1 <- p %>% add_absolute_targets(3)
+
+# create problem with varying targets for each feature
+targets <- c(1, 2, 3, 2, 1)
+p2 <- p %>% add_absolute_targets(targets)
+# \dontrun{
+# solve problem
+s <- stack(solve(p1), solve(p2))
+
+# plot solution
+plot(s, main = c("equal targets", "varying targets"), axes = FALSE,
+     box = FALSE)
+
+# }
+
+# create a problem with multiple management zones
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create a problem with targets that specify an equal amount of each feature
+# to be represented in each zone
+p4_targets <- matrix(2, nrow = number_of_features(sim_features_zones),
+                     ncol = number_of_zones(sim_features_zones),
+                     dimnames = list(feature_names(sim_features_zones),
+                                     zone_names(sim_features_zones)))
+print(p4_targets)
+#>           zone_1 zone_2 zone_3
+#> feature_1      2      2      2
+#> feature_2      2      2      2
+#> feature_3      2      2      2
+#> feature_4      2      2      2
+#> feature_5      2      2      2
+
+p4 <- p3 %>% add_absolute_targets(p4_targets)
+
+# solve problem
+# \dontrun{
+# solve problem
+s4 <- solve(p4)
+
+# plot solution (pixel values correspond to zone identifiers)
+plot(category_layer(s4), main = c("equal targets"))
+
+# }
+# create a problem with targets that require a varying amount of each
+# feature to be represented in each zone
+p5_targets <- matrix(rpois(15, 1),
+                     nrow = number_of_features(sim_features_zones),
+                     ncol = number_of_zones(sim_features_zones),
+                     dimnames = list(feature_names(sim_features_zones),
+                                     zone_names(sim_features_zones)))
+print(p5_targets)
+#>           zone_1 zone_2 zone_3
+#> feature_1      2      0      0
+#> feature_2      1      1      2
+#> feature_3      3      3      2
+#> feature_4      1      2      0
+#> feature_5      2      1      1
+
+p5 <- p3 %>% add_absolute_targets(p4_targets)
+# solve problem
+# \dontrun{
+# solve problem
+s5 <- solve(p5)
+
+# plot solution (pixel values correspond to zone identifiers)
+plot(category_layer(s5), main = c("varying targets"))
+
+# }
+
 
                                                                        
+
                                                                        +
                                                                    -
                                                                    - - - - - - - - - - + diff --git a/docs/reference/add_binary_decisions.html b/docs/reference/add_binary_decisions.html index 49f1b5b3e..9ad03482e 100644 --- a/docs/reference/add_binary_decisions.html +++ b/docs/reference/add_binary_decisions.html @@ -1,105 +1,22 @@ - - - - - - - -Add binary decisions — add_binary_decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add binary decisions — add_binary_decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
                                                                    -
                                                                    -

                                                                    Add binary decisions

                                                                    - Source: R/add_binary_decisions.R + Source: R/add_binary_decisions.R
                                                                    -

                                                                    Add a binary decision to a conservation planning problem(). +

                                                                    Add a binary decision to a conservation planning problem(). This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem then this decision class will be used by default.

                                                                    - 
                                                                    add_binary_decisions(x)
                                                                    - -

                                                                    Arguments

                                                                    - - - - - - -
                                                                    x

                                                                    problem() (i.e. ConservationProblem) object.

                                                                    +
                                                                    Usage,
                                                                    add_binary_decisions(x)
                                                                    -

                                                                    Value

                                                                    - -

                                                                    Object (i.e. ConservationProblem) with the decisions added +

                                                                    +

                                                                    Arguments

                                                                    +
                                                                    x
                                                                    +

                                                                    problem() (i.e., ConservationProblem) object.

                                                                    +
                                                                    +
                                                                    +

                                                                    Value

                                                                    +

                                                                    Object (i.e., ConservationProblem) with the decisions added to it.

                                                                    -

                                                                    Details

                                                                    - +
                                                                    +
                                                                    +

                                                                    Details

                                                                    Conservation planning problems involve making decisions on planning -units. These decisions are then associated with actions (e.g. turning a +units. These decisions are then associated with actions (e.g., turning a planning unit into a protected area). Only a single decision should be added to a ConservationProblem object. Note that if multiple decisions are added to a problem object, then the last one to be added will be used.

                                                                    -

                                                                    See also

                                                                    - -

                                                                    See decisions for an overview of all functions for adding decisions.

                                                                    +
                                                                    +
                                                                    +

                                                                    See also

                                                                    +

                                                                    See decisions for an overview of all functions for adding decisions.

                                                                    Other decisions: -add_default_decisions(), -add_proportion_decisions(), -add_semicontinuous_decisions()

                                                                    +add_default_decisions(), +add_proportion_decisions(), +add_semicontinuous_decisions()

                                                                    +
                                                                    -

                                                                    Examples

                                                                    - 
                                                                    # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem with binary decisions
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution")
-
-# }
-# build multi-zone conservation problem with binary decisions
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s2 <- solve(p2)
-
-# print solution
-print(s2)
-#> class      : RasterStack 
-#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> names      : zone_1, zone_2, zone_3 
-#> min values :      0,      0,      0 
-#> max values :      1,      1,      1 
-#> 
-
-# plot solution
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
                                                                    
+    
                                                                    Examples
                                                                    
+    
                                                                    # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem with binary decisions
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution")
+
+# }
+# build multi-zone conservation problem with binary decisions
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s2 <- solve(p2)
+
+# print solution
+print(s2)
+#> class      : RasterStack 
+#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> names      : zone_1, zone_2, zone_3 
+#> min values :      0,      0,      0 
+#> max values :      1,      1,      1 
+#> 
+
+# plot solution
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
                                                                    
+
                                                                    +
                                                                    -
                                                                    - - - - - - - - - - + diff --git a/docs/reference/add_boundary_penalties.html b/docs/reference/add_boundary_penalties.html index da9b544a9..4d28a6a60 100644 --- a/docs/reference/add_boundary_penalties.html +++ b/docs/reference/add_boundary_penalties.html @@ -1,103 +1,20 @@ - - - - - - - -Add boundary penalties — add_boundary_penalties • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add boundary penalties — add_boundary_penalties • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
                                                                    -
                                                                    -

                                                                    Add boundary penalties

                                                                    - Source: R/add_boundary_penalties.R + Source: R/add_boundary_penalties.R
                                                                    -

                                                                    Add penalties to a conservation planning problem() to favor solutions +

                                                                    Add penalties to a conservation planning problem() to favor solutions that spatially clump planning units together based on the overall boundary length (perimeter).

                                                                    - 
                                                                    add_boundary_penalties(
-  x,
-  penalty,
-  edge_factor = rep(0.5, number_of_zones(x)),
-  zones = diag(number_of_zones(x)),
-  data = NULL
-)
                                                                    - -

                                                                    Arguments

                                                                    - - - - - - - - - - - - - - - - - - - - - - -
                                                                    x

                                                                    problem() (i.e. ConservationProblem) object.

                                                                    penalty

                                                                    numeric penalty that is used to scale the importance +

                                                                    Usage,
                                                                    add_boundary_penalties(
+  x,
+  penalty,
+  edge_factor = rep(0.5, number_of_zones(x)),
+  zones = diag(number_of_zones(x)),
+  data = NULL
+)
                                                                    + +
                                                                    +

                                                                    Arguments

                                                                    +
                                                                    x
                                                                    +

                                                                    problem() (i.e., ConservationProblem) object.

                                                                    +
                                                                    penalty
                                                                    +

                                                                    numeric penalty that is used to scale the importance of selecting planning units that are spatially clumped together compared -to the main problem objective (e.g. solution cost when the argument to -x has a minimum set objective per add_min_set_objective()). +to the main problem objective (e.g., solution cost when the argument to +x has a minimum set objective per add_min_set_objective()). Higher penalty values prefer solutions with a higher degree of spatial clumping, and smaller penalty values prefer solutions with a smaller degree of clumping. Note that negative penalty values prefer solutions that are more spread out. This parameter is equivalent to the boundary length modifier (BLM) -parameter in Marxan.

                                                                    edge_factor

                                                                    numeric proportion to scale +parameter in Marxan.

                                                                    +
                                                                    edge_factor
                                                                    +

                                                                    numeric proportion to scale planning unit edges (borders) that do not have any neighboring planning units. For example, an edge factor of 0.5 is commonly used to avoid overly penalizing planning units along a coastline. Note that this argument must have an element for each zone in the argument -to x.

                                                                    zones

                                                                    matrix or Matrix object describing the +to x.

                                                                    +
                                                                    zones
                                                                    +

                                                                    matrix or Matrix object describing the clumping scheme for different zones. Each row and column corresponds to a different zone in the argument to x, and cell values indicate the relative importance of clumping planning units that are allocated to @@ -236,78 +145,79 @@

                                                                    Arg allocated to the same zone. Cell values must range between 1 and -1, where negative values favor solutions that spread out planning units. The default argument to zones is an identity -matrix (i.e. a matrix with ones along the matrix diagonal and zeros +matrix (i.e., a matrix with ones along the matrix diagonal and zeros elsewhere), so that penalties are incurred when neighboring planning units are not assigned to the same zone. If the cells along the matrix diagonal contain markedly smaller values than those found elsewhere in the matrix, then solutions are preferred that surround planning units with those allocated to different zones -(i.e. greater spatial fragmentation).

                                                                    data

                                                                    NULL, data.frame, matrix, or Matrix +(i.e., greater spatial fragmentation).

                                                                    +
                                                                    data
                                                                    +

                                                                    NULL, data.frame, matrix, or Matrix object containing the boundary data. These data describe the total amount of boundary (perimeter) length for each planning unit, and the amount of boundary (perimeter) length shared between different -planning units (i.e. planning units that are adjacent to each other). -See the Data format section for more information.

                                                                    - -

                                                                    Value

                                                                    - -

                                                                    Object (i.e. ConservationProblem) with the penalties +planning units (i.e., planning units that are adjacent to each other). +See the Data format section for more information.

    -
    - - - - -
    -
    -
    -

    Management Zones

    - - - Source: vignettes/zones.Rmd - - -
    - - - -
    -

    -Introduction

    -

    One of the main aims in conservation planning is to identify the most cost-effective set of areas to manage biodiversity (Margules & Pressey 2000). To achieve this, prioritizations are generally created to identify areas for expanding protected area systems. However, many real-world conservation problems do not simply involve deciding if an area should be protected or not (e.g. Klein et al. 2009; Stigner et al. 2016). Instead, many real-world problems involve a range of different management categories and the goal is to determine which areas should be allocated to which management category. For example, a manager might have a range of different methods (e.g. baiting or trapping at various intensities) for controlling invasive pests in a set of different areas (e.g. Cattarino et al. 2018). They would need a prioritization that shows which control methods should be implemented in which areas. In this particular case, a binary prioritization showing which areas contain the most biodiversity is simply not helpful. Furthermore, many real-world problems require decisions that meet multiple, and sometimes conflicting, objectives from different stakeholders. For example, a manager might need to implement a set of no-take and partial-take areas to prevent overfishing, but also ensure that there still remain plenty of areas for fishing activities (e.g. Wilson et al. 2010; Klein et al. 2013). Popularized by Marxan with Zones (Watts et al. 2009), this concept has become known as “zones” and is becoming increasingly important in conservation planning.

    -

    The aim of this vignette is to showcase the zones functionality of the prioritizr R package. It will assume a certain level of familiarity with conservation planning terminology and the prioritizr R package. We recommend reading the prioritizr vignette first if you don’t have much experience in either of these topics.

    -
    -
    -

    -Usage

    -
    -

    -Simple minimum set problem

    -

    In the prioritizr R package, all conservation planning problems—including those which contain multiple management zones or actions—are initialized using the problem function. To refresh our memory on how we can construct problems using the prioritizr R package, let us quickly construct a simple conservation planning problem. This problem will use the simulated built-in planning unit and feature data distributed with the package. It will have a minimum set objective, targets which require that solution secure to 10 % of the habitat in the study area for each feature, and binary decision variables indicating that planning units are selected or not selected for protection.

    -
    -# load prioritizr package
-library(prioritizr)
    -
    ## Loading required package: raster
    -
    ## Loading required package: sp
    -
    ## Loading required package: sf
    -
    ## Linking to GEOS 3.9.0, GDAL 3.2.2, PROJ 7.2.1
    -
    ## Loading required package: proto
    -
    -# load data
-data(sim_pu_raster, sim_features)
-
-# create targets for each of the five features
-t1 <- rep(0.1, 5)
-
-# build single-zone problem
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(t1) %>%
-      add_binary_decisions()
-
-# print problem
-print(p1)
    -
    ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
    -
    -# solve problem
-s1 <- solve(p1)
    -
    ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 5 rows, 90 columns and 450 nonzeros
-## Model fingerprint: 0x6442bf6e
-## Variable types: 0 continuous, 90 integer (90 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-01, 9e-01]
-##   Objective range  [2e+02, 2e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [3e+00, 8e+00]
-## Found heuristic solution: objective 2337.9617505
-## Presolve time: 0.00s
-## Presolved: 5 rows, 90 columns, 450 nonzeros
-## Variable types: 0 continuous, 90 integer (90 binary)
-## Found heuristic solution: objective 2332.1003790
-## Root relaxation presolved: 5 rows, 90 columns, 450 nonzeros
-## 
-## 
-## Root relaxation: objective 1.931582e+03, 12 iterations, 0.00 seconds (0.00 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 1931.58191    0    4 2332.10038 1931.58191  17.2%     -    0s
-## H    0     0                    1987.3985265 1931.58191  2.81%     -    0s
-## 
-## Explored 1 nodes (12 simplex iterations) in 0.00 seconds (0.00 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 3: 1987.4 2332.1 2337.96 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 1.987398526526e+03, best bound 1.931581908865e+03, gap 2.8085%
    -
    -# calculate feature representation
-r1 <- eval_feature_representation_summary(p1, s1)
-print(r1)
    -
    ## # A tibble: 5 × 5
-##   summary feature total_amount absolute_held relative_held
-##   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-## 1 overall layer.1         83.3          8.91         0.107
-## 2 overall layer.2         31.2          3.13         0.100
-## 3 overall layer.3         72.0          7.34         0.102
-## 4 overall layer.4         42.7          4.35         0.102
-## 5 overall layer.5         56.7          6.01         0.106
    -
    -# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
    -

    -
    -
    -

    -Adding management zones

    -

    Now let us imagine that instead of having a single management zone (e.g. protected area), we have two management zones. Similar to the example above, we require a solution that secures 10 % of the habitat in the study area for each feature in the first management zone. But we also require a solution that secures 5 % of the habitat in the study area for each feature in the second management zone. Each planning unit must be allocated to either zone or not selected for management at all. In this example, each planning unit costs the same when it is allocated to either of the two zones. We can formulate and solve this problem using the following code.

    -
    -# create a matrix with the targets
-# here each column corresponds to a different zone,
-# each row corresponds to a different feature, and
-# each cell value corresponds to the target
-t2 <- matrix(NA, ncol = 2, nrow = 5)
-t2[, 1] <- 0.1
-t2[, 2] <- 0.05
-
-# print targets
-print(t2)
    -
    ##      [,1] [,2]
-## [1,]  0.1 0.05
-## [2,]  0.1 0.05
-## [3,]  0.1 0.05
-## [4,]  0.1 0.05
-## [5,]  0.1 0.05
    -
    -# create a zones object that contains the amount of each feature
-# in each planning unit when it is allocated to each zone
-# since our zones pertain to the same habitat data, we will
-# to specify the same habitat data for each zone
-z2 <- zones("zone 1" = sim_features, "zone 2" = sim_features)
-
-# print zones
-print(z2)
    -
    ## Zones
-##   zones: zone 1, zone 2 (2 zones)
-##   features: 1, 2, 3, ... (5 features)
-##   data type: RasterStack
    -
    -# create a raster stack with the planning unit data
-# since our planning unit costs are the same for each zone,
-# we will create a stack with two replicates of the cost data
-pu2 <- stack(sim_pu_raster, sim_pu_raster)
-
-# print stack
-print(pu2)
    -
    ## class      : RasterStack 
-## dimensions : 10, 10, 100, 2  (nrow, ncol, ncell, nlayers)
-## resolution : 0.1, 0.1  (x, y)
-## extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-## crs        : NA 
-## names      :  layer.1,  layer.2 
-## min values : 190.1328, 190.1328 
-## max values : 215.8638, 215.8638
    -
    -# build two-zone problem
-p2 <- problem(pu2, z2) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(t2) %>%
-      add_binary_decisions()
-
-# print problem
-print(p2)
    -
    ## Conservation Problem
-##   zones:          zone 1, zone 2 (2 zones)
-##   planning units: RasterStack (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       1, 2, 3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.05, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
    -
    -# solve problem
-s2 <- solve(p2)
    -
    ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 100 rows, 180 columns and 1080 nonzeros
-## Model fingerprint: 0xbdab1647
-## Variable types: 0 continuous, 180 integer (180 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-01, 1e+00]
-##   Objective range  [2e+02, 2e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [1e+00, 8e+00]
-## Found heuristic solution: objective 3568.4931394
-## Presolve time: 0.00s
-## Presolved: 100 rows, 180 columns, 1080 nonzeros
-## Variable types: 0 continuous, 180 integer (180 binary)
-## Found heuristic solution: objective 3440.6550560
-## Root relaxation presolved: 100 rows, 180 columns, 1080 nonzeros
-## 
-## 
-## Root relaxation: objective 2.911333e+03, 80 iterations, 0.00 seconds (0.00 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 2911.33335    0   10 3440.65506 2911.33335  15.4%     -    0s
-## H    0     0                    3003.8743974 2911.33335  3.08%     -    0s
-## 
-## Explored 1 nodes (83 simplex iterations) in 0.00 seconds (0.00 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 3: 3003.87 3440.66 3568.49 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 3.003874397435e+03, best bound 2.911333350606e+03, gap 3.0807%
    -
    -# calculate feature representation
-r2 <- eval_feature_representation_summary(p2, s2)
-print(r2)
    -
    ## # A tibble: 15 × 5
-##    summary feature total_amount absolute_held relative_held
-##    <chr>   <chr>          <dbl>         <dbl>         <dbl>
-##  1 overall 1              167.          13.3         0.0799
-##  2 overall 2               62.4          4.75        0.0761
-##  3 overall 3              144.          10.9         0.0760
-##  4 overall 4               85.3          6.44        0.0755
-##  5 overall 5              113.           9.03        0.0796
-##  6 zone 1  1               83.3          8.87        0.106 
-##  7 zone 1  2               31.2          3.18        0.102 
-##  8 zone 1  3               72.0          7.22        0.100 
-##  9 zone 1  4               42.7          4.27        0.100 
-## 10 zone 1  5               56.7          6.07        0.107 
-## 11 zone 2  1               83.3          4.44        0.0533
-## 12 zone 2  2               31.2          1.57        0.0504
-## 13 zone 2  3               72.0          3.72        0.0517
-## 14 zone 2  4               42.7          2.17        0.0508
-## 15 zone 2  5               56.7          2.96        0.0521
    -
    -# plot solution
-# here we use the category layer function to generate raster showing the zone
-# that each planning unit was allocated. Specifically, pixels with the
-# value 1 are allocated to "zone 1" and pixels with the value 2 are allocated
-# to "zone 2". Thus units depicted in gray are not allocated
-# to any zone, units depicted in yellow are allocated to zone 1, and units
-# depicted in green are allocated to zone 2
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
    -

    -
    -
    -

    -Multiple zones with varying costs

    -

    Real-world problems often have different costs for managing planning units under different zones. These problems also tend to have different expected amounts of each feature when planning units are managed differently. So let us consider a slightly more complex example. Similar to before we will have two management zones. But this time, the cost of managing each planning unit is different depending on which management zone it is assigned to in the solution. Furthermore, when we assign a planning unit to the second zone, we only expect to end up with half of the habitat we would get if we managed the unit in the first zone (e.g. because the second zone is a partial-take zone and the first zone is a no-take zone). We will use the same target data as in the previous example.

    -
    -# create new planning unit and cost data
-data(sim_pu_zones_stack)
-pu3 <- sim_pu_zones_stack[[1:2]]
-
-# plot cost data
-plot(pu3, main = c("zone 1", "zone 2"), axes = FALSE, box = FALSE)
    -

    -
    -# create problem
-p3 <- problem(pu3, zones(sim_features, sim_features * 0.5)) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(t2) %>%
-      add_binary_decisions()
-
-# print problem
-print(p3)
    -
    ## Conservation Problem
-##   zones:          1, 2 (2 zones)
-##   planning units: RasterStack (90 units)
-##   cost:           min: 182.60173, max: 221.36296
-##   features:       1, 2, 3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.05, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
    -
    -# solve problem
-s3 <- solve(p3)
    -
    ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 100 rows, 180 columns and 1080 nonzeros
-## Model fingerprint: 0x07455a48
-## Variable types: 0 continuous, 180 integer (180 binary)
-## Coefficient statistics:
-##   Matrix range     [1e-01, 1e+00]
-##   Objective range  [2e+02, 2e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [8e-01, 8e+00]
-## Found heuristic solution: objective 3667.7708672
-## Presolve time: 0.00s
-## Presolved: 100 rows, 180 columns, 1080 nonzeros
-## Variable types: 0 continuous, 180 integer (180 binary)
-## Found heuristic solution: objective 3388.0248890
-## Root relaxation presolved: 100 rows, 180 columns, 1080 nonzeros
-## 
-## 
-## Root relaxation: objective 2.884872e+03, 38 iterations, 0.00 seconds (0.00 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 2884.87200    0    8 3388.02489 2884.87200  14.9%     -    0s
-## H    0     0                    2958.1201508 2884.87200  2.48%     -    0s
-## 
-## Explored 1 nodes (38 simplex iterations) in 0.00 seconds (0.00 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 3: 2958.12 3388.02 3667.77 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 2.958120150795e+03, best bound 2.884871999973e+03, gap 2.4762%
    -
    -# calculate feature representation
-r3 <- eval_feature_representation_summary(p3, s3)
-print(r3)
    -
    ## # A tibble: 15 × 5
-##    summary feature total_amount absolute_held relative_held
-##    <chr>   <chr>          <dbl>         <dbl>         <dbl>
-##  1 overall 1              125.         11.1          0.0891
-##  2 overall 2               46.8         3.92         0.0838
-##  3 overall 3              108.          9.28         0.0860
-##  4 overall 4               64.0         5.37         0.0839
-##  5 overall 5               85.1         7.46         0.0877
-##  6 1       1               83.3         8.94         0.107 
-##  7 1       2               31.2         3.13         0.100 
-##  8 1       3               72.0         7.42         0.103 
-##  9 1       4               42.7         4.29         0.101 
-## 10 1       5               56.7         6.01         0.106 
-## 11 2       1               41.6         2.19         0.0527
-## 12 2       2               15.6         0.794        0.0509
-## 13 2       3               36.0         1.87         0.0519
-## 14 2       4               21.3         1.08         0.0505
-## 15 2       5               28.4         1.44         0.0509
    -
    -# plot solution
-plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
    -

    -
    -
    -

    -Multiple zones with complex targets

    -

    So far, we have dealt with problems where each feature has a target that pertains to a single zone. But sometimes we have targets that pertain to multiple zones. For example, what if we were in charge of managing pest control in a set of areas and we had three different pest control methods we could implement in any given planning unit. We could (1) set up a few traps in a given planning unit and make 10 % of the habitat in the unit pest-free, (2) set up a lot of traps and make 50 % of the habitat in the unit pest-free, or (3) drop baits over a given planning unit and make 80 % of the planning unit pest-free. Each of these different actions has a different cost, with a few low intensity trapping costing $100 per planning unit, a high intensity trapping costing $300, and baiting costing $200 (please note these costs aren’t meant to be realistic). After defining our management actions and costs, we require a solution that will yield 8 units of pest free habitat per feature. It’s important to note that unlike the previous examples, here we don’t have targets for each feature in each zone, but rather our targets are for each feature and across multiple zones. In other words, we don’t really care which management actions we implement, we just want the set of actions that will meet our targets for minimum expenditure. We can formulate and solve this problem using the following code.

    -
    -# create planning unit data with costs
-pu4 <- stack(Which(!is.na(sim_pu_raster)) * 100,
-             Which(!is.na(sim_pu_raster)) * 300,
-             Which(!is.na(sim_pu_raster)) * 200)
-names(pu4) <- c("few.traps", "many.traps", "baiting")
-
-# plot planning unit data
-plot(pu4, nr = 1, axes = FALSE, box = FALSE)
    -

    -
    -# create targets
-t4 <- tibble::tibble(feature = names(sim_features),
-                     zone = list(names(pu4))[rep(1, 5)],
-                     target = rep(8, 5),
-                     type = rep("absolute", 5))
-
-# print targets
-print(t4)
    -
    ## # A tibble: 5 × 4
-##   feature zone      target type    
-##   <chr>   <list>     <dbl> <chr>   
-## 1 layer.1 <chr [3]>      8 absolute
-## 2 layer.2 <chr [3]>      8 absolute
-## 3 layer.3 <chr [3]>      8 absolute
-## 4 layer.4 <chr [3]>      8 absolute
-## 5 layer.5 <chr [3]>      8 absolute
    -
    -# create problem
-p4 <- problem(pu4, zones(few.traps = sim_features * 0.1,
-                         many.traps = sim_features * 0.5,
-                         baiting = sim_features * 0.8,
-                         feature_names = names(sim_features))) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(t4) %>%
-      add_binary_decisions()
-
-# print problem
-print(p4)
    -
    ## Conservation Problem
-##   zones:          few.traps, many.traps, baiting (3 zones)
-##   planning units: RasterStack (100 units)
-##   cost:           min: 0, max: 300
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Absolute targets [targets (min: 8, max: 8)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
    -
    -# solve problem
-s4 <- solve(p4)
    -
    ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 105 rows, 300 columns and 1800 nonzeros
-## Model fingerprint: 0xd67e7fdc
-## Variable types: 0 continuous, 300 integer (300 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-02, 1e+00]
-##   Objective range  [1e+02, 3e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [1e+00, 8e+00]
-## Found heuristic solution: objective 9400.0000000
-## Presolve removed 14 rows and 120 columns
-## Presolve time: 0.00s
-## Presolved: 91 rows, 180 columns, 360 nonzeros
-## Found heuristic solution: objective 4800.0000000
-## Variable types: 0 continuous, 180 integer (180 binary)
-## Root relaxation presolved: 91 rows, 180 columns, 360 nonzeros
-## 
-## 
-## Root relaxation: objective 3.663237e+03, 1 iterations, 0.00 seconds (0.00 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 3663.23657    0    1 4800.00000 3663.23657  23.7%     -    0s
-## H    0     0                    3800.0000000 3663.23657  3.60%     -    0s
-## 
-## Explored 1 nodes (1 simplex iterations) in 0.00 seconds (0.00 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 3: 3800 4800 9400 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 3.800000000000e+03, best bound 3.700000000000e+03, gap 2.6316%
    -
    -# calculate feature representation
-r4 <- eval_feature_representation_summary(p4, s4)
-print(r4)
    -
    ## # A tibble: 20 × 5
-##    summary    feature total_amount absolute_held relative_held
-##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
-##  1 overall    layer.1       117.           18.3          0.157
-##  2 overall    layer.2        43.7           8.19         0.187
-##  3 overall    layer.3       101.           15.2          0.151
-##  4 overall    layer.4        59.7          11.6          0.194
-##  5 overall    layer.5        79.4          12.7          0.161
-##  6 few.traps  layer.1         8.33          0            0    
-##  7 few.traps  layer.2         3.12          0            0    
-##  8 few.traps  layer.3         7.20          0            0    
-##  9 few.traps  layer.4         4.27          0            0    
-## 10 few.traps  layer.5         5.67          0            0    
-## 11 many.traps layer.1        41.6           0            0    
-## 12 many.traps layer.2        15.6           0            0    
-## 13 many.traps layer.3        36.0           0            0    
-## 14 many.traps layer.4        21.3           0            0    
-## 15 many.traps layer.5        28.4           0            0    
-## 16 baiting    layer.1        66.6          18.3          0.275
-## 17 baiting    layer.2        25.0           8.19         0.328
-## 18 baiting    layer.3        57.6          15.2          0.264
-## 19 baiting    layer.4        34.1          11.6          0.340
-## 20 baiting    layer.5        45.4          12.7          0.281
    -
    -# plot solution
-plot(category_layer(s4), main = "solution", axes = FALSE, box = FALSE)
    -

    -
    -
    -

    -Multiple zones with extra constraints

    -

    So it looks like baiting is the way to go! Except that we might recall that we can’t use baits in most of the planning units because they contain native species that are susceptible to baits. So now we need to specify that which of our planning units cannot be assigned to the third zone (baiting) to obtain a more useful solution.

    -
    -# create data.frame to specify that we cannot bait in the first 40 units
-l5 <- data.frame(pu = seq(1, 80),
-                 zone = "baiting",
-                 status = 0)
-
-# preview locked data
-head(l5)
    -
    ##   pu    zone status
-## 1  1 baiting      0
-## 2  2 baiting      0
-## 3  3 baiting      0
-## 4  4 baiting      0
-## 5  5 baiting      0
-## 6  6 baiting      0
    -
    -# create problem
-p5 <- problem(pu4, zones(few.traps = sim_features * 0.1,
-                         many.traps = sim_features * 0.5,
-                         baiting = sim_features * 0.8,
-                         feature_names = names(sim_features))) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(t4) %>%
-      add_manual_locked_constraints(l5) %>%
-      add_binary_decisions()
-
-# print problem
-print(p5)
    -
    ## Conservation Problem
-##   zones:          few.traps, many.traps, baiting (3 zones)
-##   planning units: RasterStack (100 units)
-##   cost:           min: 0, max: 300
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Absolute targets [targets (min: 8, max: 8)]
-##   decisions:      Binary decision 
-##   constraints:    <Manually locked planning units [80 locked units]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
    -
    -# solve problem
-s5 <- solve(p5)
    -
    ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 105 rows, 300 columns and 1800 nonzeros
-## Model fingerprint: 0x4ad99e4b
-## Variable types: 0 continuous, 300 integer (300 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-02, 1e+00]
-##   Objective range  [1e+02, 3e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [1e+00, 8e+00]
-## Found heuristic solution: objective 13600.000000
-## Presolve removed 14 rows and 120 columns
-## Presolve time: 0.00s
-## Presolved: 91 rows, 180 columns, 360 nonzeros
-## Found heuristic solution: objective 9600.0000000
-## Variable types: 0 continuous, 180 integer (180 binary)
-## Root relaxation presolved: 91 rows, 180 columns, 360 nonzeros
-## 
-## 
-## Root relaxation: objective 6.938068e+03, 1 iterations, 0.00 seconds (0.00 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 6938.06818    0    1 9600.00000 6938.06818  27.7%     -    0s
-## H    0     0                    7000.0000000 6938.06818  0.88%     -    0s
-##      0     0 6938.06818    0    1 7000.00000 6938.06818  0.88%     -    0s
-## 
-## Explored 1 nodes (1 simplex iterations) in 0.00 seconds (0.00 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 3: 7000 9600 13600 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 7.000000000000e+03, best bound 7.000000000000e+03, gap 0.0000%
    -
    -# calculate feature representation
-r5 <- eval_feature_representation_summary(p5, s5)
-print(r5)
    -
    ## # A tibble: 20 × 5
-##    summary    feature total_amount absolute_held relative_held
-##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
-##  1 overall    layer.1       117.           21.8          0.187
-##  2 overall    layer.2        43.7           8.04         0.184
-##  3 overall    layer.3       101.           17.7          0.176
-##  4 overall    layer.4        59.7          10.9          0.182
-##  5 overall    layer.5        79.4          15.2          0.192
-##  6 few.traps  layer.1         8.33          0            0    
-##  7 few.traps  layer.2         3.12          0            0    
-##  8 few.traps  layer.3         7.20          0            0    
-##  9 few.traps  layer.4         4.27          0            0    
-## 10 few.traps  layer.5         5.67          0            0    
-## 11 many.traps layer.1        41.6           7.40         0.178
-## 12 many.traps layer.2        15.6           3.42         0.219
-## 13 many.traps layer.3        36.0           6.00         0.167
-## 14 many.traps layer.4        21.3           4.84         0.227
-## 15 many.traps layer.5        28.4           5.26         0.186
-## 16 baiting    layer.1        66.6          14.4          0.217
-## 17 baiting    layer.2        25.0           4.62         0.185
-## 18 baiting    layer.3        57.6          11.7          0.203
-## 19 baiting    layer.4        34.1           6.05         0.177
-## 20 baiting    layer.5        45.4           9.98         0.220
    -
    -# plot solution
-plot(category_layer(s5), main = "solution", axes = FALSE, box = FALSE)
    -

    -
    -
    -

    -Multiple zones with fragmentation penalties

    -

    So now the best strategy seems to be a combination of high intensity trapping and baiting. But we can also see that this solution is fairly fragmented, so we can add penalties to cluster managed planning units together. Here we will add penalties that will cluster the planning units allocated to the two trapping zones together, and penalties that will cluster the planning units allocated to the baiting zone together. We will also set an overall penalty factor to 640 to strongly penalize fragmented solutions.

    -
    -# create matrix that describe boundary penalties between planning units
-# allocated to different zones
-z6 <- diag(3)
-z6[1, 2] <- 1
-z6[2, 1] <- 1
-colnames(z6) <- c("few.traps", "many.traps", "baiting")
-rownames(z6) <- colnames(z6)
-
-# print matrix
-print(z6)
    -
    ##            few.traps many.traps baiting
-## few.traps          1          1       0
-## many.traps         1          1       0
-## baiting            0          0       1
    -
    -# create problem
-p6 <- problem(pu4, zones("few.traps" = sim_features * 0.1,
-                         "many.traps" = sim_features * 0.5,
-                         "baiting" = sim_features * 0.8,
-                         feature_names = names(sim_features))) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(t4) %>%
-      add_manual_locked_constraints(l5) %>%
-      add_boundary_penalties(penalty = 640, zones = z6) %>%
-      add_binary_decisions()
-
-# print problem
-print(p6)
    -
    ## Conservation Problem
-##   zones:          few.traps, many.traps, baiting (3 zones)
-##   planning units: RasterStack (100 units)
-##   cost:           min: 0, max: 300
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Absolute targets [targets (min: 8, max: 8)]
-##   decisions:      Binary decision 
-##   constraints:    <Manually locked planning units [80 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (640), zones]>
-##   portfolio:      default
-##   solver:         default
    -
    -# solve problem
-s6 <- solve(p6)
    -
    ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 1905 rows, 1200 columns and 5400 nonzeros
-## Model fingerprint: 0xb44cc86f
-## Variable types: 0 continuous, 1200 integer (1200 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-02, 1e+00]
-##   Objective range  [1e+02, 6e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [1e+00, 8e+00]
-## Found heuristic solution: objective 20096.000000
-## Presolve removed 1028 rows and 232 columns
-## Presolve time: 0.01s
-## Presolved: 877 rows, 968 columns, 2712 nonzeros
-## Variable types: 0 continuous, 968 integer (968 binary)
-## Found heuristic solution: objective 19632.000000
-## Root relaxation presolved: 877 rows, 968 columns, 2712 nonzeros
-## 
-## 
-## Root relaxation: objective 1.005410e+04, 569 iterations, 0.01 seconds (0.01 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 10054.0986    0   57 19632.0000 10054.0986  48.8%     -    0s
-## H    0     0                    11300.000000 10054.0986  11.0%     -    0s
-## H    0     0                    10588.000000 10054.0986  5.04%     -    0s
-## 
-## Explored 1 nodes (819 simplex iterations) in 0.02 seconds (0.03 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 4: 10588 11300 19632 20096 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 1.058800000000e+04, best bound 1.005600000000e+04, gap 5.0246%
    -
    -# calculate feature representation
-r6 <- eval_feature_representation_summary(p6, s6)
-print(r6)
    -
    ## # A tibble: 20 × 5
-##    summary    feature total_amount absolute_held relative_held
-##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
-##  1 overall    layer.1       117.           22.5          0.193
-##  2 overall    layer.2        43.7           8.06         0.184
-##  3 overall    layer.3       101.           18.0          0.179
-##  4 overall    layer.4        59.7          11.6          0.193
-##  5 overall    layer.5        79.4          15.6          0.197
-##  6 few.traps  layer.1         8.33          0            0    
-##  7 few.traps  layer.2         3.12          0            0    
-##  8 few.traps  layer.3         7.20          0            0    
-##  9 few.traps  layer.4         4.27          0            0    
-## 10 few.traps  layer.5         5.67          0            0    
-## 11 many.traps layer.1        41.6           8.01         0.192
-## 12 many.traps layer.2        15.6           3.44         0.221
-## 13 many.traps layer.3        36.0           6.31         0.175
-## 14 many.traps layer.4        21.3           5.50         0.258
-## 15 many.traps layer.5        28.4           5.62         0.198
-## 16 baiting    layer.1        66.6          14.4          0.217
-## 17 baiting    layer.2        25.0           4.62         0.185
-## 18 baiting    layer.3        57.6          11.7          0.203
-## 19 baiting    layer.4        34.1           6.05         0.177
-## 20 baiting    layer.5        45.4           9.98         0.220
    -
    -# plot solution
-plot(category_layer(s6), main = "solution", axes = FALSE, box = FALSE)
    -

    -

    Finally, it appears we might have a viable solution for this made-up conservation problem.

    -
    -
    -

    -Multiple zones with fragmentation penalties and mandatory allocations

    -

    Finally, we might be interested in conservation planning scenarios where every single planning unit must be allocated to a management zone. This is often the case when developing land-use plans where every single planning unit needs to be allocated to a specific management zone. Though it makes less sense here, let’s see what happens to the solution if we needed to do at least one form of control in every single planning unit.

    -
    -# create matrix that describe boundary penalties between planning units
-# allocated to different zones
-p7 <- problem(pu4, zones("few.traps" = sim_features * 0.1,
-                         "many.traps" = sim_features * 0.5,
-                         "baiting" = sim_features * 0.8,
-                         feature_names = names(sim_features))) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(t4) %>%
-      add_mandatory_allocation_constraints() %>%
-      add_manual_locked_constraints(l5) %>%
-      add_boundary_penalties(penalty = 640, zones = z6) %>%
-      add_binary_decisions()
-
-# print problem
-print(p7)
    -
    ## Conservation Problem
-##   zones:          few.traps, many.traps, baiting (3 zones)
-##   planning units: RasterStack (100 units)
-##   cost:           min: 0, max: 300
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Absolute targets [targets (min: 8, max: 8)]
-##   decisions:      Binary decision 
-##   constraints:    <Mandatory allocation constraints [apply constraints? (1)]
-##                    Manually locked planning units [80 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (640), zones]>
-##   portfolio:      default
-##   solver:         default
    -
    -# solve problem
-s7 <- solve(p7)
    -
    ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 1905 rows, 1200 columns and 5400 nonzeros
-## Model fingerprint: 0x89a9dafb
-## Variable types: 0 continuous, 1200 integer (1200 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-02, 1e+00]
-##   Objective range  [1e+02, 6e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [1e+00, 8e+00]
-## Found heuristic solution: objective 19600.000000
-## Presolve removed 1120 rows and 324 columns
-## Presolve time: 0.01s
-## Presolved: 785 rows, 876 columns, 2448 nonzeros
-## Variable types: 0 continuous, 876 integer (876 binary)
-## Found heuristic solution: objective 18988.000000
-## Root relaxation presolved: 785 rows, 876 columns, 2448 nonzeros
-## 
-## 
-## Root relaxation: objective 1.323093e+04, 274 iterations, 0.00 seconds (0.00 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 13230.9255    0   95 18988.0000 13230.9255  30.3%     -    0s
-## H    0     0                    13260.000000 13230.9255  0.22%     -    0s
-## 
-## Explored 1 nodes (412 simplex iterations) in 0.02 seconds (0.03 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 3: 13260 18988 19600 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 1.326000000000e+04, best bound 1.323200000000e+04, gap 0.2112%
    -
    -# calculate feature representation
-r7 <- eval_feature_representation_summary(p7, s7)
-print(r7)
    -
    ## # A tibble: 20 × 5
-##    summary    feature total_amount absolute_held relative_held
-##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
-##  1 overall    layer.1       117.           23.4         0.201 
-##  2 overall    layer.2        43.7           8.04        0.184 
-##  3 overall    layer.3       101.           19.4         0.192 
-##  4 overall    layer.4        59.7          10.9         0.182 
-##  5 overall    layer.5        79.4          16.1         0.203 
-##  6 few.traps  layer.1         8.33          5.92        0.711 
-##  7 few.traps  layer.2         3.12          2.33        0.745 
-##  8 few.traps  layer.3         7.20          5.25        0.730 
-##  9 few.traps  layer.4         4.27          3.18        0.745 
-## 10 few.traps  layer.5         5.67          4.00        0.706 
-## 11 many.traps layer.1        41.6           3.02        0.0725
-## 12 many.traps layer.2        15.6           1.09        0.0700
-## 13 many.traps layer.3        36.0           2.41        0.0670
-## 14 many.traps layer.4        21.3           1.66        0.0779
-## 15 many.traps layer.5        28.4           2.11        0.0743
-## 16 baiting    layer.1        66.6          14.4         0.217 
-## 17 baiting    layer.2        25.0           4.62        0.185 
-## 18 baiting    layer.3        57.6          11.7         0.203 
-## 19 baiting    layer.4        34.1           6.05        0.177 
-## 20 baiting    layer.5        45.4           9.98        0.220
    -
    -# plot solution
-plot(category_layer(s7), main = "solution", axes = FALSE, box = FALSE)
    -

    -
    -
    -
    -

    -Conclusion

    -

    Hopefully, this vignette has provided an informative introduction to building and solving problems with multiple zones using the prioritizr R package. Although we have examined only a few different functions here, almost every single function for modifying conservation planning problems is compatible with problems that contain zones. It’s worth noting that working with multiple zones is a lot trickier than working with a single zone, so we would recommend playing around with the code in the Examples sections of the help pages to get a feel for what different functions do when they are applied to problems with multiple zones.

    -
    -
    -

    -References

    -
    -
    -Cattarino, L., Hermoso, V., Carwardine, J., Adams, V.M., Kennard, M.J. & Linke, S. (2018). Information uncertainty influences conservation outcomes when prioritizing multi-action management efforts. Journal of Applied Ecology, Available at: https://doi.org/10.1111/1365–2664.13147. -
    -
    -Klein, C.J., Tulloch, V.J., Halpern, B.S., Selkoe, K.A., Watts, M.E., Steinback, C., Scholz, A. & Possingham, H.P. (2013). Tradeoffs in marine reserve design: Habitat condition, representation, and socioeconomic costs. Conservation Letters, 6, 324–332. -
    -
    -Klein, C., Wilson, K., Watts, M., Stein, J., Berry, S., Carwardine, J., Smith, M.S., Mackey, B. & Possingham, H. (2009). Incorporating ecological and evolutionary processes into continental-scale conservation planning. Ecological Applications, 19, 206–217. -
    -
    -Margules, C.R. & Pressey, R.L. (2000). Systematic conservation planning. Nature, 405, 243–253. -
    -
    -Stigner, M.G., Beyer, H.L., Klein, C.J. & Fuller, R.A. (2016). Reconciling recreational use and conservation values in a coastal protected area. Journal of Applied Ecology, 53, 1206–1214. -
    -
    -Watts, M.E., Ball, I.R., Stewart, R.S., Klein, C.J., Wilson, K., Steinback, C., Lourival, R., Kircher, L. & Possingham, H.P. (2009). Marxan with Zones: Software for optimal conservation based land- and sea-use zoning. Environmental Modelling & Software, 24, 1513–1521. -
    -
    -Wilson, K.A., Meijaard, E., Drummond, S., Grantham, H.S., Boitani, L., Catullo, G., Christie, L., Dennis, R., Dutton, I., Falcucci, A. & others. (2010). Conserving biodiversity in production landscapes. Ecological Applications, 20, 1721–1732. -
    -
    -
    -
    - - - -
    - - - - -
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    - - - - -
    -
    -
    -

    Tasmania Tutorial

    - - - Source: vignettes/tasmania.Rmd - - -
    - - - -
    -

    -Introduction

    -

    The aim of this tutorial is to provide a worked example of how vector-based data can be used to develop conservation prioritizations using the prioritizr R package. It is also written for conservation planners that have used the Marxan decision support tool (Ball et al. 2009) and are interested in applying the prioritizr R package to their own work. The dataset used in this tutorial was obtained from the Introduction to Marxan course. This data was originally a subset of a larger spatial prioritization project performed under contract to Australia’s Department of Environment and Water Resources (Klein et al. 2007).

    -

    Please note that this tutorial uses data from the prioritizrdata R, so ensure that it is installed before trying out the code yourself.

    -
    -
    -

    -Exploring the data

    -

    This dataset contains two items. First, a spatial planning unit layer that has an attribute table which contains three columns: integer unique identifiers (“id”), unimproved land values (“cost”), and their existing level of protection (“status”). Units with 50 % or more of their area contained in protected areas are associated with a status of 2, otherwise they are associated with a value of 0. If you are familiar with the Marxan decision support tool, then you will notice that these columns are formatted in a similar manner to the input data for Marxan. For Marxan input data, planning units must be described in a table containing one row for each planning unit with a unique identifier and the corresponding cost.

    -

    The second item in this dataset is the raster-based feature data. Specifically, the feature data is expressed as a stack of rasters (termed a RasterStack object). Here each layer in the stack represents the distribution of a different vegetation class in Tasmania, Australia. There are 62 vegetation classes in total. For a given layer, pixel values indicate the presence (value of 1) or absence (value of 0) of the vegetation class in an area.

    -

    First, load the required packages and the data.

    -
    -# load packages
-library(prioritizrdata)
-library(prioritizr)
-
-# load planning unit data
-data(tas_pu)
-
-# load conservation feature data
-data(tas_features)
    -

    Now, let’s have a look at the planning unit data.

    -
    -# print planning unit data
-print(tas_pu)
    -
    ## class       : SpatialPolygonsDataFrame 
-## features    : 1130 
-## extent      : 298809.6, 613818.8, 5167775, 5502544  (xmin, xmax, ymin, ymax)
-## crs         : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
-## variables   : 5
-## names       :   id,              cost, status, locked_in, locked_out 
-## min values  :    1, 0.192488262910798,      0,         0,          0 
-## max values  : 1130,  61.9272727272727,      2,         1,          0
    -
    -# plot map of planning unit costs
-plot(st_as_sf(tas_pu[, "cost"]), main = "Planning unit costs")
    -

    -

    Next, let examine the feature data. Here we will only plot the first four features as an example. The pixel values denote the presence or absence of each feature within the extent of the study area.

    -
    -# print planning unit data
-print(tas_features)
    -
    ## class      : RasterStack 
-## dimensions : 398, 359, 142882, 62  (nrow, ncol, ncell, nlayers)
-## resolution : 1000, 1000  (x, y)
-## extent     : 288801.7, 647801.7, 5142976, 5540976  (xmin, xmax, ymin, ymax)
-## crs        : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
-## names      : tas_features.1, tas_features.2, tas_features.3, tas_features.4, tas_features.5, tas_features.6, tas_features.7, tas_features.8, tas_features.9, tas_features.10, tas_features.11, tas_features.12, tas_features.13, tas_features.14, tas_features.15, ... 
-## min values :              0,              0,              0,              0,              0,              0,              0,              0,              0,               0,               0,               0,               0,               0,               0, ... 
-## max values :              1,              1,              1,              1,              1,              1,              1,              1,              1,               1,               1,               1,               1,               1,               1, ...
    -
    -# plot map of the first four vegetation classes
-plot(tas_features[[1:4]], main = paste("Feature", 1:4))
    -

    -

    The planning units in this example are a spatial polygon layer—not a raster—and so there can be considerable flexibility in the shape of the planning units. That said, there is a trade-off with the efficiency of data pre-processing in vector-based planning unit data compared to raster-based planning unit data. Vector-based planning unit data generally require more time to complete pre-processing computations (e.g. overlaying the planning unit data with the feature data, or generating boundary data). As a consequence, we generally recommend using raster-based planning unit data where possible to reduce processing time—but note that this is not possible when not all planning units are equal-sized squares. Another strategy is to complete the pre-processing in other software environments (e.g. ArcGIS) and use the pre-processed data directly with the prioritizr package.

    -
    -
    -

    -Marxan problem formulation

    -

    Here, we will provide an example of using the marxan_problem function to build and solve a typical Marxan conservation planning problem. Then we will show how this same problem can be built and solved using the fully customizable problem function as a comparison.

    -

    The dataset used in this example follows many of the conventions used by the Marxan decision support tool. As a consequence, it is not too difficult to format the data for use with the marxan_problem function. The marxan_problem function is essentially a wrapper to the problem function. This means that when we solve problems created using the marxan_problem function, we will solve them using exact algorithms and not the simulated annealing algorithm used by Marxan.

    -

    All problem objects formulated with marxan_problem use the minimum set objective. Targets can be either relative or absolute, and planning units can be specified for masking in or out using the locked_in and locked_out arguments. To favor clumped solutions, use the penalty argument to impose a penalty on solutions with high boundary lengths (equivalent to the Boundary Length Modifier (BLM) used in Marxan), and the edge_factor argument to scale the penalty for edges that do not have neighboring planning units, such as the coastline. For simplicity we set all of the targets at the same level, 17 %, to reflect the Aichi biodiversity target to “safeguard” at least 17% of terrestrial ecosystems by 2020. For example, to prioritize planning units in Tasmania that meet the 17 % representation target at the least cost.

    -

    First, we will convert the vector-based planning unit data and raster-based feature data into the tabular formats required by the marxan_problem function. These formats are very similar to the formats used by Marxan.

    -
    -# create table with planning unit data
-pu_data <- tas_pu@data
-
-# print first six rows
-head(pu_data)
    -
    ##   id     cost status locked_in locked_out
-## 0  1 60.24638      0     FALSE      FALSE
-## 1  2 19.86301      0     FALSE      FALSE
-## 2  3 59.68051      0     FALSE      FALSE
-## 3  4 32.41614      0     FALSE      FALSE
-## 4  5 26.17706      0     FALSE      FALSE
-## 5  6 51.26218      0     FALSE      FALSE
    -
    -# create table with the feature identifiers, names, and targets
-spec_data <- data.frame(id = seq_len(nlayers(tas_features)),
-                        name = paste0("veg", seq_len(nlayers(tas_features))),
-                        prop = 0.17)
-
-# print first six rows
-head(spec_data)
    -
    ##   id name prop
-## 1  1 veg1 0.17
-## 2  2 veg2 0.17
-## 3  3 veg3 0.17
-## 4  4 veg4 0.17
-## 5  5 veg5 0.17
-## 6  6 veg6 0.17
    -
    -# create table with the planning unit vs. feature data
-puvspr_data <- rij_matrix(tas_pu, tas_features)
-puvspr_data <- as(puvspr_data, "dgTMatrix")
-puvspr_data <- data.frame(pu = puvspr_data@j + 1, species = puvspr_data@i + 1,
-                          amount = puvspr_data@x)
-
-# print first six rows
-head(puvspr_data)
    -
    ##   pu species       amount
-## 1  3      54 1.000000e+00
-## 2  3      59 1.165971e+01
-## 3  5      30 1.000000e+00
-## 4  6      27 1.000000e+00
-## 5  6      35 1.000000e+00
-## 6  6      59 3.635182e-05
    -
    -# create table with the boundary data
-bound_data <- boundary_matrix(tas_pu)
-bound_data <- as(bound_data, "dgTMatrix")
-bound_data <- data.frame(id1 = bound_data@i + 1, id2 = bound_data@j + 1,
-                         boundary = bound_data@x)
-# print first six rows
-head(bound_data)
    -
    ##   id1 id2   boundary
-## 1   1   1  6314.6621
-## 2   3   1  3922.9264
-## 3   6   1   150.3778
-## 4   2   2 23958.6982
-## 5   4   2  3233.3056
-## 6   7   2  4639.9220
    -

    Now that we have converted the data to tabular format, we can use the marxan_problem function to create a conservation planning problem.

    -
    -# create problem
-p1 <- marxan_problem(pu_data, spec_data, puvspr_data, bound_data,
-                     blm = 0.0005)
-
-# print problem
-print(p1)
    -
    ## Conservation Problem
-##   planning units: data.frame (1130 units)
-##   cost:           min: 0.19249, max: 61.92727
-##   features:       veg1, veg2, veg3, ... (62 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      default
-##   constraints:    <Locked in planning units [257 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (5e-04), zones]>
-##   portfolio:      default
-##   solver:         default
    -

    Next, we can solve the problem (see ?solve for more information). The prioritizr R package supports three different exact algorithm software packages: gurobi, Rsymphony, and lpsymphony. There are costs and benefits associated with each of these different solvers, but each software should return similar results. Note that you will need at least one of these package installed on your system to solve problems. We recommend using the gurobi solver if possible, and have used this solver when building this tutorial. After solving the problem, we will calculate some statistics to describe the solution. Note that the planning unit selections are stored in the “solution_1” column of the solution object.

    -
    -# solve problem
-s1 <- solve(p1)
    -
    ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 6358 rows, 4278 columns and 14496 nonzeros
-## Model fingerprint: 0x96b70d15
-## Variable types: 0 continuous, 4278 integer (4278 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-06, 4e+01]
-##   Objective range  [5e-02, 2e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [1e-01, 1e+02]
-## Found heuristic solution: objective 30263.129158
-## Found heuristic solution: objective 12512.071934
-## Presolve removed 3428 rows and 2241 columns
-## Presolve time: 0.03s
-## Presolved: 2930 rows, 2037 columns, 6882 nonzeros
-## Found heuristic solution: objective 11751.436316
-## Variable types: 0 continuous, 2037 integer (2037 binary)
-## Found heuristic solution: objective 11425.978431
-## Root relaxation presolved: 2930 rows, 2037 columns, 6882 nonzeros
-## 
-## 
-## Root relaxation: objective 1.081359e+04, 715 iterations, 0.02 seconds (0.03 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 10813.5861    0  135 11425.9784 10813.5861  5.36%     -    0s
-## 
-## Explored 1 nodes (715 simplex iterations) in 0.05 seconds (0.08 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 4: 11426 11751.4 12512.1 30263.1 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 1.142597843052e+04, best bound 1.081358611386e+04, gap 5.3596%
    -
    -# print first six rows of solution object
-head(s1)
    -
    ##   id     cost status locked_in locked_out solution_1
-## 0  1 60.24638      0     FALSE      FALSE          0
-## 1  2 19.86301      0     FALSE      FALSE          0
-## 2  3 59.68051      0     FALSE      FALSE          0
-## 3  4 32.41614      0     FALSE      FALSE          0
-## 4  5 26.17706      0     FALSE      FALSE          0
-## 5  6 51.26218      0     FALSE      FALSE          0
    -
    -# count number of planning units in solution
-sum(s1$solution_1)
    -
    ## [1] 315
    -
    -# proportion of planning units in solution
-mean(s1$solution_1)
    -
    ## [1] 0.2787611
    -
    -# calculate feature representation
-r1 <- eval_feature_representation_summary(p1, s1[, "solution_1", drop = FALSE])
-print(r1)
    -
    ## # A tibble: 62 × 5
-##    summary feature total_amount absolute_held relative_held
-##    <chr>   <chr>          <dbl>         <dbl>         <dbl>
-##  1 overall veg1            33.9          5.97         0.176
-##  2 overall veg2           170.          42.8          0.252
-##  3 overall veg3            24.0          5.63         0.235
-##  4 overall veg4            32.8          8.37         0.256
-##  5 overall veg5            24.8          4.98         0.201
-##  6 overall veg6            22.0          7.10         0.323
-##  7 overall veg7            16.4          3.06         0.187
-##  8 overall veg8            43.0          8.12         0.189
-##  9 overall veg9           388.          78.9          0.203
-## 10 overall veg10           14.5          4.02         0.277
-## # … with 52 more rows
    -
    -# visualize the solution by converting the solution to a spatial object
-s1 <- SpatialPolygonsDataFrame(as(tas_pu, "SpatialPolygons"), data = s1)
-s1$solution_1 <- factor(s1$solution_1)
-plot(st_as_sf(s1[, "solution_1"]), pal = c("grey90", "darkgreen"),
-    main = "marxan_problem solution")
    -

    -
    -
    -

    -General problem formulation

    -

    Now we will formulate the exact same problem using the problem function and the spatially referenced data. We recommend using this approach instead of the marxan_problem because it is more verbose and you can specify exactly how the conservation planning problem should be formulated.

    -
    -# build problem
-p2 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_locked_in_constraints("locked_in") %>%
-      add_binary_decisions() %>%
-      add_boundary_penalties(penalty = 0.0005, edge_factor = 1)
-
-# print the problem
-print(p2)
    -
    ## Conservation Problem
-##   planning units: SpatialPolygonsDataFrame (1130 units)
-##   cost:           min: 0.19249, max: 61.92727
-##   features:       tas_features.1, tas_features.2, tas_features.3, ... (62 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      Binary decision 
-##   constraints:    <Locked in planning units [257 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (5e-04), zones]>
-##   portfolio:      default
-##   solver:         default
    -
    -# solve problem
-s2 <- solve(p2)
    -
    ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 6358 rows, 4278 columns and 14496 nonzeros
-## Model fingerprint: 0x96b70d15
-## Variable types: 0 continuous, 4278 integer (4278 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-06, 4e+01]
-##   Objective range  [5e-02, 2e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [1e-01, 1e+02]
-## Found heuristic solution: objective 30263.129158
-## Found heuristic solution: objective 12512.071934
-## Presolve removed 3428 rows and 2241 columns
-## Presolve time: 0.03s
-## Presolved: 2930 rows, 2037 columns, 6882 nonzeros
-## Found heuristic solution: objective 11751.436316
-## Variable types: 0 continuous, 2037 integer (2037 binary)
-## Found heuristic solution: objective 11425.978431
-## Root relaxation presolved: 2930 rows, 2037 columns, 6882 nonzeros
-## 
-## 
-## Root relaxation: objective 1.081359e+04, 715 iterations, 0.02 seconds (0.03 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 10813.5861    0  135 11425.9784 10813.5861  5.36%     -    0s
-## 
-## Explored 1 nodes (715 simplex iterations) in 0.06 seconds (0.08 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 4: 11426 11751.4 12512.1 30263.1 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 1.142597843052e+04, best bound 1.081358611386e+04, gap 5.3596%
    -
    -# calculate feature representation
-r2 <- eval_feature_representation_summary(p2, s2[, "solution_1"])
-print(r2)
    -
    ## # A tibble: 62 × 5
-##    summary feature         total_amount absolute_held relative_held
-##    <chr>   <chr>                  <dbl>         <dbl>         <dbl>
-##  1 overall tas_features.1          33.9          5.97         0.176
-##  2 overall tas_features.2         170.          42.8          0.252
-##  3 overall tas_features.3          24.0          5.63         0.235
-##  4 overall tas_features.4          32.8          8.37         0.256
-##  5 overall tas_features.5          24.8          4.98         0.201
-##  6 overall tas_features.6          22.0          7.10         0.323
-##  7 overall tas_features.7          16.4          3.06         0.187
-##  8 overall tas_features.8          43.0          8.12         0.189
-##  9 overall tas_features.9         388.          78.9          0.203
-## 10 overall tas_features.10         14.5          4.02         0.277
-## # … with 52 more rows
    -
    -# visualize solution
-s2$solution_1 <- factor(s2$solution_1)
-plot(st_as_sf(s2[, "solution_1"]), pal = c("grey90", "darkgreen"),
-    main = "problem solution")
    -

    -
    -
    -

    -Selection frequencies

    -

    Similar to the Marxan decision support tool, we can generate a portfolio of solutions and compute the planning unit selection frequencies to understand their relative importance. This can be useful when trying to understand which planning units in the solution are the most irreplaceable. To do this, we will create a portfolio containing 1000 solutions within 20% of optimality, and calculate the number of times that each planning unit was selected. Note that this requires the Gurobi software to be installed.

    -
    -# create new problem with a portfolio added to it
-p3 <- p2 %>%
-      add_gap_portfolio(number_solutions = 1000, pool_gap = 0.2)
-
-# print problem
-print(p3)
    -
    ## Conservation Problem
-##   planning units: SpatialPolygonsDataFrame (1130 units)
-##   cost:           min: 0.19249, max: 61.92727
-##   features:       tas_features.1, tas_features.2, tas_features.3, ... (62 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      Binary decision 
-##   constraints:    <Locked in planning units [257 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (5e-04), zones]>
-##   portfolio:      Gap portfolio [number_solutions (1000), pool_gap (0.2)]
-##   solver:         default
    -
    -# generate solutions
-s3 <- solve(p3)
-
-# find column numbers with the solutions
-solution_columns <- which(grepl("solution", names(s3)))
-
-# calculate selection frequencies
-s3$selection_frequencies <- rowSums(as.matrix(s3@data[, solution_columns]))
    -
    -# plot first four solutions in the portfolio
-s3$solution_1 <- factor(s3$solution_1)
-s3$solution_2 <- factor(s3$solution_2)
-s3$solution_3 <- factor(s3$solution_3)
-s3$solution_4 <- factor(s3$solution_4)
-plot(st_as_sf(s3[, c("solution_1", "solution_2", "solution_3", "solution_4")]),
-  pal = c("grey90", "darkgreen"))
    -

    -
    -# plot histogram of selection frequencies
-hist(s3$selection_frequencies, main = "Selection frequencies",
-     xlab = "Number of times units were selected")
    -

    -
    -# plot spatial distribution of the selection frequencies
-plot(st_as_sf(s3[, "selection_frequencies"]), main = "Selection frequencies")
    -

    -
    -
    -

    -References

    -
    -
    -Ball, I.R., Possingham, H. & Watts, M.E. (2009). Marxan and relatives: Software for spatial conservation prioritisation. Spatial Conservation Prioritisation: Quantitative Methods & Computational Tools (eds A. Moilanen, K.A. Wilson & H. Possingham), pp. 185–189. Oxford University Press, Oxford, UK. -
    -
    -Klein, C., Carwardine, J., Wilson, K., Watts, M. & Possingham, H. (2007). Spatial Prioritization Approaches for the Conservation of Biodiversity in Australia: Considering Conservation Costs, Ecological & Evolutionary Processes, and Large-Intact Areas. Report to the Department of Environment; Water Resources. -
    -
    -
    -
    - - - -
    - - - - -

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--- a/docs/articles/solver_benchmark_files/header-attrs-2.11/header-attrs.js +++ /dev/null @@ -1,12 +0,0 @@ -// Pandoc 2.9 adds attributes on both header and div. 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    +
    +

    Value

    +

    Object (i.e., ConservationProblem) with the penalties added to it.

    -

    Details

    - +
    +
    +

    Details

    This function adds penalties to a conservation planning problem to penalize fragmented solutions. It was is inspired by Ball et al. (2009) and Beyer et al. (2016). The penalty argument is equivalent to the boundary length modifier (BLM) used in -Marxan. +Marxan. Note that this function can only be used to represent symmetric relationships between planning units. If asymmetric relationships are required, use the -add_connectivity_penalties() function.

    -

    Data format

    - +add_connectivity_penalties() function.

    +
    +
    +

    Data format

    The argument to data can be specified using the following formats. Note that boundary data must always describe symmetric relationships between planning units.

    -
    - -
    data as a NULL value

    indicating that the data should be -automatically calculated using the boundary_matrix() function. +

    data as a NULL value
    +

    indicating that the data should be +automatically calculated using the boundary_matrix() function. This argument is the default. Note that the boundary data must be supplied using one of the other formats below if the planning unit data in the argument to x do not explicitly contain spatial information -(e.g. planning unit data are a data.frame or numeric class).

    +(e.g., planning unit data are a data.frame or numeric class).

    -
    data as a matrix/Matrix object

    where rows and columns represent + +

    data as a matrix/Matrix object
    +

    where rows and columns represent different planning units and the value of each cell represents the amount of shared boundary length between two different planning units. Cells that occur along the matrix diagonal represent the amount of exposed boundary associated with each planning unit that has -no neighbor (e.g. these value might pertain to boundaries along a +no neighbor (e.g., these value might pertain to boundaries along a coastline).

    -
    data as a data.frame object

    with the columns "id1", + +

    data as a data.frame object
    +

    with the columns "id1", "id2", and "boundary". The "id1" and "id2" columns contain identifiers (indices) for a pair of planning units, and the "boundary" column contains the amount of shared boundary length between these two planning units. This format follows the the standard Marxan format for boundary -data (i.e. per the "bound.dat" file).

    +data (i.e., per the "bound.dat" file).

    -
    - -

    Mathematical formulation

    +
    +
    +

    Mathematical formulation

    The boundary penalties are implemented using the following equations. Let @@ -315,11 +225,11 @@

    boundary_matrix()), and \(W_{zz}\) represent the matrix argument to zones.

    $$ \sum_{i}^{I} \sum_{j}^{I} \sum_{z}^{Z} (\mathit{ifelse}(i == j, E_z, 1) @@ -329,8 +239,9 @@

    References

    - +
    +
    +

    References

    Ball IR, Possingham HP, and Watts M (2009) Marxan and relatives: Software for spatial conservation prioritisation in Spatial conservation prioritisation: Quantitative methods and computational tools. Eds Moilanen @@ -338,152 +249,151 @@

    R

    Beyer HL, Dujardin Y, Watts ME, and Possingham HP (2016) Solving conservation planning problems with integer linear programming. Ecological Modelling, 228: 14--22.

    -

    See also

    - -

    See penalties for an overview of all functions for adding penalties.

    +
    +
    +

    See also

    +

    See penalties for an overview of all functions for adding penalties.

    Other penalties: -add_connectivity_penalties(), -add_feature_weights(), -add_linear_penalties()

    +add_connectivity_penalties(), +add_feature_weights(), +add_linear_penalties()

    +
    -

    Examples

    - 
    # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with low boundary penalties
-p2 <- p1 %>% add_boundary_penalties(50, 1)
-
-# create problem with high boundary penalties but outer edges receive
-# half the penalty as inner edges
-p3 <- p1 %>% add_boundary_penalties(500, 0.5)
-
-# create a problem using precomputed boundary data
-bmat <- boundary_matrix(sim_pu_raster)
-p4 <- p1 %>% add_boundary_penalties(50, 1, data = bmat)
-
-# \dontrun{
-# solve problems
-s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
-
-# plot solutions
-plot(s, main = c("basic solution", "small penalties", "high penalties",
-                 "precomputed data"), axes = FALSE, box = FALSE)
-
-# }
-# create minimal problem with multiple zones and limit the run-time for
-# solver to 10 seconds so this example doesn't take too long
-p5 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(0.2, nrow = 5, ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(time_limit = 10, verbose = FALSE)
-
-# create zone matrix which favors clumping planning units that are
-# allocated to the same zone together - note that this is the default
-zm6 <- diag(3)
-print(zm6)
-#>      [,1] [,2] [,3]
-#> [1,]    1    0    0
-#> [2,]    0    1    0
-#> [3,]    0    0    1
-
-# create problem with the zone matrix and low penalties
-p6 <- p5 %>% add_boundary_penalties(50, zone = zm6)
-
-# create another problem with the same zone matrix and higher penalties
-p7 <- p5 %>% add_boundary_penalties(500, zone = zm6)
-
-# create zone matrix which favors clumping units that are allocated to
-# different zones together
-zm8 <- matrix(1, ncol = 3, nrow = 3)
-diag(zm8) <- 0
-print(zm8)
-#>      [,1] [,2] [,3]
-#> [1,]    0    1    1
-#> [2,]    1    0    1
-#> [3,]    1    1    0
-
-# create problem with the zone matrix
-p8 <- p5 %>% add_boundary_penalties(500, zone = zm8)
-
-# create zone matrix which strongly favors clumping units
-# that are allocated to the same zone together. It will also prefer
-# clumping planning units in zones 1 and 2 together over having
-# these planning units with no neighbors in the solution
-zm9 <- diag(3)
-zm9[upper.tri(zm9)] <- c(0.3, 0, 0)
-zm9[lower.tri(zm9)] <- zm9[upper.tri(zm9)]
-print(zm9)
-#>      [,1] [,2] [,3]
-#> [1,]  1.0  0.3    0
-#> [2,]  0.3  1.0    0
-#> [3,]  0.0  0.0    1
-
-# create problem with the zone matrix
-p9 <- p5 %>% add_boundary_penalties(500, zone = zm9)
-
-# create zone matrix which favors clumping planning units in zones 1 and 2
-# together, and favors planning units in zone 3 being spread out
-# (i.e. negative clumping)
-zm10 <- diag(3)
-zm10[3, 3] <- -1
-print(zm10)
-#>      [,1] [,2] [,3]
-#> [1,]    1    0    0
-#> [2,]    0    1    0
-#> [3,]    0    0   -1
-
-# create problem with the zone matrix
-p10 <- p5 %>% add_boundary_penalties(500, zone = zm10)
-
-# \dontrun{
-# solve problems
-s2 <- stack(category_layer(solve(p5)), category_layer(solve(p6)),
-            category_layer(solve(p7)), category_layer(solve(p8)),
-            category_layer(solve(p9)), category_layer(solve(p10)))
-
-# plot solutions
-plot(s2, main = c("basic solution", "within zone clumping (low)",
-                  "within zone clumping (high)", "between zone clumping",
-                  "within + between clumping", "negative clumping"),
-     axes = FALSE, box = FALSE)
-
-# }
+    
    
+    
    Examples
    
+    
    # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with low boundary penalties
+p2 <- p1 %>% add_boundary_penalties(50, 1)
+
+# create problem with high boundary penalties but outer edges receive
+# half the penalty as inner edges
+p3 <- p1 %>% add_boundary_penalties(500, 0.5)
+
+# create a problem using precomputed boundary data
+bmat <- boundary_matrix(sim_pu_raster)
+p4 <- p1 %>% add_boundary_penalties(50, 1, data = bmat)
+
+# \dontrun{
+# solve problems
+s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
+
+# plot solutions
+plot(s, main = c("basic solution", "small penalties", "high penalties",
+                 "precomputed data"), axes = FALSE, box = FALSE)
+
+# }
+# create minimal problem with multiple zones and limit the run-time for
+# solver to 10 seconds so this example doesn't take too long
+p5 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(0.2, nrow = 5, ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(time_limit = 10, verbose = FALSE)
+
+# create zone matrix which favors clumping planning units that are
+# allocated to the same zone together - note that this is the default
+zm6 <- diag(3)
+print(zm6)
+#>      [,1] [,2] [,3]
+#> [1,]    1    0    0
+#> [2,]    0    1    0
+#> [3,]    0    0    1
+
+# create problem with the zone matrix and low penalties
+p6 <- p5 %>% add_boundary_penalties(50, zone = zm6)
+
+# create another problem with the same zone matrix and higher penalties
+p7 <- p5 %>% add_boundary_penalties(500, zone = zm6)
+
+# create zone matrix which favors clumping units that are allocated to
+# different zones together
+zm8 <- matrix(1, ncol = 3, nrow = 3)
+diag(zm8) <- 0
+print(zm8)
+#>      [,1] [,2] [,3]
+#> [1,]    0    1    1
+#> [2,]    1    0    1
+#> [3,]    1    1    0
+
+# create problem with the zone matrix
+p8 <- p5 %>% add_boundary_penalties(500, zone = zm8)
+
+# create zone matrix which strongly favors clumping units
+# that are allocated to the same zone together. It will also prefer
+# clumping planning units in zones 1 and 2 together over having
+# these planning units with no neighbors in the solution
+zm9 <- diag(3)
+zm9[upper.tri(zm9)] <- c(0.3, 0, 0)
+zm9[lower.tri(zm9)] <- zm9[upper.tri(zm9)]
+print(zm9)
+#>      [,1] [,2] [,3]
+#> [1,]  1.0  0.3    0
+#> [2,]  0.3  1.0    0
+#> [3,]  0.0  0.0    1
+
+# create problem with the zone matrix
+p9 <- p5 %>% add_boundary_penalties(500, zone = zm9)
+
+# create zone matrix which favors clumping planning units in zones 1 and 2
+# together, and favors planning units in zone 3 being spread out
+# (i.e., negative clumping)
+zm10 <- diag(3)
+zm10[3, 3] <- -1
+print(zm10)
+#>      [,1] [,2] [,3]
+#> [1,]    1    0    0
+#> [2,]    0    1    0
+#> [3,]    0    0   -1
+
+# create problem with the zone matrix
+p10 <- p5 %>% add_boundary_penalties(500, zone = zm10)
+
+# \dontrun{
+# solve problems
+s2 <- stack(category_layer(solve(p5)), category_layer(solve(p6)),
+            category_layer(solve(p7)), category_layer(solve(p8)),
+            category_layer(solve(p9)), category_layer(solve(p10)))
+
+# plot solutions
+plot(s2, main = c("basic solution", "within zone clumping (low)",
+                  "within zone clumping (high)", "between zone clumping",
+                  "within + between clumping", "negative clumping"),
+     axes = FALSE, box = FALSE)
+
+# }
 
    
+
    +
    -
    - - - - - - - - - - + diff --git a/docs/reference/add_cbc_solver.html b/docs/reference/add_cbc_solver.html index 00b97e4a8..6abea23eb 100644 --- a/docs/reference/add_cbc_solver.html +++ b/docs/reference/add_cbc_solver.html @@ -1,108 +1,25 @@ - - - - - - - -Add a CBC solver — add_cbc_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a CBC solver — add_cbc_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
    -
    -

    Add a CBC solver

    - Source: R/add_cbc_solver.R + Source: R/add_cbc_solver.R
    -

    Specify that the CBC +

    Specify that the CBC (COIN-OR branch and cut) software (Forrest & Lougee-Heimer 2005) should be used to solve a conservation planning -problem(). +problem(). This function can also be used to customize the behavior of the solver. It requires the rcbc package to be installed -(only available on GitHub, +(only available on GitHub, see below for installation instructions).

    - 
    add_cbc_solver(
-  x,
-  gap = 0.1,
-  time_limit = .Machine$integer.max,
-  presolve = TRUE,
-  threads = 1,
-  first_feasible = FALSE,
-  start_solution = NULL,
-  verbose = TRUE
-)
    - -

    Arguments

    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    x

    problem() (i.e. ConservationProblem) object.

    gap

    numeric gap to optimality. This gap is relative +

    Usage,
    add_cbc_solver(
+  x,
+  gap = 0.1,
+  time_limit = .Machine$integer.max,
+  presolve = TRUE,
+  threads = 1,
+  first_feasible = FALSE,
+  start_solution = NULL,
+  verbose = TRUE
+)
    + +
    +

    Arguments

    +
    x
    +

    problem() (i.e., ConservationProblem) object.

    +
    gap
    +

    numeric gap to optimality. This gap is relative and expresses the acceptable deviance from the optimal objective. For example, a value of 0.01 will result in the solver stopping when it has found a solution within 1% of optimality. Additionally, a value of 0 will result in the solver stopping when it has found an optimal solution. -The default value is 0.1 (i.e. 10% from optimality).

    time_limit

    numeric time limit (seconds) for generating solutions. +The default value is 0.1 (i.e., 10% from optimality).

    +
    time_limit
    +

    numeric time limit (seconds) for generating solutions. The solver will return the current best solution when this time limit is exceeded. The default value is the largest integer value -(i.e. .Machine$integer.max), effectively meaning that solver -will keep running until a solution within the optimality gap is found.

    presolve

    logical attempt to simplify the -problem before solving it? Defaults to TRUE.

    threads

    integer number of threads to use for the -optimization algorithm. The default value is 1.

    first_feasible

    logical should the first feasible solution be +(i.e., .Machine$integer.max), effectively meaning that solver +will keep running until a solution within the optimality gap is found.

    +
    presolve
    +

    logical attempt to simplify the +problem before solving it? Defaults to TRUE.

    +
    threads
    +

    integer number of threads to use for the +optimization algorithm. The default value is 1.

    +
    first_feasible
    +

    logical should the first feasible solution be be returned? If first_feasible is set to TRUE, the solver will return the first solution it encounters that meets all the constraints, regardless of solution quality. Note that the first feasible solution is not an arbitrary solution, rather it is derived from the relaxed solution, and is therefore often reasonably close to optimality. -Defaults to FALSE.

    start_solution

    NULL or object containing the starting solution +Defaults to FALSE.

    +
    start_solution
    +

    NULL or object containing the starting solution for the solver. Defaults to NULL such that no starting solution is used. To specify a starting solution, the argument to start_solution should -be in the same format as the planning units (i.e. a NULL, numeric, -matrix, data.frame, Raster, Spatial, -or sf::sf() object). -See the Start solution format section for more information.

    verbose

    logical should information be printed while solving -optimization problems? Defaults to TRUE.

    - -

    Value

    - -

    Object (i.e. ConservationProblem) with the solver +be in the same format as the planning units (i.e., a NULL, numeric, +matrix, data.frame, Raster, Spatial, +or sf::sf() object). +See the Start solution format section for more information.

    +
    verbose
    +

    logical should information be printed while solving +optimization problems? Defaults to TRUE.

    +
    +
    +

    Value

    +

    Object (i.e., ConservationProblem) with the solver added to it.

    -

    Details

    - -

    CBC is an +

    +
    +

    Details

    +

    CBC is an open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. Although formal benchmarks examining the performance of this solver for conservation planning problems have yet to be completed, preliminary analyses suggest that it performs much faster than the other open-source -solvers (i.e. add_rsymphony_solver(), add_rsymphony_solver()), and +solvers (i.e., add_rsymphony_solver(), add_rsymphony_solver()), and so we recommend using this solver if the Gurobi and IBM CPLEX solvers are unavailable.

    -

    Installation

    - +
    +
    +

    Installation

    The rcbc package is required to use this solver. Since the rcbc package is not available on the the Comprehensive R Archive Network (CRAN), it must be installed from -its GitHub repository. To -install the rcbc package, please use the following code:

    if (!require(remotes)) install.packages("remotes")
-remotes::install_github("dirkschumacher/rcbc")
-
    +its GitHub repository. To +install the rcbc package, please use the following code:

    if (!require(remotes)) install.packages("remotes")
+remotes::install_github("dirkschumacher/rcbc")

    Note that you may also need to install several dependencies -- such as the -Rtools software +Rtools software or system libraries -- prior to installing the rcbc package. For further details on installing this package, please consult -official installation instructions for the package.

    -

    Start solution format

    - +official installation instructions for the package.

    +
    +
    +

    Start solution format

    Broadly speaking, the argument to start_solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

    -
    - -
    x has numeric planning units

    The argument to start_solution must be a +

    x has numeric planning units
    +

    The argument to start_solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to start_solution.

    -
    x has matrix planning units

    The argument to start_solution must be a + +

    x has matrix planning units
    +

    The argument to start_solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -329,8 +231,10 @@

    Raster planning units +

    The argument to start_solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -338,35 +242,41 @@

    sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

    -
    x has Spatial planning units

    The argument to start_solution -must be a Spatial object with each column corresponding to a + +

    x has Spatial planning units
    +

    The argument to start_solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to start_solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

    -
    x has sf::sf() planning units

    The argument to start_solution must be -a sf::sf() object with each column corresponding to a different + +

    x has sf::sf() planning units
    +

    The argument to start_solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to start_solution must also have the same @@ -375,85 +285,84 @@

    References

    +

    +
    +

    References

    Forrest J and Lougee-Heimer R (2005) CBC User Guide. In Emerging theory, Methods, and Applications (pp. 257--277). INFORMS, Catonsville, MD. -doi: 10.1287/educ.1053.0020 +doi: 10.1287/educ.1053.0020 .

    -

    See also

    - -

    See solvers for an overview of all functions for adding a solver.

    +
    +
    +

    See also

    +

    See solvers for an overview of all functions for adding a solver.

    Other solvers: -add_cplex_solver(), -add_default_solver(), -add_gurobi_solver(), -add_lsymphony_solver, -add_rsymphony_solver()

    +add_cplex_solver(), +add_default_solver(), +add_gurobi_solver(), +add_lsymphony_solver, +add_rsymphony_solver()

    +
    -

    Examples

    - 
    # \dontrun{
-# load data
-data(sim_pu_raster, sim_features)
-
-# create problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.1) %>%
-     add_binary_decisions() %>%
-     add_cbc_solver(gap = 0, verbose = FALSE)
-
-# generate solution %>%
-s <- solve(p)
-
-# plot solution
-plot(s, main = "solution", axes = FALSE, box = FALSE)
-
-
-# create a similar problem with boundary length penalties and
-# specify the solution from the previous run as a starting solution
-p2 <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.1) %>%
-     add_boundary_penalties(10) %>%
-     add_binary_decisions() %>%
-     add_cbc_solver(gap = 0, start_solution = s, verbose = FALSE)
-
-# generate solution
-s2 <- solve(p2)
-
-# plot solution
-plot(s2, main = "solution with boundary penalties", axes = FALSE,
-     box = FALSE)
-
-# }
+    
    
+    
    Examples
    
+    
    # \dontrun{
+# load data
+data(sim_pu_raster, sim_features)
+
+# create problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.1) %>%
+     add_binary_decisions() %>%
+     add_cbc_solver(gap = 0, verbose = FALSE)
+
+# generate solution %>%
+s <- solve(p)
+
+# plot solution
+plot(s, main = "solution", axes = FALSE, box = FALSE)
+
+
+# create a similar problem with boundary length penalties and
+# specify the solution from the previous run as a starting solution
+p2 <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.1) %>%
+     add_boundary_penalties(10) %>%
+     add_binary_decisions() %>%
+     add_cbc_solver(gap = 0, start_solution = s, verbose = FALSE)
+
+# generate solution
+s2 <- solve(p2)
+
+# plot solution
+plot(s2, main = "solution with boundary penalties", axes = FALSE,
+     box = FALSE)
+
+# }
 
    
+
    +
    -
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zxUj(X+{ZAaQYJ;&oM;$9N*7GLKrwT%-a}0Jp|f@)3FDw=i60${VJ|QR4xEUfW=kSw zJ|PC*+-7NA-fHHIQ&nv+sye$C8+;4n{T2-vIJe4>D=&48#nwuQJB;RHJY|k6xwhtc ztnTaK4pG(lxPsDt&pSmBcbsqpD6huMO@L4Wkmuq!?@Xg7^#+bxqTmpDr-&9dBdGP| zRGN;huS}TS;*4tE$B7GV0;^qULnu_eU$it6Z5^`3@vAf_C=xZAziieyVRus3kJg4s zl*g1&tsw0hpX z+1t4Hg19WDB$8lQZ=2eRlZgk;PGf$CUG?PiEbNOhGb@-qd;+>X=I!7jw>=`u!i=^ - - - - - - -Add connectivity penalties — add_connectivity_penalties • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add connectivity penalties — add_connectivity_penalties • prioritizr - - - - - - - - - - - - - - +

      -
      -

      Add connectivity penalties

      - Source: R/add_connectivity_penalties.R + Source: R/add_connectivity_penalties.R
      -

      Add penalties to a conservation planning problem() to favor +

      Add penalties to a conservation planning problem() to favor solutions that select planning units with high connectivity between them.

      - 
      # S4 method for ConservationProblem,ANY,ANY,matrix
-add_connectivity_penalties(x, penalty, zones, data)
+    
      Usage,
      # S4 method for ConservationProblem,ANY,ANY,matrix
+add_connectivity_penalties(x, penalty, zones, data)
 
-# S4 method for ConservationProblem,ANY,ANY,Matrix
-add_connectivity_penalties(x, penalty, zones, data)
+# S4 method for ConservationProblem,ANY,ANY,Matrix
+add_connectivity_penalties(x, penalty, zones, data)
 
-# S4 method for ConservationProblem,ANY,ANY,data.frame
-add_connectivity_penalties(x, penalty, zones, data)
+# S4 method for ConservationProblem,ANY,ANY,data.frame
+add_connectivity_penalties(x, penalty, zones, data)
 
-# S4 method for ConservationProblem,ANY,ANY,dgCMatrix
-add_connectivity_penalties(x, penalty, zones, data)
+# S4 method for ConservationProblem,ANY,ANY,dgCMatrix
+add_connectivity_penalties(x, penalty, zones, data)
 
-# S4 method for ConservationProblem,ANY,ANY,array
-add_connectivity_penalties(x, penalty, zones, data)
      
+# S4 method for ConservationProblem,ANY,ANY,array
+add_connectivity_penalties(x, penalty, zones, data)
      -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      penalty

      numeric penalty that is used to scale the importance +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      penalty
      +

      numeric penalty that is used to scale the importance of selecting planning units with strong connectivity between them compared -to the main problem objective (e.g. solution cost when the argument to +to the main problem objective (e.g., solution cost when the argument to x has a minimum set objective set using -add_min_set_objective()). Higher penalty values +add_min_set_objective()). Higher penalty values can be used to obtain solutions with a high degree of connectivity, and smaller penalty values can be used to obtain solutions with a small degree of connectivity. Note that negative penalty values can -be used to obtain solutions that have very little connectivity.

      zones

      matrix or Matrix object describing the +be used to obtain solutions that have very little connectivity.

      +
      zones
      +

      matrix or Matrix object describing the level of connectivity between different zones. Each row and column corresponds to a different zone in the argument to x, and cell values indicate the level of connectivity between each combination @@ -230,47 +141,44 @@

      Arg the level of connectivity between planning units allocated to the same zone. Cell values must lay between 1 and -1, where negative values favor solutions with weak connectivity. The default argument to -zones is an identity matrix (i.e. a matrix with ones along the +zones is an identity matrix (i.e., a matrix with ones along the matrix diagonal and zeros elsewhere), so that planning units are only considered to be connected when they are allocated to the same zone. This argument is required when the argument to data is a matrix or Matrix object. If the argument to data is an array or data.frame with zone data, this argument -must explicitly be set to NULL otherwise an error will be thrown.

      data

      matrix, Matrix, data.frame, or +must explicitly be set to NULL otherwise an error will be thrown.

      +
      data
      +

      matrix, Matrix, data.frame, or array object containing connectivity data. The connectivity values correspond to the strength of connectivity between different planning units. Thus connections between planning units that are associated with higher values are more favorable in the solution. -See the Data format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the penalties +See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the penalties added to it.

      -

      Details

      - +
      +
      +

      Details

      This function adds penalties to conservation planning problem to penalize solutions that have low connectivity. Specifically, it favors pair-wise connections between planning units that have high connectivity values. It was inspired by Beger et al. (2010) and can symmetric and asymmetric connectivity relationships between planning units.

      -

      Data format

      - +
      +
      +

      Data format

      The argument to data can be specified using several different formats. These formats can be used to describe symmetric or asymmetric relationships between planning units.

      -
      - -
      data as a matrix/Matrix object

      where rows and columns represent +

      data as a matrix/Matrix object
      +

      where rows and columns represent different planning units and the value of each cell represents the strength of connectivity between two different planning units. Cells that occur along the matrix diagonal are treated as weights which @@ -280,13 +188,15 @@

      zones is to treat planning units allocated to different zones as having zero connectivity.

      -
      data as a data.frame object

      containing the fields (columns) + +

      data as a data.frame object
      +

      containing the fields (columns) "id1", "id2", and "boundary". Here, each row denotes the connectivity between two planning units following the Marxan format. The data can be used to denote symmetric or asymmetric relationships between planning units. By default, input data is assumed to be symmetric unless asymmetric data is -also included (e.g. if data is present for planning units 2 and 3, then +also included (e.g., if data is present for planning units 2 and 3, then the same amount of connectivity is expected for planning units 3 and 2, unless connectivity data is also provided for planning units 3 and 2). If the argument to x contains multiple zones, then the columns @@ -296,10 +206,12 @@

      "zone2" are present, then the argument to zones must be NULL.

      -
      data as an array object

      containing four-dimensions where cell values + +

      data as an array object
      +

      containing four-dimensions where cell values indicate the strength of connectivity between planning units when they are assigned to specific management zones. The first two -dimensions (i.e. rows and columns) indicate the strength of +dimensions (i.e., rows and columns) indicate the strength of connectivity between different planning units and the second two dimensions indicate the different management zones. Thus the data[1, 2, 3, 4] indicates the strength of @@ -307,10 +219,10 @@

      -
      - -

      Mathematical formulation

      +
      +
      +

      Mathematical formulation

      The connectivity penalties are implemented using the following equations. @@ -318,7 +230,7 @@

      References

      - +
      +
      +

      References

      Beger M, Linke S, Watts M, Game E, Treml E, Ball I, and Possingham, HP (2010) Incorporating asymmetric connectivity into spatial decision making for conservation, Conservation Letters, 3: 359--368.

      -

      See also

      - -

      See penalties for an overview of all functions for adding penalties.

      +
      +
      +

      See also

      +

      See penalties for an overview of all functions for adding penalties.

      Other penalties: -add_boundary_penalties(), -add_feature_weights(), -add_linear_penalties()

      +add_boundary_penalties(), +add_feature_weights(), +add_linear_penalties()

      +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(600)
-
-# load Matrix package for visualizing matrices
-require(Matrix)
-#> Loading required package: Matrix
-
-# load data
-data(sim_pu_polygons, sim_pu_zones_stack, sim_features, sim_features_zones)
-
-# define function to rescale values between zero and one so that we
-# can compare solutions from different connectivity matrices
-rescale <- function(x, to = c(0, 1), from = range(x, na.rm = TRUE)) {
-  (x - from[1]) / diff(from) * diff(to) + to[1]
-}
-
-# create basic problem
-p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_default_solver(verbose = FALSE)
-
-# create a symmetric connectivity matrix where the connectivity between
-# two planning units corresponds to their shared boundary length
-b_matrix <- boundary_matrix(sim_pu_polygons)
-
-# standardize matrix values to lay between zero and one
-b_matrix[] <- rescale(b_matrix[])
-
-# visualize connectivity matrix
-# \dontrun{
-image(b_matrix)
-
-# }
-# create a symmetric connectivity matrix where the connectivity between
-# two planning units corresponds to their spatial proximity
-# i.e. planning units that are further apart share less connectivity
-centroids <- rgeos::gCentroid(sim_pu_polygons, byid = TRUE)
-d_matrix <- (1 / (as(dist(centroids@coords), "Matrix") + 1))
-
-# standardize matrix values to lay between zero and one
-d_matrix[] <- rescale(d_matrix[])
-
-# remove connections between planning units without connectivity to
-# reduce run-time
-d_matrix[d_matrix < 0.7] <- 0
-
-# visualize connectivity matrix
-# \dontrun{
-image(d_matrix)
-
-# }
-# create a symmetric connectivity matrix where the connectivity
-# between adjacent two planning units corresponds to their combined
-# value in a field in the planning unit attribute data
-# for example, this field could describe the extent of native vegetation in
-# each planning unit and we could use connectivity penalties to identify
-# solutions that cluster planning units together that both contain large
-# amounts of native vegetation
-c_matrix <- connectivity_matrix(sim_pu_polygons, "cost")
-
-# standardize matrix values to lay between zero and one
-c_matrix[] <- rescale(c_matrix[])
-
-# visualize connectivity matrix
-# \dontrun{
-image(c_matrix)
-
-# }
-# create an asymmetric connectivity matrix. Here, connectivity occurs between
-# adjacent planning units and, due to rivers flowing southwards
-# through the study area, connectivity from northern planning units to
-# southern planning units is ten times stronger than the reverse.
-ac_matrix <- matrix(0, length(sim_pu_polygons), length(sim_pu_polygons))
-ac_matrix <- as(ac_matrix, "Matrix")
-adjacent_units <- rgeos::gIntersects(sim_pu_polygons, byid = TRUE)
-for (i in seq_len(length(sim_pu_polygons))) {
-  for (j in seq_len(length(sim_pu_polygons))) {
-    # find if planning units are adjacent
-    if (adjacent_units[i, j]) {
-      # find if planning units lay north and south of each other
-      # i.e. they have the same x-coordinate
-      if (centroids@coords[i, 1] == centroids@coords[j, 1]) {
-        if (centroids@coords[i, 2] > centroids@coords[j, 2]) {
-          # if i is north of j add 10 units of connectivity
-          ac_matrix[i, j] <- ac_matrix[i, j] + 10
-        } else if (centroids@coords[i, 2] < centroids@coords[j, 2]) {
-          # if i is south of j add 1 unit of connectivity
-          ac_matrix[i, j] <- ac_matrix[i, j] + 1
-        }
-      }
-    }
-  }
-}
-
-# standardize matrix values to lay between zero and one
-ac_matrix[] <- rescale(ac_matrix[])
-
-# visualize asymmetric connectivity matrix
-# \dontrun{
-image(ac_matrix)
-
-# }
-# create penalties
-penalties <- c(10, 25)
-
-# create problems using the different connectivity matrices and penalties
-p2 <- list(p1,
-           p1 %>% add_connectivity_penalties(penalties[1], data = b_matrix),
-           p1 %>% add_connectivity_penalties(penalties[2], data = b_matrix),
-           p1 %>% add_connectivity_penalties(penalties[1], data = d_matrix),
-           p1 %>% add_connectivity_penalties(penalties[2], data = d_matrix),
-           p1 %>% add_connectivity_penalties(penalties[1], data = c_matrix),
-           p1 %>% add_connectivity_penalties(penalties[2], data = c_matrix),
-           p1 %>% add_connectivity_penalties(penalties[1], data = ac_matrix),
-           p1 %>% add_connectivity_penalties(penalties[2], data = ac_matrix))
-
-# assign names to the problems
-names(p2) <- c("basic problem",
-               paste0("b_matrix (", penalties,")"),
-               paste0("d_matrix (", penalties,")"),
-               paste0("c_matrix (", penalties,")"),
-               paste0("ac_matrix (", penalties,")"))
-# \dontrun{
-# solve problems
-s2 <- lapply(p2, solve)
-
-# plot solutions
-par(mfrow = c(3, 3))
-for (i in seq_along(s2)) {
-  plot(s2[[i]], main = names(p2)[i], cex = 1.5, col = "white")
-  plot(s2[[i]][s2[[i]]$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-}
-
-# }
-
-# create minimal multi-zone problem and limit solver to one minute
-# to obtain solutions in a short period of time
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(0.15, nrow = 5, ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(time_limit = 60, verbose = FALSE)
-
-# create matrix showing which planning units are adjacent to other units
-a_matrix <- adjacency_matrix(sim_pu_zones_stack)
-
-# visualize matrix
-# \dontrun{
-image(a_matrix)
-
-# }
-# create a zone matrix where connectivities are only present between
-# planning units that are allocated to the same zone
-zm1 <- as(diag(3), "Matrix")
-
-# print zone matrix
-print(zm1)
-#>      [,1] [,2] [,3]
-#> [1,]    1    .    .
-#> [2,]    .    1    .
-#> [3,]    .    .    1
-
-# create a zone matrix where connectivities are strongest between
-# planning units allocated to different zones
-zm2 <- matrix(1, ncol = 3, nrow = 3)
-diag(zm2) <- 0
-zm2 <- as(zm2, "Matrix")
-
-# print zone matrix
-print(zm2)
-#> 3 x 3 Matrix of class "dsyMatrix"
-#>      [,1] [,2] [,3]
-#> [1,]    0    1    1
-#> [2,]    1    0    1
-#> [3,]    1    1    0
-
-# create a zone matrix that indicates that connectivities between planning
-# units assigned to the same zone are much higher than connectivities
-# assigned to different zones
-zm3 <- matrix(0.1, ncol = 3, nrow = 3)
-diag(zm3) <- 1
-zm3 <- as(zm3, "Matrix")
-
-# print zone matrix
-print(zm3)
-#> 3 x 3 Matrix of class "dsyMatrix"
-#>      [,1] [,2] [,3]
-#> [1,]  1.0  0.1  0.1
-#> [2,]  0.1  1.0  0.1
-#> [3,]  0.1  0.1  1.0
-
-# create a zone matrix that indicates that connectivities between planning
-# units allocated to zone 1 are very high, connectivities between planning
-# units allocated to zones 1 and 2 are moderately high, and connectivities
-# planning units allocated to other zones are low
-zm4 <- matrix(0.1, ncol = 3, nrow = 3)
-zm4[1, 1] <- 1
-zm4[1, 2] <- 0.5
-zm4[2, 1] <- 0.5
-zm4 <- as(zm4, "Matrix")
-
-# print zone matrix
-print(zm4)
-#> 3 x 3 Matrix of class "dsyMatrix"
-#>      [,1] [,2] [,3]
-#> [1,]  1.0  0.5  0.1
-#> [2,]  0.5  0.1  0.1
-#> [3,]  0.1  0.1  0.1
-
-# create a zone matrix with strong connectivities between planning units
-# allocated to the same zone, moderate connectivities between planning
-# unit allocated to zone 1 and zone 2, and negative connectivities between
-# planning units allocated to zone 3 and the other two zones
-zm5 <- matrix(-1, ncol = 3, nrow = 3)
-zm5[1, 2] <- 0.5
-zm5[2, 1] <- 0.5
-diag(zm5) <- 1
-zm5 <- as(zm5, "Matrix")
-
-# print zone matrix
-print(zm5)
-#> 3 x 3 Matrix of class "dsyMatrix"
-#>      [,1] [,2] [,3]
-#> [1,]  1.0  0.5   -1
-#> [2,]  0.5  1.0   -1
-#> [3,] -1.0 -1.0    1
-
-# create vector of penalties to use creating problems
-penalties2 <- c(5, 15)
-
-# create multi-zone problems using the adjacent connectivity matrix and
-# different zone matrices
-p4 <- list(
-  p3,
-  p3 %>% add_connectivity_penalties(penalties2[1], zm1, a_matrix),
-  p3 %>% add_connectivity_penalties(penalties2[2], zm1, a_matrix),
-  p3 %>% add_connectivity_penalties(penalties2[1], zm2, a_matrix),
-  p3 %>% add_connectivity_penalties(penalties2[2], zm2, a_matrix),
-  p3 %>% add_connectivity_penalties(penalties2[1], zm3, a_matrix),
-  p3 %>% add_connectivity_penalties(penalties2[2], zm3, a_matrix),
-  p3 %>% add_connectivity_penalties(penalties2[1], zm4, a_matrix),
-  p3 %>% add_connectivity_penalties(penalties2[2], zm4, a_matrix),
-  p3 %>% add_connectivity_penalties(penalties2[1], zm5, a_matrix),
-  p3 %>% add_connectivity_penalties(penalties2[2], zm5, a_matrix))
-
-# assign names to the problems
-names(p4) <- c("basic problem",
-               paste0("zm", rep(seq_len(5), each = 2), " (",
-                      rep(penalties2, 2), ")"))
-# \dontrun{
-# solve problems
-s4 <- lapply(p4, solve)
-s4 <- lapply(s4, category_layer)
-s4 <- stack(s4)
-
-# plot solutions
-plot(s4, main = names(p4), axes = FALSE, box = FALSE)
-
-# }
-
-# create an array to manually specify the connectivities between
-# each planning unit when they are allocated to each different zone
-# for real-world problems, these connectivities would be generated using
-# data - but here these connectivity values are assigned as random
-# ones or zeros
-c_array <- array(0, c(rep(ncell(sim_pu_zones_stack[[1]]), 2), 3, 3))
-for (z1 in seq_len(3))
-  for (z2 in seq_len(3))
-    c_array[, , z1, z2] <- round(runif(ncell(sim_pu_zones_stack[[1]]) ^ 2,
-                                       0, 0.505))
-
-# create a problem with the manually specified connectivity array
-# note that the zones argument is set to NULL because the connectivity
-# data is an array
-p5 <- list(p3,
-           p3 %>% add_connectivity_penalties(15, zones = NULL, c_array))
-
-
-# assign names to the problems
-names(p5) <- c("basic problem", "connectivity array")
-# \dontrun{
-# solve problems
-s5 <- lapply(p5, solve)
-s5 <- lapply(s5, category_layer)
-s5 <- stack(s5)
-
-# plot solutions
-plot(s5, main = names(p5), axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(600)
+
+# load Matrix package for visualizing matrices
+require(Matrix)
+#> Loading required package: Matrix
+
+# load data
+data(sim_pu_polygons, sim_pu_zones_stack, sim_features, sim_features_zones)
+
+# define function to rescale values between zero and one so that we
+# can compare solutions from different connectivity matrices
+rescale <- function(x, to = c(0, 1), from = range(x, na.rm = TRUE)) {
+  (x - from[1]) / diff(from) * diff(to) + to[1]
+}
+
+# create basic problem
+p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_default_solver(verbose = FALSE)
+
+# create a symmetric connectivity matrix where the connectivity between
+# two planning units corresponds to their shared boundary length
+b_matrix <- boundary_matrix(sim_pu_polygons)
+
+# standardize matrix values to lay between zero and one
+b_matrix[] <- rescale(b_matrix[])
+
+# visualize connectivity matrix
+# \dontrun{
+image(b_matrix)
+
+# }
+# create a symmetric connectivity matrix where the connectivity between
+# two planning units corresponds to their spatial proximity
+# i.e., planning units that are further apart share less connectivity
+centroids <- rgeos::gCentroid(sim_pu_polygons, byid = TRUE)
+d_matrix <- (1 / (as(dist(centroids@coords), "Matrix") + 1))
+
+# standardize matrix values to lay between zero and one
+d_matrix[] <- rescale(d_matrix[])
+
+# remove connections between planning units without connectivity to
+# reduce run-time
+d_matrix[d_matrix < 0.7] <- 0
+
+# visualize connectivity matrix
+# \dontrun{
+image(d_matrix)
+
+# }
+# create a symmetric connectivity matrix where the connectivity
+# between adjacent two planning units corresponds to their combined
+# value in a field in the planning unit attribute data
+# for example, this field could describe the extent of native vegetation in
+# each planning unit and we could use connectivity penalties to identify
+# solutions that cluster planning units together that both contain large
+# amounts of native vegetation
+c_matrix <- connectivity_matrix(sim_pu_polygons, "cost")
+
+# standardize matrix values to lay between zero and one
+c_matrix[] <- rescale(c_matrix[])
+
+# visualize connectivity matrix
+# \dontrun{
+image(c_matrix)
+
+# }
+# create an asymmetric connectivity matrix. Here, connectivity occurs between
+# adjacent planning units and, due to rivers flowing southwards
+# through the study area, connectivity from northern planning units to
+# southern planning units is ten times stronger than the reverse.
+ac_matrix <- matrix(0, length(sim_pu_polygons), length(sim_pu_polygons))
+ac_matrix <- as(ac_matrix, "Matrix")
+adjacent_units <- rgeos::gIntersects(sim_pu_polygons, byid = TRUE)
+for (i in seq_len(length(sim_pu_polygons))) {
+  for (j in seq_len(length(sim_pu_polygons))) {
+    # find if planning units are adjacent
+    if (adjacent_units[i, j]) {
+      # find if planning units lay north and south of each other
+      # i.e., they have the same x-coordinate
+      if (centroids@coords[i, 1] == centroids@coords[j, 1]) {
+        if (centroids@coords[i, 2] > centroids@coords[j, 2]) {
+          # if i is north of j add 10 units of connectivity
+          ac_matrix[i, j] <- ac_matrix[i, j] + 10
+        } else if (centroids@coords[i, 2] < centroids@coords[j, 2]) {
+          # if i is south of j add 1 unit of connectivity
+          ac_matrix[i, j] <- ac_matrix[i, j] + 1
+        }
+      }
+    }
+  }
+}
+
+# standardize matrix values to lay between zero and one
+ac_matrix[] <- rescale(ac_matrix[])
+
+# visualize asymmetric connectivity matrix
+# \dontrun{
+image(ac_matrix)
+
+# }
+# create penalties
+penalties <- c(10, 25)
+
+# create problems using the different connectivity matrices and penalties
+p2 <- list(p1,
+           p1 %>% add_connectivity_penalties(penalties[1], data = b_matrix),
+           p1 %>% add_connectivity_penalties(penalties[2], data = b_matrix),
+           p1 %>% add_connectivity_penalties(penalties[1], data = d_matrix),
+           p1 %>% add_connectivity_penalties(penalties[2], data = d_matrix),
+           p1 %>% add_connectivity_penalties(penalties[1], data = c_matrix),
+           p1 %>% add_connectivity_penalties(penalties[2], data = c_matrix),
+           p1 %>% add_connectivity_penalties(penalties[1], data = ac_matrix),
+           p1 %>% add_connectivity_penalties(penalties[2], data = ac_matrix))
+
+# assign names to the problems
+names(p2) <- c("basic problem",
+               paste0("b_matrix (", penalties,")"),
+               paste0("d_matrix (", penalties,")"),
+               paste0("c_matrix (", penalties,")"),
+               paste0("ac_matrix (", penalties,")"))
+# \dontrun{
+# solve problems
+s2 <- lapply(p2, solve)
+
+# plot solutions
+par(mfrow = c(3, 3))
+for (i in seq_along(s2)) {
+  plot(s2[[i]], main = names(p2)[i], cex = 1.5, col = "white")
+  plot(s2[[i]][s2[[i]]$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+}
+
+# }
+
+# create minimal multi-zone problem and limit solver to one minute
+# to obtain solutions in a short period of time
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(0.15, nrow = 5, ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(time_limit = 60, verbose = FALSE)
+
+# create matrix showing which planning units are adjacent to other units
+a_matrix <- adjacency_matrix(sim_pu_zones_stack)
+
+# visualize matrix
+# \dontrun{
+image(a_matrix)
+
+# }
+# create a zone matrix where connectivities are only present between
+# planning units that are allocated to the same zone
+zm1 <- as(diag(3), "Matrix")
+
+# print zone matrix
+print(zm1)
+#>      [,1] [,2] [,3]
+#> [1,]    1    .    .
+#> [2,]    .    1    .
+#> [3,]    .    .    1
+
+# create a zone matrix where connectivities are strongest between
+# planning units allocated to different zones
+zm2 <- matrix(1, ncol = 3, nrow = 3)
+diag(zm2) <- 0
+zm2 <- as(zm2, "Matrix")
+
+# print zone matrix
+print(zm2)
+#> 3 x 3 Matrix of class "dsyMatrix"
+#>      [,1] [,2] [,3]
+#> [1,]    0    1    1
+#> [2,]    1    0    1
+#> [3,]    1    1    0
+
+# create a zone matrix that indicates that connectivities between planning
+# units assigned to the same zone are much higher than connectivities
+# assigned to different zones
+zm3 <- matrix(0.1, ncol = 3, nrow = 3)
+diag(zm3) <- 1
+zm3 <- as(zm3, "Matrix")
+
+# print zone matrix
+print(zm3)
+#> 3 x 3 Matrix of class "dsyMatrix"
+#>      [,1] [,2] [,3]
+#> [1,]  1.0  0.1  0.1
+#> [2,]  0.1  1.0  0.1
+#> [3,]  0.1  0.1  1.0
+
+# create a zone matrix that indicates that connectivities between planning
+# units allocated to zone 1 are very high, connectivities between planning
+# units allocated to zones 1 and 2 are moderately high, and connectivities
+# planning units allocated to other zones are low
+zm4 <- matrix(0.1, ncol = 3, nrow = 3)
+zm4[1, 1] <- 1
+zm4[1, 2] <- 0.5
+zm4[2, 1] <- 0.5
+zm4 <- as(zm4, "Matrix")
+
+# print zone matrix
+print(zm4)
+#> 3 x 3 Matrix of class "dsyMatrix"
+#>      [,1] [,2] [,3]
+#> [1,]  1.0  0.5  0.1
+#> [2,]  0.5  0.1  0.1
+#> [3,]  0.1  0.1  0.1
+
+# create a zone matrix with strong connectivities between planning units
+# allocated to the same zone, moderate connectivities between planning
+# unit allocated to zone 1 and zone 2, and negative connectivities between
+# planning units allocated to zone 3 and the other two zones
+zm5 <- matrix(-1, ncol = 3, nrow = 3)
+zm5[1, 2] <- 0.5
+zm5[2, 1] <- 0.5
+diag(zm5) <- 1
+zm5 <- as(zm5, "Matrix")
+
+# print zone matrix
+print(zm5)
+#> 3 x 3 Matrix of class "dsyMatrix"
+#>      [,1] [,2] [,3]
+#> [1,]  1.0  0.5   -1
+#> [2,]  0.5  1.0   -1
+#> [3,] -1.0 -1.0    1
+
+# create vector of penalties to use creating problems
+penalties2 <- c(5, 15)
+
+# create multi-zone problems using the adjacent connectivity matrix and
+# different zone matrices
+p4 <- list(
+  p3,
+  p3 %>% add_connectivity_penalties(penalties2[1], zm1, a_matrix),
+  p3 %>% add_connectivity_penalties(penalties2[2], zm1, a_matrix),
+  p3 %>% add_connectivity_penalties(penalties2[1], zm2, a_matrix),
+  p3 %>% add_connectivity_penalties(penalties2[2], zm2, a_matrix),
+  p3 %>% add_connectivity_penalties(penalties2[1], zm3, a_matrix),
+  p3 %>% add_connectivity_penalties(penalties2[2], zm3, a_matrix),
+  p3 %>% add_connectivity_penalties(penalties2[1], zm4, a_matrix),
+  p3 %>% add_connectivity_penalties(penalties2[2], zm4, a_matrix),
+  p3 %>% add_connectivity_penalties(penalties2[1], zm5, a_matrix),
+  p3 %>% add_connectivity_penalties(penalties2[2], zm5, a_matrix))
+
+# assign names to the problems
+names(p4) <- c("basic problem",
+               paste0("zm", rep(seq_len(5), each = 2), " (",
+                      rep(penalties2, 2), ")"))
+# \dontrun{
+# solve problems
+s4 <- lapply(p4, solve)
+s4 <- lapply(s4, category_layer)
+s4 <- stack(s4)
+
+# plot solutions
+plot(s4, main = names(p4), axes = FALSE, box = FALSE)
+
+# }
+
+# create an array to manually specify the connectivities between
+# each planning unit when they are allocated to each different zone
+# for real-world problems, these connectivities would be generated using
+# data - but here these connectivity values are assigned as random
+# ones or zeros
+c_array <- array(0, c(rep(ncell(sim_pu_zones_stack[[1]]), 2), 3, 3))
+for (z1 in seq_len(3))
+  for (z2 in seq_len(3))
+    c_array[, , z1, z2] <- round(runif(ncell(sim_pu_zones_stack[[1]]) ^ 2,
+                                       0, 0.505))
+
+# create a problem with the manually specified connectivity array
+# note that the zones argument is set to NULL because the connectivity
+# data is an array
+p5 <- list(p3,
+           p3 %>% add_connectivity_penalties(15, zones = NULL, c_array))
+
+
+# assign names to the problems
+names(p5) <- c("basic problem", "connectivity array")
+# \dontrun{
+# solve problems
+s5 <- lapply(p5, solve)
+s5 <- lapply(s5, category_layer)
+s5 <- stack(s5)
+
+# plot solutions
+plot(s5, main = names(p5), axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_contiguity_constraints.html b/docs/reference/add_contiguity_constraints.html index b9450b2af..4fc61ab91 100644 --- a/docs/reference/add_contiguity_constraints.html +++ b/docs/reference/add_contiguity_constraints.html @@ -1,103 +1,20 @@ - - - - - - - -Add contiguity constraints — add_contiguity_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add contiguity constraints — add_contiguity_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add contiguity constraints

      - Source: R/add_contiguity_constraints.R + Source: R/add_contiguity_constraints.R
      -

      Add constraints to a conservation planning problem() to ensure +

      Add constraints to a conservation planning problem() to ensure that all selected planning units are spatially connected with each other and form a single contiguous unit.

      - 
      # S4 method for ConservationProblem,ANY,ANY
-add_contiguity_constraints(x, zones, data)
+    
      Usage,
      # S4 method for ConservationProblem,ANY,ANY
+add_contiguity_constraints(x, zones, data)
 
-# S4 method for ConservationProblem,ANY,data.frame
-add_contiguity_constraints(x, zones, data)
+# S4 method for ConservationProblem,ANY,data.frame
+add_contiguity_constraints(x, zones, data)
 
-# S4 method for ConservationProblem,ANY,matrix
-add_contiguity_constraints(x, zones, data)
      
+# S4 method for ConservationProblem,ANY,matrix
+add_contiguity_constraints(x, zones, data)
      -

      Arguments

      - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      zones

      matrix or Matrix object describing the +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      zones
      +

      matrix or Matrix object describing the connection scheme for different zones. Each row and column corresponds to a different zone in the argument to x, and cell values must -contain binary numeric values (i.e. one or zero) that indicate +contain binary numeric values (i.e., one or zero) that indicate if connected planning units (as specified in the argument to data) should be still considered connected if they are allocated to different zones. The cell values along the diagonal @@ -218,54 +131,55 @@

      Arg arguments to zones must be symmetric, and that a row or column has a value of one then the diagonal element for that row or column must also have a value of one. The default argument to zones is an identity -matrix (i.e. a matrix with ones along the matrix diagonal and zeros +matrix (i.e., a matrix with ones along the matrix diagonal and zeros elsewhere), so that planning units are only considered connected if they -are both allocated to the same zone.

      data

      NULL, matrix, Matrix, data.frame +are both allocated to the same zone.

      +
      data
      +

      NULL, matrix, Matrix, data.frame object showing which planning units are connected with each other. The argument defaults to NULL which means that the connection data is calculated automatically using the -adjacency_matrix() function. -See the Data format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the constraints +adjacency_matrix() function. +See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the constraints added to it.

      -

      Details

      - +
      +
      +

      Details

      This function uses connection data to identify solutions that form a single contiguous unit. It was inspired by the mathematical formulations detailed in Önal and Briers (2006).

      -

      Data format

      - +
      +
      +

      Data format

      The argument to data can be specified using the following formats.

      -
      - -
      data as a NULL value

      indicating that connection data should be -calculated automatically using the adjacency_matrix() function. +

      data as a NULL value
      +

      indicating that connection data should be +calculated automatically using the adjacency_matrix() function. This is the default argument. Note that the connection data must be manually defined using one of the other formats below when the planning unit data -in the argument to x is not spatially referenced (e.g. +in the argument to x is not spatially referenced (e.g., in data.frame or numeric format).

      -
      data as a matrix/Matrix object

      where rows and columns represent + +

      data as a matrix/Matrix object
      +

      where rows and columns represent different planning units and the value of each cell indicates if the two planning units are connected or not. Cell values should be binary -numeric values (i.e. one or zero). Cells that occur along the +numeric values (i.e., one or zero). Cells that occur along the matrix diagonal have no effect on the solution at all because each planning unit cannot be a connected with itself.

      -
      data as a data.frame object

      containing the fields (columns) + +

      data as a data.frame object
      +

      containing the fields (columns) "id1", "id2", and "boundary". Here, each row denotes the connectivity between two planning units following the Marxan format. The field boundary should contain @@ -274,209 +188,209 @@

      -
      - -

      Notes

      +
      +
      +

      Notes

      In early versions, this function was named as the -add_connected_constraints() function.

      -

      References

      - +add_connected_constraints() function.

      +
      +
      +

      References

      Önal H and Briers RA (2006) Optimal selection of a connected reserve network. Operations Research, 54: 379--388.

      -

      See also

      - -

      See constraints for an overview of all functions for adding constraints.

      +
      + +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with added connected constraints
-p2 <- p1 %>% add_contiguity_constraints()
-# \dontrun{
-# solve problems
-s <- stack(solve(p1), solve(p2))
-
-# plot solutions
-plot(s, main = c("basic solution", "connected solution"), axes = FALSE,
-     box = FALSE)
-
-# }
-# create minimal problem with multiple zones, and limit the solver to
-# 30 seconds to obtain solutions in a feasible period of time
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(0.2, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(time_limit = 30, verbose = FALSE)
-
-# create problem with added constraints to ensure that the planning units
-# allocated to each zone form a separate contiguous unit
-z4 <- diag(3)
-print(z4)
-#>      [,1] [,2] [,3]
-#> [1,]    1    0    0
-#> [2,]    0    1    0
-#> [3,]    0    0    1
-p4 <- p3 %>% add_contiguity_constraints(z4)
-
-# create problem with added constraints to ensure that the planning
-# units allocated to each zone form a separate contiguous unit,
-# except for planning units allocated to zone 2 which do not need
-# form a single contiguous unit
-z5 <- diag(3)
-z5[3, 3] <- 0
-print(z5)
-#>      [,1] [,2] [,3]
-#> [1,]    1    0    0
-#> [2,]    0    1    0
-#> [3,]    0    0    0
-p5 <- p3 %>% add_contiguity_constraints(z5)
-
-# create problem with added constraints that ensure that the planning
-# units allocated to zones 1 and 2 form a contiguous unit
-z6 <- diag(3)
-z6[1, 2] <- 1
-z6[2, 1] <- 1
-print(z6)
-#>      [,1] [,2] [,3]
-#> [1,]    1    1    0
-#> [2,]    1    1    0
-#> [3,]    0    0    1
-p6 <- p3 %>% add_contiguity_constraints(z6)
-# \dontrun{
-# solve problems
-s2 <- lapply(list(p3, p4, p5, p6), solve)
-s2 <- lapply(s2, category_layer)
-s2 <- stack(s2)
-
-# plot solutions
-plot(s2, axes = FALSE, box = FALSE,
-     main = c("basic solution", "p4", "p5", "p6"))
-
-# }
-# create a problem that has a main "reserve zone" and a secondary
-# "corridor zone" to connect up import areas. Here, each feature has a
-# target of 30% of its distribution. If a planning unit is allocated to the
-# "reserve zone", then the prioritization accrues 100% of the amount of
-# each feature in the planning unit. If a planning unit is allocated to the
-# "corridor zone" then the prioritization accrues 40% of the amount of each
-# feature in the planning unit. Also, the cost of managing a planning unit
-# in the "corridor zone" is 45% of that when it is managed as the
-# "reserve zone". Finally, the problem has constraints which
-# ensure that all of the selected planning units form a single contiguous
-# unit, so that the planning units allocated to the "corridor zone" can
-# link up the planning units allocated to the "reserve zone"
-
-# create planning unit data
-pus <- sim_pu_zones_stack[[c(1, 1)]]
-pus[[2]] <- pus[[2]] * 0.45
-print(pus)
-#> class      : RasterStack 
-#> dimensions : 10, 10, 100, 2  (nrow, ncol, ncell, nlayers)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> names      : layer.1.1, layer.1.2 
-#> min values : 190.13276,  85.55974 
-#> max values : 215.86384,  97.13873 
-#> 
-
-# create biodiversity data
-fts <- zones(sim_features, sim_features * 0.4,
-             feature_names = names(sim_features),
-             zone_names = c("reserve zone", "corridor zone"))
-print(fts)
-#> Zones
-#>   zones: reserve zone, corridor zone (2 zones)
-#>   features: layer.1, layer.2, layer.3, ... (5 features)
-#>   data type: RasterStack
-
-# create targets
-targets <- tibble::tibble(feature = names(sim_features),
-                          zone = list(zone_names(fts))[rep(1, 5)],
-                          target = cellStats(sim_features, "sum") * 0.2,
-                          type = rep("absolute", 5))
-print(targets)
-#> # A tibble: 5 × 4
-#>   feature zone      target type    
-#>   <chr>   <list>     <dbl> <chr>   
-#> 1 layer.1 <chr [2]>  16.7  absolute
-#> 2 layer.2 <chr [2]>   6.24 absolute
-#> 3 layer.3 <chr [2]>  14.4  absolute
-#> 4 layer.4 <chr [2]>   8.53 absolute
-#> 5 layer.5 <chr [2]>  11.3  absolute
-
-# create zones matrix
-z7 <- matrix(1, ncol = 2, nrow = 2)
-print(z7)
-#>      [,1] [,2]
-#> [1,]    1    1
-#> [2,]    1    1
-
-# create problem
-p7 <- problem(pus, fts) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(targets) %>%
-      add_contiguity_constraints(z7) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problems
-s7 <- category_layer(solve(p7))
-
-# plot solutions
-plot(s7, "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with added connected constraints
+p2 <- p1 %>% add_contiguity_constraints()
+# \dontrun{
+# solve problems
+s <- stack(solve(p1), solve(p2))
+
+# plot solutions
+plot(s, main = c("basic solution", "connected solution"), axes = FALSE,
+     box = FALSE)
+
+# }
+# create minimal problem with multiple zones, and limit the solver to
+# 30 seconds to obtain solutions in a feasible period of time
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(0.2, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(time_limit = 30, verbose = FALSE)
+
+# create problem with added constraints to ensure that the planning units
+# allocated to each zone form a separate contiguous unit
+z4 <- diag(3)
+print(z4)
+#>      [,1] [,2] [,3]
+#> [1,]    1    0    0
+#> [2,]    0    1    0
+#> [3,]    0    0    1
+p4 <- p3 %>% add_contiguity_constraints(z4)
+
+# create problem with added constraints to ensure that the planning
+# units allocated to each zone form a separate contiguous unit,
+# except for planning units allocated to zone 2 which do not need
+# form a single contiguous unit
+z5 <- diag(3)
+z5[3, 3] <- 0
+print(z5)
+#>      [,1] [,2] [,3]
+#> [1,]    1    0    0
+#> [2,]    0    1    0
+#> [3,]    0    0    0
+p5 <- p3 %>% add_contiguity_constraints(z5)
+
+# create problem with added constraints that ensure that the planning
+# units allocated to zones 1 and 2 form a contiguous unit
+z6 <- diag(3)
+z6[1, 2] <- 1
+z6[2, 1] <- 1
+print(z6)
+#>      [,1] [,2] [,3]
+#> [1,]    1    1    0
+#> [2,]    1    1    0
+#> [3,]    0    0    1
+p6 <- p3 %>% add_contiguity_constraints(z6)
+# \dontrun{
+# solve problems
+s2 <- lapply(list(p3, p4, p5, p6), solve)
+s2 <- lapply(s2, category_layer)
+s2 <- stack(s2)
+
+# plot solutions
+plot(s2, axes = FALSE, box = FALSE,
+     main = c("basic solution", "p4", "p5", "p6"))
+
+# }
+# create a problem that has a main "reserve zone" and a secondary
+# "corridor zone" to connect up import areas. Here, each feature has a
+# target of 30% of its distribution. If a planning unit is allocated to the
+# "reserve zone", then the prioritization accrues 100% of the amount of
+# each feature in the planning unit. If a planning unit is allocated to the
+# "corridor zone" then the prioritization accrues 40% of the amount of each
+# feature in the planning unit. Also, the cost of managing a planning unit
+# in the "corridor zone" is 45% of that when it is managed as the
+# "reserve zone". Finally, the problem has constraints which
+# ensure that all of the selected planning units form a single contiguous
+# unit, so that the planning units allocated to the "corridor zone" can
+# link up the planning units allocated to the "reserve zone"
+
+# create planning unit data
+pus <- sim_pu_zones_stack[[c(1, 1)]]
+pus[[2]] <- pus[[2]] * 0.45
+print(pus)
+#> class      : RasterStack 
+#> dimensions : 10, 10, 100, 2  (nrow, ncol, ncell, nlayers)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> names      : layer.1.1, layer.1.2 
+#> min values : 190.13276,  85.55974 
+#> max values : 215.86384,  97.13873 
+#> 
+
+# create biodiversity data
+fts <- zones(sim_features, sim_features * 0.4,
+             feature_names = names(sim_features),
+             zone_names = c("reserve zone", "corridor zone"))
+print(fts)
+#> Zones
+#>   zones: reserve zone, corridor zone (2 zones)
+#>   features: layer.1, layer.2, layer.3, ... (5 features)
+#>   data type: RasterStack
+
+# create targets
+targets <- tibble::tibble(feature = names(sim_features),
+                          zone = list(zone_names(fts))[rep(1, 5)],
+                          target = cellStats(sim_features, "sum") * 0.2,
+                          type = rep("absolute", 5))
+print(targets)
+#> # A tibble: 5 × 4
+#>   feature zone      target type    
+#>   <chr>   <list>     <dbl> <chr>   
+#> 1 layer.1 <chr [2]>  16.7  absolute
+#> 2 layer.2 <chr [2]>   6.24 absolute
+#> 3 layer.3 <chr [2]>  14.4  absolute
+#> 4 layer.4 <chr [2]>   8.53 absolute
+#> 5 layer.5 <chr [2]>  11.3  absolute
+
+# create zones matrix
+z7 <- matrix(1, ncol = 2, nrow = 2)
+print(z7)
+#>      [,1] [,2]
+#> [1,]    1    1
+#> [2,]    1    1
+
+# create problem
+p7 <- problem(pus, fts) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(targets) %>%
+      add_contiguity_constraints(z7) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problems
+s7 <- category_layer(solve(p7))
+
+# plot solutions
+plot(s7, "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_cplex_solver.html b/docs/reference/add_cplex_solver.html index 11dccd2be..ba8a91e12 100644 --- a/docs/reference/add_cplex_solver.html +++ b/docs/reference/add_cplex_solver.html @@ -1,106 +1,23 @@ - - - - - - - -Add a CPLEX solver — add_cplex_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a CPLEX solver — add_cplex_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add a CPLEX solver

      - Source: R/add_cplex_solver.R + Source: R/add_cplex_solver.R

      Specify that the -IBM CPLEX software -(IBM 2017) should be used to solve a conservation planning problem(). +IBM CPLEX software +(IBM 2017) should be used to solve a conservation planning problem(). This function can also be used to customize the behavior of the solver. It requires the cplexAPI package to be installed (see below for installation instructions).

      - 
      add_cplex_solver(
-  x,
-  gap = 0.1,
-  time_limit = .Machine$integer.max,
-  presolve = TRUE,
-  threads = 1,
-  verbose = TRUE
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      gap

      numeric gap to optimality. This gap is relative +

      Usage,
      add_cplex_solver(
+  x,
+  gap = 0.1,
+  time_limit = .Machine$integer.max,
+  presolve = TRUE,
+  threads = 1,
+  verbose = TRUE
+)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      gap
      +

      numeric gap to optimality. This gap is relative and expresses the acceptable deviance from the optimal objective. For example, a value of 0.01 will result in the solver stopping when it has found a solution within 1% of optimality. Additionally, a value of 0 will result in the solver stopping when it has found an optimal solution. -The default value is 0.1 (i.e. 10% from optimality).

      time_limit

      numeric time limit (seconds) for generating solutions. +The default value is 0.1 (i.e., 10% from optimality).

      +
      time_limit
      +

      numeric time limit (seconds) for generating solutions. The solver will return the current best solution when this time limit is exceeded. The default value is the largest integer value -(i.e. .Machine$integer.max), effectively meaning that solver -will keep running until a solution within the optimality gap is found.

      presolve

      logical attempt to simplify the -problem before solving it? Defaults to TRUE.

      threads

      integer number of threads to use for the -optimization algorithm. The default value is 1.

      verbose

      logical should information be printed while solving -optimization problems? Defaults to TRUE.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the solver +(i.e., .Machine$integer.max), effectively meaning that solver +will keep running until a solution within the optimality gap is found.

      +
      presolve
      +

      logical attempt to simplify the +problem before solving it? Defaults to TRUE.

      +
      threads
      +

      integer number of threads to use for the +optimization algorithm. The default value is 1.

      +
      verbose
      +

      logical should information be printed while solving +optimization problems? Defaults to TRUE.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the solver added to it.

      -

      Details

      - -

      IBM CPLEX is a +

      +
      +

      Details

      +

      IBM CPLEX is a commercial optimization software. It is faster than -the available open source solvers (e.g. add_lpsymphony_solver() and -add_rsymphony_solver(). +the available open source solvers (e.g., add_lpsymphony_solver() and +add_rsymphony_solver(). Although formal benchmarks examining the performance of this solver for conservation planning problems have yet to be completed, preliminary analyses suggest that it performs slightly slower than the Gurobi -solver (i.e. add_gurobi_solver()). +solver (i.e., add_gurobi_solver()). We recommend using this solver if the Gurobi solver is not available. Licenses are available for the IBM CPLEX software to academics at no cost -(see https://www.ibm.com/products/ilog-cplex-optimization-studio).

      -

      Installation

      - +(see https://www.ibm.com/products/ilog-cplex-optimization-studio).

      +
      + +
      +

      References

      IBM (2017) IBM ILOG CPLEX Optimization Studio CPLEX User's Manual. Version 12 Release 8. IBM ILOG CPLEX Division, Incline Village, NV.

      -

      See also

      - -

      See solvers for an overview of all functions for adding a solver.

      +
      +
      +

      See also

      +

      See solvers for an overview of all functions for adding a solver.

      Other solvers: -add_cbc_solver(), -add_default_solver(), -add_gurobi_solver(), -add_lsymphony_solver, -add_rsymphony_solver()

      +add_cbc_solver(), +add_default_solver(), +add_gurobi_solver(), +add_lsymphony_solver, +add_rsymphony_solver()

      +
      -

      Examples

      - 
      # \dontrun{
-# load data
-data(sim_pu_raster, sim_features)
-
-# create problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.1) %>%
-     add_binary_decisions() %>%
-     add_cplex_solver(gap = 0.1, time_limit = 5, verbose = FALSE)
-
-# generate solution
-s <- solve(p)
-
-# plot solution
-plot(s, main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# load data
+data(sim_pu_raster, sim_features)
+
+# create problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.1) %>%
+     add_binary_decisions() %>%
+     add_cplex_solver(gap = 0.1, time_limit = 5, verbose = FALSE)
+
+# generate solution
+s <- solve(p)
+
+# plot solution
+plot(s, main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_cuts_portfolio.html b/docs/reference/add_cuts_portfolio.html index 0fe5f6f88..8a5780b75 100644 --- a/docs/reference/add_cuts_portfolio.html +++ b/docs/reference/add_cuts_portfolio.html @@ -1,105 +1,22 @@ - - - - - - - -Add Bender's cuts portfolio — add_cuts_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add Bender's cuts portfolio — add_cuts_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add Bender's cuts portfolio

      - Source: R/add_cuts_portfolio.R + Source: R/add_cuts_portfolio.R

      Generate a portfolio of solutions for a conservation planning -problem() using Bender's cuts (discussed in Rodrigues +problem() using Bender's cuts (discussed in Rodrigues et al. 2000). This is recommended as a replacement for -add_gap_portfolio() when the Gurobi software is not +add_gap_portfolio() when the Gurobi software is not available.

      - 
      add_cuts_portfolio(x, number_solutions = 10L)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      number_solutions

      integer number of attempts to generate -different solutions. Defaults to 10.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the portfolio +

      Usage,
      add_cuts_portfolio(x, number_solutions = 10L)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      number_solutions
      +

      integer number of attempts to generate +different solutions. Defaults to 10.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the portfolio added to it.

      -

      Details

      - +
      +
      +

      Details

      This strategy for generating a portfolio of solutions involves solving the problem multiple times and adding additional constraints to forbid previously obtained solutions. In general, this strategy is most useful when problems take a long time to solve and benefit from having multiple threads allocated for solving an individual problem.

      -

      Notes

      - +
      +
      +

      Notes

      In early versions (< 4.0.1), this function was only compatible with -Gurobi (i.e. add_gurobi_solver()). To provide functionality with +Gurobi (i.e., add_gurobi_solver()). To provide functionality with exact algorithm solvers, this function now adds constraints to the problem formulation to generate multiple solutions.

      -

      References

      - +
      +
      +

      References

      Rodrigues AS, Cerdeira OJ, and Gaston KJ (2000) Flexibility, efficiency, and accountability: adapting reserve selection algorithms to more complex conservation problems. Ecography, 23: 565--574.

      -

      See also

      - -

      See portfolios for an overview of all functions for adding a portfolio.

      +
      +
      +

      See also

      +

      See portfolios for an overview of all functions for adding a portfolio.

      Other portfolios: -add_extra_portfolio(), -add_gap_portfolio(), -add_shuffle_portfolio(), -add_top_portfolio()

      +add_extra_portfolio(), +add_gap_portfolio(), +add_shuffle_portfolio(), +add_top_portfolio()

      +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem with cuts portfolio
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_cuts_portfolio(10) %>%
-      add_default_solver(gap = 0.2, verbose = FALSE)
-
-# \dontrun{
-# solve problem and generate 10 solutions within 20% of optimality
-s1 <- solve(p1)
-
-# plot solutions in portfolio
-plot(stack(s1), axes = FALSE, box = FALSE)
-
-# }
-# build multi-zone conservation problem with cuts portfolio
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_cuts_portfolio(10) %>%
-      add_default_solver(gap = 0.2, verbose = FALSE)
-
-# \dontrun{
-# solve the problem
-s2 <- solve(p2)
-
-# print solution
-str(s2, max.level = 1)
-#> List of 10
-#>  $ solution_1 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_2 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_3 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_4 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_5 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_6 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_7 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_8 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_9 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_10:Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  - attr(*, "objective")= Named num [1:10] 11601 11815 11790 11820 11618 ...
-#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
-#>  - attr(*, "status")= Named chr [1:10] "OPTIMAL" "OPTIMAL" "OPTIMAL" "OPTIMAL" ...
-#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
-#>  - attr(*, "runtime")= Named num [1:10] 0.007 0.006 0.007 0.007 0.007 ...
-#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
-
-# plot solutions in portfolio
-plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
-     box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem with cuts portfolio
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_cuts_portfolio(10) %>%
+      add_default_solver(gap = 0.2, verbose = FALSE)
+
+# \dontrun{
+# solve problem and generate 10 solutions within 20% of optimality
+s1 <- solve(p1)
+
+# plot solutions in portfolio
+plot(stack(s1), axes = FALSE, box = FALSE)
+
+# }
+# build multi-zone conservation problem with cuts portfolio
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_cuts_portfolio(10) %>%
+      add_default_solver(gap = 0.2, verbose = FALSE)
+
+# \dontrun{
+# solve the problem
+s2 <- solve(p2)
+
+# print solution
+str(s2, max.level = 1)
+#> List of 10
+#>  $ solution_1 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_2 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_3 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_4 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_5 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_6 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_7 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_8 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_9 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_10:Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  - attr(*, "objective")= Named num [1:10] 11601 11815 11790 11820 11618 ...
+#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
+#>  - attr(*, "status")= Named chr [1:10] "OPTIMAL" "OPTIMAL" "OPTIMAL" "OPTIMAL" ...
+#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
+#>  - attr(*, "runtime")= Named num [1:10] 0.026 0.006 0.007 0.006 0.007 ...
+#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
+
+# plot solutions in portfolio
+plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
+     box = FALSE)
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/add_default_decisions.html b/docs/reference/add_default_decisions.html index 335c3c602..7ca4eb629 100644 --- a/docs/reference/add_default_decisions.html +++ b/docs/reference/add_default_decisions.html @@ -1,103 +1,20 @@ - - - - - - - -Add default decisions — add_default_decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add default decisions — add_default_decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add default decisions

      - Source: R/add_default_decisions.R + Source: R/add_default_decisions.R

      This function adds the default decision types to a conservation planning -problem(). The default types are binary and are added using -the add_binary_decisions() function.

      +problem(). The default types are binary and are added using +the add_binary_decisions() function.

      - 
      add_default_decisions(x)
      - -

      Arguments

      - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      +
      Usage,
      add_default_decisions(x)
      -

      Value

      - -

      Object (i.e. ConservationProblem) with the decisions added +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the decisions added to it.

      -

      See also

      - -

      See decisions for an overview of all functions for adding decisions.

      +
      +
      +

      See also

      +

      See decisions for an overview of all functions for adding decisions.

      Other decisions: -add_binary_decisions(), -add_proportion_decisions(), -add_semicontinuous_decisions()

      +add_binary_decisions(), +add_proportion_decisions(), +add_semicontinuous_decisions()

      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_default_solver.html b/docs/reference/add_default_solver.html index 7126da15a..9c1ad2a2a 100644 --- a/docs/reference/add_default_solver.html +++ b/docs/reference/add_default_solver.html @@ -1,106 +1,23 @@ - - - - - - - -Add a default solver — add_default_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a default solver — add_default_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add a default solver

      - Source: R/add_default_solver.R + Source: R/add_default_solver.R

      Identify the best solver currently installed on the system and specify that -it should be used to solve a conservation planning problem(). +it should be used to solve a conservation planning problem(). For information on the performance of different solvers, please see Schuster et al. (2020) for benchmarks comparing the run time and solution quality of some of the available solvers when applied to different sized datasets.

      - 
      add_default_solver(x, ...)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      ...

      arguments passed to the solver.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the solver +

      Usage,
      add_default_solver(x, ...)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      ...
      +

      arguments passed to the solver.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the solver added to it.

      -

      Details

      - +
      +
      +

      Details

      Ranked from best to worst, the available solvers that can be used are: -add_gurobi_solver(), add_cplex_solver(), add_cbc_solver(), -add_lpsymphony_solver(), and finally add_rsymphony_solver().

      -

      References

      - +add_gurobi_solver(), add_cplex_solver(), add_cbc_solver(), +add_lpsymphony_solver(), and finally add_rsymphony_solver().

      +
      +
      +

      References

      Schuster R, Hanson JO, Strimas-Mackey M, and Bennett JR (2020). Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems. PeerJ, 8: e9258.

      -

      See also

      - -

      See solvers for an overview of all functions for adding a solver.

      +
      +
      +

      See also

      +

      See solvers for an overview of all functions for adding a solver.

      Other solvers: -add_cbc_solver(), -add_cplex_solver(), -add_gurobi_solver(), -add_lsymphony_solver, -add_rsymphony_solver()

      +add_cbc_solver(), +add_cplex_solver(), +add_gurobi_solver(), +add_lsymphony_solver, +add_rsymphony_solver()

      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_extra_portfolio.html b/docs/reference/add_extra_portfolio.html index 1f5d6725f..aca66fd97 100644 --- a/docs/reference/add_extra_portfolio.html +++ b/docs/reference/add_extra_portfolio.html @@ -1,106 +1,23 @@ - - - - - - - -Add an extra portfolio — add_extra_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add an extra portfolio — add_extra_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add an extra portfolio

      - Source: R/add_extra_portfolio.R + Source: R/add_extra_portfolio.R

      Generate a portfolio of solutions for a conservation planning -problem() by storing feasible solutions +problem() by storing feasible solutions discovered during the optimization process. This method is useful for quickly obtaining multiple solutions, but does not provide any guarantees on the number of solutions, or the quality of solutions.

      - 
      add_extra_portfolio(x)
      - -

      Arguments

      - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      +
      Usage,
      add_extra_portfolio(x)
      -

      Value

      - -

      Object (i.e. ConservationProblem) with the portfolio +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the portfolio added to it.

      -

      Details

      - +
      +
      +

      Details

      This strategy for generating a portfolio requires problems to -be solved using the Gurobi software suite (i.e. using -add_gurobi_solver(). Specifically, version 8.0.0 (or greater) +be solved using the Gurobi software suite (i.e., using +add_gurobi_solver(). Specifically, version 8.0.0 (or greater) of the gurobi package must be installed.

      -

      See also

      - -

      See portfolios for an overview of all functions for adding a portfolio.

      +
      +
      +

      See also

      +

      See portfolios for an overview of all functions for adding a portfolio.

      Other portfolios: -add_cuts_portfolio(), -add_gap_portfolio(), -add_shuffle_portfolio(), -add_top_portfolio()

      +add_cuts_portfolio(), +add_gap_portfolio(), +add_shuffle_portfolio(), +add_top_portfolio()

      +
      -

      Examples

      - 
      # \dontrun{
-# set seed for reproducibility
-set.seed(600)
-
-# load data
-data(sim_pu_raster, sim_features)
-
-# create minimal problem with a portfolio for extra solutions
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.05) %>%
-      add_extra_portfolio() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem and generate portfolio
-s1 <- solve(p1)
-
-# print number of solutions found
-print(length(s1))
-#> [1] 10
-
-# plot solutions
-plot(stack(s1), axes = FALSE, box = FALSE)
-
-
-# create multi-zone problem with a portfolio for extra solutions
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_extra_portfolio() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem and generate portfolio
-s2 <- solve(p2)
-
-# print number of solutions found
-print(length(s2))
-#> [1] 10
-
-# plot solutions in portfolio
-plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
-     box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# set seed for reproducibility
+set.seed(600)
+
+# load data
+data(sim_pu_raster, sim_features)
+
+# create minimal problem with a portfolio for extra solutions
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.05) %>%
+      add_extra_portfolio() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem and generate portfolio
+s1 <- solve(p1)
+
+# print number of solutions found
+print(length(s1))
+#> [1] 10
+
+# plot solutions
+plot(stack(s1), axes = FALSE, box = FALSE)
+
+
+# create multi-zone problem with a portfolio for extra solutions
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_extra_portfolio() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem and generate portfolio
+s2 <- solve(p2)
+
+# print number of solutions found
+print(length(s2))
+#> [1] 10
+
+# plot solutions in portfolio
+plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
+     box = FALSE)
+
+# }
 
      
+
      +
      -
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b/docs/reference/add_feature_contiguity_constraints.html index b71bf3e09..f4368a743 100644 --- a/docs/reference/add_feature_contiguity_constraints.html +++ b/docs/reference/add_feature_contiguity_constraints.html @@ -1,61 +1,5 @@ - - - - - - - -Add feature contiguity constraints — add_feature_contiguity_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add feature contiguity constraints — add_feature_contiguity_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add feature contiguity constraints

      - Source: R/add_feature_contiguity_constraints.R + Source: R/add_feature_contiguity_constraints.R
      -

      Add constraints to a problem() to ensure that each feature is +

      Add constraints to a problem() to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of those implemented in the -add_contiguity_constraints() function, because they ensure that +add_contiguity_constraints() function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit. Additionally, this function can use data showing the distribution of dispersible habitat for each @@ -200,32 +117,28 @@

      Add feature contiguity constraints

      designated for their conservation.

      - 
      # S4 method for ConservationProblem,ANY,Matrix
-add_feature_contiguity_constraints(x, zones, data)
+    
      Usage,
      # S4 method for ConservationProblem,ANY,Matrix
+add_feature_contiguity_constraints(x, zones, data)
 
-# S4 method for ConservationProblem,ANY,data.frame
-add_feature_contiguity_constraints(x, zones, data)
+# S4 method for ConservationProblem,ANY,data.frame
+add_feature_contiguity_constraints(x, zones, data)
 
-# S4 method for ConservationProblem,ANY,matrix
-add_feature_contiguity_constraints(x, zones, data)
+# S4 method for ConservationProblem,ANY,matrix
+add_feature_contiguity_constraints(x, zones, data)
 
-# S4 method for ConservationProblem,ANY,ANY
-add_feature_contiguity_constraints(x, zones, data)
      
+# S4 method for ConservationProblem,ANY,ANY
+add_feature_contiguity_constraints(x, zones, data)
      -

      Arguments

      - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      zones

      matrix, Matrix or list object describing +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      zones
      +

      matrix, Matrix or list object describing the connection scheme for different zones. For matrix or and Matrix arguments, each row and column corresponds to a different zone in the argument to x, and cell values must -contain binary numeric values (i.e. one or zero) that indicate +contain binary numeric values (i.e., one or zero) that indicate if connected planning units (as specified in the argument to data) should be still considered connected if they are allocated to different zones. The cell values along the diagonal @@ -238,13 +151,11 @@

      Arg be a list of matrix or Matrix objects that shows the specific scheme for each feature using the conventions described above. The default argument to zones is an identity -matrix (i.e. a matrix with ones along the matrix diagonal and zeros +matrix (i.e., a matrix with ones along the matrix diagonal and zeros elsewhere), so that planning units are only considered connected if they -are both allocated to the same zone.

      data

      NULL, matrix, Matrix, data.frame +are both allocated to the same zone.

      +
      data
      +

      NULL, matrix, Matrix, data.frame or list of matrix, Matrix, or data.frame objects. The argument to data shows which planning units should be treated as being connected when implementing constraints to ensure that features @@ -253,18 +164,17 @@

      Arg which sets of planning units should be treated as being connected for which features using a list of objects. The default argument is NULL which means that the connection data is calculated -automatically using the adjacency_matrix() function and so +automatically using the adjacency_matrix() function and so all adjacent planning units are treated as being connected for all -features. See the Data format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the constraints +features. See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the constraints added to it.

      -

      Details

      - +
      +
      +

      Details

      This function uses connection data to identify solutions that represent features in contiguous units of dispersible habitat. It was inspired by the mathematical formulations detailed in @@ -275,34 +185,38 @@

      Details cannot be used with feature data that have negative vales. Please note that adding these constraints to a problem will drastically increase the amount of time required to solve it.

      -

      Data format

      - +
      +
      +

      Data format

      The argument to data can be specified using the following formats.

      -
      - -
      data as a NULL value

      connection +

      data as a NULL value
      +

      connection data should be calculated automatically -using the adjacency_matrix() function. This is the default +using the adjacency_matrix() function. This is the default argument and means that all adjacent planning units are treated as potentially dispersible for all features. Note that the connection data must be manually defined using one of the other formats below when the planning unit data -in the argument to x is not spatially referenced (e.g. +in the argument to x is not spatially referenced (e.g., in data.frame or numeric format).

      -
      data as amatrix/Matrix object

      where rows and columns represent + +

      data as amatrix/Matrix object
      +

      where rows and columns represent different planning units and the value of each cell indicates if the two planning units are connected or not. Cell values should be binary -numeric values (i.e. one or zero). Cells that occur along the +numeric values (i.e., one or zero). Cells that occur along the matrix diagonal have no effect on the solution at all because each planning unit cannot be a connected with itself. Note that pairs of connected planning units are treated as being potentially dispersible for all features.

      -
      data as a data.frame object

      containing the fields (columns) + +

      data as a data.frame object
      +

      containing the fields (columns) "id1", "id2", and "boundary". Here, each row denotes the connectivity between two planning units following the Marxan format. The field boundary should contain @@ -311,13 +225,15 @@

      -
      data as a list object

      containing matrix, Matrix, or + +

      data as a list object
      +

      containing matrix, Matrix, or data.frame objects showing which planning units should be treated as connected for each feature. Each element in the list should correspond to a different feature (specifically, @@ -326,15 +242,16 @@

      -
      - -

      Notes

      +
      +
      +

      Notes

      In early versions, it was named as the add_corridor_constraints function.

      -

      References

      - +
      +
      +

      References

      Önal H and Briers RA (2006) Optimal selection of a connected reserve network. Operations Research, 54: 379--388.

      Cardeira JO, Pinto LS, Cabeza M and Gaston KJ (2010) Species specific @@ -343,162 +260,161 @@

      R

      Hanson JO, Fuller RA, & Rhodes JR (2019) Conventional methods for enhancing connectivity in conservation planning do not always maintain gene flow. Journal of Applied Ecology, 56: 913--922.

      -

      See also

      - -

      See constraints for an overview of all functions for adding constraints.

      +
      + +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
-
-# create minimal problem
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.3) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with contiguity constraints
-p2 <- p1 %>% add_contiguity_constraints()
-
-# create problem with constraints to represent features in contiguous
-# units
-p3 <- p1 %>% add_feature_contiguity_constraints()
-
-# create problem with constraints to represent features in contiguous
-# units that contain highly suitable habitat values
-# (specifically in the top 1.5th percentile)
-cm4 <- lapply(seq_len(nlayers(sim_features)), function(i) {
-  # create connectivity matrix using the i'th feature's habitat data
-  m <- connectivity_matrix(sim_pu_raster, sim_features[[i]])
-  # convert matrix to TRUE/FALSE values in top 20th percentile
-  m <- m > quantile(as.vector(m), 1 - 0.015, names = FALSE)
-  # convert matrix from TRUE/FALSE to sparse matrix with 0/1s
-  m <- as(m, "dgCMatrix")
-  # remove 0s from the sparse matrix
-  m <- Matrix::drop0(m)
-  # return matrix
-  m
-})
-p4 <- p1 %>% add_feature_contiguity_constraints(data = cm4)
-# \dontrun{
-# solve problems
-s1 <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
-
-# plot solutions
-plot(s1,  axes = FALSE, box = FALSE,
-     main = c("basic solution", "contiguity constraints",
-              "feature contiguity constraints",
-              "feature contiguity constraints with data"))
-
-# }
-# create minimal problem with multiple zones, and limit the solver to
-# 30 seconds to obtain solutions in a feasible period of time
-p5 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(time_limit = 30, verbose = FALSE)
-
-# create problem with contiguity constraints that specify that the
-# planning units used to conserve each feature in different management
-# zones must form separate contiguous units
-p6 <- p5 %>% add_feature_contiguity_constraints(diag(3))
-
-# create problem with contiguity constraints that specify that the
-# planning units used to conserve each feature must form a single
-# contiguous unit if the planning units are allocated to zones 1 and 2
-# and do not need to form a single contiguous unit if they are allocated
-# to zone 3
-zm7 <- matrix(0, ncol = 3, nrow = 3)
-zm7[seq_len(2), seq_len(2)] <- 1
-print(zm7)
-#>      [,1] [,2] [,3]
-#> [1,]    1    1    0
-#> [2,]    1    1    0
-#> [3,]    0    0    0
-p7 <- p5 %>% add_feature_contiguity_constraints(zm7)
-
-# create problem with contiguity constraints that specify that all of
-# the planning units in all three of the zones must conserve first feature
-# in a single contiguous unit but the planning units used to conserve the
-# remaining features do not need to be contiguous in any way
-zm8 <- lapply(seq_len(number_of_features(sim_features_zones)), function(i)
-  matrix(ifelse(i == 1, 1, 0), ncol = 3, nrow = 3))
-print(zm8)
-#> [[1]]
-#>      [,1] [,2] [,3]
-#> [1,]    1    1    1
-#> [2,]    1    1    1
-#> [3,]    1    1    1
-#> 
-#> [[2]]
-#>      [,1] [,2] [,3]
-#> [1,]    0    0    0
-#> [2,]    0    0    0
-#> [3,]    0    0    0
-#> 
-#> [[3]]
-#>      [,1] [,2] [,3]
-#> [1,]    0    0    0
-#> [2,]    0    0    0
-#> [3,]    0    0    0
-#> 
-#> [[4]]
-#>      [,1] [,2] [,3]
-#> [1,]    0    0    0
-#> [2,]    0    0    0
-#> [3,]    0    0    0
-#> 
-#> [[5]]
-#>      [,1] [,2] [,3]
-#> [1,]    0    0    0
-#> [2,]    0    0    0
-#> [3,]    0    0    0
-#> 
-p8 <- p5 %>% add_feature_contiguity_constraints(zm8)
-# \dontrun{
-# solve problems
-s2 <- lapply(list(p5, p6, p7, p8), solve)
-s2 <- stack(lapply(s2, category_layer))
-
-# plot solutions
-plot(s2, main = c("p5", "p6", "p7", "p8"), axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
+
+# create minimal problem
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.3) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with contiguity constraints
+p2 <- p1 %>% add_contiguity_constraints()
+
+# create problem with constraints to represent features in contiguous
+# units
+p3 <- p1 %>% add_feature_contiguity_constraints()
+
+# create problem with constraints to represent features in contiguous
+# units that contain highly suitable habitat values
+# (specifically in the top 1.5th percentile)
+cm4 <- lapply(seq_len(nlayers(sim_features)), function(i) {
+  # create connectivity matrix using the i'th feature's habitat data
+  m <- connectivity_matrix(sim_pu_raster, sim_features[[i]])
+  # convert matrix to TRUE/FALSE values in top 20th percentile
+  m <- m > quantile(as.vector(m), 1 - 0.015, names = FALSE)
+  # convert matrix from TRUE/FALSE to sparse matrix with 0/1s
+  m <- as(m, "dgCMatrix")
+  # remove 0s from the sparse matrix
+  m <- Matrix::drop0(m)
+  # return matrix
+  m
+})
+p4 <- p1 %>% add_feature_contiguity_constraints(data = cm4)
+# \dontrun{
+# solve problems
+s1 <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
+
+# plot solutions
+plot(s1,  axes = FALSE, box = FALSE,
+     main = c("basic solution", "contiguity constraints",
+              "feature contiguity constraints",
+              "feature contiguity constraints with data"))
+
+# }
+# create minimal problem with multiple zones, and limit the solver to
+# 30 seconds to obtain solutions in a feasible period of time
+p5 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(time_limit = 30, verbose = FALSE)
+
+# create problem with contiguity constraints that specify that the
+# planning units used to conserve each feature in different management
+# zones must form separate contiguous units
+p6 <- p5 %>% add_feature_contiguity_constraints(diag(3))
+
+# create problem with contiguity constraints that specify that the
+# planning units used to conserve each feature must form a single
+# contiguous unit if the planning units are allocated to zones 1 and 2
+# and do not need to form a single contiguous unit if they are allocated
+# to zone 3
+zm7 <- matrix(0, ncol = 3, nrow = 3)
+zm7[seq_len(2), seq_len(2)] <- 1
+print(zm7)
+#>      [,1] [,2] [,3]
+#> [1,]    1    1    0
+#> [2,]    1    1    0
+#> [3,]    0    0    0
+p7 <- p5 %>% add_feature_contiguity_constraints(zm7)
+
+# create problem with contiguity constraints that specify that all of
+# the planning units in all three of the zones must conserve first feature
+# in a single contiguous unit but the planning units used to conserve the
+# remaining features do not need to be contiguous in any way
+zm8 <- lapply(seq_len(number_of_features(sim_features_zones)), function(i)
+  matrix(ifelse(i == 1, 1, 0), ncol = 3, nrow = 3))
+print(zm8)
+#> [[1]]
+#>      [,1] [,2] [,3]
+#> [1,]    1    1    1
+#> [2,]    1    1    1
+#> [3,]    1    1    1
+#> 
+#> [[2]]
+#>      [,1] [,2] [,3]
+#> [1,]    0    0    0
+#> [2,]    0    0    0
+#> [3,]    0    0    0
+#> 
+#> [[3]]
+#>      [,1] [,2] [,3]
+#> [1,]    0    0    0
+#> [2,]    0    0    0
+#> [3,]    0    0    0
+#> 
+#> [[4]]
+#>      [,1] [,2] [,3]
+#> [1,]    0    0    0
+#> [2,]    0    0    0
+#> [3,]    0    0    0
+#> 
+#> [[5]]
+#>      [,1] [,2] [,3]
+#> [1,]    0    0    0
+#> [2,]    0    0    0
+#> [3,]    0    0    0
+#> 
+p8 <- p5 %>% add_feature_contiguity_constraints(zm8)
+# \dontrun{
+# solve problems
+s2 <- lapply(list(p5, p6, p7, p8), solve)
+s2 <- stack(lapply(s2, category_layer))
+
+# plot solutions
+plot(s2, main = c("p5", "p6", "p7", "p8"), axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_feature_weights.html b/docs/reference/add_feature_weights.html index 2d828339a..6901f679c 100644 --- a/docs/reference/add_feature_weights.html +++ b/docs/reference/add_feature_weights.html @@ -1,108 +1,25 @@ - - - - - - - -Add feature weights — add_feature_weights • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add feature weights — add_feature_weights • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add feature weights

      - Source: R/add_feature_weights.R + Source: R/add_feature_weights.R
      @@ -198,36 +115,31 @@

      Add feature weights

      about how the budget should be allocated.

      - 
      # S4 method for ConservationProblem,numeric
-add_feature_weights(x, weights)
-
-# S4 method for ConservationProblem,matrix
-add_feature_weights(x, weights)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      weights

      numeric or matrix of weights. -See the Weights format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the weights +

      Usage,
      # S4 method for ConservationProblem,numeric
+add_feature_weights(x, weights)
+
+# S4 method for ConservationProblem,matrix
+add_feature_weights(x, weights)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      weights
      +

      numeric or matrix of weights. +See the Weights format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the weights added to it.

      -

      Details

      - +
      +
      +

      Details

      Weights can only be applied to problems that have an objective -that is budget limited (e.g. add_max_cover_objective()). +that is budget limited (e.g., add_max_cover_objective()). They can be applied to problems that aim to maximize phylogenetic -representation (add_max_phylo_div_objective()) to favor the +representation (add_max_phylo_div_objective()) to favor the representation of specific features over the representation of some phylogenetic branches. Weights cannot be negative values and must have values that are equal to or larger than zero. @@ -236,262 +148,262 @@

      Details that the optimization process will favor cheaper solutions over solutions that meet feature targets (or occurrences) when feature weights are lower than 0.01.

      -

      Weights format

      - +
      +
      +

      Weights format

      The argument to weights can be specified using the following formats.

      -
      - -
      weights as a numeric vector

      containing weights for each feature. +

      weights as a numeric vector
      +

      containing weights for each feature. Note that this format cannot be used to specify weights for problems with multiple zones.

      -
      weights as a matrix object

      containing weights + +

      weights as a matrix object
      +

      containing weights for each feature in each zone. Here, each row corresponds to a different feature in argument to x, each column corresponds to a different zone in argument to x, and each cell contains the weight value for a given feature that the solution can to secure in a given zone. Note that if the problem contains targets created using -add_manual_targets() then a matrix should be +add_manual_targets() then a matrix should be supplied containing a single column that indicates that weight for fulfilling each target.

      -
      - -

      See also

      -

      See penalties for an overview of all functions for adding penalties.

      +
      +
      +

      See also

      +

      See penalties for an overview of all functions for adding penalties.

      Other penalties: -add_boundary_penalties(), -add_connectivity_penalties(), -add_linear_penalties()

      +add_boundary_penalties(), +add_connectivity_penalties(), +add_linear_penalties()

      +
      -

      Examples

      - 
      # load ape package
-require(ape)
-#> Loading required package: ape
-#> 
-#> Attaching package: ‘ape’
-#> The following objects are masked from ‘package:raster’:
-#> 
-#>     rotate, zoom
-
-# load data
-data(sim_pu_raster, sim_features, sim_phylogeny, sim_pu_zones_stack,
-     sim_features_zones)
-
-# create minimal problem that aims to maximize the number of features
-# adequately conserved given a total budget of 3800. Here, each feature
-# needs 20% of its habitat for it to be considered adequately conserved
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_features_objective(budget = 3800) %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create weights that assign higher importance to features with less
-# suitable habitat in the study area
-(w2 <- exp((1 / cellStats(sim_features, "sum")) * 200))
-#>   layer.1   layer.2   layer.3   layer.4   layer.5 
-#>  11.03585 606.63186  16.11015 108.65716  34.01731 
-
-# create problem using rarity weights
-p2 <- p1 %>% add_feature_weights(w2)
-
-# create manually specified weights that assign higher importance to
-# certain features. These weights could be based on a pre-calculated index
-# (e.g. an index measuring extinction risk where higher values
-# denote higher extinction risk)
-w3 <- c(0, 0, 0, 100, 200)
-p3 <- p1 %>% add_feature_weights(w3)
-# \dontrun{
-# solve problems
-s1 <- stack(solve(p1), solve(p2), solve(p3))
-
-# plot solutions
-plot(s1, main = c("equal weights", "rarity weights", "manual weights"),
-     axes = FALSE, box = FALSE)
-
-# }
-
-# plot the example phylogeny
-# \dontrun{
-par(mfrow = c(1, 1))
-plot(sim_phylogeny, main = "simulated phylogeny")
-
-# }
-# create problem with a maximum phylogenetic diversity objective,
-# where each feature needs 10% of its distribution to be secured for
-# it to be adequately conserved and a total budget of 1900
-p4 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_phylo_div_objective(1900, sim_phylogeny) %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s4 <- solve(p4)
-
-# plot solution
-plot(s4, main = "solution", axes = FALSE, box = FALSE)
-
-
-# find out which features have their targets met
-r4 <- eval_target_coverage_summary(p4, s4)
-print(r4, width = Inf)
-#> # A tibble: 5 × 9
-#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
-#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
-#> 1 layer.1 FALSE         83.3            8.33          7.35              0.975
-#> 2 layer.2 TRUE          31.2            3.12          3.13              0    
-#> 3 layer.3 FALSE         72.0            7.20          5.78              1.42 
-#> 4 layer.4 TRUE          42.7            4.27          4.50              0    
-#> 5 layer.5 FALSE         56.7            5.67          5.24              0.431
-#>   relative_target relative_held relative_shortfall
-#>             <dbl>         <dbl>              <dbl>
-#> 1             0.1        0.0883            0.0117 
-#> 2             0.1        0.100             0      
-#> 3             0.1        0.0803            0.0197 
-#> 4             0.1        0.106             0      
-#> 5             0.1        0.0924            0.00760
-
-# plot the example phylogeny and color the represented features in red
-plot(sim_phylogeny, main = "represented features",
-     tip.color = replace(rep("black", nlayers(sim_features)),
-                         which(r4$met), "red"))
-
-# }
-# we can see here that the third feature ("layer.3", i.e.
-# sim_features[[3]]) is not represented in the solution. Let us pretend
-# that it is absolutely critical this feature is adequately conserved
-# in the solution. For example, this feature could represent a species
-# that plays important role in the ecosystem, or a species that is
-# important commercial activities (e.g. eco-tourism). So, to generate
-# a solution that conserves the third feature whilst also aiming to
-# maximize phylogenetic diversity, we will create a set of weights that
-# assign a particularly high weighting to the third feature
-w5 <- c(0, 0, 1000, 0, 0)
-
-# we can see that this weighting (i.e. w5[3]) has a much higher value than
-# the branch lengths in the phylogeny so solutions that represent this
-# feature be much closer to optimality
-print(sim_phylogeny$edge.length)
-#> [1] 1.42105185 0.34712544 0.04100098 0.30612447 0.30612447 0.59604770 1.17212960
-#> [8] 1.17212960
-# \dontrun{
-# create problem with high weighting for the third feature and solve it
-s5 <- p4 %>% add_feature_weights(w5) %>% solve()
-
-# plot solution
-plot(s5, main = "solution", axes = FALSE, box = FALSE)
-
-
-# find which features have their targets met
-r5 <- eval_target_coverage_summary(p4, s5)
-print(r5, width = Inf)
-#> # A tibble: 5 × 9
-#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
-#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
-#> 1 layer.1 FALSE         83.3            8.33          7.35              0.975
-#> 2 layer.2 TRUE          31.2            3.12          3.13              0    
-#> 3 layer.3 FALSE         72.0            7.20          5.78              1.42 
-#> 4 layer.4 TRUE          42.7            4.27          4.50              0    
-#> 5 layer.5 FALSE         56.7            5.67          5.24              0.431
-#>   relative_target relative_held relative_shortfall
-#>             <dbl>         <dbl>              <dbl>
-#> 1             0.1        0.0883            0.0117 
-#> 2             0.1        0.100             0      
-#> 3             0.1        0.0803            0.0197 
-#> 4             0.1        0.106             0      
-#> 5             0.1        0.0924            0.00760
-
-# plot the example phylogeny and color the represented features in red
-# here we can see that this solution only adequately conserves the
-# third feature. This means that, given the budget, we are faced with the
-# trade-off of conserving either the third feature, or a phylogenetically
-# diverse set of three different features.
-plot(sim_phylogeny, main = "represented features",
-     tip.color = replace(rep("black", nlayers(sim_features)),
-                         which(r5$met), "red"))
-
-# }
-# create multi-zone problem with maximum features objective,
-# with 10% representation targets for each feature, and set
-# a budget such that the total maximum expenditure in all zones
-# cannot exceed 3000
-p6 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_max_features_objective(3000) %>%
-      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create weights that assign equal weighting for the representation
-# of each feature in each zone except that it does not matter if
-# feature 1 is represented in zone 1 and it really important
-# that feature 3 is really in zone 1
-w7 <- matrix(1, ncol = 3, nrow = 5)
-w7[1, 1] <- 0
-w7[3, 1] <- 100
-
-# create problem with weights
-p7 <- p6 %>% add_feature_weights(w7)
-# \dontrun{
-# solve problems
-s6 <- solve(p6)
-s7 <- solve(p7)
-
-# plot solutions
-plot(stack(category_layer(s6), category_layer(s7)),
-     main = c("equal weights", "manual weights"), axes = FALSE, box = FALSE)
-
-# }
-# create minimal problem to show the correct method for setting
-# weights for problems with manual targets
-p8 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_features_objective(budget = 3000) %>%
-      add_manual_targets(data.frame(feature = c("layer.1", "layer.4"),
-                                    type = "relative",
-                                    target = 0.1)) %>%
-      add_feature_weights(matrix(c(1, 200), ncol = 1)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s8 <- solve(p8)
-
-# plot solution
-plot(s8, main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load ape package
+require(ape)
+#> Loading required package: ape
+#> 
+#> Attaching package: ‘ape’
+#> The following objects are masked from ‘package:raster’:
+#> 
+#>     rotate, zoom
+
+# load data
+data(sim_pu_raster, sim_features, sim_phylogeny, sim_pu_zones_stack,
+     sim_features_zones)
+
+# create minimal problem that aims to maximize the number of features
+# adequately conserved given a total budget of 3800. Here, each feature
+# needs 20% of its habitat for it to be considered adequately conserved
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_features_objective(budget = 3800) %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create weights that assign higher importance to features with less
+# suitable habitat in the study area
+(w2 <- exp((1 / cellStats(sim_features, "sum")) * 200))
+#>   layer.1   layer.2   layer.3   layer.4   layer.5 
+#>  11.03585 606.63186  16.11015 108.65716  34.01731 
+
+# create problem using rarity weights
+p2 <- p1 %>% add_feature_weights(w2)
+
+# create manually specified weights that assign higher importance to
+# certain features. These weights could be based on a pre-calculated index
+# (e.g., an index measuring extinction risk where higher values
+# denote higher extinction risk)
+w3 <- c(0, 0, 0, 100, 200)
+p3 <- p1 %>% add_feature_weights(w3)
+# \dontrun{
+# solve problems
+s1 <- stack(solve(p1), solve(p2), solve(p3))
+
+# plot solutions
+plot(s1, main = c("equal weights", "rarity weights", "manual weights"),
+     axes = FALSE, box = FALSE)
+
+# }
+
+# plot the example phylogeny
+# \dontrun{
+par(mfrow = c(1, 1))
+plot(sim_phylogeny, main = "simulated phylogeny")
+
+# }
+# create problem with a maximum phylogenetic diversity objective,
+# where each feature needs 10% of its distribution to be secured for
+# it to be adequately conserved and a total budget of 1900
+p4 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_phylo_div_objective(1900, sim_phylogeny) %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s4 <- solve(p4)
+
+# plot solution
+plot(s4, main = "solution", axes = FALSE, box = FALSE)
+
+
+# find out which features have their targets met
+r4 <- eval_target_coverage_summary(p4, s4)
+print(r4, width = Inf)
+#> # A tibble: 5 × 9
+#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
+#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
+#> 1 layer.1 FALSE         83.3            8.33          7.35              0.975
+#> 2 layer.2 TRUE          31.2            3.12          3.13              0    
+#> 3 layer.3 FALSE         72.0            7.20          5.78              1.42 
+#> 4 layer.4 TRUE          42.7            4.27          4.50              0    
+#> 5 layer.5 FALSE         56.7            5.67          5.24              0.431
+#>   relative_target relative_held relative_shortfall
+#>             <dbl>         <dbl>              <dbl>
+#> 1             0.1        0.0883            0.0117 
+#> 2             0.1        0.100             0      
+#> 3             0.1        0.0803            0.0197 
+#> 4             0.1        0.106             0      
+#> 5             0.1        0.0924            0.00760
+
+# plot the example phylogeny and color the represented features in red
+plot(sim_phylogeny, main = "represented features",
+     tip.color = replace(rep("black", nlayers(sim_features)),
+                         which(r4$met), "red"))
+
+# }
+# we can see here that the third feature ("layer.3", i.e.,
+# sim_features[[3]]) is not represented in the solution. Let us pretend
+# that it is absolutely critical this feature is adequately conserved
+# in the solution. For example, this feature could represent a species
+# that plays important role in the ecosystem, or a species that is
+# important commercial activities (e.g., eco-tourism). So, to generate
+# a solution that conserves the third feature whilst also aiming to
+# maximize phylogenetic diversity, we will create a set of weights that
+# assign a particularly high weighting to the third feature
+w5 <- c(0, 0, 1000, 0, 0)
+
+# we can see that this weighting (i.e., w5[3]) has a much higher value than
+# the branch lengths in the phylogeny so solutions that represent this
+# feature be much closer to optimality
+print(sim_phylogeny$edge.length)
+#> [1] 1.42105185 0.34712544 0.04100098 0.30612447 0.30612447 0.59604770 1.17212960
+#> [8] 1.17212960
+# \dontrun{
+# create problem with high weighting for the third feature and solve it
+s5 <- p4 %>% add_feature_weights(w5) %>% solve()
+
+# plot solution
+plot(s5, main = "solution", axes = FALSE, box = FALSE)
+
+
+# find which features have their targets met
+r5 <- eval_target_coverage_summary(p4, s5)
+print(r5, width = Inf)
+#> # A tibble: 5 × 9
+#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
+#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
+#> 1 layer.1 FALSE         83.3            8.33          7.35              0.975
+#> 2 layer.2 TRUE          31.2            3.12          3.13              0    
+#> 3 layer.3 FALSE         72.0            7.20          5.78              1.42 
+#> 4 layer.4 TRUE          42.7            4.27          4.50              0    
+#> 5 layer.5 FALSE         56.7            5.67          5.24              0.431
+#>   relative_target relative_held relative_shortfall
+#>             <dbl>         <dbl>              <dbl>
+#> 1             0.1        0.0883            0.0117 
+#> 2             0.1        0.100             0      
+#> 3             0.1        0.0803            0.0197 
+#> 4             0.1        0.106             0      
+#> 5             0.1        0.0924            0.00760
+
+# plot the example phylogeny and color the represented features in red
+# here we can see that this solution only adequately conserves the
+# third feature. This means that, given the budget, we are faced with the
+# trade-off of conserving either the third feature, or a phylogenetically
+# diverse set of three different features.
+plot(sim_phylogeny, main = "represented features",
+     tip.color = replace(rep("black", nlayers(sim_features)),
+                         which(r5$met), "red"))
+
+# }
+# create multi-zone problem with maximum features objective,
+# with 10% representation targets for each feature, and set
+# a budget such that the total maximum expenditure in all zones
+# cannot exceed 3000
+p6 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_max_features_objective(3000) %>%
+      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create weights that assign equal weighting for the representation
+# of each feature in each zone except that it does not matter if
+# feature 1 is represented in zone 1 and it really important
+# that feature 3 is really in zone 1
+w7 <- matrix(1, ncol = 3, nrow = 5)
+w7[1, 1] <- 0
+w7[3, 1] <- 100
+
+# create problem with weights
+p7 <- p6 %>% add_feature_weights(w7)
+# \dontrun{
+# solve problems
+s6 <- solve(p6)
+s7 <- solve(p7)
+
+# plot solutions
+plot(stack(category_layer(s6), category_layer(s7)),
+     main = c("equal weights", "manual weights"), axes = FALSE, box = FALSE)
+
+# }
+# create minimal problem to show the correct method for setting
+# weights for problems with manual targets
+p8 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_features_objective(budget = 3000) %>%
+      add_manual_targets(data.frame(feature = c("layer.1", "layer.4"),
+                                    type = "relative",
+                                    target = 0.1)) %>%
+      add_feature_weights(matrix(c(1, 200), ncol = 1)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s8 <- solve(p8)
+
+# plot solution
+plot(s8, main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_gap_portfolio.html b/docs/reference/add_gap_portfolio.html index f027ee2fe..3a162e15c 100644 --- a/docs/reference/add_gap_portfolio.html +++ b/docs/reference/add_gap_portfolio.html @@ -1,106 +1,23 @@ - - - - - - - -Add a gap portfolio — add_gap_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a gap portfolio — add_gap_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add a gap portfolio

      - Source: R/add_gap_portfolio.R + Source: R/add_gap_portfolio.R

      Generate a portfolio of solutions for a conservation planning -problem() by finding a certain number of solutions that +problem() by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is useful for generating multiple solutions that can be used to calculate selection frequencies for moderate and large-sized problems (similar to Marxan).

      - 
      add_gap_portfolio(x, number_solutions, pool_gap = 0.1)
      +
      Usage,
      add_gap_portfolio(x, number_solutions, pool_gap = 0.1)
      -

      Arguments

      - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      number_solutions

      integer number of solutions required.

      pool_gap

      numeric gap to optimality for solutions in the portfolio. +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      number_solutions
      +

      integer number of solutions required.

      +
      pool_gap
      +

      numeric gap to optimality for solutions in the portfolio. This relative gap specifies a threshold worst-case performance for solutions in the portfolio. For example, value of 0.1 will result in the portfolio returning solutions that are within 10% of an optimal solution. -Note that the gap specified in the solver (i.e. -add_gurobi_solver() must be less than or equal to the gap -specified to generate the portfolio. Defaults to 0.1.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the portfolio +Note that the gap specified in the solver (i.e., +add_gurobi_solver() must be less than or equal to the gap +specified to generate the portfolio. Defaults to 0.1.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the portfolio added to it.

      -

      Details

      - +
      +
      +

      Details

      This strategy for generating a portfolio requires problems to -be solved using the Gurobi software suite (i.e. using -add_gurobi_solver(). Specifically, version 9.0.0 (or greater) +be solved using the Gurobi software suite (i.e., using +add_gurobi_solver(). Specifically, version 9.0.0 (or greater) of the gurobi package must be installed. Note that the number of solutions returned may be less than the argument to number_solutions, if the total number of solutions that meet the optimality gap is less than the number of solutions requested. Also, note that this portfolio function only works with problems -that have binary decisions (i.e. specified using add_binary_decisions()).

      -

      See also

      - -

      See portfolios for an overview of all functions for adding a portfolio.

      +that have binary decisions (i.e., specified using +add_binary_decisions()).

      +
      +
      +

      See also

      +

      See portfolios for an overview of all functions for adding a portfolio.

      Other portfolios: -add_cuts_portfolio(), -add_extra_portfolio(), -add_shuffle_portfolio(), -add_top_portfolio()

      +add_cuts_portfolio(), +add_extra_portfolio(), +add_shuffle_portfolio(), +add_top_portfolio()

      +
      -

      Examples

      - 
      # \dontrun{
-# set seed for reproducibility
-set.seed(600)
-
-# load data
-data(sim_pu_raster, sim_features)
-
-# create minimal problem with a portfolio containing 10 solutions within 20%
-# of optimality
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.05) %>%
-      add_gap_portfolio(number_solutions = 5, pool_gap = 0.2) %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem and generate portfolio
-s1 <- solve(p1)
-
-# print number of solutions found
-print(length(s1))
-#> [1] 5
-
-# plot solutions
-plot(stack(s1), axes = FALSE, box = FALSE)
-
-
-# create multi-zone  problem with a portfolio containing 10 solutions within
-# 20% of optimality
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_gap_portfolio(number_solutions = 5, pool_gap = 0.2) %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem and generate portfolio
-s2 <- solve(p2)
-
-# print number of solutions found
-print(length(s2))
-#> [1] 5
-
-# plot solutions in portfolio
-plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
-     box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# set seed for reproducibility
+set.seed(600)
+
+# load data
+data(sim_pu_raster, sim_features)
+
+# create minimal problem with a portfolio containing 10 solutions within 20%
+# of optimality
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.05) %>%
+      add_gap_portfolio(number_solutions = 5, pool_gap = 0.2) %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem and generate portfolio
+s1 <- solve(p1)
+
+# print number of solutions found
+print(length(s1))
+#> [1] 5
+
+# plot solutions
+plot(stack(s1), axes = FALSE, box = FALSE)
+
+
+# create multi-zone  problem with a portfolio containing 10 solutions within
+# 20% of optimality
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_gap_portfolio(number_solutions = 5, pool_gap = 0.2) %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem and generate portfolio
+s2 <- solve(p2)
+
+# print number of solutions found
+print(length(s2))
+#> [1] 5
+
+# plot solutions in portfolio
+plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
+     box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_gurobi_solver.html b/docs/reference/add_gurobi_solver.html index ad0df63dd..a3cdc4b32 100644 --- a/docs/reference/add_gurobi_solver.html +++ b/docs/reference/add_gurobi_solver.html @@ -1,106 +1,23 @@ - - - - - - - -Add a Gurobi solver — add_gurobi_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a Gurobi solver — add_gurobi_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add a Gurobi solver

      - Source: R/add_gurobi_solver.R + Source: R/add_gurobi_solver.R
      -

      Specify that the Gurobi software +

      Specify that the Gurobi software (Gurobi Optimization LLC 2021) should be used to solve a -conservation planning problem(). This function can also be used to +conservation planning problem(). This function can also be used to customize the behavior of the solver. It requires the gurobi package to be installed (see below for installation instructions).

      - 
      add_gurobi_solver(
-  x,
-  gap = 0.1,
-  time_limit = .Machine$integer.max,
-  presolve = 2,
-  threads = 1,
-  first_feasible = FALSE,
-  numeric_focus = FALSE,
-  node_file_start = Inf,
-  start_solution = NULL,
-  verbose = TRUE
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      gap

      numeric gap to optimality. This gap is relative +

      Usage,
      add_gurobi_solver(
+  x,
+  gap = 0.1,
+  time_limit = .Machine$integer.max,
+  presolve = 2,
+  threads = 1,
+  first_feasible = FALSE,
+  numeric_focus = FALSE,
+  node_file_start = Inf,
+  start_solution = NULL,
+  verbose = TRUE
+)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      gap
      +

      numeric gap to optimality. This gap is relative and expresses the acceptable deviance from the optimal objective. For example, a value of 0.01 will result in the solver stopping when it has found a solution within 1% of optimality. Additionally, a value of 0 will result in the solver stopping when it has found an optimal solution. -The default value is 0.1 (i.e. 10% from optimality).

      time_limit

      numeric time limit (seconds) for generating solutions. +The default value is 0.1 (i.e., 10% from optimality).

      +
      time_limit
      +

      numeric time limit (seconds) for generating solutions. The solver will return the current best solution when this time limit is exceeded. The default value is the largest integer value -(i.e. .Machine$integer.max), effectively meaning that solver -will keep running until a solution within the optimality gap is found.

      presolve

      integer number indicating how intensively the +(i.e., .Machine$integer.max), effectively meaning that solver +will keep running until a solution within the optimality gap is found.

      +
      presolve
      +

      integer number indicating how intensively the solver should try to simplify the problem before solving it. Available options are: (-1) automatically determine the intensity of pre-solving, (0) disable pre-solving, (1) conservative level of pre-solving, and (2) very aggressive level of pre-solving . -The default value is 2.

      threads

      integer number of threads to use for the -optimization algorithm. The default value is 1.

      first_feasible

      logical should the first feasible solution be +The default value is 2.

      +
      threads
      +

      integer number of threads to use for the +optimization algorithm. The default value is 1.

      +
      first_feasible
      +

      logical should the first feasible solution be be returned? If first_feasible is set to TRUE, the solver will return the first solution it encounters that meets all the constraints, regardless of solution quality. Note that the first feasible solution is not an arbitrary solution, rather it is derived from the relaxed solution, and is therefore often reasonably close to optimality. -Defaults to FALSE.

      numeric_focus

      logical should extra attention be paid +Defaults to FALSE.

      +
      numeric_focus
      +

      logical should extra attention be paid to verifying the accuracy of numerical calculations? This may be useful when dealing problems that may suffer from numerical instability issues. Beware that it will likely substantially increase run time (sets the Gurobi NumericFocus parameter -to 3). Defaults to FALSE.

      node_file_start

      numeric threshold amount of memory (in GB). +to 3). Defaults to FALSE.

      +
      node_file_start
      +

      numeric threshold amount of memory (in GB). Once the amount of memory (RAM) used to store information for solving the optimization problem exceeds this parameter value, the solver will begin storing this information on disk (using the *Gurobi( NodeFileStart parameter). This functionality is useful if the system has insufficient memory to -solve a given problem (e.g. solving the problem with default settings +solve a given problem (e.g., solving the problem with default settings yields the OUT OF MEMORY error message) and a system with more memory is not readily available. For example, a value of 4 indicates that the solver will start using the disk after it uses more than 4 GB of memory to store information on solving the problem. Defaults to Inf such that the solver will not attempt -to store information on disk when solving a given problem.

      start_solution

      NULL or object containing the starting solution +to store information on disk when solving a given problem.

      +
      start_solution
      +

      NULL or object containing the starting solution for the solver. Defaults to NULL such that no starting solution is used. To specify a starting solution, the argument to start_solution should -be in the same format as the planning units (i.e. a NULL, numeric, -matrix, data.frame, Raster, Spatial, -or sf::sf() object). -See the Start solution format section for more information.

      verbose

      logical should information be printed while solving -optimization problems? Defaults to TRUE.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the solver +be in the same format as the planning units (i.e., a NULL, numeric, +matrix, data.frame, Raster, Spatial, +or sf::sf() object). +See the Start solution format section for more information.

      +
      verbose
      +

      logical should information be printed while solving +optimization problems? Defaults to TRUE.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the solver added to it.

      -

      Details

      - -

      Gurobi is a +

      +
      +

      Details

      +

      Gurobi is a state-of-the-art commercial optimization software with an R package interface. It is by far the fastest of the solvers available for generating prioritizations, however, it is not freely @@ -316,34 +212,36 @@

      Details please see Schuster et al. (2020) for benchmarks comparing the run time and solution quality of different solvers when applied to different sized datasets.

      -

      Installation

      - +
      +
      +

      Installation

      Please see the Gurobi Installation Guide vignette for details on installing the Gurobi software and the gurobi package. -You can access this vignette online -or using the following code:

      vignette("gurobi_installation", package = "prioritizr")
-
      - -

      Start solution format

      +You can access this vignette online +or using the following code:

      vignette("gurobi_installation", package = "prioritizr")
      +
      +
      +

      Start solution format

      Broadly speaking, the argument to start_solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to start_solution must be a +

      x has numeric planning units
      +

      The argument to start_solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to start_solution.

      -
      x has matrix planning units

      The argument to start_solution must be a + +

      x has matrix planning units
      +

      The argument to start_solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -351,8 +249,10 @@

      Raster planning units +

      The argument to start_solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -360,35 +260,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

      -
      x has Spatial planning units

      The argument to start_solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to start_solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to start_solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

      -
      x has sf::sf() planning units

      The argument to start_solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to start_solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to start_solution must also have the same @@ -397,86 +303,85 @@

      References

      +

      +
      +

      References

      Gurobi Optimization LLC (2021) Gurobi Optimizer Reference Manual. -https://www.gurobi.com.

      +https://www.gurobi.com.

      Schuster R, Hanson JO, Strimas-Mackey M, and Bennett JR (2020). Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems. PeerJ, 8: e9258.

      -

      See also

      - -

      See solvers for an overview of all functions for adding a solver.

      +
      +
      +

      See also

      +

      See solvers for an overview of all functions for adding a solver.

      Other solvers: -add_cbc_solver(), -add_cplex_solver(), -add_default_solver(), -add_lsymphony_solver, -add_rsymphony_solver()

      +add_cbc_solver(), +add_cplex_solver(), +add_default_solver(), +add_lsymphony_solver, +add_rsymphony_solver()

      +
      -

      Examples

      - 
      # \dontrun{
-# load data
-data(sim_pu_raster, sim_features)
-
-# create problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.1) %>%
-     add_binary_decisions() %>%
-     add_gurobi_solver(gap = 0, verbose = FALSE)
-
-# generate solution
-s <- solve(p)
-
-# plot solution
-plot(s, main = "solution", axes = FALSE, box = FALSE)
-
-
-# create a similar problem with boundary length penalties and
-# specify the solution from the previous run as a starting solution
-p2 <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.1) %>%
-     add_boundary_penalties(10) %>%
-     add_binary_decisions() %>%
-     add_gurobi_solver(gap = 0, start_solution = s, verbose = FALSE)
-
-# generate solution
-s2 <- solve(p2)
-
-# plot solution
-plot(s2, main = "solution with boundary penalties", axes = FALSE,
-     box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# load data
+data(sim_pu_raster, sim_features)
+
+# create problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.1) %>%
+     add_binary_decisions() %>%
+     add_gurobi_solver(gap = 0, verbose = FALSE)
+
+# generate solution
+s <- solve(p)
+
+# plot solution
+plot(s, main = "solution", axes = FALSE, box = FALSE)
+
+
+# create a similar problem with boundary length penalties and
+# specify the solution from the previous run as a starting solution
+p2 <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.1) %>%
+     add_boundary_penalties(10) %>%
+     add_binary_decisions() %>%
+     add_gurobi_solver(gap = 0, start_solution = s, verbose = FALSE)
+
+# generate solution
+s2 <- solve(p2)
+
+# plot solution
+plot(s2, main = "solution with boundary penalties", axes = FALSE,
+     box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_linear_constraints.html b/docs/reference/add_linear_constraints.html index 49a0e4931..25c84981f 100644 --- a/docs/reference/add_linear_constraints.html +++ b/docs/reference/add_linear_constraints.html @@ -1,102 +1,19 @@ - - - - - - - -Add linear constraints — add_linear_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add linear constraints — add_linear_constraints • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Add linear constraints

      - Source: R/add_linear_constraints.R + Source: R/add_linear_constraints.R
      -

      Add constraints to a conservation planning problem() to ensure +

      Add constraints to a conservation planning problem() to ensure that all selected planning units meet certain criteria.

      - 
      # S4 method for ConservationProblem,ANY,ANY,character
-add_linear_constraints(x, threshold, sense, data)
+    
      Usage,
      # S4 method for ConservationProblem,ANY,ANY,character
+add_linear_constraints(x, threshold, sense, data)
 
-# S4 method for ConservationProblem,ANY,ANY,numeric
-add_linear_constraints(x, threshold, sense, data)
+# S4 method for ConservationProblem,ANY,ANY,numeric
+add_linear_constraints(x, threshold, sense, data)
 
-# S4 method for ConservationProblem,ANY,ANY,matrix
-add_linear_constraints(x, threshold, sense, data)
+# S4 method for ConservationProblem,ANY,ANY,matrix
+add_linear_constraints(x, threshold, sense, data)
 
-# S4 method for ConservationProblem,ANY,ANY,Matrix
-add_linear_constraints(x, threshold, sense, data)
+# S4 method for ConservationProblem,ANY,ANY,Matrix
+add_linear_constraints(x, threshold, sense, data)
 
-# S4 method for ConservationProblem,ANY,ANY,Raster
-add_linear_constraints(x, threshold, sense, data)
+# S4 method for ConservationProblem,ANY,ANY,Raster
+add_linear_constraints(x, threshold, sense, data)
 
-# S4 method for ConservationProblem,ANY,ANY,dgCMatrix
-add_linear_constraints(x, threshold, sense, data)
      
+# S4 method for ConservationProblem,ANY,ANY,dgCMatrix
+add_linear_constraints(x, threshold, sense, data)
      -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      threshold

      numeric value. +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      threshold
      +

      numeric value. This threshold value is also known as a "right-hand-side" value -per integer programming terminology.

      sense

      character sense for the constraint. Available -options include ">=", "<=", or "=" values.

      data

      character, numeric, -Raster, matrix, or Matrix object +per integer programming terminology.

      +
      sense
      +

      character sense for the constraint. Available +options include ">=", "<=", or "=" values.

      +
      data
      +

      character, numeric, +Raster, matrix, or Matrix object containing the constraint values. These constraint values are also known as constraint coefficients per integer programming terminology. -See the Data format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the constraints +See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the constraints added to it.

      -

      Details

      - +
      +
      +

      Details

      This function adds general purpose constraints that can be used to ensure that solutions meet certain criteria (see Examples section below for details). For example, these constraints can be used to add multiple budgets. They can also be used to ensure that the total number of planning units -allocated to a certain administrative area (e.g. country) does not exceed -a certain threshold (e.g. 30% of its total area). Furthermore, +allocated to a certain administrative area (e.g., country) does not exceed +a certain threshold (e.g., 30% of its total area). Furthermore, they can also be used to ensure that features have a minimal level -of representation (e.g. 30%) when using an objective +of representation (e.g., 30%) when using an objective function that aims to enhance feature representation given a budget -(e.g. add_min_shortfall_objective()).

      -

      Mathematical formulation

      - +(e.g., add_min_shortfall_objective()).

      +
      +
      +

      Mathematical formulation

      The linear constraints are implemented using the following @@ -259,29 +168,29 @@

      Data format

      - +
      +
      +

      Data format

      The argument to data can be specified using the following formats.

      -
      - -
      data as character vector

      containing field (column) name(s) that +

      data as character vector
      +

      containing field (column) name(s) that contain penalty values for planning units. This format is only compatible if the planning units in the argument to x are a -Spatial, sf::sf(), or +Spatial, sf::sf(), or data.frame object. The fields (columns) must have numeric values, and must not contain any missing (NA) values. For problems that contain a single zone, the argument to data must @@ -289,28 +198,34 @@

      data must contain a field name for each zone.

      -
      data as a numeric vector

      containing values for + +

      data as a numeric vector
      +

      containing values for planning units. These values must not contain any missing (NA) values. Note that this format is only available for planning units that contain a single zone.

      -
      data as a matrix/Matrix object

      containing numeric values + +

      data as a matrix/Matrix object
      +

      containing numeric values that specify data for each planning unit. Each row corresponds to a planning unit, each column corresponds to a zone, and each cell indicates the data for penalizing a planning unit when it is allocated to a given zone.

      -
      data as a Raster object

      containing values for planning + +

      data as a Raster object
      +

      containing values for planning units. This format is only compatible if the planning units in the argument to x are -Spatial, sf::sf(), or -Raster objects. -If the planning unit data are a Spatial or -sf::sf() object, then the values are calculated by overlaying the +Spatial, sf::sf(), or +Raster objects. +If the planning unit data are a Spatial or +sf::sf() object, then the values are calculated by overlaying the planning units with the argument to data and calculating the sum of the values associated with each planning unit. If the planning unit data are a -Raster object then the values are calculated by extracting the +Raster object then the values are calculated by extracting the cell values (note that the planning unit data and the argument to data must have exactly the same dimensionality, extent, and missingness). @@ -318,189 +233,187 @@

      -
      - -

      See also

      -

      See constraints for an overview of all functions for adding constraints.

      +
      +
      +

      See also

      +

      See constraints for an overview of all functions for adding constraints.

      Other constraints: -add_contiguity_constraints(), -add_feature_contiguity_constraints(), -add_locked_in_constraints(), -add_locked_out_constraints(), -add_mandatory_allocation_constraints,ConservationProblem-method, -add_manual_bounded_constraints(), -add_manual_locked_constraints()

      - -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# \dontrun{
-# create a baseline problem with minimum shortfall objective
-p0 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_shortfall_objective(1800) %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve problem
-s0 <- solve(p0)
-
-# plot solution
-plot(s0, main = "solution", axes = FALSE, box = FALSE)
-
-
-# now let's create some modified versions of this baseline problem by
-# adding additional criteria using linear constraints
-
-# first, let's create a modified version of p0 that contains
-# an additional budget of 1600 based on a secondary cost dataset
-
-# create a secondary cost dataset by simulating values
-# (note this requires the RandomFields package to be installed)
-sim_pu_raster2 <- simulate_cost(sim_pu_raster)
-
-# plot the primary cost dataset (sim_pu_raster) and
-# the secondary cost dataset (sim_pu_raster2)
-plot(stack(sim_pu_raster, sim_pu_raster2),
-     main = c("sim_pu_raster", "sim_pu_raster2"),
-     axes = FALSE, box = FALSE)
-
-
-# create a modified version of p0 with linear constraints that
-# specify that the planning units in the solution must not have
-# values in sim_pu_raster2 that sum to a total greater than 1600
-p1 <- p0 %>%
-      add_linear_constraints(threshold = 1600,
-                             sense = "<=",
-                             data = sim_pu_raster2)
-
-# solve problem
-s1 <- solve(p1)
-
-# plot solutions s1 and s2 to compare them
-plot(stack(s0, s1), main = c("s0", "s1"), axes = FALSE, box = FALSE)
-
-
-# second, let's create a modified version of p0 that contains
-# additional constraints to ensure that each feature has
-# at least 8% of its overall distribution represented by the solution
-
-# to achieve this, we need to calculate the total amount of each feature
-# within the planning units so we can, in turn, set the constraint thresholds
-feat_abund <- feature_abundances(p0)$absolute_abundance
-
-# create a modified version of p0 with additional constraints for each
-# feature to specify that the planning units in the solution must
-# secure at least 8% of the total abundance for each feature
-p2 <- p0
-for (i in seq_len(nlayers(sim_features))) {
-  p2 <- p2 %>%
-        add_linear_constraints(threshold = feat_abund[i] * 0.08,
-                               sense = ">=",
-                               data = sim_features[[i]])
-}
-
-# overall, p2 could be described as an optimization problem
-# that maximizes feature representation as much as possible
-# towards securing 20% of the total amount of each feature,
-# whilst ensuring that (i) the total cost of the solution does
-# not exceed 1800 (per cost values in sim_pu_raster) and (ii)
-# the solution secures at least 8% of the total amount of each feature
-# (if 20% is not possible due to the budget)
-
-# solve problem
-s2 <- solve(p2)
-
-# plot solutions s0 and s2 to compare them
-plot(stack(s0, s2), main = c("s1", "s2"), axes = FALSE, box = FALSE)
-
-
-# third, let's create a modified version of p0 that contains
-# additional constraints to ensure that the solution equitably
-# distributes conservation effort across different administrative areas
-# (e.g. countries) within the study region
-
-# to begin with, we will simulate a dataset describing the spatial extent of
-# four different administrative areas across the study region
-sim_admin <- sim_pu_raster
-sim_admin <- aggregate(sim_admin, fact = 5)
-values(sim_admin) <- seq_along(values(sim_admin))
-sim_admin <- resample(sim_admin, sim_pu_raster, method = "ngb")
-sim_admin <- mask(sim_admin, sim_pu_raster)
-
-# plot administrative areas layer,
-# we can see that the administrative areas subdivide
-# the study region into four quadrants, and the sim_admin object is a
-# RasterLayer with integer values denoting ids for the administrative areas
-plot(sim_admin)
-
-
-# next we will convert the sim_admin RasterLayer object into a RasterStack
-# object (with a layer for each administrative area) indicating which
-# planning units belong to each administrative area using binary
-# (presence/absence) values
-sim_admin2 <- binary_stack(sim_admin)
-
-# plot administrative areas stack
-plot(sim_admin2)
-
-
-# we will now calculate the total amount of planning units associated
-# with each administrative area, so that we can set the constraint threshold
-
-# since we are using raster data, we won't bother explicitly
-# accounting for the total area of each planning unit (because all
-# planning units have the same area in raster formats) -- but if we were
-# using vector data then we would need to account for the area of each unit
-admin_total <- rowSums(rij_matrix(sim_pu_raster, sim_admin2))
-
-# create a modified version of p0 with additional constraints for each
-# administrative area to specify that the planning units in the solution must
-# not encompass more than 10% of the total extent of the administrative
-# area
-p3 <- p0
-for (i in seq_len(nlayers(sim_admin2))) {
-  p3 <- p3 %>%
-        add_linear_constraints(threshold = admin_total[i] * 0.1,
-                               sense = "<=",
-                               data = sim_admin2[[i]])
-}
-
-# solve problem
-s3 <- solve(p3)
-
-# plot solutions s0 and s3 to compare them
-plot(stack(s0, s3), main = c("s0", "s3"), axes = FALSE, box = FALSE)
-
-# }
-
+add_contiguity_constraints(),
+add_feature_contiguity_constraints(),
+add_locked_in_constraints(),
+add_locked_out_constraints(),
+add_mandatory_allocation_constraints,ConservationProblem-method,
+add_manual_bounded_constraints(),
+add_manual_locked_constraints()
      +
      + +
      +

      Examples

      + 
      # load data
+data(sim_pu_raster, sim_features)
+
+# \dontrun{
+# create a baseline problem with minimum shortfall objective
+p0 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_shortfall_objective(1800) %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve problem
+s0 <- solve(p0)
+
+# plot solution
+plot(s0, main = "solution", axes = FALSE, box = FALSE)
+
+
+# now let's create some modified versions of this baseline problem by
+# adding additional criteria using linear constraints
+
+# first, let's create a modified version of p0 that contains
+# an additional budget of 1600 based on a secondary cost dataset
+
+# create a secondary cost dataset by simulating values
+# (note this requires the RandomFields package to be installed)
+sim_pu_raster2 <- simulate_cost(sim_pu_raster)
+
+# plot the primary cost dataset (sim_pu_raster) and
+# the secondary cost dataset (sim_pu_raster2)
+plot(stack(sim_pu_raster, sim_pu_raster2),
+     main = c("sim_pu_raster", "sim_pu_raster2"),
+     axes = FALSE, box = FALSE)
+
+
+# create a modified version of p0 with linear constraints that
+# specify that the planning units in the solution must not have
+# values in sim_pu_raster2 that sum to a total greater than 1600
+p1 <- p0 %>%
+      add_linear_constraints(threshold = 1600,
+                             sense = "<=",
+                             data = sim_pu_raster2)
+
+# solve problem
+s1 <- solve(p1)
+
+# plot solutions s1 and s2 to compare them
+plot(stack(s0, s1), main = c("s0", "s1"), axes = FALSE, box = FALSE)
+
+
+# second, let's create a modified version of p0 that contains
+# additional constraints to ensure that each feature has
+# at least 8% of its overall distribution represented by the solution
+
+# to achieve this, we need to calculate the total amount of each feature
+# within the planning units so we can, in turn, set the constraint thresholds
+feat_abund <- feature_abundances(p0)$absolute_abundance
+
+# create a modified version of p0 with additional constraints for each
+# feature to specify that the planning units in the solution must
+# secure at least 8% of the total abundance for each feature
+p2 <- p0
+for (i in seq_len(nlayers(sim_features))) {
+  p2 <- p2 %>%
+        add_linear_constraints(threshold = feat_abund[i] * 0.08,
+                               sense = ">=",
+                               data = sim_features[[i]])
+}
+
+# overall, p2 could be described as an optimization problem
+# that maximizes feature representation as much as possible
+# towards securing 20% of the total amount of each feature,
+# whilst ensuring that (i) the total cost of the solution does
+# not exceed 1800 (per cost values in sim_pu_raster) and (ii)
+# the solution secures at least 8% of the total amount of each feature
+# (if 20% is not possible due to the budget)
+
+# solve problem
+s2 <- solve(p2)
+
+# plot solutions s0 and s2 to compare them
+plot(stack(s0, s2), main = c("s1", "s2"), axes = FALSE, box = FALSE)
+
+
+# third, let's create a modified version of p0 that contains
+# additional constraints to ensure that the solution equitably
+# distributes conservation effort across different administrative areas
+# (e.g., countries) within the study region
+
+# to begin with, we will simulate a dataset describing the spatial extent of
+# four different administrative areas across the study region
+sim_admin <- sim_pu_raster
+sim_admin <- aggregate(sim_admin, fact = 5)
+values(sim_admin) <- seq_along(values(sim_admin))
+sim_admin <- resample(sim_admin, sim_pu_raster, method = "ngb")
+sim_admin <- mask(sim_admin, sim_pu_raster)
+
+# plot administrative areas layer,
+# we can see that the administrative areas subdivide
+# the study region into four quadrants, and the sim_admin object is a
+# RasterLayer with integer values denoting ids for the administrative areas
+plot(sim_admin)
+
+
+# next we will convert the sim_admin RasterLayer object into a RasterStack
+# object (with a layer for each administrative area) indicating which
+# planning units belong to each administrative area using binary
+# (presence/absence) values
+sim_admin2 <- binary_stack(sim_admin)
+
+# plot administrative areas stack
+plot(sim_admin2)
+
+
+# we will now calculate the total amount of planning units associated
+# with each administrative area, so that we can set the constraint threshold
+
+# since we are using raster data, we won't bother explicitly
+# accounting for the total area of each planning unit (because all
+# planning units have the same area in raster formats) -- but if we were
+# using vector data then we would need to account for the area of each unit
+admin_total <- rowSums(rij_matrix(sim_pu_raster, sim_admin2))
+
+# create a modified version of p0 with additional constraints for each
+# administrative area to specify that the planning units in the solution must
+# not encompass more than 10% of the total extent of the administrative
+# area
+p3 <- p0
+for (i in seq_len(nlayers(sim_admin2))) {
+  p3 <- p3 %>%
+        add_linear_constraints(threshold = admin_total[i] * 0.1,
+                               sense = "<=",
+                               data = sim_admin2[[i]])
+}
+
+# solve problem
+s3 <- solve(p3)
+
+# plot solutions s0 and s3 to compare them
+plot(stack(s0, s3), main = c("s0", "s3"), axes = FALSE, box = FALSE)
+
+# }
+
      +
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zb!smd| z3^lXtZcL7oBjK0B0>wPz`HR9@_X^Cv2h#qNR`elA z{nr7y&lCZ$M;jnu?mBQ3^z+i(7<=_}|EEm|Lh|7$_~iZ^WX8s`XNc{DJ#ACjsYgX` zoT3bIb*EnuBQMw4_XTEl#kdHwMvgjSpj6z=}nnkks|u2{SSZ>Q+s>cmO!n8n;dpNG6BD3fM z;j6aJr~9|n=8Xx?svmS4J?Y$CIlV>kN)o@7J8p72@WzW;pJ(4vE2?n}OyNH&metaT}|SNgq{O(Sy_&WJ3!30n_ip4LZORb>{P`)kkKXa)JY z%00&|we&`pvTeFhG|{ej4Z#l-^-Na`hD2KSO%S2=$cLf=<}Fq$XWSU#OE$zMyji?r ztxH({tx}*5jtTr(sc-Ebh&a)7{j?>|#R#GjP}w^UTV - - - - - - -Add locked out constraints — add_locked_out_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add locked out constraints — add_locked_out_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - + - - - - - - - - - - - + diff --git a/docs/reference/add_loglinear_targets.html b/docs/reference/add_loglinear_targets.html index 46ae1e8aa..074d92a55 100644 --- a/docs/reference/add_loglinear_targets.html +++ b/docs/reference/add_loglinear_targets.html @@ -1,106 +1,23 @@ - - - - - - - -Add targets using log-linear scaling — add_loglinear_targets • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add targets using log-linear scaling — add_loglinear_targets • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add targets using log-linear scaling

      - Source: R/add_loglinear_targets.R + Source: R/add_loglinear_targets.R
      -

      Add targets to a conservation planning problem() by log-linearly +

      Add targets to a conservation planning problem() by log-linearly interpolating the targets between thresholds based on the total amount of each feature in the study area (Rodrigues et al. 2004). Additionally, caps can be applied to targets to prevent features with massive @@ -194,73 +111,56 @@

      Add targets using log-linear scaling

      in solutions (Butchart et al. 2015).

      - 
      add_loglinear_targets(
-  x,
-  lower_bound_amount,
-  lower_bound_target,
-  upper_bound_amount,
-  upper_bound_target,
-  cap_amount = NULL,
-  cap_target = NULL,
-  abundances = feature_abundances(x, na.rm = FALSE)$absolute_abundance
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      lower_bound_amount

      numeric threshold.

      lower_bound_target

      numeric relative target that should be +

      Usage,
      add_loglinear_targets(
+  x,
+  lower_bound_amount,
+  lower_bound_target,
+  upper_bound_amount,
+  upper_bound_target,
+  cap_amount = NULL,
+  cap_target = NULL,
+  abundances = feature_abundances(x, na.rm = FALSE)$absolute_abundance
+)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      lower_bound_amount
      +

      numeric threshold.

      +
      lower_bound_target
      +

      numeric relative target that should be applied to features with a total amount that is less -than or equal to lower_bound_amount.

      upper_bound_amount

      numeric threshold.

      upper_bound_target

      numeric relative target that should be +than or equal to lower_bound_amount.

      +
      upper_bound_amount
      +

      numeric threshold.

      +
      upper_bound_target
      +

      numeric relative target that should be applied to features with a total amount that is greater -than or equal to upper_bound_amount.

      cap_amount

      numeric total amount at which targets should be -capped. Defaults to NULL so that targets are not capped.

      cap_target

      numeric amount-based target to apply to features +than or equal to upper_bound_amount.

      +
      cap_amount
      +

      numeric total amount at which targets should be +capped. Defaults to NULL so that targets are not capped.

      +
      cap_target
      +

      numeric amount-based target to apply to features which have a total amount greater than argument to cap_amount. -Defaults to NULL so that targets are not capped.

      abundances

      numeric total amount of each feature to +Defaults to NULL so that targets are not capped.

      +
      abundances
      +

      numeric total amount of each feature to use when calculating the targets. Defaults to the feature abundances in the -study area (calculated using the feature_abundances() function.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the targets added +study area (calculated using the feature_abundances() function.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the targets added to it.

      -

      Details

      - +
      +
      +

      Details

      Targets are used to specify the minimum amount or proportion of a feature's distribution that needs to be protected. All conservation planning problems require adding targets with the exception of the maximum -cover problem (see add_max_cover_objective()), which maximizes +cover problem (see add_max_cover_objective()), which maximizes all features in the solution and therefore does not require targets.

      Seven parameters are used to calculate the targets: lower_bound_amount specifies the first range size threshold, @@ -276,20 +176,22 @@

      Details that should be used when calculating the targets.

      The target calculations do not account for the size of each planning unit. Therefore, the feature data should account for -the size of each planning unit if this is important (e.g. pixel values in -the argument to features in the function problem() could +the size of each planning unit if this is important (e.g., pixel values in +the argument to features in the function problem() could correspond to amount of land occupied by the feature in \(km^2\) units). Additionally, the function can only be applied to -ConservationProblem objects that are associated with a +ConservationProblem objects that are associated with a single zone.

      -

      Notes

      - +
      +
      +

      Notes

      Early versions (< 5.0.2.4) used different equations for calculating targets.

      -

      References

      - +
      +
      +

      References

      Rodrigues ASL, Akcakaya HR, Andelman SJ, Bakarr MI, Boitani L, Brooks TM, Chanson JS, Fishpool LDC, da Fonseca GAB, Gaston KJ, and others (2004) Global gap analysis: priority regions for expanding the global @@ -298,58 +200,57 @@

      R Buchanan, GM, Angulo A, Balmford A, Bertzky B, and others (2015) Shortfalls and solutions for meeting national and global conservation area targets. Conservation Letters, 8: 329--337.

      -

      See also

      - -

      See targets for an overview of all functions for adding targets.

      +
      +
      +

      See also

      +

      See targets for an overview of all functions for adding targets.

      Other targets: -add_absolute_targets(), -add_manual_targets(), -add_relative_targets()

      +add_absolute_targets(), +add_manual_targets(), +add_relative_targets()

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create problem using loglinear targets
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_loglinear_targets(10, 0.9, 100, 0.2) %>%
-     add_binary_decisions() %>%
-     add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s <- solve(p)
-
-# plot solution
-plot(s, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create problem using loglinear targets
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_loglinear_targets(10, 0.9, 100, 0.2) %>%
+     add_binary_decisions() %>%
+     add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s <- solve(p)
+
+# plot solution
+plot(s, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_lsymphony_solver.html b/docs/reference/add_lsymphony_solver.html index ecf54f0b2..fa85e7289 100644 --- a/docs/reference/add_lsymphony_solver.html +++ b/docs/reference/add_lsymphony_solver.html @@ -1,106 +1,23 @@ - - - - - - - -Add a SYMPHONY solver with lpsymphony — add_lsymphony_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a SYMPHONY solver with lpsymphony — add_lsymphony_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add a SYMPHONY solver with lpsymphony

      - Source: R/add_lpsymphony_solver.R + Source: R/add_lpsymphony_solver.R
      -

      Specify that the SYMPHONY +

      Specify that the SYMPHONY software (Ralphs & Güzelsoy 2005) -- using the lpsymphony package -- -should be used to solve a conservation planning problem(). +should be used to solve a conservation planning problem(). This function can also be used to customize the behavior of the solver. It requires the lpsymphony package to be installed (see below for installation instructions).

      - 
      add_lpsymphony_solver(
-  x,
-  gap = 0.1,
-  time_limit = .Machine$integer.max,
-  first_feasible = FALSE,
-  verbose = TRUE
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      gap

      numeric gap to optimality. This gap is relative +

      Usage,
      add_lpsymphony_solver(
+  x,
+  gap = 0.1,
+  time_limit = .Machine$integer.max,
+  first_feasible = FALSE,
+  verbose = TRUE
+)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      gap
      +

      numeric gap to optimality. This gap is relative and expresses the acceptable deviance from the optimal objective. For example, a value of 0.01 will result in the solver stopping when it has found a solution within 1% of optimality. Additionally, a value of 0 will result in the solver stopping when it has found an optimal solution. -The default value is 0.1 (i.e. 10% from optimality).

      time_limit

      numeric time limit (seconds) for generating solutions. +The default value is 0.1 (i.e., 10% from optimality).

      +
      time_limit
      +

      numeric time limit (seconds) for generating solutions. The solver will return the current best solution when this time limit is exceeded. The default value is the largest integer value -(i.e. .Machine$integer.max), effectively meaning that solver -will keep running until a solution within the optimality gap is found.

      first_feasible

      logical should the first feasible solution be +(i.e., .Machine$integer.max), effectively meaning that solver +will keep running until a solution within the optimality gap is found.

      +
      first_feasible
      +

      logical should the first feasible solution be be returned? If first_feasible is set to TRUE, the solver will return the first solution it encounters that meets all the constraints, regardless of solution quality. Note that the first feasible solution is not an arbitrary solution, rather it is derived from the relaxed solution, and is therefore often reasonably close to optimality. -Defaults to FALSE.

      verbose

      logical should information be printed while solving -optimization problems? Defaults to TRUE.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the solver +Defaults to FALSE.

      +
      verbose
      +

      logical should information be printed while solving +optimization problems? Defaults to TRUE.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the solver added to it.

      -

      Details

      - -

      SYMPHONY is an +

      +
      +

      Details

      +

      SYMPHONY is an open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. This solver is provided because it may be easier to install @@ -260,84 +166,84 @@

      Details lpsymphony package will solve problems using parallel processing (unlike the Rsymphony package). As a consequence, this solver will likely generate solutions much faster than the -add_rsymphony_solver(). +add_rsymphony_solver(). Although formal benchmarks examining the performance of this solver have yet to be completed, please see Schuster et al. (2020) for benchmarks comparing the run time and solution quality of the Rsymphony solver.

      -

      Installation

      - +
      +
      +

      Installation

      The lpsymphony package is distributed through -Bioconductor. -To install the lpsymphony package, please use the following code:

      if (!require(remotes)) install.packages("remotes")
-remotes::install_bioc("lpsymphony")
-
      - -

      References

      +Bioconductor. +To install the lpsymphony package, please use the following code:

      if (!require(remotes)) install.packages("remotes")
+remotes::install_bioc("lpsymphony")
      +
      +
      +

      References

      Ralphs TK and Güzelsoy M (2005) The SYMPHONY callable library for mixed integer programming. In The Next Wave in Computing, Optimization, and Decision Technologies (pp. 61--76). Springer, Boston, MA.

      Schuster R, Hanson JO, Strimas-Mackey M, and Bennett JR (2020). Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems. PeerJ, 8: e9258.

      -

      See also

      - -

      See solvers for an overview of all functions for adding a solver.

      +
      +
      +

      See also

      +

      See solvers for an overview of all functions for adding a solver.

      Other solvers: -add_cbc_solver(), -add_cplex_solver(), -add_default_solver(), -add_gurobi_solver(), -add_rsymphony_solver()

      +add_cbc_solver(), +add_cplex_solver(), +add_default_solver(), +add_gurobi_solver(), +add_rsymphony_solver()

      +
      -

      Examples

      - 
      # \dontrun{
-# load data
-data(sim_pu_raster, sim_features)
-
-# create problem
-p <- problem(sim_pu_raster, sim_features) %>%
-  add_min_set_objective() %>%
-  add_relative_targets(0.05) %>%
-  add_proportion_decisions() %>%
-  add_lpsymphony_solver(time_limit = 5, verbose = FALSE)
-
-# generate solution
-s <- solve(p)
-
-# plot solution
-plot(s, main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# load data
+data(sim_pu_raster, sim_features)
+
+# create problem
+p <- problem(sim_pu_raster, sim_features) %>%
+  add_min_set_objective() %>%
+  add_relative_targets(0.05) %>%
+  add_proportion_decisions() %>%
+  add_lpsymphony_solver(time_limit = 5, verbose = FALSE)
+
+# generate solution
+s <- solve(p)
+
+# plot solution
+plot(s, main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_mandatory_allocation_constraints.html b/docs/reference/add_mandatory_allocation_constraints.html index 959f164f3..2b53f0308 100644 --- a/docs/reference/add_mandatory_allocation_constraints.html +++ b/docs/reference/add_mandatory_allocation_constraints.html @@ -1,103 +1,20 @@ - - - - - - - -Add mandatory allocation constraints — add_mandatory_allocation_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add mandatory allocation constraints — add_mandatory_allocation_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add mandatory allocation constraints

      - Source: R/add_mandatory_allocation_constraints.R + Source: R/add_mandatory_allocation_constraints.R
      @@ -188,110 +105,106 @@

      Add mandatory allocation constraints

      with problems that contain multiple zones.

      - 
      # S4 method for ConservationProblem
-add_mandatory_allocation_constraints(x)
      - -

      Arguments

      - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the constraints +

      Usage,
      # S4 method for ConservationProblem
+add_mandatory_allocation_constraints(x)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the constraints added to it.

      -

      Details

      - -

      For a conservation planning problem() with multiple +

      +
      +

      Details

      +

      For a conservation planning problem() with multiple management zones, it may sometimes be desirable to obtain a solution that assigns each and every single planning unit to a zone. For example, when developing land-use plans, some decision makers may require that each and every single parcel of land has been allocated a specific land-use type. In other words are no "left over" areas. Although it might seem tempting to simply solve the problem and manually assign "left over" planning units -to a default zone afterwards (e.g. an "other", "urban", or "grazing" +to a default zone afterwards (e.g., an "other", "urban", or "grazing" land-use), this could result in highly sub-optimal solutions if there penalties for siting the default land-use adjacent to other zones. Instead, this function can be used to specify that all planning units in a -problem with multiple zones must be allocated to a management zone (i.e. +problem with multiple zones must be allocated to a management zone (i.e., zone allocation is mandatory).

      -

      See also

      - -

      See constraints for an overview of all functions for adding constraints.

      +
      + +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_zones_stack, sim_features_zones)
-
-# create multi-zone problem with minimum set objective
-targets_matrix <- matrix(rpois(15, 1), nrow = 5, ncol = 3)
-
-# create minimal problem with minimum set objective
-p1 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_absolute_targets(targets_matrix) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create another problem that is the same as p1, but has constraints
-# to mandate that every planning unit in the solution is assigned to
-# zone
-p2 <- p1 %>% add_mandatory_allocation_constraints()
-# \dontrun{
-# solve problems
-s1 <- solve(p1)
-s2 <- solve(p2)
-
-# convert solutions into category layers, where each pixel is assigned
- # value indicating which zone it was assigned to in the zone
-c1 <- category_layer(s1)
-c2 <- category_layer(s2)
-
-# plot solution category layers
-plot(stack(c1, c2), main = c("default", "mandatory allocation"),
-     axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_zones_stack, sim_features_zones)
+
+# create multi-zone problem with minimum set objective
+targets_matrix <- matrix(rpois(15, 1), nrow = 5, ncol = 3)
+
+# create minimal problem with minimum set objective
+p1 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_absolute_targets(targets_matrix) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create another problem that is the same as p1, but has constraints
+# to mandate that every planning unit in the solution is assigned to
+# zone
+p2 <- p1 %>% add_mandatory_allocation_constraints()
+# \dontrun{
+# solve problems
+s1 <- solve(p1)
+s2 <- solve(p2)
+
+# convert solutions into category layers, where each pixel is assigned
+ # value indicating which zone it was assigned to in the zone
+c1 <- category_layer(s1)
+c2 <- category_layer(s2)
+
+# plot solution category layers
+plot(stack(c1, c2), main = c("default", "mandatory allocation"),
+     axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
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      -
      -

      Add manually specified bound constraints

      - Source: R/add_manual_bounded_constraints.R + Source: R/add_manual_bounded_constraints.R
      -

      Add constraints to a conservation planning problem() to ensure -that the planning unit values (e.g. proportion, binary) in a solution +

      Add constraints to a conservation planning problem() to ensure +that the planning unit values (e.g., proportion, binary) in a solution range between specific lower and upper bounds. This function offers more -fine-grained control than the add_manual_locked_constraints() +fine-grained control than the add_manual_locked_constraints() function and is is most useful for problems involving proportion-type or semi-continuous decisions.

      - 
      add_manual_bounded_constraints(x, data)
-
-# S4 method for ConservationProblem,data.frame
-add_manual_bounded_constraints(x, data)
-
-# S4 method for ConservationProblem,tbl_df
-add_manual_bounded_constraints(x, data)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      data

      data.frame or tibble::tibble() object. -See the Data format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the constraints +

      Usage,
      add_manual_bounded_constraints(x, data)
+
+# S4 method for ConservationProblem,data.frame
+add_manual_bounded_constraints(x, data)
+
+# S4 method for ConservationProblem,tbl_df
+add_manual_bounded_constraints(x, data)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      data
      +

      data.frame or tibble::tibble() object. +See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the constraints added to it.

      -

      Data format

      - +
      +
      +

      Data format

      The argument to data should be a data.frame with the following fields (columns):

      -
      +
      pu
      +

      integer planning unit identifier.

      -
      pu

      integer planning unit identifier.

      -
      zone

      character names of zones. Note that this +

      zone
      +

      character names of zones. Note that this argument is optional for arguments to x that contain a single zone.

      -
      lower

      numeric values indicating the minimum + +

      lower
      +

      numeric values indicating the minimum value that each planning unit can be allocated to in each zone in the solution.

      -
      upper

      numeric values indicating the maximum + +

      upper
      +

      numeric values indicating the maximum value that each planning unit can be allocated to in each zone in the solution.

      -
      - -

      See also

      -

      See constraints for an overview of all functions for adding constraints.

      +
      + +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_polygons, sim_features, sim_pu_zones_polygons,
-     sim_features_zones)
-
-# create minimal problem
-p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with locked in constraints using add_locked_constraints
-p2 <- p1 %>% add_locked_in_constraints("locked_in")
-
-# create identical problem using add_manual_bounded_constraints
-bounds_data <- data.frame(pu = which(sim_pu_polygons$locked_in),
-                          lower = 1, upper = 1)
-
-p3 <- p1 %>% add_manual_bounded_constraints(bounds_data)
-# \dontrun{
-# solve problems
-s1 <- solve(p1)
-s2 <- solve(p2)
-s3 <- solve(p3)
-
-# plot solutions
-par(mfrow = c(1,3), mar = c(0, 0, 4.1, 0))
-plot(s1, main = "none locked in")
-plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s2, main = "add_locked_in_constraints")
-plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s3, main = "add_bounds_constraints")
-plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-# }
-# create minimal problem with multiple zones
-p4 <- problem(sim_pu_zones_polygons, sim_features_zones,
-              c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create data.frame with the following constraints:
-# planning units 1, 2, and 3 must be allocated to zone 1 in the solution
-# planning units 4, and 5 must be allocated to zone 2 in the solution
-# planning units 8 and 9 must not be allocated to zone 3 in the solution
-bounds_data2 <- data.frame(pu = c(1, 2, 3, 4, 5, 8, 9),
-                           zone = c(rep("zone_1", 3), rep("zone_2", 2),
-                                    rep("zone_3", 2)),
-                           lower = c(rep(1, 5), rep(0, 2)),
-                           upper = c(rep(1, 5), rep(0, 2)))
-
-# print bounds data
-print(bounds_data2)
-#>   pu   zone lower upper
-#> 1  1 zone_1     1     1
-#> 2  2 zone_1     1     1
-#> 3  3 zone_1     1     1
-#> 4  4 zone_2     1     1
-#> 5  5 zone_2     1     1
-#> 6  8 zone_3     0     0
-#> 7  9 zone_3     0     0
-
-# create problem with added constraints
-p5 <- p4 %>% add_manual_bounded_constraints(bounds_data2)
-# \dontrun{
-# solve problem
-s4 <- solve(p4)
-s5 <- solve(p5)
-
-# create two new columns representing the zone id that each planning unit
-# was allocated to in the two solutions
-s4$solution <- category_vector(s4@data[, c("solution_1_zone_1",
-                                           "solution_1_zone_2",
-                                           "solution_1_zone_3")])
-s4$solution <- factor(s4$solution)
-
-s4$solution_bounded <- category_vector(s5@data[, c("solution_1_zone_1",
-                                                   "solution_1_zone_2",
-                                                   "solution_1_zone_3")])
-s4$solution_bounded <- factor(s4$solution_bounded)
-
-# plot solutions
-spplot(s4, zcol = c("solution", "solution_bounded"), axes = FALSE,
-       box = FALSE)
-
-# }
-
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_polygons, sim_features, sim_pu_zones_polygons,
+     sim_features_zones)
+
+# create minimal problem
+p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with locked in constraints using add_locked_constraints
+p2 <- p1 %>% add_locked_in_constraints("locked_in")
+
+# create identical problem using add_manual_bounded_constraints
+bounds_data <- data.frame(pu = which(sim_pu_polygons$locked_in),
+                          lower = 1, upper = 1)
+
+p3 <- p1 %>% add_manual_bounded_constraints(bounds_data)
+# \dontrun{
+# solve problems
+s1 <- solve(p1)
+s2 <- solve(p2)
+s3 <- solve(p3)
+
+# plot solutions
+par(mfrow = c(1,3), mar = c(0, 0, 4.1, 0))
+plot(s1, main = "none locked in")
+plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s2, main = "add_locked_in_constraints")
+plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s3, main = "add_bounds_constraints")
+plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+# }
+# create minimal problem with multiple zones
+p4 <- problem(sim_pu_zones_polygons, sim_features_zones,
+              c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create data.frame with the following constraints:
+# planning units 1, 2, and 3 must be allocated to zone 1 in the solution
+# planning units 4, and 5 must be allocated to zone 2 in the solution
+# planning units 8 and 9 must not be allocated to zone 3 in the solution
+bounds_data2 <- data.frame(pu = c(1, 2, 3, 4, 5, 8, 9),
+                           zone = c(rep("zone_1", 3), rep("zone_2", 2),
+                                    rep("zone_3", 2)),
+                           lower = c(rep(1, 5), rep(0, 2)),
+                           upper = c(rep(1, 5), rep(0, 2)))
+
+# print bounds data
+print(bounds_data2)
+#>   pu   zone lower upper
+#> 1  1 zone_1     1     1
+#> 2  2 zone_1     1     1
+#> 3  3 zone_1     1     1
+#> 4  4 zone_2     1     1
+#> 5  5 zone_2     1     1
+#> 6  8 zone_3     0     0
+#> 7  9 zone_3     0     0
+
+# create problem with added constraints
+p5 <- p4 %>% add_manual_bounded_constraints(bounds_data2)
+# \dontrun{
+# solve problem
+s4 <- solve(p4)
+s5 <- solve(p5)
+
+# create two new columns representing the zone id that each planning unit
+# was allocated to in the two solutions
+s4$solution <- category_vector(s4@data[, c("solution_1_zone_1",
+                                           "solution_1_zone_2",
+                                           "solution_1_zone_3")])
+s4$solution <- factor(s4$solution)
+
+s4$solution_bounded <- category_vector(s5@data[, c("solution_1_zone_1",
+                                                   "solution_1_zone_2",
+                                                   "solution_1_zone_3")])
+s4$solution_bounded <- factor(s4$solution_bounded)
+
+# plot solutions
+spplot(s4, zcol = c("solution", "solution_bounded"), axes = FALSE,
+       box = FALSE)
+
+# }
+
 
      
+
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zK$A3x!-e{|W#?l~f20D()T;F+Jf$!v+g1y%!MvNiV*U0ACndd{apM;lgMhHT@{rGnj>e*Yu3@O4$Q|G)^mfch)c^zJ0OJ;rVbGx<>rauz}D zf)@37e=mp-5zE2n%6zetZyQ7RUI!_bOx>3+*rkKmb(~`};pZw9sOdA^P%3JqC{D$8 x6J*@h4sYf7xq3?@{jZ{{?6WpnCuS diff --git a/docs/reference/add_manual_locked_constraints.html b/docs/reference/add_manual_locked_constraints.html index 342e2ae41..5da6d2e3c 100644 --- a/docs/reference/add_manual_locked_constraints.html +++ b/docs/reference/add_manual_locked_constraints.html @@ -1,105 +1,22 @@ - - - - - - - -Add manually specified locked constraints — add_manual_locked_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add manually specified locked constraints — add_manual_locked_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add manually specified locked constraints

      - Source: R/add_manual_locked_constraints.R + Source: R/add_manual_locked_constraints.R
      -

      Add constraints to a conservation planning problem() to ensure +

      Add constraints to a conservation planning problem() to ensure that solutions allocate (or do not allocate) specific planning units to specific management zones. This function offers more fine-grained control -than the add_locked_in_constraints() and -add_locked_out_constraints() functions.

      +than the add_locked_in_constraints() and +add_locked_out_constraints() functions.

      - 
      add_manual_locked_constraints(x, data)
-
-# S4 method for ConservationProblem,data.frame
-add_manual_locked_constraints(x, data)
-
-# S4 method for ConservationProblem,tbl_df
-add_manual_locked_constraints(x, data)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      data

      data.frame or tibble::tibble() object. -See the Data format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the constraints +

      Usage,
      add_manual_locked_constraints(x, data)
+
+# S4 method for ConservationProblem,data.frame
+add_manual_locked_constraints(x, data)
+
+# S4 method for ConservationProblem,tbl_df
+add_manual_locked_constraints(x, data)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      data
      +

      data.frame or tibble::tibble() object. +See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the constraints added to it.

      -

      Data format

      - +
      +
      +

      Data format

      The argument to data should be a data.frame with the following fields (columns):

      -
      +
      pu
      +

      integer planning unit identifier.

      -
      pu

      integer planning unit identifier.

      -
      zone

      character names of zones. Note that this +

      zone
      +

      character names of zones. Note that this argument is optional for arguments to x that contain a single zone.

      -
      status

      numeric values indicating how much + +

      status
      +

      numeric values indicating how much of each planning unit should be allocated to each zone in the solution. -For example, the numeric values could be binary values (i.e. zero +For example, the numeric values could be binary values (i.e., zero or one) for problems containing binary-type decision variables -(using the add_binary_decisions() function). Alternatively, -the numeric values could be proportions (e.g. 0.5) for problems +(using the add_binary_decisions() function). Alternatively, +the numeric values could be proportions (e.g., 0.5) for problems containing proportion-type decision variables (using the -add_proportion_decisions()).

      - +add_proportion_decisions()).

      -
      -

      See also

      -

      See constraints for an overview of all functions for adding constraints.

      +
      + +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_polygons, sim_features, sim_pu_zones_polygons,
-     sim_features_zones)
-
-# create minimal problem
-p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with locked in constraints using add_locked_constraints
-p2 <- p1 %>% add_locked_in_constraints("locked_in")
-
-# create identical problem using add_manual_locked_constraints
-locked_data <- data.frame(pu = which(sim_pu_polygons$locked_in),
-                          status = 1)
-
-p3 <- p1 %>% add_manual_locked_constraints(locked_data)
-# \dontrun{
-# solve problems
-s1 <- solve(p1)
-s2 <- solve(p2)
-s3 <- solve(p3)
-
-# plot solutions
-par(mfrow = c(1,3), mar = c(0, 0, 4.1, 0))
-plot(s1, main = "none locked in")
-plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s2, main = "add_locked_in_constraints")
-plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s3, main = "add_manual_constraints")
-plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-# }
-# create minimal problem with multiple zones
-p4 <- problem(sim_pu_zones_polygons, sim_features_zones,
-              c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create data.frame with the following constraints:
-# planning units 1, 2, and 3 must be allocated to zone 1 in the solution
-# planning units 4, and 5 must be allocated to zone 2 in the solution
-# planning units 8 and 9 must not be allocated to zone 3 in the solution
-locked_data2 <- data.frame(pu = c(1, 2, 3, 4, 5, 8, 9),
-                           zone = c(rep("zone_1", 3), rep("zone_2", 2),
-                                    rep("zone_3", 2)),
-                           status = c(rep(1, 5), rep(0, 2)))
-
-# print locked constraint data
-print(locked_data2)
-#>   pu   zone status
-#> 1  1 zone_1      1
-#> 2  2 zone_1      1
-#> 3  3 zone_1      1
-#> 4  4 zone_2      1
-#> 5  5 zone_2      1
-#> 6  8 zone_3      0
-#> 7  9 zone_3      0
-
-# create problem with added constraints
-p5 <- p4 %>% add_manual_locked_constraints(locked_data2)
-# \dontrun{
-# solve problem
-s4 <- solve(p4)
-s5 <- solve(p5)
-
-# create two new columns representing the zone id that each planning unit
-# was allocated to in the two solutions
-s4$solution <- category_vector(s4@data[, c("solution_1_zone_1",
-                                           "solution_1_zone_2",
-                                           "solution_1_zone_3")])
-s4$solution <- factor(s4$solution)
-
-s4$solution_locked <- category_vector(s5@data[, c("solution_1_zone_1",
-                                                  "solution_1_zone_2",
-                                                  "solution_1_zone_3")])
-s4$solution_locked <- factor(s4$solution_locked)
-
-# plot solutions
-spplot(s4, zcol = c("solution", "solution_locked"), axes = FALSE,
-       box = FALSE)
-
-# }
-
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_polygons, sim_features, sim_pu_zones_polygons,
+     sim_features_zones)
+
+# create minimal problem
+p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with locked in constraints using add_locked_constraints
+p2 <- p1 %>% add_locked_in_constraints("locked_in")
+
+# create identical problem using add_manual_locked_constraints
+locked_data <- data.frame(pu = which(sim_pu_polygons$locked_in),
+                          status = 1)
+
+p3 <- p1 %>% add_manual_locked_constraints(locked_data)
+# \dontrun{
+# solve problems
+s1 <- solve(p1)
+s2 <- solve(p2)
+s3 <- solve(p3)
+
+# plot solutions
+par(mfrow = c(1,3), mar = c(0, 0, 4.1, 0))
+plot(s1, main = "none locked in")
+plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s2, main = "add_locked_in_constraints")
+plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s3, main = "add_manual_constraints")
+plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+# }
+# create minimal problem with multiple zones
+p4 <- problem(sim_pu_zones_polygons, sim_features_zones,
+              c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create data.frame with the following constraints:
+# planning units 1, 2, and 3 must be allocated to zone 1 in the solution
+# planning units 4, and 5 must be allocated to zone 2 in the solution
+# planning units 8 and 9 must not be allocated to zone 3 in the solution
+locked_data2 <- data.frame(pu = c(1, 2, 3, 4, 5, 8, 9),
+                           zone = c(rep("zone_1", 3), rep("zone_2", 2),
+                                    rep("zone_3", 2)),
+                           status = c(rep(1, 5), rep(0, 2)))
+
+# print locked constraint data
+print(locked_data2)
+#>   pu   zone status
+#> 1  1 zone_1      1
+#> 2  2 zone_1      1
+#> 3  3 zone_1      1
+#> 4  4 zone_2      1
+#> 5  5 zone_2      1
+#> 6  8 zone_3      0
+#> 7  9 zone_3      0
+
+# create problem with added constraints
+p5 <- p4 %>% add_manual_locked_constraints(locked_data2)
+# \dontrun{
+# solve problem
+s4 <- solve(p4)
+s5 <- solve(p5)
+
+# create two new columns representing the zone id that each planning unit
+# was allocated to in the two solutions
+s4$solution <- category_vector(s4@data[, c("solution_1_zone_1",
+                                           "solution_1_zone_2",
+                                           "solution_1_zone_3")])
+s4$solution <- factor(s4$solution)
+
+s4$solution_locked <- category_vector(s5@data[, c("solution_1_zone_1",
+                                                  "solution_1_zone_2",
+                                                  "solution_1_zone_3")])
+s4$solution_locked <- factor(s4$solution_locked)
+
+# plot solutions
+spplot(s4, zcol = c("solution", "solution_locked"), axes = FALSE,
+       box = FALSE)
+
+# }
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_manual_targets.html b/docs/reference/add_manual_targets.html index 8b8506292..ba460b2bd 100644 --- a/docs/reference/add_manual_targets.html +++ b/docs/reference/add_manual_targets.html @@ -1,61 +1,5 @@ - - - - - - - -Add manual targets — add_manual_targets • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add manual targets — add_manual_targets • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Add manual targets

      - Source: R/add_manual_targets.R + Source: R/add_manual_targets.R
      -

      Set targets for a conservation planning problem() by manually +

      Set targets for a conservation planning problem() by manually specifying all the required information for each target. This function is useful because it can be used to customize all aspects of a target. For most cases, targets can be specified using the -add_absolute_targets() and add_relative_targets() +add_absolute_targets() and add_relative_targets() functions. However, this function can be used to (i) mix absolute and relative targets for different features and zones, (ii) set targets that pertain to the allocations of planning units in multiple zones, and (iii) -set targets that require different senses (e.g. targets which specify the +set targets that require different senses (e.g., targets which specify the solution should not exceed a certain quantity using "<=" values).

      - 
      add_manual_targets(x, targets)
-
-# S4 method for ConservationProblem,data.frame
-add_manual_targets(x, targets)
-
-# S4 method for ConservationProblem,tbl_df
-add_manual_targets(x, targets)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      targets

      data.frame or tibble::tibble() object. -See the Target data format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the targets added +

      Usage,
      add_manual_targets(x, targets)
+
+# S4 method for ConservationProblem,data.frame
+add_manual_targets(x, targets)
+
+# S4 method for ConservationProblem,tbl_df
+add_manual_targets(x, targets)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      targets
      +

      data.frame or tibble::tibble() object. +See the Target data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the targets added to it.

      -

      Details

      - +
      +
      +

      Details

      Targets are used to specify the minimum amount or proportion of a feature's distribution that needs to be protected. Most conservation planning problems require targets with the exception of the maximum cover -(see add_max_cover_objective()) and maximum utility -(see add_max_utility_objective()) problems. Attempting to solve +(see add_max_cover_objective()) and maximum utility +(see add_max_utility_objective()) problems. Attempting to solve problems with objectives that require targets without specifying targets will throw an error.

      For problems associated with multiple management zones, this function can @@ -251,211 +163,217 @@

      Details potentially, be met through allocating all planning units to any specific management zone, or through allocating the planning units to different combinations of management zones.

      -

      Targets format

      - +
      +
      +

      Targets format

      The targets argument should be a data.frame with the following fields (columns):

      -
      - -
      feature

      character name of features in argument +

      feature
      +

      character name of features in argument to x.

      -
      zone

      character name of zones in argument to + +

      zone
      +

      character name of zones in argument to x. This field (column) is optional for arguments to x that do not contain multiple zones.

      -
      type

      character describing the type of target. + +

      type
      +

      character describing the type of target. Acceptable values include "absolute" and "relative". -These values correspond to add_absolute_targets(), -and add_relative_targets() respectively.

      +These values correspond to add_absolute_targets(), +and add_relative_targets() respectively.

      -
      sense

      character sense of the target. Acceptable + +

      sense
      +

      character sense of the target. Acceptable values include: ">=", "<=", and "=". This field (column) is optional and if it is missing then target senses will default to ">=" values.

      -
      target

      numeric target threshold.

      +
      target
      +

      numeric target threshold.

      -
      -

      See also

      -

      See targets for an overview of all functions for adding targets.

      +
      +
      +

      See also

      +

      See targets for an overview of all functions for adding targets.

      Other targets: -add_absolute_targets(), -add_loglinear_targets(), -add_relative_targets()

      +add_absolute_targets(), +add_loglinear_targets(), +add_relative_targets()

      +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create problem with 10% relative targets
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-# }
-# create equivalent problem using add_manual_targets
-p2 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(data.frame(feature = names(sim_features),
-                                    type = "relative", sense = ">=",
-                                    target = 0.1)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# plot solution
-plot(s2, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create problem with targets set for only a few features
-p3 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(data.frame(
-        feature = names(sim_features)[1:3], type = "relative",
-        sense = ">=", target = 0.1)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s3 <- solve(p3)
-
-# plot solution
-plot(s3, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create problem that aims to secure at least 10% of the habitat for one
-# feature whilst ensuring that the solution does not capture more than
-# 20 units habitat for different feature
-# create problem with targets set for only a few features
-p4 <- problem(sim_pu_raster, sim_features[[1:2]]) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(data.frame(
-        feature = names(sim_features)[1:2], type = "relative",
-        sense = c(">=", "<="), target = c(0.1, 0.2))) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s4 <- solve(p4)
-
-# plot solution
-plot(s4, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create a multi-zone problem that requires a specific amount of each
-# feature in each zone
-targets_matrix <- matrix(rpois(15, 1), nrow = 5, ncol = 3)
-
-p5 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_absolute_targets(targets_matrix) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s5 <- solve(p5)
-
-# plot solution
-plot(category_layer(s5), main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create equivalent problem using add_manual_targets
-targets_dataframe <- expand.grid(feature = feature_names(sim_features_zones),
-                                 zone = zone_names(sim_features_zones),
-                                 sense = ">=", type = "absolute")
-targets_dataframe$target <- c(targets_matrix)
-
-p6 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(targets_dataframe) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s6 <- solve(p6)
-
-# plot solution
-plot(category_layer(s6), main = "solution", axes = FALSE, box = FALSE)
-# }
-# create a problem that requires a total of 20 units of habitat to be
-# captured for two species. This can be achieved through representing
-# habitat in two zones. The first zone represents a full restoration of the
-# habitat and a second zone represents a partial restoration of the habitat
-# Thus only half of the benefit that would have been gained from the full
-# restoration is obtained when planning units are allocated a partial
-# restoration
-
-# create data
-spp_zone1 <- as.list(sim_features_zones)[[1]][[1:2]]
-spp_zone2 <- spp_zone1 * 0.5
-costs <- sim_pu_zones_stack[[1:2]]
-
-# create targets
-targets_dataframe2 <- tibble::tibble(
-  feature = names(spp_zone1), zone = list(c("z1", "z2"), c("z1", "z2")),
-  sense = c(">=", ">="), type = c("absolute", "absolute"),
-  target = c(20, 20))
-
-# create problem
-p7 <- problem(costs, zones(spp_zone1, spp_zone2,
-                           feature_names = names(spp_zone1),
-                           zone_names = c("z1", "z2"))) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(targets_dataframe2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s7 <- solve(p7)
-
-# plot solution
-plot(category_layer(s7), main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create problem with 10% relative targets
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+# }
+# create equivalent problem using add_manual_targets
+p2 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(data.frame(feature = names(sim_features),
+                                    type = "relative", sense = ">=",
+                                    target = 0.1)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# plot solution
+plot(s2, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create problem with targets set for only a few features
+p3 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(data.frame(
+        feature = names(sim_features)[1:3], type = "relative",
+        sense = ">=", target = 0.1)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s3 <- solve(p3)
+
+# plot solution
+plot(s3, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create problem that aims to secure at least 10% of the habitat for one
+# feature whilst ensuring that the solution does not capture more than
+# 20 units habitat for different feature
+# create problem with targets set for only a few features
+p4 <- problem(sim_pu_raster, sim_features[[1:2]]) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(data.frame(
+        feature = names(sim_features)[1:2], type = "relative",
+        sense = c(">=", "<="), target = c(0.1, 0.2))) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s4 <- solve(p4)
+
+# plot solution
+plot(s4, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create a multi-zone problem that requires a specific amount of each
+# feature in each zone
+targets_matrix <- matrix(rpois(15, 1), nrow = 5, ncol = 3)
+
+p5 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_absolute_targets(targets_matrix) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s5 <- solve(p5)
+
+# plot solution
+plot(category_layer(s5), main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create equivalent problem using add_manual_targets
+targets_dataframe <- expand.grid(feature = feature_names(sim_features_zones),
+                                 zone = zone_names(sim_features_zones),
+                                 sense = ">=", type = "absolute")
+targets_dataframe$target <- c(targets_matrix)
+
+p6 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(targets_dataframe) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s6 <- solve(p6)
+
+# plot solution
+plot(category_layer(s6), main = "solution", axes = FALSE, box = FALSE)
+# }
+# create a problem that requires a total of 20 units of habitat to be
+# captured for two species. This can be achieved through representing
+# habitat in two zones. The first zone represents a full restoration of the
+# habitat and a second zone represents a partial restoration of the habitat
+# Thus only half of the benefit that would have been gained from the full
+# restoration is obtained when planning units are allocated a partial
+# restoration
+
+# create data
+spp_zone1 <- as.list(sim_features_zones)[[1]][[1:2]]
+spp_zone2 <- spp_zone1 * 0.5
+costs <- sim_pu_zones_stack[[1:2]]
+
+# create targets
+targets_dataframe2 <- tibble::tibble(
+  feature = names(spp_zone1), zone = list(c("z1", "z2"), c("z1", "z2")),
+  sense = c(">=", ">="), type = c("absolute", "absolute"),
+  target = c(20, 20))
+
+# create problem
+p7 <- problem(costs, zones(spp_zone1, spp_zone2,
+                           feature_names = names(spp_zone1),
+                           zone_names = c("z1", "z2"))) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(targets_dataframe2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s7 <- solve(p7)
+
+# plot solution
+plot(category_layer(s7), main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/add_max_cover_objective.html b/docs/reference/add_max_cover_objective.html index 7cef56f8f..6c9f84b01 100644 --- a/docs/reference/add_max_cover_objective.html +++ b/docs/reference/add_max_cover_objective.html @@ -1,105 +1,22 @@ - - - - - - - -Add maximum coverage objective — add_max_cover_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add maximum coverage objective — add_max_cover_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add maximum coverage objective

      - Source: R/add_max_cover_objective.R + Source: R/add_max_cover_objective.R
      -

      Set the objective of a conservation planning problem() to +

      Set the objective of a conservation planning problem() to represent at least one instance of as many features as possible within a given budget. This objective does not use targets, and feature weights should be used instead to increase the representation of certain features by a solution.

      - 
      add_max_cover_objective(x, budget)
      +
      Usage,
      add_max_cover_objective(x, budget)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      budget

      numeric value specifying the maximum expenditure of +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      budget
      +

      numeric value specifying the maximum expenditure of the prioritization. For problems with multiple zones, the argument to budget can be a single numeric value to specify a budget for the entire solution or a numeric vector to specify -a budget for each each management zone.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the objective +a budget for each each management zone.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the objective added to it.

      -

      Details

      - +
      +
      +

      Details

      The maximum coverage objective seeks to find the set of planning units that maximizes the number of represented features, while keeping cost within a fixed budget. Here, features are treated as being represented if the reserve system contains at least a single instance of a feature -(i.e. an amount greater than 1). This formulation has often been +(i.e., an amount greater than 1). This formulation has often been used in conservation planning problems dealing with binary biodiversity data that indicate the presence/absence of suitable habitat -(e.g. Church & Velle 1974). Additionally, weights can be used to favor the +(e.g., Church & Velle 1974). Additionally, weights can be used to favor the representation of certain features over other features (see -add_feature_weights()). Check out the -add_max_features_objective() for a more +add_feature_weights()). Check out the +add_max_features_objective() for a more generalized formulation which can accommodate user-specified representation targets.

      -

      Mathematical formulation

      - +
      +
      +

      Mathematical formulation

      This objective is based on the maximum coverage reserve @@ -244,137 +157,138 @@

      decisions variable (e.g., specifying whether planning unit \(i\) has been selected (1) or not (0)), \(r_{ij}\) is the amount of feature \(j\) in planning unit \(i\), \(y_j\) indicates if the solution has meet the target \(t_j\) for feature \(j\), and \(w_j\) is the weight for feature \(j\) (defaults to 1 for all features; see -add_feature_weights() to specify weights). Additionally, +add_feature_weights() to specify weights). Additionally, \(B\) is the budget allocated for the solution, \(c_i\) is the cost of planning unit \(i\), and \(s\) is a scaling factor used to shrink the costs so that the problem will return a cheapest solution when there are multiple solutions that represent the same amount of all features within the budget.

      -

      Notes

      - +
      +
      +

      Notes

      In early versions (< 3.0.0.0), the mathematical formulation underpinning this function was very different. Specifically, as described above, the function now follows the formulations outlined in Church et al. (1996). The old formulation is now provided by the -add_max_utility_objective() function.

      -

      References

      - +add_max_utility_objective() function.

      +
      +
      +

      References

      Church RL and Velle CR (1974) The maximum covering location problem. Regional Science, 32: 101--118.

      Church RL, Stoms DM, and Davis FW (1996) Reserve selection as a maximum covering location problem. Biological Conservation, 76: 105--112.

      -

      See also

      - -

      See objectives for an overview of all functions for adding objectives. -Also, see add_feature_weights() to specify weights for different features.

      +
      + +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
-
-# threshold the feature data to generate binary biodiversity data
-sim_binary_features <- sim_features
-thresholds <- raster::quantile(sim_features, probs = 0.95, names = FALSE,
-                               na.rm = TRUE)
-for (i in seq_len(raster::nlayers(sim_features)))
-  sim_binary_features[[i]] <- as.numeric(raster::values(sim_features[[i]]) >
-                                         thresholds[[i]])
-
-# create problem with maximum utility objective
-p1 <- problem(sim_pu_raster, sim_binary_features) %>%
-      add_max_cover_objective(500) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# threshold the multi-zone feature data to generate binary biodiversity data
-sim_binary_features_zones <- sim_features_zones
-for (z in number_of_zones(sim_features_zones)) {
-  thresholds <- raster::quantile(sim_features_zones[[z]], probs = 0.95,
-                                 names = FALSE, na.rm = TRUE)
-  for (i in seq_len(number_of_features(sim_features_zones))) {
-    sim_binary_features_zones[[z]][[i]] <- as.numeric(
-      raster::values(sim_features_zones[[z]][[i]]) > thresholds[[i]])
-  }
-}
-
-# create multi-zone problem with maximum utility objective that
-# has a single budget for all zones
-p2 <- problem(sim_pu_zones_stack, sim_binary_features_zones) %>%
-      add_max_cover_objective(800) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# plot solution
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# create multi-zone problem with maximum utility objective that
-# has separate budgets for each zone
-p3 <- problem(sim_pu_zones_stack, sim_binary_features_zones) %>%
-      add_max_cover_objective(c(400, 400, 400)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s3 <- solve(p3)
-
-# plot solution
-plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
+
+# threshold the feature data to generate binary biodiversity data
+sim_binary_features <- sim_features
+thresholds <- raster::quantile(sim_features, probs = 0.95, names = FALSE,
+                               na.rm = TRUE)
+for (i in seq_len(raster::nlayers(sim_features)))
+  sim_binary_features[[i]] <- as.numeric(raster::values(sim_features[[i]]) >
+                                         thresholds[[i]])
+
+# create problem with maximum utility objective
+p1 <- problem(sim_pu_raster, sim_binary_features) %>%
+      add_max_cover_objective(500) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# threshold the multi-zone feature data to generate binary biodiversity data
+sim_binary_features_zones <- sim_features_zones
+for (z in number_of_zones(sim_features_zones)) {
+  thresholds <- raster::quantile(sim_features_zones[[z]], probs = 0.95,
+                                 names = FALSE, na.rm = TRUE)
+  for (i in seq_len(number_of_features(sim_features_zones))) {
+    sim_binary_features_zones[[z]][[i]] <- as.numeric(
+      raster::values(sim_features_zones[[z]][[i]]) > thresholds[[i]])
+  }
+}
+
+# create multi-zone problem with maximum utility objective that
+# has a single budget for all zones
+p2 <- problem(sim_pu_zones_stack, sim_binary_features_zones) %>%
+      add_max_cover_objective(800) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# plot solution
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# create multi-zone problem with maximum utility objective that
+# has separate budgets for each zone
+p3 <- problem(sim_pu_zones_stack, sim_binary_features_zones) %>%
+      add_max_cover_objective(c(400, 400, 400)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s3 <- solve(p3)
+
+# plot solution
+plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_max_features_objective.html b/docs/reference/add_max_features_objective.html index a904a1a65..effa84e2a 100644 --- a/docs/reference/add_max_features_objective.html +++ b/docs/reference/add_max_features_objective.html @@ -1,103 +1,20 @@ - - - - - - - -Add maximum feature representation objective — add_max_features_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add maximum feature representation objective — add_max_features_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add maximum feature representation objective

      - Source: R/add_max_features_objective.R + Source: R/add_max_features_objective.R
      -

      Set the objective of a conservation planning problem() to +

      Set the objective of a conservation planning problem() to fulfill as many targets as possible while ensuring that the cost of the solution does not exceed a budget.

      - 
      add_max_features_objective(x, budget)
      +
      Usage,
      add_max_features_objective(x, budget)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      budget

      numeric value specifying the maximum expenditure of +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      budget
      +

      numeric value specifying the maximum expenditure of the prioritization. For problems with multiple zones, the argument to budget can be (i) a single numeric value to specify a single budget for the entire solution or (ii) a numeric vector to specify -a separate budget for each management zone.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the objective +a separate budget for each management zone.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the objective added to it.

      -

      Details

      - +
      +
      +

      Details

      The maximum feature representation objective is an enhanced version of the -maximum coverage objective add_max_cover_objective() because +maximum coverage objective add_max_cover_objective() because targets can be used to ensure that a certain amount of each feature is required in order for them to be adequately represented (similar to the -minimum set objective (see add_min_set_objective()). This +minimum set objective (see add_min_set_objective()). This objective finds the set of planning units that meets representation targets for as many features as possible while staying within a fixed budget (inspired by Cabeza and Moilanen 2001). Additionally, weights can be used -add_feature_weights()). If multiple solutions can meet the same +add_feature_weights()). If multiple solutions can meet the same number of weighted targets while staying within budget, the cheapest solution is returned.

      -

      Mathematical formulation

      - +
      +
      +

      Mathematical formulation

      This objective can be expressed mathematically for a set of planning units @@ -235,115 +148,115 @@

      decisions variable (e.g., specifying whether planning unit \(i\) has been selected (1) or not (0)), \(r_{ij}\) is the amount of feature \(j\) in planning unit \(i\), \(t_j\) is the representation target for feature \(j\), \(y_j\) indicates if the solution has meet the target \(t_j\) for feature \(j\), and \(w_j\) is the weight for feature \(j\) (defaults to 1 for all features; see -add_feature_weights() to specify weights). Additionally, +add_feature_weights() to specify weights). Additionally, \(B\) is the budget allocated for the solution, \(c_i\) is the cost of planning unit \(i\), and \(s\) is a scaling factor used to shrink the costs so that the problem will return a cheapest solution when there are multiple solutions that represent the same amount of all features within the budget.

      -

      References

      - +
      +
      +

      References

      Cabeza M and Moilanen A (2001) Design of reserve networks and the persistence of biodiversity. Trends in Ecology & Evolution, 16: 242--248.

      -

      See also

      - -

      See objectives for an overview of all functions for adding objectives. -Also, see targets for an overview of all functions for adding targets, and -add_feature_weights() to specify weights for different features.

      +
      +
      +

      See also

      +

      See objectives for an overview of all functions for adding objectives. +Also, see targets for an overview of all functions for adding targets, and +add_feature_weights() to specify weights for different features.

      Other objectives: -add_max_cover_objective(), -add_max_phylo_div_objective(), -add_max_phylo_end_objective(), -add_max_utility_objective(), -add_min_largest_shortfall_objective(), -add_min_set_objective(), -add_min_shortfall_objective()

      +add_max_cover_objective(), +add_max_phylo_div_objective(), +add_max_phylo_end_objective(), +add_max_utility_objective(), +add_min_largest_shortfall_objective(), +add_min_set_objective(), +add_min_shortfall_objective()

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
-
-# create problem with maximum features objective
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_features_objective(1800) %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# create multi-zone problem with maximum features objective,
-# with 10% representation targets for each feature, and set
-# a budget such that the total maximum expenditure in all zones
-# cannot exceed 3000
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_max_features_objective(3000) %>%
-      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# plot solution
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create multi-zone problem with maximum features objective,
-# with 10% representation targets for each feature, and set
-# separate budgets for each management zone
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_max_features_objective(c(3000, 3000, 3000)) %>%
-      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s3 <- solve(p3)
-
-# plot solution
-plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
+
+# create problem with maximum features objective
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_features_objective(1800) %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# create multi-zone problem with maximum features objective,
+# with 10% representation targets for each feature, and set
+# a budget such that the total maximum expenditure in all zones
+# cannot exceed 3000
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_max_features_objective(3000) %>%
+      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# plot solution
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create multi-zone problem with maximum features objective,
+# with 10% representation targets for each feature, and set
+# separate budgets for each management zone
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_max_features_objective(c(3000, 3000, 3000)) %>%
+      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s3 <- solve(p3)
+
+# plot solution
+plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_max_phylo_div_objective.html b/docs/reference/add_max_phylo_div_objective.html index cd6cb2848..d0ed7b206 100644 --- a/docs/reference/add_max_phylo_div_objective.html +++ b/docs/reference/add_max_phylo_div_objective.html @@ -1,108 +1,25 @@ - - - - - - - -Add maximum phylogenetic diversity objective — add_max_phylo_div_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add maximum phylogenetic diversity objective — add_max_phylo_div_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add maximum phylogenetic diversity objective

      - Source: R/add_max_phylo_div_objective.R + Source: R/add_max_phylo_div_objective.R
      -

      Set the objective of a conservation planning problem() to +

      Set the objective of a conservation planning problem() to maximize the phylogenetic diversity of the features represented in the solution subject to a budget. This objective is similar to -add_max_features_objective() except +add_max_features_objective() except that emphasis is placed on representing a phylogenetically diverse set of species, rather than as many features as possible (subject to weights). This function was inspired by Faith (1992) and Rodrigues et al. (2002).

      - 
      add_max_phylo_div_objective(x, budget, tree)
      +
      Usage,
      add_max_phylo_div_objective(x, budget, tree)
      -

      Arguments

      - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      budget

      numeric value specifying the maximum expenditure of +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      budget
      +

      numeric value specifying the maximum expenditure of the prioritization. For problems with multiple zones, the argument to budget can be (i) a single numeric value to specify a single budget for the entire solution or (ii) a numeric vector to specify -a separate budget for each management zone.

      tree

      phylo() object specifying a phylogenetic tree -for the conservation features.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the objective +a separate budget for each management zone.

      +
      tree
      +

      phylo() object specifying a phylogenetic tree +for the conservation features.

      + +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the objective added to it.

      -

      Details

      - +
      +
      +

      Details

      The maximum phylogenetic diversity objective finds the set of planning units that meets representation targets for a phylogenetic tree while staying within a fixed budget. If multiple solutions can meet all targets while staying within budget, the cheapest solution is chosen. Note that this objective is similar to the maximum -features objective (add_max_features_objective()) in that it +features objective (add_max_features_objective()) in that it allows for both a budget and targets to be set for each feature. However, unlike the maximum feature objective, the aim of this objective is to maximize the total phylogenetic diversity of the targets met in the @@ -253,8 +163,9 @@

      Details Here each target corresponds to a single feature and can be met through the total amount of habitat in planning units present to the three zones.

      -

      Mathematical formulation

      - +
      +
      +

      Mathematical formulation

      This objective can be expressed mathematically for a set of planning units @@ -266,7 +177,7 @@

      decisions variable (e.g., specifying whether planning unit \(i\) has been selected (1) or not (0)), \(r_{ij}\) is the amount of feature \(j\) in planning unit \(i\), \(t_j\) is the representation target for feature @@ -283,209 +194,210 @@

      Notes

      - +
      +
      +

      Notes

      In early versions, this function was named as the add_max_phylo_div_objective function.

      -

      References

      - +
      +
      +

      References

      Faith DP (1992) Conservation evaluation and phylogenetic diversity. Biological Conservation, 61: 1--10.

      Rodrigues ASL and Gaston KJ (2002) Maximising phylogenetic diversity in the selection of networks of conservation areas. Biological Conservation, 105: 103--111.

      -

      See also

      - -

      See objectives for an overview of all functions for adding objectives. -Also, see targets for an overview of all functions for adding targets, and -add_feature_weights() to specify weights for different features.

      +
      +
      +

      See also

      +

      See objectives for an overview of all functions for adding objectives. +Also, see targets for an overview of all functions for adding targets, and +add_feature_weights() to specify weights for different features.

      Other objectives: -add_max_cover_objective(), -add_max_features_objective(), -add_max_phylo_end_objective(), -add_max_utility_objective(), -add_min_largest_shortfall_objective(), -add_min_set_objective(), -add_min_shortfall_objective()

      +add_max_cover_objective(), +add_max_features_objective(), +add_max_phylo_end_objective(), +add_max_utility_objective(), +add_min_largest_shortfall_objective(), +add_min_set_objective(), +add_min_shortfall_objective()

      +
      -

      Examples

      - 
      # load ape package
-require(ape)
-
-# load data
-data(sim_pu_raster, sim_features, sim_phylogeny, sim_pu_zones_stack,
-     sim_features_zones)
-
-# plot the simulated phylogeny
-# \dontrun{
-par(mfrow = c(1, 1))
-plot(sim_phylogeny, main = "phylogeny")
-
-# }
-# create problem with a maximum phylogenetic diversity objective,
-# where each feature needs 10% of its distribution to be secured for
-# it to be adequately conserved and a total budget of 1900
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_phylo_div_objective(1900, sim_phylogeny) %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# find out which features have their targets met
-r1 <- eval_target_coverage_summary(p1, s1)
-print(r1, width = Inf)
-#> # A tibble: 5 × 9
-#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
-#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
-#> 1 layer.1 FALSE         83.3            8.33          7.35              0.975
-#> 2 layer.2 TRUE          31.2            3.12          3.13              0    
-#> 3 layer.3 FALSE         72.0            7.20          5.78              1.42 
-#> 4 layer.4 TRUE          42.7            4.27          4.50              0    
-#> 5 layer.5 FALSE         56.7            5.67          5.24              0.431
-#>   relative_target relative_held relative_shortfall
-#>             <dbl>         <dbl>              <dbl>
-#> 1             0.1        0.0883            0.0117 
-#> 2             0.1        0.100             0      
-#> 3             0.1        0.0803            0.0197 
-#> 4             0.1        0.106             0      
-#> 5             0.1        0.0924            0.00760
-
-# plot the phylogeny and color the adequately represented features in red
-plot(sim_phylogeny, main = "adequately represented features",
-     tip.color = replace(
-       rep("black", nlayers(sim_features)),
-       sim_phylogeny$tip.label %in% r1$feature[r1$met],
-       "red"))
-
-# }
-# rename the features in the example phylogeny for use with the
-# multi-zone data
-sim_phylogeny$tip.label <- feature_names(sim_features_zones)
-
-# create targets for a multi-zone problem. Here, each feature needs a total
-# of 10 units of habitat to be conserved among the three zones to be
-# considered adequately conserved
-targets <- tibble::tibble(
-  feature = feature_names(sim_features_zones),
-  zone = list(zone_names(sim_features_zones))[rep(1,
-          number_of_features(sim_features_zones))],
-  type = rep("absolute", number_of_features(sim_features_zones)),
-  target = rep(10, number_of_features(sim_features_zones)))
-
-# create a multi-zone problem with a maximum phylogenetic diversity
-# objective, where the total expenditure in all zones is 5000.
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_max_phylo_div_objective(5000, sim_phylogeny) %>%
-      add_manual_targets(targets) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# plot solution
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
-
-
-# find out which features have their targets met
-r2 <- eval_target_coverage_summary(p2, s2)
-print(r2, width = Inf)
-#> # A tibble: 5 × 11
-#>   feature   zone      sense met   total_amount absolute_target absolute_held
-#>   <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
-#> 1 feature_1 <chr [3]> >=    TRUE         250.               10         17.6 
-#> 2 feature_2 <chr [3]> >=    FALSE         93.6              10          6.66
-#> 3 feature_3 <chr [3]> >=    TRUE         216.               10         14.0 
-#> 4 feature_4 <chr [3]> >=    TRUE         128.               10         10.0 
-#> 5 feature_5 <chr [3]> >=    TRUE         170.               10         12.4 
-#>   absolute_shortfall relative_target relative_held relative_shortfall
-#>                <dbl>           <dbl>         <dbl>              <dbl>
-#> 1               0             0.0400        0.0706             0     
-#> 2               3.34          0.107         0.0712             0.0356
-#> 3               0             0.0463        0.0646             0     
-#> 4               0             0.0781        0.0784             0     
-#> 5               0             0.0588        0.0731             0     
-
-# plot the phylogeny and color the adequately represented features in red
-plot(sim_phylogeny, main = "adequately represented features",
-     tip.color = replace(rep("black", nlayers(sim_features)),
-                         which(r2$met), "red"))
-
-# }
-# create a multi-zone problem with a maximum phylogenetic diversity
-# objective, where each zone has a separate budget.
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_max_phylo_div_objective(c(2500, 500, 2000), sim_phylogeny) %>%
-      add_manual_targets(targets) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s3 <- solve(p3)
-
-# plot solution
-plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
-
-
-# find out which features have their targets met
-r3 <- eval_target_coverage_summary(p3, s3)
-print(r3, width = Inf)
-#> # A tibble: 5 × 11
-#>   feature   zone      sense met   total_amount absolute_target absolute_held
-#>   <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
-#> 1 feature_1 <chr [3]> >=    TRUE         250.               10         15.6 
-#> 2 feature_2 <chr [3]> >=    FALSE         93.6              10          7.23
-#> 3 feature_3 <chr [3]> >=    TRUE         216.               10         12.9 
-#> 4 feature_4 <chr [3]> >=    TRUE         128.               10         10.1 
-#> 5 feature_5 <chr [3]> >=    TRUE         170.               10         10.8 
-#>   absolute_shortfall relative_target relative_held relative_shortfall
-#>                <dbl>           <dbl>         <dbl>              <dbl>
-#> 1               0             0.0400        0.0624             0     
-#> 2               2.77          0.107         0.0772             0.0296
-#> 3               0             0.0463        0.0598             0     
-#> 4               0             0.0781        0.0788             0     
-#> 5               0             0.0588        0.0636             0     
-
-# plot the phylogeny and color the adequately represented features in red
-plot(sim_phylogeny, main = "adequately represented features",
-     tip.color = replace(rep("black", nlayers(sim_features)),
-                         which(r3$met), "red"))
-
-# }
+    
      
+    
      Examples
      
+    
      # load ape package
+require(ape)
+
+# load data
+data(sim_pu_raster, sim_features, sim_phylogeny, sim_pu_zones_stack,
+     sim_features_zones)
+
+# plot the simulated phylogeny
+# \dontrun{
+par(mfrow = c(1, 1))
+plot(sim_phylogeny, main = "phylogeny")
+
+# }
+# create problem with a maximum phylogenetic diversity objective,
+# where each feature needs 10% of its distribution to be secured for
+# it to be adequately conserved and a total budget of 1900
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_phylo_div_objective(1900, sim_phylogeny) %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# find out which features have their targets met
+r1 <- eval_target_coverage_summary(p1, s1)
+print(r1, width = Inf)
+#> # A tibble: 5 × 9
+#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
+#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
+#> 1 layer.1 FALSE         83.3            8.33          7.35              0.975
+#> 2 layer.2 TRUE          31.2            3.12          3.13              0    
+#> 3 layer.3 FALSE         72.0            7.20          5.78              1.42 
+#> 4 layer.4 TRUE          42.7            4.27          4.50              0    
+#> 5 layer.5 FALSE         56.7            5.67          5.24              0.431
+#>   relative_target relative_held relative_shortfall
+#>             <dbl>         <dbl>              <dbl>
+#> 1             0.1        0.0883            0.0117 
+#> 2             0.1        0.100             0      
+#> 3             0.1        0.0803            0.0197 
+#> 4             0.1        0.106             0      
+#> 5             0.1        0.0924            0.00760
+
+# plot the phylogeny and color the adequately represented features in red
+plot(sim_phylogeny, main = "adequately represented features",
+     tip.color = replace(
+       rep("black", nlayers(sim_features)),
+       sim_phylogeny$tip.label %in% r1$feature[r1$met],
+       "red"))
+
+# }
+# rename the features in the example phylogeny for use with the
+# multi-zone data
+sim_phylogeny$tip.label <- feature_names(sim_features_zones)
+
+# create targets for a multi-zone problem. Here, each feature needs a total
+# of 10 units of habitat to be conserved among the three zones to be
+# considered adequately conserved
+targets <- tibble::tibble(
+  feature = feature_names(sim_features_zones),
+  zone = list(zone_names(sim_features_zones))[rep(1,
+          number_of_features(sim_features_zones))],
+  type = rep("absolute", number_of_features(sim_features_zones)),
+  target = rep(10, number_of_features(sim_features_zones)))
+
+# create a multi-zone problem with a maximum phylogenetic diversity
+# objective, where the total expenditure in all zones is 5000.
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_max_phylo_div_objective(5000, sim_phylogeny) %>%
+      add_manual_targets(targets) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# plot solution
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+
+
+# find out which features have their targets met
+r2 <- eval_target_coverage_summary(p2, s2)
+print(r2, width = Inf)
+#> # A tibble: 5 × 11
+#>   feature   zone      sense met   total_amount absolute_target absolute_held
+#>   <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
+#> 1 feature_1 <chr [3]> >=    TRUE         250.               10         17.6 
+#> 2 feature_2 <chr [3]> >=    FALSE         93.6              10          6.66
+#> 3 feature_3 <chr [3]> >=    TRUE         216.               10         14.0 
+#> 4 feature_4 <chr [3]> >=    TRUE         128.               10         10.0 
+#> 5 feature_5 <chr [3]> >=    TRUE         170.               10         12.4 
+#>   absolute_shortfall relative_target relative_held relative_shortfall
+#>                <dbl>           <dbl>         <dbl>              <dbl>
+#> 1               0             0.0400        0.0706             0     
+#> 2               3.34          0.107         0.0712             0.0356
+#> 3               0             0.0463        0.0646             0     
+#> 4               0             0.0781        0.0784             0     
+#> 5               0             0.0588        0.0731             0     
+
+# plot the phylogeny and color the adequately represented features in red
+plot(sim_phylogeny, main = "adequately represented features",
+     tip.color = replace(rep("black", nlayers(sim_features)),
+                         which(r2$met), "red"))
+
+# }
+# create a multi-zone problem with a maximum phylogenetic diversity
+# objective, where each zone has a separate budget.
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_max_phylo_div_objective(c(2500, 500, 2000), sim_phylogeny) %>%
+      add_manual_targets(targets) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s3 <- solve(p3)
+
+# plot solution
+plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
+
+
+# find out which features have their targets met
+r3 <- eval_target_coverage_summary(p3, s3)
+print(r3, width = Inf)
+#> # A tibble: 5 × 11
+#>   feature   zone      sense met   total_amount absolute_target absolute_held
+#>   <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
+#> 1 feature_1 <chr [3]> >=    TRUE         250.               10         15.6 
+#> 2 feature_2 <chr [3]> >=    FALSE         93.6              10          7.23
+#> 3 feature_3 <chr [3]> >=    TRUE         216.               10         12.9 
+#> 4 feature_4 <chr [3]> >=    TRUE         128.               10         10.1 
+#> 5 feature_5 <chr [3]> >=    TRUE         170.               10         10.8 
+#>   absolute_shortfall relative_target relative_held relative_shortfall
+#>                <dbl>           <dbl>         <dbl>              <dbl>
+#> 1               0             0.0400        0.0624             0     
+#> 2               2.77          0.107         0.0772             0.0296
+#> 3               0             0.0463        0.0598             0     
+#> 4               0             0.0781        0.0788             0     
+#> 5               0             0.0588        0.0636             0     
+
+# plot the phylogeny and color the adequately represented features in red
+plot(sim_phylogeny, main = "adequately represented features",
+     tip.color = replace(rep("black", nlayers(sim_features)),
+                         which(r3$met), "red"))
+
+# }
 
      
+
      + - - - - - - - - - - - + diff --git a/docs/reference/add_max_phylo_end_objective.html b/docs/reference/add_max_phylo_end_objective.html index 58c690d1f..489d47c4a 100644 --- a/docs/reference/add_max_phylo_end_objective.html +++ b/docs/reference/add_max_phylo_end_objective.html @@ -1,108 +1,25 @@ - - - - - - - -Add maximum phylogenetic endemism objective — add_max_phylo_end_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add maximum phylogenetic endemism objective — add_max_phylo_end_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add maximum phylogenetic endemism objective

      - Source: R/add_max_phylo_end_objective.R + Source: R/add_max_phylo_end_objective.R
      -

      Set the objective of a conservation planning problem() to +

      Set the objective of a conservation planning problem() to maximize the phylogenetic endemism of the features represented in the solution subject to a budget. This objective is similar to add_max_phylo_end_objective() except @@ -198,42 +115,35 @@

      Add maximum phylogenetic endemism objective

      Rodrigues et al. (2002), and Rosauer et al. (2009).

      - 
      add_max_phylo_end_objective(x, budget, tree)
      +
      Usage,
      add_max_phylo_end_objective(x, budget, tree)
      -

      Arguments

      - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      budget

      numeric value specifying the maximum expenditure of +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      budget
      +

      numeric value specifying the maximum expenditure of the prioritization. For problems with multiple zones, the argument to budget can be (i) a single numeric value to specify a single budget for the entire solution or (ii) a numeric vector to specify -a separate budget for each management zone.

      tree

      phylo() object specifying a phylogenetic tree -for the conservation features.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the objective +a separate budget for each management zone.

      +
      tree
      +

      phylo() object specifying a phylogenetic tree +for the conservation features.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the objective added to it.

      -

      Details

      - +
      +
      +

      Details

      The maximum phylogenetic endemism objective finds the set of planning units that meets representation targets for a phylogenetic tree while staying within a fixed budget. If multiple solutions can meet all targets while staying within budget, the cheapest solution is chosen. Note that this objective is similar to the maximum -features objective (add_max_features_objective()) in that it +features objective (add_max_features_objective()) in that it allows for both a budget and targets to be set for each feature. However, unlike the maximum feature objective, the aim of this objective is to maximize the total phylogenetic endemism of the targets met in the @@ -253,8 +163,9 @@

      Details Here each target corresponds to a single feature and can be met through the total amount of habitat in planning units present to the three zones.

      -

      Mathematical formulation

      - +
      +
      +

      Mathematical formulation

      This objective can be expressed mathematically for a set of planning units @@ -266,7 +177,7 @@

      decisions variable (e.g., specifying whether planning unit \(i\) has been selected (1) or not (0)), \(r_{ij}\) is the amount of feature \(j\) in planning unit \(i\), \(t_j\) is the representation target for feature @@ -287,8 +198,9 @@

      References

      - +
      +
      +

      References

      Faith DP (1992) Conservation evaluation and phylogenetic diversity. Biological Conservation, 61: 1--10.

      Rodrigues ASL and Gaston KJ (2002) Maximising phylogenetic diversity in the @@ -298,196 +210,195 @@

      R Phylogenetic endemism: a new approach for identifying geographical concentrations of evolutionary history. Molecular Ecology, 18: 4061--4072.

      -

      See also

      - -

      See objectives for an overview of all functions for adding objectives. -Also, see targets for an overview of all functions for adding targets, and -add_feature_weights() to specify weights for different features.

      +
      +
      +

      See also

      +

      See objectives for an overview of all functions for adding objectives. +Also, see targets for an overview of all functions for adding targets, and +add_feature_weights() to specify weights for different features.

      Other objectives: -add_max_cover_objective(), -add_max_features_objective(), -add_max_phylo_div_objective(), -add_max_utility_objective(), -add_min_largest_shortfall_objective(), -add_min_set_objective(), -add_min_shortfall_objective()

      +add_max_cover_objective(), +add_max_features_objective(), +add_max_phylo_div_objective(), +add_max_utility_objective(), +add_min_largest_shortfall_objective(), +add_min_set_objective(), +add_min_shortfall_objective()

      +
      -

      Examples

      - 
      # load ape package
-require(ape)
-
-# load data
-data(sim_pu_raster, sim_features, sim_phylogeny, sim_pu_zones_stack,
-     sim_features_zones)
-
-# plot the simulated phylogeny
-# \dontrun{
-par(mfrow = c(1, 1))
-plot(sim_phylogeny, main = "phylogeny")
-
-# }
-# create problem with a maximum phylogenetic endemism objective,
-# where each feature needs 10% of its distribution to be secured for
-# it to be adequately conserved and a total budget of 1900
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_phylo_end_objective(1900, sim_phylogeny) %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# find out which features have their targets met
-r1 <- eval_target_coverage_summary(p1, s1)
-print(r1, width = Inf)
-#> # A tibble: 5 × 9
-#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
-#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
-#> 1 layer.1 FALSE         83.3            8.33          7.71              0.618
-#> 2 layer.2 FALSE         31.2            3.12          2.35              0.775
-#> 3 layer.3 FALSE         72.0            7.20          5.81              1.38 
-#> 4 layer.4 TRUE          42.7            4.27          4.28              0    
-#> 5 layer.5 TRUE          56.7            5.67          5.77              0    
-#>   relative_target relative_held relative_shortfall
-#>             <dbl>         <dbl>              <dbl>
-#> 1             0.1        0.0926            0.00742
-#> 2             0.1        0.0752            0.0248 
-#> 3             0.1        0.0808            0.0192 
-#> 4             0.1        0.100             0      
-#> 5             0.1        0.102             0      
-
-# plot the phylogeny and color the adequately represented features in red
-plot(sim_phylogeny, main = "adequately represented features",
-     tip.color = replace(
-       rep("black", nlayers(sim_features)),
-       sim_phylogeny$tip.label %in% r1$feature[r1$met],
-       "red"))
-
-# }
-# rename the features in the example phylogeny for use with the
-# multi-zone data
-sim_phylogeny$tip.label <- feature_names(sim_features_zones)
-
-# create targets for a multi-zone problem. Here, each feature needs a total
-# of 10 units of habitat to be conserved among the three zones to be
-# considered adequately conserved
-targets <- tibble::tibble(
-  feature = feature_names(sim_features_zones),
-  zone = list(zone_names(sim_features_zones))[rep(1,
-          number_of_features(sim_features_zones))],
-  type = rep("absolute", number_of_features(sim_features_zones)),
-  target = rep(10, number_of_features(sim_features_zones)))
-
-# create a multi-zone problem with a maximum phylogenetic endemism
-# objective, where the total expenditure in all zones is 5000.
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_max_phylo_end_objective(5000, sim_phylogeny) %>%
-      add_manual_targets(targets) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# plot solution
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
-
-
-# find out which features have their targets met
-r2 <- eval_target_coverage_summary(p2, s2)
-print(r2, width = Inf)
-#> # A tibble: 5 × 11
-#>   feature   zone      sense met   total_amount absolute_target absolute_held
-#>   <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
-#> 1 feature_1 <chr [3]> >=    TRUE         250.               10         19.6 
-#> 2 feature_2 <chr [3]> >=    FALSE         93.6              10          6.72
-#> 3 feature_3 <chr [3]> >=    TRUE         216.               10         16.3 
-#> 4 feature_4 <chr [3]> >=    TRUE         128.               10         10.0 
-#> 5 feature_5 <chr [3]> >=    TRUE         170.               10         13.7 
-#>   absolute_shortfall relative_target relative_held relative_shortfall
-#>                <dbl>           <dbl>         <dbl>              <dbl>
-#> 1               0             0.0400        0.0786             0     
-#> 2               3.28          0.107         0.0717             0.0351
-#> 3               0             0.0463        0.0753             0     
-#> 4               0             0.0781        0.0782             0     
-#> 5               0             0.0588        0.0807             0     
-
-# plot the phylogeny and color the adequately represented features in red
-plot(sim_phylogeny, main = "adequately represented features",
-     tip.color = replace(rep("black", nlayers(sim_features)),
-                         which(r2$met), "red"))
-
-# }
-# create a multi-zone problem with a maximum phylogenetic endemism
-# objective, where each zone has a separate budget.
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_max_phylo_end_objective(c(2500, 500, 2000), sim_phylogeny) %>%
-      add_manual_targets(targets) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s3 <- solve(p3)
-
-# plot solution
-plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
-
-
-# find out which features have their targets met
-r3 <- eval_target_coverage_summary(p3, s3)
-print(r3, width = Inf)
-#> # A tibble: 5 × 11
-#>   feature   zone      sense met   total_amount absolute_target absolute_held
-#>   <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
-#> 1 feature_1 <chr [3]> >=    TRUE         250.               10         15.7 
-#> 2 feature_2 <chr [3]> >=    FALSE         93.6              10          5.73
-#> 3 feature_3 <chr [3]> >=    TRUE         216.               10         12.1 
-#> 4 feature_4 <chr [3]> >=    TRUE         128.               10         10.0 
-#> 5 feature_5 <chr [3]> >=    TRUE         170.               10         11.4 
-#>   absolute_shortfall relative_target relative_held relative_shortfall
-#>                <dbl>           <dbl>         <dbl>              <dbl>
-#> 1               0             0.0400        0.0628             0     
-#> 2               4.27          0.107         0.0612             0.0456
-#> 3               0             0.0463        0.0559             0     
-#> 4               0             0.0781        0.0782             0     
-#> 5               0             0.0588        0.0669             0     
-
-# plot the phylogeny and color the adequately represented features in red
-plot(sim_phylogeny, main = "adequately represented features",
-     tip.color = replace(rep("black", nlayers(sim_features)),
-                         which(r3$met), "red"))
-
-# }
+    
      
+    
      Examples
      
+    
      # load ape package
+require(ape)
+
+# load data
+data(sim_pu_raster, sim_features, sim_phylogeny, sim_pu_zones_stack,
+     sim_features_zones)
+
+# plot the simulated phylogeny
+# \dontrun{
+par(mfrow = c(1, 1))
+plot(sim_phylogeny, main = "phylogeny")
+
+# }
+# create problem with a maximum phylogenetic endemism objective,
+# where each feature needs 10% of its distribution to be secured for
+# it to be adequately conserved and a total budget of 1900
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_phylo_end_objective(1900, sim_phylogeny) %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# find out which features have their targets met
+r1 <- eval_target_coverage_summary(p1, s1)
+print(r1, width = Inf)
+#> # A tibble: 5 × 9
+#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
+#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
+#> 1 layer.1 FALSE         83.3            8.33          7.71              0.618
+#> 2 layer.2 FALSE         31.2            3.12          2.35              0.775
+#> 3 layer.3 FALSE         72.0            7.20          5.81              1.38 
+#> 4 layer.4 TRUE          42.7            4.27          4.28              0    
+#> 5 layer.5 TRUE          56.7            5.67          5.77              0    
+#>   relative_target relative_held relative_shortfall
+#>             <dbl>         <dbl>              <dbl>
+#> 1             0.1        0.0926            0.00742
+#> 2             0.1        0.0752            0.0248 
+#> 3             0.1        0.0808            0.0192 
+#> 4             0.1        0.100             0      
+#> 5             0.1        0.102             0      
+
+# plot the phylogeny and color the adequately represented features in red
+plot(sim_phylogeny, main = "adequately represented features",
+     tip.color = replace(
+       rep("black", nlayers(sim_features)),
+       sim_phylogeny$tip.label %in% r1$feature[r1$met],
+       "red"))
+
+# }
+# rename the features in the example phylogeny for use with the
+# multi-zone data
+sim_phylogeny$tip.label <- feature_names(sim_features_zones)
+
+# create targets for a multi-zone problem. Here, each feature needs a total
+# of 10 units of habitat to be conserved among the three zones to be
+# considered adequately conserved
+targets <- tibble::tibble(
+  feature = feature_names(sim_features_zones),
+  zone = list(zone_names(sim_features_zones))[rep(1,
+          number_of_features(sim_features_zones))],
+  type = rep("absolute", number_of_features(sim_features_zones)),
+  target = rep(10, number_of_features(sim_features_zones)))
+
+# create a multi-zone problem with a maximum phylogenetic endemism
+# objective, where the total expenditure in all zones is 5000.
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_max_phylo_end_objective(5000, sim_phylogeny) %>%
+      add_manual_targets(targets) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# plot solution
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+
+
+# find out which features have their targets met
+r2 <- eval_target_coverage_summary(p2, s2)
+print(r2, width = Inf)
+#> # A tibble: 5 × 11
+#>   feature   zone      sense met   total_amount absolute_target absolute_held
+#>   <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
+#> 1 feature_1 <chr [3]> >=    TRUE         250.               10         19.6 
+#> 2 feature_2 <chr [3]> >=    FALSE         93.6              10          6.72
+#> 3 feature_3 <chr [3]> >=    TRUE         216.               10         16.3 
+#> 4 feature_4 <chr [3]> >=    TRUE         128.               10         10.0 
+#> 5 feature_5 <chr [3]> >=    TRUE         170.               10         13.7 
+#>   absolute_shortfall relative_target relative_held relative_shortfall
+#>                <dbl>           <dbl>         <dbl>              <dbl>
+#> 1               0             0.0400        0.0786             0     
+#> 2               3.28          0.107         0.0717             0.0351
+#> 3               0             0.0463        0.0753             0     
+#> 4               0             0.0781        0.0782             0     
+#> 5               0             0.0588        0.0807             0     
+
+# plot the phylogeny and color the adequately represented features in red
+plot(sim_phylogeny, main = "adequately represented features",
+     tip.color = replace(rep("black", nlayers(sim_features)),
+                         which(r2$met), "red"))
+
+# }
+# create a multi-zone problem with a maximum phylogenetic endemism
+# objective, where each zone has a separate budget.
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_max_phylo_end_objective(c(2500, 500, 2000), sim_phylogeny) %>%
+      add_manual_targets(targets) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s3 <- solve(p3)
+
+# plot solution
+plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
+
+
+# find out which features have their targets met
+r3 <- eval_target_coverage_summary(p3, s3)
+print(r3, width = Inf)
+#> # A tibble: 5 × 11
+#>   feature   zone      sense met   total_amount absolute_target absolute_held
+#>   <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
+#> 1 feature_1 <chr [3]> >=    TRUE         250.               10         15.7 
+#> 2 feature_2 <chr [3]> >=    FALSE         93.6              10          5.73
+#> 3 feature_3 <chr [3]> >=    TRUE         216.               10         12.1 
+#> 4 feature_4 <chr [3]> >=    TRUE         128.               10         10.0 
+#> 5 feature_5 <chr [3]> >=    TRUE         170.               10         11.4 
+#>   absolute_shortfall relative_target relative_held relative_shortfall
+#>                <dbl>           <dbl>         <dbl>              <dbl>
+#> 1               0             0.0400        0.0628             0     
+#> 2               4.27          0.107         0.0612             0.0456
+#> 3               0             0.0463        0.0559             0     
+#> 4               0             0.0781        0.0782             0     
+#> 5               0             0.0588        0.0669             0     
+
+# plot the phylogeny and color the adequately represented features in red
+plot(sim_phylogeny, main = "adequately represented features",
+     tip.color = replace(rep("black", nlayers(sim_features)),
+                         which(r3$met), "red"))
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_max_utility_objective.html b/docs/reference/add_max_utility_objective.html index 073f5c7c9..258e31805 100644 --- a/docs/reference/add_max_utility_objective.html +++ b/docs/reference/add_max_utility_objective.html @@ -1,108 +1,25 @@ - - - - - - - -Add maximum utility objective — add_max_utility_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add maximum utility objective — add_max_utility_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add maximum utility objective

      - Source: R/add_max_utility_objective.R + Source: R/add_max_utility_objective.R
      -

      Set the objective of a conservation planning problem() to +

      Set the objective of a conservation planning problem() to secure as much of the features as possible without exceeding a budget. This objective does not use targets, and feature weights should be used instead to increase the representation of certain @@ -198,39 +115,35 @@

      Add maximum utility objective

      just a few features.

      - 
      add_max_utility_objective(x, budget)
      +
      Usage,
      add_max_utility_objective(x, budget)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      budget

      numeric value specifying the maximum expenditure of +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      budget
      +

      numeric value specifying the maximum expenditure of the prioritization. For problems with multiple zones, the argument to budget can be (i) a single numeric value to specify a single budget for the entire solution or (ii) a numeric vector to specify -a separate budget for each management zone.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the objective +a separate budget for each management zone.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the objective added to it.

      -

      Details

      - +
      +
      +

      Details

      The maximum utility objective seeks to maximize the overall level of representation across a suite of conservation features, while keeping cost within a fixed budget. Additionally, weights can be used to favor the representation of certain features over other features (see -add_feature_weights()).

      -

      Mathematical formulation

      - +add_feature_weights()).

      +
      +
      +

      Mathematical formulation

      This objective can be expressed mathematically for a set of planning units @@ -240,110 +153,110 @@

      decisions variable (e.g., specifying whether planning unit \(i\) has been selected (1) or not (0)), \(r_{ij}\) is the amount of feature \(j\) in planning unit \(i\), \(A_j\) is the amount of feature \(j\) represented in in the solution, and \(w_j\) is the weight for feature \(j\) (defaults to 1 for all features; see -add_feature_weights() +add_feature_weights() to specify weights). Additionally, \(B\) is the budget allocated for the solution, \(c_i\) is the cost of planning unit \(i\), and \(s\) is a scaling factor used to shrink the costs so that the problem will return a cheapest solution when there are multiple solutions that represent the same amount of all features within the budget.

      -

      Notes

      - +
      +
      +

      Notes

      In early versions (< 3.0.0.0), this function was named as the add_max_cover_objective function. It was renamed to avoid confusion with existing terminology.

      -

      See also

      - -

      See objectives for an overview of all functions for adding objectives. -Also, see add_feature_weights() to specify weights for different features.

      +
      + +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
-
-# create problem with maximum utility objective
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_utility_objective(5000) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# create multi-zone problem with maximum utility objective that
-# has a single budget for all zones
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_max_utility_objective(5000) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# plot solution
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# create multi-zone problem with maximum utility objective that
-# has separate budgets for each zone
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_max_utility_objective(c(1000, 2000, 3000)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-# \dontrun{
-# solve problem
-s3 <- solve(p3)
-
-# plot solution
-plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
+
+# create problem with maximum utility objective
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_utility_objective(5000) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# create multi-zone problem with maximum utility objective that
+# has a single budget for all zones
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_max_utility_objective(5000) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# plot solution
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# create multi-zone problem with maximum utility objective that
+# has separate budgets for each zone
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_max_utility_objective(c(1000, 2000, 3000)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+# \dontrun{
+# solve problem
+s3 <- solve(p3)
+
+# plot solution
+plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_min_largest_shortfall_objective.html b/docs/reference/add_min_largest_shortfall_objective.html index 76965913b..f44cd4d2f 100644 --- a/docs/reference/add_min_largest_shortfall_objective.html +++ b/docs/reference/add_min_largest_shortfall_objective.html @@ -1,107 +1,24 @@ - - - - - - - -Add minimum largest shortfall objective — add_min_largest_shortfall_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add minimum largest shortfall objective — add_min_largest_shortfall_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add minimum largest shortfall objective

      - Source: R/add_min_largest_shortfall_objective.R + Source: R/add_min_largest_shortfall_objective.R
      -

      Set the objective of a conservation planning problem() to +

      Set the objective of a conservation planning problem() to minimize the largest target shortfall while ensuring that the cost of the solution does not exceed a budget. Note that if the target shortfall for a single feature cannot be decreased beyond a certain -point (e.g. because all remaining planning units occupied by that feature +point (e.g., because all remaining planning units occupied by that feature are too costly or are locked out), then solutions may only use a small proportion of the specified budget.

      - 
      add_min_largest_shortfall_objective(x, budget)
      +
      Usage,
      add_min_largest_shortfall_objective(x, budget)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      budget

      numeric value specifying the maximum expenditure of +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      budget
      +

      numeric value specifying the maximum expenditure of the prioritization. For problems with multiple zones, the argument to budget can be (i) a single numeric value to specify a single budget for the entire solution or (ii) a numeric vector to specify -a separate budget for each management zone.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the objective +a separate budget for each management zone.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the objective added to it.

      -

      Details

      - +
      +
      +

      Details

      The minimum largest shortfall objective aims to find the set of planning units that minimize the largest shortfall for any of the representation targets---that is, the fraction of each target that remains unmet---for as many features as possible while staying within a fixed budget. This objective is different from the -minimum shortfall objective (add_min_shortfall_objective()) because this +minimum shortfall objective (add_min_shortfall_objective()) because this objective minimizes the largest (maximum) target shortfall, whereas the minimum shortfall objective minimizes the total (weighted sum) of the target shortfalls. Note that this objective function is not compatible with feature weights -(add_feature_weights()).

      -

      Mathematical formulation

      - +(add_feature_weights()).

      +
      +
      +

      Mathematical formulation

      This objective can be expressed mathematically for a set of planning units @@ -244,7 +157,7 @@

      decisions variable (e.g., specifying whether planning unit \(i\) has been selected (1) or not (0)), \(r_{ij}\) is the amount of feature \(j\) in planning unit \(i\), and \(t_j\) is the representation target for feature @@ -256,97 +169,96 @@

      See also

      - -

      See objectives for an overview of all functions for adding objectives. -Also, see targets for an overview of all functions for adding targets, and -add_feature_weights() to specify weights for different features.

      +
      +
      +

      See also

      +

      See objectives for an overview of all functions for adding objectives. +Also, see targets for an overview of all functions for adding targets, and +add_feature_weights() to specify weights for different features.

      Other objectives: -add_max_cover_objective(), -add_max_features_objective(), -add_max_phylo_div_objective(), -add_max_phylo_end_objective(), -add_max_utility_objective(), -add_min_set_objective(), -add_min_shortfall_objective()

      +add_max_cover_objective(), +add_max_features_objective(), +add_max_phylo_div_objective(), +add_max_phylo_end_objective(), +add_max_utility_objective(), +add_min_set_objective(), +add_min_shortfall_objective()

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
-
-# create problem with minimum largest shortfall objective
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_largest_shortfall_objective(1800) %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# create multi-zone problem with minimum largest shortfall objective,
-# with 10% representation targets for each feature, and set
-# a budget such that the total maximum expenditure in all zones
-# cannot exceed 3000
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_largest_shortfall_objective(3000) %>%
-      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# plot solution
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create multi-zone problem with minimum largest shortfall objective,
-# with 10% representation targets for each feature, and set
-# separate budgets for each management zone
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_largest_shortfall_objective(c(3000, 3000, 3000)) %>%
-      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s3 <- solve(p3)
-
-# plot solution
-plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
+
+# create problem with minimum largest shortfall objective
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_largest_shortfall_objective(1800) %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# create multi-zone problem with minimum largest shortfall objective,
+# with 10% representation targets for each feature, and set
+# a budget such that the total maximum expenditure in all zones
+# cannot exceed 3000
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_largest_shortfall_objective(3000) %>%
+      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# plot solution
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create multi-zone problem with minimum largest shortfall objective,
+# with 10% representation targets for each feature, and set
+# separate budgets for each management zone
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_largest_shortfall_objective(c(3000, 3000, 3000)) %>%
+      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s3 <- solve(p3)
+
+# plot solution
+plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_min_set_objective.html b/docs/reference/add_min_set_objective.html index b90a8d506..abd8e557a 100644 --- a/docs/reference/add_min_set_objective.html +++ b/docs/reference/add_min_set_objective.html @@ -1,104 +1,21 @@ - - - - - - - -Add minimum set objective — add_min_set_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add minimum set objective — add_min_set_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add minimum set objective

      - Source: R/add_min_set_objective.R + Source: R/add_min_set_objective.R
      -

      Set the objective of a conservation planning problem() to -minimize the cost of the solution whilst ensuring that all targets are met. +

      Set the objective of a conservation planning problem() to +minimize the cost of the solution whilst ensuring that all targets are met. This objective is similar to that used in Marxan and is detailed in Rodrigues et al. (2000).

      - 
      add_min_set_objective(x)
      - -

      Arguments

      - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      +
      Usage,
      add_min_set_objective(x)
      -

      Value

      - -

      Object (i.e. ConservationProblem) with the objective +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the objective added to it.

      -

      Details

      - +
      +
      +

      Details

      The minimum set objective -- in the the context of systematic reserve design -- seeks to find the set of planning units that minimizes the overall cost of a reserve network, while meeting a set of representation @@ -215,8 +129,9 @@

      Details (BLM) set to zero. The difference between this objective and the Marxan software is that the targets for the features will always be met (and as such it does not use Species Penalty Factors).

      -

      Mathematical formulation

      - +
      +
      +

      Mathematical formulation

      This objective can be expressed @@ -225,7 +140,7 @@

      decisions variable (e.g., specifying whether planning unit \(i\) has been selected (1) or not (0)), \(c_i\) is the cost of planning unit \(i\), \(r_{ij}\) is the amount of feature \(j\) in planning unit @@ -233,87 +148,87 @@

      References

      - +
      +
      +

      References

      Rodrigues AS, Cerdeira OJ, and Gaston KJ (2000) Flexibility, efficiency, and accountability: adapting reserve selection algorithms to more complex conservation problems. Ecography, 23: 565--574.

      -

      See also

      - -

      See objectives for an overview of all functions for adding objectives. -Also see targets for an overview of all functions for adding targets.

      +
      + +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem with minimum set objective
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# create multi-zone problem with minimum set objective
-targets_matrix <- matrix(rpois(15, 1), nrow = 5, ncol = 3)
-
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_absolute_targets(targets_matrix) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# plot solution
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem with minimum set objective
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# create multi-zone problem with minimum set objective
+targets_matrix <- matrix(rpois(15, 1), nrow = 5, ncol = 3)
+
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_absolute_targets(targets_matrix) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# plot solution
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/add_min_shortfall_objective.html b/docs/reference/add_min_shortfall_objective.html index efd570c99..c37a87560 100644 --- a/docs/reference/add_min_shortfall_objective.html +++ b/docs/reference/add_min_shortfall_objective.html @@ -1,103 +1,20 @@ - - - - - - - -Add minimum shortfall objective — add_min_shortfall_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add minimum shortfall objective — add_min_shortfall_objective • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add minimum shortfall objective

      - Source: R/add_min_shortfall_objective.R + Source: R/add_min_shortfall_objective.R
      -

      Set the objective of a conservation planning problem() to -minimize the overall shortfall for as many targets as possible while +

      Set the objective of a conservation planning problem() to +minimize the overall shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget.

      - 
      add_min_shortfall_objective(x, budget)
      +
      Usage,
      add_min_shortfall_objective(x, budget)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      budget

      numeric value specifying the maximum expenditure of +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      budget
      +

      numeric value specifying the maximum expenditure of the prioritization. For problems with multiple zones, the argument to budget can be (i) a single numeric value to specify a single budget for the entire solution or (ii) a numeric vector to specify -a separate budget for each management zone.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the objective +a separate budget for each management zone.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the objective added to it.

      -

      Details

      - +
      +
      +

      Details

      The minimum shortfall objective aims to find the set of planning units that minimize the overall (weighted sum) shortfall for the @@ -221,9 +133,10 @@

      Details fixed budget (inspired by Table 1, equation IV, Arponen et al. 2005). Additionally, weights can be used to favor the representation of certain features over other features (see -add_feature_weights().

      -

      Mathematical formulation

      - +add_feature_weights().

      +
      +
      +

      Mathematical formulation

      This objective can be expressed mathematically for a set of planning units @@ -233,114 +146,114 @@

      decisions variable (e.g., specifying whether planning unit \(i\) has been selected (1) or not (0)), \(r_{ij}\) is the amount of feature \(j\) in planning unit \(i\), \(t_j\) is the representation target for feature \(j\), \(y_j\) denotes the representation shortfall for the target \(t_j\) for feature \(j\), and \(w_j\) is the weight for feature \(j\) (defaults to 1 for all features; see -add_feature_weights() to specify weights). Additionally, +add_feature_weights() to specify weights). Additionally, \(B\) is the budget allocated for the solution, \(c_i\) is the cost of planning unit \(i\). Note that \(y_j\) is a continuous variable bounded between zero and infinity, and denotes the shortfall for target \(j\).

      -

      References

      - +
      +
      +

      References

      Arponen A, Heikkinen RK, Thomas CD, and Moilanen A (2005) The value of biodiversity in reserve selection: representation, species weighting, and benefit functions. Conservation Biology, 19: 2009--2014.

      -

      See also

      - -

      See objectives for an overview of all functions for adding objectives. -Also, see targets for an overview of all functions for adding targets, and -add_feature_weights() to specify weights for different features.

      +
      +
      +

      See also

      +

      See objectives for an overview of all functions for adding objectives. +Also, see targets for an overview of all functions for adding targets, and +add_feature_weights() to specify weights for different features.

      Other objectives: -add_max_cover_objective(), -add_max_features_objective(), -add_max_phylo_div_objective(), -add_max_phylo_end_objective(), -add_max_utility_objective(), -add_min_largest_shortfall_objective(), -add_min_set_objective()

      +add_max_cover_objective(), +add_max_features_objective(), +add_max_phylo_div_objective(), +add_max_phylo_end_objective(), +add_max_utility_objective(), +add_min_largest_shortfall_objective(), +add_min_set_objective()

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
-
-# create problem with minimum shortfall objective
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_shortfall_objective(1800) %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# create multi-zone problem with minimum shortfall objective,
-# with 10% representation targets for each feature, and set
-# a budget such that the total maximum expenditure in all zones
-# cannot exceed 3000
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_shortfall_objective(3000) %>%
-      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# plot solution
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create multi-zone problem with minimum shortfall objective,
-# with 10% representation targets for each feature, and set
-# separate budgets for each management zone
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_shortfall_objective(c(3000, 3000, 3000)) %>%
-      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s3 <- solve(p3)
-
-# plot solution
-plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
+
+# create problem with minimum shortfall objective
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_shortfall_objective(1800) %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# create multi-zone problem with minimum shortfall objective,
+# with 10% representation targets for each feature, and set
+# a budget such that the total maximum expenditure in all zones
+# cannot exceed 3000
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_shortfall_objective(3000) %>%
+      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# plot solution
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create multi-zone problem with minimum shortfall objective,
+# with 10% representation targets for each feature, and set
+# separate budgets for each management zone
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_shortfall_objective(c(3000, 3000, 3000)) %>%
+      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s3 <- solve(p3)
+
+# plot solution
+plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_neighbor_constraints.html b/docs/reference/add_neighbor_constraints.html index fbc2353c5..ba32413ad 100644 --- a/docs/reference/add_neighbor_constraints.html +++ b/docs/reference/add_neighbor_constraints.html @@ -1,103 +1,20 @@ - - - - - - - -Add neighbor constraints — add_neighbor_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add neighbor constraints — add_neighbor_constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add neighbor constraints

      - Source: R/add_neighbor_constraints.R + Source: R/add_neighbor_constraints.R
      -

      Add constraints to a conservation planning problem() to ensure +

      Add constraints to a conservation planning problem() to ensure that all selected planning units in the solution have at least a certain number of neighbors that are also selected in the solution.

      - 
      # S4 method for ConservationProblem,ANY,ANY,ANY
-add_neighbor_constraints(x, k, zones, data)
+    
      Usage,
      # S4 method for ConservationProblem,ANY,ANY,ANY
+add_neighbor_constraints(x, k, zones, data)
 
-# S4 method for ConservationProblem,ANY,ANY,data.frame
-add_neighbor_constraints(x, k, zones, data)
+# S4 method for ConservationProblem,ANY,ANY,data.frame
+add_neighbor_constraints(x, k, zones, data)
 
-# S4 method for ConservationProblem,ANY,ANY,matrix
-add_neighbor_constraints(x, k, zones, data)
+# S4 method for ConservationProblem,ANY,ANY,matrix
+add_neighbor_constraints(x, k, zones, data)
 
-# S4 method for ConservationProblem,ANY,ANY,array
-add_neighbor_constraints(x, k, zones, data)
      
+# S4 method for ConservationProblem,ANY,ANY,array
+add_neighbor_constraints(x, k, zones, data)
      -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      k

      integer minimum number of neighbors for selected +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      k
      +

      integer minimum number of neighbors for selected planning units in the solution. For problems with multiple zones, -the argument to k must have an element for each zone.

      zones

      matrix or Matrix object describing the +the argument to k must have an element for each zone.

      +
      zones
      +

      matrix or Matrix object describing the neighborhood scheme for different zones. Each row and column corresponds to a different zone in the argument to x, and cell values must -contain binary numeric values (i.e. one or zero) that indicate +contain binary numeric values (i.e., one or zero) that indicate if neighboring planning units (as specified in the argument to data) should be considered neighbors if they are allocated to different zones. The cell values along the diagonal of the matrix indicate if planning units that are allocated to the same zone should be considered neighbors or not. The default argument to -zones is an identity matrix (i.e. a matrix with ones along the +zones is an identity matrix (i.e., a matrix with ones along the matrix diagonal and zeros elsewhere), so that planning units are -only considered neighbors if they are both allocated to the same zone.

      data

      NULL, matrix, Matrix, data.frame, or +only considered neighbors if they are both allocated to the same zone.

      +
      data
      +

      NULL, matrix, Matrix, data.frame, or array object showing which planning units are neighbors with each other. The argument defaults to NULL which means that the neighborhood data is calculated automatically using the -adjacency_matrix() function. -See the Data format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the constraints +adjacency_matrix() function. +See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the constraints added to it.

      -

      Details

      - +
      +
      +

      Details

      This function uses neighborhood data identify solutions that surround planning units with a minimum number of neighbors. It was inspired by the mathematical formulations detailed in Billionnet (2013) and Beyer et al. (2016).

      -

      Data format

      - +
      +
      +

      Data format

      The argument to data can be specified using the following formats:

      -
      - -
      data as a NULL value

      neighborhood data should be calculated +

      data as a NULL value
      +

      neighborhood data should be calculated automatically -using the adjacency_matrix() function. This is the default +using the adjacency_matrix() function. This is the default argument. Note that the neighborhood data must be manually defined using one of the other formats below when the planning unit data -in the argument to x is not spatially referenced (e.g. +in the argument to x is not spatially referenced (e.g., in data.frame or numeric format).

      -
      data as a matrix/Matrix object

      where rows and columns represent + +

      data as a matrix/Matrix object
      +

      where rows and columns represent different planning units and the value of each cell indicates if the two planning units are neighbors or not. Cell values should be binary -numeric values (i.e. one or zero). Cells that occur along the +numeric values (i.e., one or zero). Cells that occur along the matrix diagonal have no effect on the solution at all because each planning unit cannot be a neighbor with itself.

      -
      data as a data.frame object

      containing the fields (columns) + +

      data as a data.frame object
      +

      containing the fields (columns) "id1", "id2", and "boundary". Here, each row denotes the connectivity between two planning units following the Marxan format. The field boundary should contain @@ -280,7 +192,7 @@

      x contains multiple zones, then the columns @@ -290,11 +202,13 @@

      "zone1" and "zone2" are present, then the argument to zones must be NULL.

      -
      data as an array object

      containing four-dimensions where binary + +

      data as an array object
      +

      containing four-dimensions where binary numeric values indicate if planning unit should be treated as being neighbors with every other planning unit when they are allocated to every combination of management zone. The first two -dimensions (i.e. rows and columns) correspond to the planning units, +dimensions (i.e., rows and columns) correspond to the planning units, and second two dimensions correspond to the management zones. For example, if the argument to data had a value of 1 at the index data[1, 2, 3, 4] this would indicate that planning unit 1 and @@ -302,134 +216,133 @@

      -
      - -

      References

      +
      +
      +

      References

      Beyer HL, Dujardin Y, Watts ME, and Possingham HP (2016) Solving conservation planning problems with integer linear programming. Ecological Modelling, 228: 14--22.

      Billionnet A (2013) Mathematical optimization ideas for biodiversity conservation. European Journal of Operational Research, 231: 514--534.

      -

      See also

      - -

      See constraints for an overview of all functions for adding constraints.

      +
      + +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with constraints that require 1 neighbor
-# and neighbors are defined using a rook-style neighborhood
-p2 <- p1 %>% add_neighbor_constraints(1)
-
-# create problem with constraints that require 2 neighbor
-# and neighbors are defined using a rook-style neighborhood
-p3 <- p1 %>% add_neighbor_constraints(2)
-
-# create problem with constraints that require 3 neighbor
-# and neighbors are defined using a queen-style neighborhood
-p4 <- p1 %>% add_neighbor_constraints(3,
-               data = adjacency_matrix(sim_pu_raster, directions = 8))
-
-# \dontrun{
-# solve problems
-s1 <- stack(list(solve(p1), solve(p2), solve(p3), solve(p4)))
-
-# plot solutions
-plot(s1, box = FALSE, axes = FALSE,
-     main = c("basic solution", "1 neighbor", "2 neighbors", "3 neighbors"))
-
-# }
-# create minimal problem with multiple zones
-p5 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem where selected planning units require at least 2 neighbors
-# for each zone and planning units are only considered neighbors if they
-# are allocated to the same zone
-z6 <- diag(3)
-print(z6)
-#>      [,1] [,2] [,3]
-#> [1,]    1    0    0
-#> [2,]    0    1    0
-#> [3,]    0    0    1
-p6 <- p5 %>% add_neighbor_constraints(rep(2, 3), z6)
-
-# create problem where the planning units in zone 1 don't explicitly require
-# any neighbors, planning units in zone 2 require at least 1 neighbors, and
-# planning units in zone 3 require at least 2 neighbors. As before, planning
-# units are still only considered neighbors if they are allocated to the
-# same zone
-p7 <- p5 %>% add_neighbor_constraints(c(0, 1, 2), z6)
-
-# create problem given the same constraints as outlined above, except
-# that when determining which selected planning units are neighbors,
-# planning units that are allocated to zone 1 and zone 2 can also treated
-# as being neighbors with each other
-z8 <- diag(3)
-z8[1, 2] <- 1
-z8[2, 1] <- 1
-print(z8)
-#>      [,1] [,2] [,3]
-#> [1,]    1    1    0
-#> [2,]    1    1    0
-#> [3,]    0    0    1
-p8 <- p5 %>% add_neighbor_constraints(c(0, 1, 2), z8)
-# \dontrun{
-# solve problems
-s2 <- list(p5, p6, p7, p8)
-s2 <- lapply(s2, solve)
-s2 <- lapply(s2, category_layer)
-s2 <- stack(s2)
-names(s2) <- c("basic problem", "p6", "p7", "p8")
-
-# plot solutions
-plot(s2, main = names(s2), box = FALSE, axes = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with constraints that require 1 neighbor
+# and neighbors are defined using a rook-style neighborhood
+p2 <- p1 %>% add_neighbor_constraints(1)
+
+# create problem with constraints that require 2 neighbor
+# and neighbors are defined using a rook-style neighborhood
+p3 <- p1 %>% add_neighbor_constraints(2)
+
+# create problem with constraints that require 3 neighbor
+# and neighbors are defined using a queen-style neighborhood
+p4 <- p1 %>% add_neighbor_constraints(3,
+               data = adjacency_matrix(sim_pu_raster, directions = 8))
+
+# \dontrun{
+# solve problems
+s1 <- stack(list(solve(p1), solve(p2), solve(p3), solve(p4)))
+
+# plot solutions
+plot(s1, box = FALSE, axes = FALSE,
+     main = c("basic solution", "1 neighbor", "2 neighbors", "3 neighbors"))
+
+# }
+# create minimal problem with multiple zones
+p5 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem where selected planning units require at least 2 neighbors
+# for each zone and planning units are only considered neighbors if they
+# are allocated to the same zone
+z6 <- diag(3)
+print(z6)
+#>      [,1] [,2] [,3]
+#> [1,]    1    0    0
+#> [2,]    0    1    0
+#> [3,]    0    0    1
+p6 <- p5 %>% add_neighbor_constraints(rep(2, 3), z6)
+
+# create problem where the planning units in zone 1 don't explicitly require
+# any neighbors, planning units in zone 2 require at least 1 neighbors, and
+# planning units in zone 3 require at least 2 neighbors. As before, planning
+# units are still only considered neighbors if they are allocated to the
+# same zone
+p7 <- p5 %>% add_neighbor_constraints(c(0, 1, 2), z6)
+
+# create problem given the same constraints as outlined above, except
+# that when determining which selected planning units are neighbors,
+# planning units that are allocated to zone 1 and zone 2 can also treated
+# as being neighbors with each other
+z8 <- diag(3)
+z8[1, 2] <- 1
+z8[2, 1] <- 1
+print(z8)
+#>      [,1] [,2] [,3]
+#> [1,]    1    1    0
+#> [2,]    1    1    0
+#> [3,]    0    0    1
+p8 <- p5 %>% add_neighbor_constraints(c(0, 1, 2), z8)
+# \dontrun{
+# solve problems
+s2 <- list(p5, p6, p7, p8)
+s2 <- lapply(s2, solve)
+s2 <- lapply(s2, category_layer)
+s2 <- stack(s2)
+names(s2) <- c("basic problem", "p6", "p7", "p8")
+
+# plot solutions
+plot(s2, main = names(s2), box = FALSE, axes = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_proportion_decisions.html b/docs/reference/add_proportion_decisions.html index ee7557c4e..08b8bdb1f 100644 --- a/docs/reference/add_proportion_decisions.html +++ b/docs/reference/add_proportion_decisions.html @@ -1,106 +1,23 @@ - - - - - - - -Add proportion decisions — add_proportion_decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add proportion decisions — add_proportion_decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add proportion decisions

      - Source: R/add_proportion_decisions.R + Source: R/add_proportion_decisions.R
      -

      Add a proportion decision to a conservation planning problem(). +

      Add a proportion decision to a conservation planning problem(). This is a relaxed decision where a part of a planning unit can be prioritized as opposed to the entire planning unit. Typically, this decision has the assumed action of buying a fraction of a planning unit to include in @@ -194,111 +111,107 @@

      Add proportion decisions

      decisions

      - 
      add_proportion_decisions(x)
      - -

      Arguments

      - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      +
      Usage,
      add_proportion_decisions(x)
      -

      Value

      - -

      Object (i.e. ConservationProblem) with the decisions added +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the decisions added to it.

      -

      Details

      - +
      +
      +

      Details

      Conservation planning problems involve making decisions on planning -units. These decisions are then associated with actions (e.g. turning a +units. These decisions are then associated with actions (e.g., turning a planning unit into a protected area). Only a single decision should be added to a ConservationProblem object. Note that if multiple decisions are added to a problem object, then the last one to be added will be used.

      -

      See also

      - -

      See decisions for an overview of all functions for adding decisions.

      +
      +
      +

      See also

      +

      See decisions for an overview of all functions for adding decisions.

      Other decisions: -add_binary_decisions(), -add_default_decisions(), -add_semicontinuous_decisions()

      +add_binary_decisions(), +add_default_decisions(), +add_semicontinuous_decisions()

      +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem with proportion decisions
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_proportion_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solutions
-plot(s1, main = "solution")
-
-# }
-# build multi-zone conservation problem with proportion decisions
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_proportion_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s2 <- solve(p2)
-
-# print solution
-print(s2)
-#> class      : RasterStack 
-#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> names      : zone_1, zone_2, zone_3 
-#> min values :      0,      0,      0 
-#> max values :      1,      1,      1 
-#> 
-
-# plot solution
-# panels show the proportion of each planning unit allocated to each zone
-plot(s2, axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem with proportion decisions
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_proportion_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solutions
+plot(s1, main = "solution")
+
+# }
+# build multi-zone conservation problem with proportion decisions
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_proportion_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s2 <- solve(p2)
+
+# print solution
+print(s2)
+#> class      : RasterStack 
+#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> names      : zone_1, zone_2, zone_3 
+#> min values :      0,      0,      0 
+#> max values :      1,      1,      1 
+#> 
+
+# plot solution
+# panels show the proportion of each planning unit allocated to each zone
+plot(s2, axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/add_relative_targets.html b/docs/reference/add_relative_targets.html index 715696564..aab1f4751 100644 --- a/docs/reference/add_relative_targets.html +++ b/docs/reference/add_relative_targets.html @@ -1,105 +1,22 @@ - - - - - - - -Add relative targets — add_relative_targets • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add relative targets — add_relative_targets • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add relative targets

      - Source: R/add_relative_targets.R + Source: R/add_relative_targets.R
      @@ -189,51 +106,46 @@

      Add relative targets

      representation of features in the study area. Please note that proportions are scaled according to the features' total abundances in the study area (including any locked out planning units, or planning units with NA -cost data) using the feature_abundances() function.

      +cost data) using the feature_abundances() function.

      - 
      add_relative_targets(x, targets)
-
-# S4 method for ConservationProblem,numeric
-add_relative_targets(x, targets)
+    
      Usage,
      add_relative_targets(x, targets)
 
-# S4 method for ConservationProblem,matrix
-add_relative_targets(x, targets)
+# S4 method for ConservationProblem,numeric
+add_relative_targets(x, targets)
 
-# S4 method for ConservationProblem,character
-add_relative_targets(x, targets)
      
+# S4 method for ConservationProblem,matrix
+add_relative_targets(x, targets)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
      x
      problem() (i.e. ConservationProblem) object.
      targets
      Object that specifies the targets for each feature.
-See the Targets format section for more information.
      
+# S4 method for ConservationProblem,character
+add_relative_targets(x, targets)
      -

      Value

      - -

      Object (i.e. ConservationProblem) with the targets added +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      targets
      +

      Object that specifies the targets for each feature. +See the Targets format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the targets added to it.

      -

      Details

      - +
      +
      +

      Details

      Targets are used to specify the minimum amount or proportion of a feature's distribution that needs to be protected. Most conservation planning problems require targets with the exception of the maximum cover -(see add_max_cover_objective()) and maximum utility -(see add_max_utility_objective()) problems. Attempting to solve +(see add_max_cover_objective()) and maximum utility +(see add_max_utility_objective()) problems. Attempting to solve problems with objectives that require targets without specifying targets will throw an error.

      For problems associated with multiple management zones, this function can be used to set targets that each pertain to a single feature and a single zone. To set targets which can be met through allocating different -planning units to multiple zones, see the add_manual_targets() +planning units to multiple zones, see the add_manual_targets() function. An example of a target that could be met through allocations to multiple zones might be where each management zone is expected to result in a different amount of a feature and the target requires that @@ -244,150 +156,152 @@

      Details potentially, be met through allocating all planning units to any specific management zone, or through allocating the planning units to different combinations of management zones.

      -

      Targets format

      - +
      +
      +

      Targets format

      The targets for a problem can be specified using the following formats.

      -
      - -
      targets as a numeric vector

      containing target values for each +

      targets as a numeric vector
      +

      containing target values for each feature. Additionally, for convenience, this format can be a single value to assign the same target to each feature. Note that this format cannot be used to specify targets for problems with multiple zones.

      -
      targets as a matrix object

      containing a target for each feature + +

      targets as a matrix object
      +

      containing a target for each feature in each zone. Here, each row corresponds to a different feature in argument to x, each column corresponds to a different zone in argument to x, and each cell contains the target value for a given feature that the solution needs to secure in a given zone.

      -
      targets as a character vector

      containing the names of fields + +

      targets as a character vector
      +

      containing the names of fields (columns) in the feature data associated with the argument to x that contain targets. This format can only be used when the feature data associated with x is a data.frame. This argument must contain a field (column) name for each zone.

      -
      - -

      See also

      -

      See targets for an overview of all functions for adding targets.

      +
      +
      +

      See also

      +

      See targets for an overview of all functions for adding targets.

      Other targets: -add_absolute_targets(), -add_loglinear_targets(), -add_manual_targets()

      +add_absolute_targets(), +add_loglinear_targets(), +add_manual_targets()

      +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features)
-
-# create base problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_binary_decisions() %>%
-     add_default_solver(verbose = FALSE)
-
-# create problem with 10% targets
-p1 <- p %>% add_relative_targets(0.1)
-
-# create problem with varying targets for each feature
-targets <- c(0.1, 0.2, 0.3, 0.4, 0.5)
-p2 <- p %>% add_relative_targets(targets)
-# \dontrun{
-# solve problem
-s <- stack(solve(p1), solve(p2))
-
-# plot solution
-plot(s, main = c("10% targets", "varying targets"), axes = FALSE,
-     box = FALSE)
-
-# }
-# create a problem with multiple management zones
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create a problem with targets that specify an equal amount of each feature
-# to be represented in each zone
-p4_targets <- matrix(0.1, nrow = 5, ncol = 3,
-                     dimnames = list(feature_names(sim_features_zones),
-                                     zone_names(sim_features_zones)))
-print(p4_targets)
-#>           zone_1 zone_2 zone_3
-#> feature_1    0.1    0.1    0.1
-#> feature_2    0.1    0.1    0.1
-#> feature_3    0.1    0.1    0.1
-#> feature_4    0.1    0.1    0.1
-#> feature_5    0.1    0.1    0.1
-
-p4 <- p3 %>% add_relative_targets(p4_targets)
-
-# solve problem
-# \dontrun{
-# solve problem
-s4 <- solve(p4)
-
-# plot solution (pixel values correspond to zone identifiers)
-plot(category_layer(s4), main = c("equal targets"))
-
-# }
-# create a problem with targets that require a varying amount of each
-# feature to be represented in each zone
-p5_targets <- matrix(runif(15, 0.01, 0.2), nrow = 5, ncol = 3,
-                     dimnames = list(feature_names(sim_features_zones),
-                                     zone_names(sim_features_zones)))
-print(p5_targets)
-#>               zone_1     zone_2     zone_3
-#> feature_1 0.16838399 0.04908221 0.06359158
-#> feature_2 0.14775224 0.10731456 0.17964011
-#> feature_3 0.19530969 0.18583855 0.15529418
-#> feature_4 0.09884473 0.16747797 0.04122594
-#> feature_5 0.16433284 0.14519964 0.14909414
-
-p5 <- p3 %>% add_relative_targets(p4_targets)
-# solve problem
-# \dontrun{
-# solve problem
-s5 <- solve(p5)
-
-# plot solution (pixel values correspond to zone identifiers)
-plot(category_layer(s5), main = c("varying targets"))
-
-# }
-
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features)
+
+# create base problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_binary_decisions() %>%
+     add_default_solver(verbose = FALSE)
+
+# create problem with 10% targets
+p1 <- p %>% add_relative_targets(0.1)
+
+# create problem with varying targets for each feature
+targets <- c(0.1, 0.2, 0.3, 0.4, 0.5)
+p2 <- p %>% add_relative_targets(targets)
+# \dontrun{
+# solve problem
+s <- stack(solve(p1), solve(p2))
+
+# plot solution
+plot(s, main = c("10% targets", "varying targets"), axes = FALSE,
+     box = FALSE)
+
+# }
+# create a problem with multiple management zones
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create a problem with targets that specify an equal amount of each feature
+# to be represented in each zone
+p4_targets <- matrix(0.1, nrow = 5, ncol = 3,
+                     dimnames = list(feature_names(sim_features_zones),
+                                     zone_names(sim_features_zones)))
+print(p4_targets)
+#>           zone_1 zone_2 zone_3
+#> feature_1    0.1    0.1    0.1
+#> feature_2    0.1    0.1    0.1
+#> feature_3    0.1    0.1    0.1
+#> feature_4    0.1    0.1    0.1
+#> feature_5    0.1    0.1    0.1
+
+p4 <- p3 %>% add_relative_targets(p4_targets)
+
+# solve problem
+# \dontrun{
+# solve problem
+s4 <- solve(p4)
+
+# plot solution (pixel values correspond to zone identifiers)
+plot(category_layer(s4), main = c("equal targets"))
+
+# }
+# create a problem with targets that require a varying amount of each
+# feature to be represented in each zone
+p5_targets <- matrix(runif(15, 0.01, 0.2), nrow = 5, ncol = 3,
+                     dimnames = list(feature_names(sim_features_zones),
+                                     zone_names(sim_features_zones)))
+print(p5_targets)
+#>               zone_1     zone_2     zone_3
+#> feature_1 0.16838399 0.04908221 0.06359158
+#> feature_2 0.14775224 0.10731456 0.17964011
+#> feature_3 0.19530969 0.18583855 0.15529418
+#> feature_4 0.09884473 0.16747797 0.04122594
+#> feature_5 0.16433284 0.14519964 0.14909414
+
+p5 <- p3 %>% add_relative_targets(p4_targets)
+# solve problem
+# \dontrun{
+# solve problem
+s5 <- solve(p5)
+
+# plot solution (pixel values correspond to zone identifiers)
+plot(category_layer(s5), main = c("varying targets"))
+
+# }
+
 
      
+
      + - - - - - - - - - - - + diff --git a/docs/reference/add_rsymphony_solver.html b/docs/reference/add_rsymphony_solver.html index c9d51a34c..e287c954d 100644 --- a/docs/reference/add_rsymphony_solver.html +++ b/docs/reference/add_rsymphony_solver.html @@ -1,105 +1,22 @@ - - - - - - - -Add a SYMPHONY solver with Rsymphony — add_rsymphony_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a SYMPHONY solver with Rsymphony — add_rsymphony_solver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add a SYMPHONY solver with Rsymphony

      - Source: R/add_rsymphony_solver.R + Source: R/add_rsymphony_solver.R
      -

      Specify that the SYMPHONY +

      Specify that the SYMPHONY software (Ralphs & Güzelsoy 2005) -- using the Rsymphony package -- -should be used to solve a conservation planning problem(). +should be used to solve a conservation planning problem(). This function can also be used to customize the behavior of the solver. It requires the Rsymphony package to be installed.

      - 
      add_rsymphony_solver(
-  x,
-  gap = 0.1,
-  time_limit = .Machine$integer.max,
-  first_feasible = FALSE,
-  verbose = TRUE
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      gap

      numeric gap to optimality. This gap is relative +

      Usage,
      add_rsymphony_solver(
+  x,
+  gap = 0.1,
+  time_limit = .Machine$integer.max,
+  first_feasible = FALSE,
+  verbose = TRUE
+)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      gap
      +

      numeric gap to optimality. This gap is relative and expresses the acceptable deviance from the optimal objective. For example, a value of 0.01 will result in the solver stopping when it has found a solution within 1% of optimality. Additionally, a value of 0 will result in the solver stopping when it has found an optimal solution. -The default value is 0.1 (i.e. 10% from optimality).

      time_limit

      numeric time limit (seconds) for generating solutions. +The default value is 0.1 (i.e., 10% from optimality).

      +
      time_limit
      +

      numeric time limit (seconds) for generating solutions. The solver will return the current best solution when this time limit is exceeded. The default value is the largest integer value -(i.e. .Machine$integer.max), effectively meaning that solver -will keep running until a solution within the optimality gap is found.

      first_feasible

      logical should the first feasible solution be +(i.e., .Machine$integer.max), effectively meaning that solver +will keep running until a solution within the optimality gap is found.

      +
      first_feasible
      +

      logical should the first feasible solution be be returned? If first_feasible is set to TRUE, the solver will return the first solution it encounters that meets all the constraints, regardless of solution quality. Note that the first feasible solution is not an arbitrary solution, rather it is derived from the relaxed solution, and is therefore often reasonably close to optimality. -Defaults to FALSE.

      verbose

      logical should information be printed while solving -optimization problems? Defaults to TRUE.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the solver +Defaults to FALSE.

      +
      verbose
      +

      logical should information be printed while solving +optimization problems? Defaults to TRUE.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the solver added to it.

      -

      Details

      - -

      SYMPHONY is an +

      +
      +

      Details

      +

      SYMPHONY is an open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. @@ -259,68 +165,68 @@

      Details please see Schuster et al. (2020) for benchmarks comparing the run time and solution quality of different solvers when applied to different sized datasets.

      -

      References

      - +
      +
      +

      References

      Ralphs TK and Güzelsoy M (2005) The SYMPHONY callable library for mixed integer programming. In The Next Wave in Computing, Optimization, and Decision Technologies (pp. 61--76). Springer, Boston, MA.

      Schuster R, Hanson JO, Strimas-Mackey M, and Bennett JR (2020). Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems. PeerJ, 8: e9258.

      -

      See also

      - -

      See solvers for an overview of all functions for adding a solver.

      +
      +
      +

      See also

      +

      See solvers for an overview of all functions for adding a solver.

      Other solvers: -add_cbc_solver(), -add_cplex_solver(), -add_default_solver(), -add_gurobi_solver(), -add_lsymphony_solver

      +add_cbc_solver(), +add_cplex_solver(), +add_default_solver(), +add_gurobi_solver(), +add_lsymphony_solver

      +
      -

      Examples

      - 
      # \dontrun{
-# load data
-data(sim_pu_raster, sim_features)
-
-# create problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.1) %>%
-     add_binary_decisions() %>%
-     add_rsymphony_solver(time_limit = 10, verbose = FALSE)
-
-# generate solution
-s <- solve(p)
-
-# plot solution
-plot(s, main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# load data
+data(sim_pu_raster, sim_features)
+
+# create problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.1) %>%
+     add_binary_decisions() %>%
+     add_rsymphony_solver(time_limit = 10, verbose = FALSE)
+
+# generate solution
+s <- solve(p)
+
+# plot solution
+plot(s, main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/add_semicontinuous_decisions.html b/docs/reference/add_semicontinuous_decisions.html index f4fe97a4b..aa57e929b 100644 --- a/docs/reference/add_semicontinuous_decisions.html +++ b/docs/reference/add_semicontinuous_decisions.html @@ -1,61 +1,5 @@ - - - - - - - -Add semi-continuous decisions — add_semicontinuous_decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add semi-continuous decisions — add_semicontinuous_decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add semi-continuous decisions

      - Source: R/add_semicontinuous_decisions.R + Source: R/add_semicontinuous_decisions.R

      Add a semi-continuous decision to a conservation planning -problem(). This is a relaxed decision where a part of a planning +problem(). This is a relaxed decision where a part of a planning unit can be prioritized, as opposed to the entire planning unit, which is -the default function (see add_binary_decisions()). -This decision is similar to the add_proportion_decisions() +the default function (see add_binary_decisions()). +This decision is similar to the add_proportion_decisions() function except that it has an upper bound parameter. By default, the decision can range from prioritizing none (0%) to all (100%) of a planning unit. However, an upper bound can be specified to ensure that at -most only a fraction (e.g. 80%) of a planning unit can be preserved. This +most only a fraction (e.g., 80%) of a planning unit can be preserved. This type of decision may be useful when it is not practical to conserve entire planning units.

      - 
      add_semicontinuous_decisions(x, upper_limit)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      upper_limit

      numeric value specifying the maximum proportion -of a planning unit that can be reserved (e.g. set to 0.8 for 80%).

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the decisions added +

      Usage,
      add_semicontinuous_decisions(x, upper_limit)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      upper_limit
      +

      numeric value specifying the maximum proportion +of a planning unit that can be reserved (e.g., set to 0.8 for 80%).

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the decisions added to it.

      -

      Details

      - +
      +
      +

      Details

      Conservation planning problems involve making decisions on planning -units. These decisions are then associated with actions (e.g. turning a +units. These decisions are then associated with actions (e.g., turning a planning unit into a protected area). Only a single decision should be added to a ConservationProblem object. Note that if multiple decisions are added to a problem object, then the last one to be added will be used.

      -

      See also

      - -

      See decisions for an overview of all functions for adding decisions.

      +
      +
      +

      See also

      +

      See decisions for an overview of all functions for adding decisions.

      Other decisions: -add_binary_decisions(), -add_default_decisions(), -add_proportion_decisions()

      +add_binary_decisions(), +add_default_decisions(), +add_proportion_decisions()

      +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem with semi-continuous decisions
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_semicontinuous_decisions(0.5) %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# plot solutions
-plot(s1, main = "solution")
-
-# }
-# build multi-zone conservation problem with semi-continuous decisions
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_semicontinuous_decisions(0.5) %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s2 <- solve(p2)
-
-# print solution
-print(s2)
-#> class      : RasterStack 
-#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> names      : zone_1, zone_2, zone_3 
-#> min values :      0,      0,      0 
-#> max values :    0.5,    0.5,    0.5 
-#> 
-
-# plot solution
-# panels show the proportion of each planning unit allocated to each zone
-plot(s2, axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem with semi-continuous decisions
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_semicontinuous_decisions(0.5) %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# plot solutions
+plot(s1, main = "solution")
+
+# }
+# build multi-zone conservation problem with semi-continuous decisions
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_semicontinuous_decisions(0.5) %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s2 <- solve(p2)
+
+# print solution
+print(s2)
+#> class      : RasterStack 
+#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> names      : zone_1, zone_2, zone_3 
+#> min values :      0,      0,      0 
+#> max values :    0.5,    0.5,    0.5 
+#> 
+
+# plot solution
+# panels show the proportion of each planning unit allocated to each zone
+plot(s2, axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/add_shuffle_portfolio.html b/docs/reference/add_shuffle_portfolio.html index 133df4c02..533a04abc 100644 --- a/docs/reference/add_shuffle_portfolio.html +++ b/docs/reference/add_shuffle_portfolio.html @@ -1,105 +1,22 @@ - - - - - - - -Add a shuffle portfolio — add_shuffle_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a shuffle portfolio — add_shuffle_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add a shuffle portfolio

      - Source: R/add_shuffle_portfolio.R + Source: R/add_shuffle_portfolio.R

      Generate a portfolio of solutions for a conservation planning -problem() by randomly reordering the data prior to +problem() by randomly reordering the data prior to solving the problem. This is recommended as a replacement for -add_top_portfolio() when the Gurobi software is not +add_top_portfolio() when the Gurobi software is not available.

      - 
      add_shuffle_portfolio(
-  x,
-  number_solutions = 10L,
-  threads = 1L,
-  remove_duplicates = TRUE
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      number_solutions

      integer number of attempts to generate -different solutions. Defaults to 10.

      threads

      integer number of threads to use for the generating -the solution portfolio. Defaults to 1.

      remove_duplicates

      logical should duplicate solutions -be removed? Defaults to TRUE.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the portfolio +

      Usage,
      add_shuffle_portfolio(
+  x,
+  number_solutions = 10L,
+  threads = 1L,
+  remove_duplicates = TRUE
+)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      number_solutions
      +

      integer number of attempts to generate +different solutions. Defaults to 10.

      +
      threads
      +

      integer number of threads to use for the generating +the solution portfolio. Defaults to 1.

      +
      remove_duplicates
      +

      logical should duplicate solutions +be removed? Defaults to TRUE.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the portfolio added to it.

      -

      Details

      - +
      +
      +

      Details

      This strategy for generating a portfolio of solutions often results in different solutions, depending on optimality gap, but may return duplicate solutions. In general, this strategy is most effective when problems are quick to solve and multiple threads are available for solving each problem separately.

      -

      See also

      - -

      See portfolios for an overview of all functions for adding a portfolio.

      +
      +
      +

      See also

      +

      See portfolios for an overview of all functions for adding a portfolio.

      Other portfolios: -add_cuts_portfolio(), -add_extra_portfolio(), -add_gap_portfolio(), -add_top_portfolio()

      +add_cuts_portfolio(), +add_extra_portfolio(), +add_gap_portfolio(), +add_top_portfolio()

      +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem with shuffle portfolio
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_shuffle_portfolio(10, remove_duplicates = FALSE) %>%
-      add_default_solver(gap = 0.2, verbose = FALSE)
-
-# \dontrun{
-# solve problem and generate 10 solutions within 20% of optimality
-s1 <- solve(p1)
-
-# plot solutions in portfolio
-plot(stack(s1), axes = FALSE, box = FALSE)
-
-# }
-# build multi-zone conservation problem with shuffle portfolio
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_shuffle_portfolio(10, remove_duplicates = FALSE) %>%
-      add_default_solver(gap = 0.2, verbose = FALSE)
-
-# \dontrun{
-# solve the problem
-s2 <- solve(p2)
-
-# print solution
-str(s2, max.level = 1)
-#> List of 10
-#>  $ solution_1 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_2 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_3 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_4 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_5 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_6 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_7 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_8 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_9 :Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  $ solution_10:Formal class 'RasterStack' [package "raster"] with 11 slots
-#>  - attr(*, "objective")= Named num [1:10] 11667 11408 11268 11080 11752 ...
-#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
-#>  - attr(*, "status")= Named chr [1:10] "OPTIMAL" "OPTIMAL" "OPTIMAL" "OPTIMAL" ...
-#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
-#>  - attr(*, "runtime")= Named num [1:10] 0.027 0.006 0.005 0.005 0.005 ...
-#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
-
-# plot solutions in portfolio
-plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
-     box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem with shuffle portfolio
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_shuffle_portfolio(10, remove_duplicates = FALSE) %>%
+      add_default_solver(gap = 0.2, verbose = FALSE)
+
+# \dontrun{
+# solve problem and generate 10 solutions within 20% of optimality
+s1 <- solve(p1)
+
+# plot solutions in portfolio
+plot(stack(s1), axes = FALSE, box = FALSE)
+
+# }
+# build multi-zone conservation problem with shuffle portfolio
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_shuffle_portfolio(10, remove_duplicates = FALSE) %>%
+      add_default_solver(gap = 0.2, verbose = FALSE)
+
+# \dontrun{
+# solve the problem
+s2 <- solve(p2)
+
+# print solution
+str(s2, max.level = 1)
+#> List of 10
+#>  $ solution_1 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_2 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_3 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_4 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_5 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_6 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_7 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_8 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_9 :Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  $ solution_10:Formal class 'RasterStack' [package "raster"] with 11 slots
+#>  - attr(*, "objective")= Named num [1:10] 11667 11408 11268 11080 11752 ...
+#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
+#>  - attr(*, "status")= Named chr [1:10] "OPTIMAL" "OPTIMAL" "OPTIMAL" "OPTIMAL" ...
+#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
+#>  - attr(*, "runtime")= Named num [1:10] 0.006 0.024 0.006 0.023 0.007 ...
+#>   ..- attr(*, "names")= chr [1:10] "solution_1" "solution_2" "solution_3" "solution_4" ...
+
+# plot solutions in portfolio
+plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
+     box = FALSE)
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/add_top_portfolio.html b/docs/reference/add_top_portfolio.html index 63f7f9c2c..bd382d78b 100644 --- a/docs/reference/add_top_portfolio.html +++ b/docs/reference/add_top_portfolio.html @@ -1,103 +1,20 @@ - - - - - - - -Add a top portfolio — add_top_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a top portfolio — add_top_portfolio • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add a top portfolio

      - Source: R/add_top_portfolio.R + Source: R/add_top_portfolio.R

      Generate a portfolio of solutions for a conservation planning -problem() by finding a pre-specified number of solutions that +problem() by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions).

      - 
      add_top_portfolio(x, number_solutions)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      number_solutions

      integer number of solutions required.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the portfolio +

      Usage,
      add_top_portfolio(x, number_solutions)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      number_solutions
      +

      integer number of solutions required.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the portfolio added to it.

      -

      Details

      - +
      +
      +

      Details

      This strategy for generating a portfolio requires problems to -be solved using the Gurobi software suite (i.e. using -add_gurobi_solver(). Specifically, version 9.0.0 (or greater) +be solved using the Gurobi software suite (i.e., using +add_gurobi_solver(). Specifically, version 9.0.0 (or greater) of the gurobi package must be installed. Note that the number of solutions returned may be less than the argument to number_solutions, if the total number of feasible solutions is less than the number of solutions requested.

      -

      See also

      - -

      See portfolios for an overview of all functions for adding a portfolio.

      +
      +
      +

      See also

      +

      See portfolios for an overview of all functions for adding a portfolio.

      Other portfolios: -add_cuts_portfolio(), -add_extra_portfolio(), -add_gap_portfolio(), -add_shuffle_portfolio()

      +add_cuts_portfolio(), +add_extra_portfolio(), +add_gap_portfolio(), +add_shuffle_portfolio()

      +
      -

      Examples

      - 
      # \dontrun{
-# set seed for reproducibility
-set.seed(600)
-
-# load data
-data(sim_pu_raster, sim_features)
-
-# create minimal problem with a portfolio for the top 5 solutions
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.05) %>%
-      add_top_portfolio(number_solutions = 5) %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem and generate portfolio
-s1 <- solve(p1)
-
-# print number of solutions found
-print(length(s1))
-#> [1] 5
-
-# plot solutions
-plot(stack(s1), axes = FALSE, box = FALSE)
-
-
-# create multi-zone problem with a portfolio for the top 5 solutions
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_top_portfolio(number_solutions = 5) %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem and generate portfolio
-s2 <- solve(p2)
-
-# print number of solutions found
-print(length(s2))
-#> [1] 5
-
-# plot solutions in portfolio
-plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
-     box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# set seed for reproducibility
+set.seed(600)
+
+# load data
+data(sim_pu_raster, sim_features)
+
+# create minimal problem with a portfolio for the top 5 solutions
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.05) %>%
+      add_top_portfolio(number_solutions = 5) %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem and generate portfolio
+s1 <- solve(p1)
+
+# print number of solutions found
+print(length(s1))
+#> [1] 5
+
+# plot solutions
+plot(stack(s1), axes = FALSE, box = FALSE)
+
+
+# create multi-zone problem with a portfolio for the top 5 solutions
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_top_portfolio(number_solutions = 5) %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem and generate portfolio
+s2 <- solve(p2)
+
+# print number of solutions found
+print(length(s2))
+#> [1] 5
+
+# plot solutions in portfolio
+plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
+     box = FALSE)
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/adjacency_matrix.html b/docs/reference/adjacency_matrix.html index 6314fc812..4391ce6e8 100644 --- a/docs/reference/adjacency_matrix.html +++ b/docs/reference/adjacency_matrix.html @@ -1,103 +1,20 @@ - - - - - - - -Adjacency matrix — adjacency_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Adjacency matrix — adjacency_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Adjacency matrix

      - Source: R/adjacency_matrix.R + Source: R/adjacency_matrix.R
      @@ -188,146 +105,137 @@

      Adjacency matrix

      with each other too.

      - 
      adjacency_matrix(x, ...)
+    
      Usage,
      adjacency_matrix(x, ...)
 
-# S3 method for Raster
-adjacency_matrix(x, directions = 4L, ...)
+# S3 method for Raster
+adjacency_matrix(x, directions = 4L, ...)
 
-# S3 method for SpatialPolygons
-adjacency_matrix(x, ...)
+# S3 method for SpatialPolygons
+adjacency_matrix(x, ...)
 
-# S3 method for SpatialLines
-adjacency_matrix(x, ...)
+# S3 method for SpatialLines
+adjacency_matrix(x, ...)
 
-# S3 method for SpatialPoints
-adjacency_matrix(x, ...)
+# S3 method for SpatialPoints
+adjacency_matrix(x, ...)
 
-# S3 method for sf
-adjacency_matrix(x, ...)
+# S3 method for sf
+adjacency_matrix(x, ...)
 
-# S3 method for default
-adjacency_matrix(x, ...)
      
+# S3 method for default
+adjacency_matrix(x, ...)
      -

      Arguments

      - - - - - - - - - - - - - - -
      x

      Raster, -SpatialPolygons, -SpatialLines, -or sf::sf() object -representing planning units.

      ...

      not used.

      directions

      integer If x is a -Raster object, the number of directions +

      +

      Arguments

      +
      x
      +

      Raster, +SpatialPolygons, +SpatialLines, +or sf::sf() object +representing planning units.

      +
      ...
      +

      not used.

      +
      directions
      +

      integer If x is a +Raster object, the number of directions in which cells should be considered adjacent: 4 (rook's case), 8 (queen's case), 16 (knight and one-cell queen moves), or "bishop" to for cells -with one-cell diagonal moves.

      - -

      Value

      - -

      dsCMatrix sparse symmetric matrix. +with one-cell diagonal moves.

      +
      +
      +

      Value

      +

      dsCMatrix sparse symmetric matrix. Each row and column represents a planning unit. Cells values indicate if different planning units are adjacent to each other or not (using ones and zeros). To reduce computational burden, cells among the matrix diagonal are set to zero. Furthermore, if the argument to x is a -Raster object, then cells with NA -values are set to zero too.

      -

      Details

      - +Raster object, then cells with NAvalues are set to zero too.

      +
      +
      +

      Details

      Spatial processing is completed using -sf::st_intersects() for Spatial and -sf::sf() objects, -and raster::adjacent() for Raster +sf::st_intersects() for Spatial and +sf::sf() objects, +and raster::adjacent() for Raster objects.

      -

      Notes

      - +
      +
      +

      Notes

      In earlier versions (< 5.0.0), this function was named as the connected_matrix function. It has been renamed to be consistent with other spatial association matrix functions.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_sf, sim_pu_lines)
-
-# create adjacency matrix using raster data
-## crop raster to 9 cells
-r <- crop(sim_pu_raster, c(0, 0.3, 0, 0.3))
-
-## make adjacency matrix
-am_raster <- adjacency_matrix(r)
-
-# create adjacency matrix using polygons (sf) data
-## subset 9 polygons
-ply <- sim_pu_sf[c(1:2, 10:12, 20:22), ]
-
-## make adjacency matrix
-am_ply <- adjacency_matrix(ply)
-
-# create adjacency matrix using lines (Spatial) data
-## subset 9 lines
-lns <- sim_pu_lines[c(1:2, 10:12, 20:22), ]
-
-## make adjacency matrix
-am_lns <- adjacency_matrix(lns)
-
-# plot data and the adjacency matrices
-# \dontrun{
-par(mfrow = c(4,2))
-
-## plot raster and adjacency matrix
-plot(r, main = "raster", axes = FALSE, box = FALSE)
-plot(raster(as.matrix(am_raster)), main = "adjacency matrix", axes = FALSE,
-     box = FALSE)
-
-## plot polygons (sf) and adjacency matrix
-plot(r, main = "polygons (sf)", axes = FALSE, box = FALSE)
-plot(raster(as.matrix(am_ply)), main = "adjacency matrix", axes = FALSE,
-    box = FALSE)
-
-## plot lines (Spatial) and adjacency matrix
-plot(r, main = "lines (Spatial)", axes = FALSE, box = FALSE)
-plot(raster(as.matrix(am_lns)), main = "adjacency matrix", axes = FALSE,
-     box = FALSE)
-# }
-
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_sf, sim_pu_lines)
+
+# create adjacency matrix using raster data
+## crop raster to 9 cells
+r <- crop(sim_pu_raster, c(0, 0.3, 0, 0.3))
+
+## make adjacency matrix
+am_raster <- adjacency_matrix(r)
+
+# create adjacency matrix using polygons (sf) data
+## subset 9 polygons
+ply <- sim_pu_sf[c(1:2, 10:12, 20:22), ]
+
+## make adjacency matrix
+am_ply <- adjacency_matrix(ply)
+
+# create adjacency matrix using lines (Spatial) data
+## subset 9 lines
+lns <- sim_pu_lines[c(1:2, 10:12, 20:22), ]
+
+## make adjacency matrix
+am_lns <- adjacency_matrix(lns)
+
+# plot data and the adjacency matrices
+# \dontrun{
+par(mfrow = c(4,2))
+
+## plot raster and adjacency matrix
+plot(r, main = "raster", axes = FALSE, box = FALSE)
+plot(raster(as.matrix(am_raster)), main = "adjacency matrix", axes = FALSE,
+     box = FALSE)
+
+## plot polygons (sf) and adjacency matrix
+plot(r, main = "polygons (sf)", axes = FALSE, box = FALSE)
+plot(raster(as.matrix(am_ply)), main = "adjacency matrix", axes = FALSE,
+    box = FALSE)
+
+## plot lines (Spatial) and adjacency matrix
+plot(r, main = "lines (Spatial)", axes = FALSE, box = FALSE)
+plot(raster(as.matrix(am_lns)), main = "adjacency matrix", axes = FALSE,
+     box = FALSE)
+# }
+
 
      
+
      + - - - - - - - - - - - + diff --git a/docs/reference/array_parameters.html b/docs/reference/array_parameters.html index 18bfc5fe5..472060104 100644 --- a/docs/reference/array_parameters.html +++ b/docs/reference/array_parameters.html @@ -1,102 +1,19 @@ - - - - - - - -Array parameters — array_parameters • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Array parameters — array_parameters • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Array parameters

      - Source: R/parameters.R + Source: R/parameters.R
      @@ -186,202 +103,193 @@

      Array parameters

      to create a parameter with conflicting settings then an error will be thrown.

      - 
      proportion_parameter_array(name, value, label)
-
-binary_parameter_array(name, value, label)
-
-integer_parameter_array(
-  name,
-  value,
-  label,
-  lower_limit = rep(as.integer(-.Machine$integer.max), length(value)),
-  upper_limit = rep(as.integer(.Machine$integer.max), length(value))
-)
-
-numeric_parameter_array(
-  name,
-  value,
-  label,
-  lower_limit = rep(.Machine$double.xmin, length(value)),
-  upper_limit = rep(.Machine$double.xmax, length(value))
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - -
      name

      character name of parameter.

      value

      numeric vector of values.

      label

      character vector of labels for each value.

      lower_limit

      numeric vector of values denoting the minimum acceptable +

      Usage,
      proportion_parameter_array(name, value, label)
+
+binary_parameter_array(name, value, label)
+
+integer_parameter_array(
+  name,
+  value,
+  label,
+  lower_limit = rep(as.integer(-.Machine$integer.max), length(value)),
+  upper_limit = rep(as.integer(.Machine$integer.max), length(value))
+)
+
+numeric_parameter_array(
+  name,
+  value,
+  label,
+  lower_limit = rep(.Machine$double.xmin, length(value)),
+  upper_limit = rep(.Machine$double.xmax, length(value))
+)
      + +
      +

      Arguments

      +
      name
      +

      character name of parameter.

      +
      value
      +

      numeric vector of values.

      +
      label
      +

      character vector of labels for each value.

      +
      lower_limit
      +

      numeric vector of values denoting the minimum acceptable value for each element in value. Defaults to the -smallest possible number on the system.

      upper_limit

      numeric vector of values denoting the maximum acceptable +smallest possible number on the system.

      +
      upper_limit
      +

      numeric vector of values denoting the maximum acceptable value for each element in value. Defaults to the -largest possible number on the system.

      - -

      Value

      - -

      ArrayParameter object.

      -

      Details

      - +largest possible number on the system.

      +
      +
      +

      Value

      +

      ArrayParameter object.

      +
      +
      +

      Details

      Below is a list of parameter generating functions and a brief -description of each.

      - -
      proportion_parameter_array

      a parameter that consists of multiple +description of each.

      proportion_parameter_array
      +

      a parameter that consists of multiple numeric values that are between zero and one.

      -
      binary_parameter_array

      a parameter that consists of multiple + +

      binary_parameter_array
      +

      a parameter that consists of multiple integer values that are either zero or one.

      -
      integer_parameter_array

      a parameter that consists of multiple + +

      integer_parameter_array
      +

      a parameter that consists of multiple integer values.

      -
      numeric_parameter_array

      a parameter that consists of multiple -numeric values.

      +
      numeric_parameter_array
      +

      a parameter that consists of multiple +numeric values.

      -
      -

      Examples

      - 
      # proportion parameter array
-p1 <- proportion_parameter_array('prop_array', c(0.1, 0.2, 0.3),
-                                 letters[1:3])
-print(p1) # print it
-#> prop_array (min: 0.1, max: 0.3)
-p1$get() # get value
-#>   value
-#> a   0.1
-#> b   0.2
-#> c   0.3
-p1$id # get id
-#> id: 79916be9-839c-4864-be8d-bc16e9226395
-invalid <- data.frame(value = 1:3, row.names=letters[1:3]) # invalid values
-p1$validate(invalid) # check invalid input is invalid
-valid <- data.frame(value = c(0.4, 0.5, 0.6), row.names=letters[1:3]) # valid
-p1$validate(valid) # check valid input is valid
-p1$set(valid) # change value to valid input
-print(p1)
-#> prop_array (min: 0.4, max: 0.6)
-
-# binary parameter array
-p2 <- binary_parameter_array('bin_array', c(0L, 1L, 0L), letters[1:3])
-print(p2) # print it
-#> bin_array (min: 0, max: 1)
-p2$get() # get value
-#>   value
-#> a     0
-#> b     1
-#> c     0
-p2$id # get id
-#> id: 955a2518-aa58-46c9-8dd0-ca5054f436e3
-invalid <- data.frame(value = 1:3, row.names=letters[1:3]) # invalid values
-p2$validate(invalid) # check invalid input is invalid
-valid <- data.frame(value = c(0L, 0L, 0L), row.names=letters[1:3]) # valid
-p2$validate(valid) # check valid input is valid
-p2$set(valid) # change value to valid input
-print(p2)
-#> bin_array (min: 0, max: 0)
-
-# integer parameter array
-p3 <- integer_parameter_array('int_array', c(1:3), letters[1:3])
-print(p3) # print it
-#> int_array (min: 1, max: 3)
-p3$get() # get value
-#>   value
-#> a     1
-#> b     2
-#> c     3
-p3$id # get id
-#> id: db018677-fca9-46df-b1fd-33a3d023bc9e
-invalid <- data.frame(value = rnorm(3), row.names=letters[1:3]) # invalid
-p3$validate(invalid) # check invalid input is invalid
-valid <- data.frame(value = 5:7, row.names=letters[1:3]) # valid
-p3$validate(valid) # check valid input is valid
-p3$set(valid) # change value to valid input
-print(p3)
-#> int_array (min: 5, max: 7)
-
-# numeric parameter array
-p4 <- numeric_parameter_array('dbl_array', c(0.1, 4, -5), letters[1:3])
-print(p4) # print it
-#> dbl_array (min: -5, max: 4)
-p4$get() # get value
-#>   value
-#> a   0.1
-#> b   4.0
-#> c  -5.0
-p4$id # get id
-#> id: d199e63a-36cf-47d9-8a05-b254f498e7d0
-invalid <- data.frame(value = c(NA, 1, 2), row.names=letters[1:3]) # invalid
-p4$validate(invalid) # check invalid input is invalid
-valid <- data.frame(value = c(1, 2, 3), row.names=letters[1:3]) # valid
-p4$validate(valid) # check valid input is valid
-p4$set(valid) # change value to valid input
-print(p4)
-#> dbl_array (min: 1, max: 3)
-
-# numeric parameter array with lower bounds
-p5 <- numeric_parameter_array('b_dbl_array', c(0.1, 4, -5), letters[1:3],
-                              lower_limit=c(0, 1, 2))
-print(p5) # print it
-#> b_dbl_array (min: -5, max: 4)
-p5$get() # get value
-#>   value
-#> a   0.1
-#> b   4.0
-#> c  -5.0
-p5$id# get id
-#> id: d2529a02-5134-4b9c-bc60-c29c27cf4f3f
-invalid <- data.frame(value = c(-1, 5, 5), row.names=letters[1:3]) # invalid
-p5$validate(invalid) # check invalid input is invalid
-valid <- data.frame(value = c(0, 1, 2), row.names=letters[1:3]) # valid
-p5$validate(valid) # check valid input is valid
-p5$set(valid) # change value to valid input
-print(p5)
-#> b_dbl_array (min: 0, max: 2)
-
+
      + +
      +

      Examples

      + 
      # proportion parameter array
+p1 <- proportion_parameter_array('prop_array', c(0.1, 0.2, 0.3),
+                                 letters[1:3])
+print(p1) # print it
+#> prop_array (min: 0.1, max: 0.3)
+p1$get() # get value
+#>   value
+#> a   0.1
+#> b   0.2
+#> c   0.3
+p1$id # get id
+#> id: d2bca11d-4367-4c50-93a1-46041bff7f53
+invalid <- data.frame(value = 1:3, row.names=letters[1:3]) # invalid values
+p1$validate(invalid) # check invalid input is invalid
+valid <- data.frame(value = c(0.4, 0.5, 0.6), row.names=letters[1:3]) # valid
+p1$validate(valid) # check valid input is valid
+p1$set(valid) # change value to valid input
+print(p1)
+#> prop_array (min: 0.4, max: 0.6)
+
+# binary parameter array
+p2 <- binary_parameter_array('bin_array', c(0L, 1L, 0L), letters[1:3])
+print(p2) # print it
+#> bin_array (min: 0, max: 1)
+p2$get() # get value
+#>   value
+#> a     0
+#> b     1
+#> c     0
+p2$id # get id
+#> id: 206b0969-b11c-4f49-b06e-760674882b5e
+invalid <- data.frame(value = 1:3, row.names=letters[1:3]) # invalid values
+p2$validate(invalid) # check invalid input is invalid
+valid <- data.frame(value = c(0L, 0L, 0L), row.names=letters[1:3]) # valid
+p2$validate(valid) # check valid input is valid
+p2$set(valid) # change value to valid input
+print(p2)
+#> bin_array (min: 0, max: 0)
+
+# integer parameter array
+p3 <- integer_parameter_array('int_array', c(1:3), letters[1:3])
+print(p3) # print it
+#> int_array (min: 1, max: 3)
+p3$get() # get value
+#>   value
+#> a     1
+#> b     2
+#> c     3
+p3$id # get id
+#> id: fb5f4dd4-0caa-46a6-a5d3-3994cd2718b7
+invalid <- data.frame(value = rnorm(3), row.names=letters[1:3]) # invalid
+p3$validate(invalid) # check invalid input is invalid
+valid <- data.frame(value = 5:7, row.names=letters[1:3]) # valid
+p3$validate(valid) # check valid input is valid
+p3$set(valid) # change value to valid input
+print(p3)
+#> int_array (min: 5, max: 7)
+
+# numeric parameter array
+p4 <- numeric_parameter_array('dbl_array', c(0.1, 4, -5), letters[1:3])
+print(p4) # print it
+#> dbl_array (min: -5, max: 4)
+p4$get() # get value
+#>   value
+#> a   0.1
+#> b   4.0
+#> c  -5.0
+p4$id # get id
+#> id: d0009519-648d-4aad-89e5-4b0f86aaffee
+invalid <- data.frame(value = c(NA, 1, 2), row.names=letters[1:3]) # invalid
+p4$validate(invalid) # check invalid input is invalid
+valid <- data.frame(value = c(1, 2, 3), row.names=letters[1:3]) # valid
+p4$validate(valid) # check valid input is valid
+p4$set(valid) # change value to valid input
+print(p4)
+#> dbl_array (min: 1, max: 3)
+
+# numeric parameter array with lower bounds
+p5 <- numeric_parameter_array('b_dbl_array', c(0.1, 4, -5), letters[1:3],
+                              lower_limit=c(0, 1, 2))
+print(p5) # print it
+#> b_dbl_array (min: -5, max: 4)
+p5$get() # get value
+#>   value
+#> a   0.1
+#> b   4.0
+#> c  -5.0
+p5$id# get id
+#> id: 274883ce-0d40-485f-89b8-f2fc2f433e5e
+invalid <- data.frame(value = c(-1, 5, 5), row.names=letters[1:3]) # invalid
+p5$validate(invalid) # check invalid input is invalid
+valid <- data.frame(value = c(0, 1, 2), row.names=letters[1:3]) # valid
+p5$validate(valid) # check valid input is valid
+p5$set(valid) # change value to valid input
+print(p5)
+#> b_dbl_array (min: 0, max: 2)
+
      +
      + - - - - - - - - - - - + diff --git a/docs/reference/as.html b/docs/reference/as.html index 88fc43b03..b66e788d2 100644 --- a/docs/reference/as.html +++ b/docs/reference/as.html @@ -1,101 +1,18 @@ - - - - - - - -Coerce object to another object — as.Id • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Coerce object to another object — as.Id • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Coerce object to another object

      - Source: R/Id.R, R/misc.R + Source: R/Id.R, R/misc.R
      @@ -184,58 +101,48 @@

      Coerce object to another object

      Coerce an object.

      - 
      as.Id(x, ...)
-
-# S3 method for character
-as.Id(x, ...)
+    
      Usage,
      as.Id(x, ...)
 
-# S3 method for Parameters
-as.list(x, ...)
+# S3 method for character
+as.Id(x, ...)
 
-# S3 method for Zones
-as.list(x, ...)
      
+# S3 method for Parameters
+as.list(x, ...)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
      x
      Object.
      ...
      unused arguments.
      
-
-    
      Value
      
+# S3 method for Zones
+as.list(x, ...)
      +
      +

      Arguments

      +
      x
      +

      Object.

      +
      ...
      +

      unused arguments.

      +
      +
      +

      Value

      An object.

      +
      + - - - - - - - - - - - + diff --git a/docs/reference/as.list.html b/docs/reference/as.list.html index f750d9c6d..282890a0a 100644 --- a/docs/reference/as.list.html +++ b/docs/reference/as.list.html @@ -1,101 +1,18 @@ - - - - - - - -Convert OptimizationProblem to list — as.list.OptimizationProblem • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Convert OptimizationProblem to list — as.list.OptimizationProblem • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Convert OptimizationProblem to list

      - Source: R/OptimizationProblem-methods.R + Source: R/OptimizationProblem-methods.R
      @@ -184,50 +101,40 @@

      Convert OptimizationProblem to list

      Convert OptimizationProblem to list

      - 
      # S3 method for OptimizationProblem
-as.list(x, ...)
      - -

      Arguments

      - - - - - - - - - - -
      x

      OptimizationProblem object.

      ...

      not used.

      - -

      Value

      - -

      list() object.

      +
      Usage,
      # S3 method for OptimizationProblem
+as.list(x, ...)
      + +
      +

      Arguments

      +
      x
      +

      OptimizationProblem object.

      +
      ...
      +

      not used.

      +
      +
      +

      Value

      +

      list() object.

      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/binary_stack.html b/docs/reference/binary_stack.html index 6dd03f2bd..d92cf65c8 100644 --- a/docs/reference/binary_stack.html +++ b/docs/reference/binary_stack.html @@ -1,104 +1,21 @@ - - - - - - - -Binary stack — binary_stack • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Binary stack — binary_stack • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Binary stack

      - Source: R/binary_stack.R + Source: R/binary_stack.R
      -

      Convert a RasterLayer object containing -categorical identifiers into a RasterStack +

      Convert a RasterLayer object containing +categorical identifiers into a RasterStack object where each layer corresponds to a different identifier and values indicate the presence/absence of that category in the input object.

      - 
      binary_stack(x)
      - -

      Arguments

      - - - - - - -
      x

      Raster object containing a single layer.

      - -

      Value

      - -

      RasterStack object.

      -

      Details

      +
      Usage,
      binary_stack(x)
      +
      +

      Arguments

      +
      x
      +

      Raster object containing a single layer.

      +
      +
      +

      Value

      +

      RasterStack object.

      +
      +
      +

      Details

      This function is provided to help manage data that encompass multiple management zones. For instance, this function may be helpful -for preparing raster data for add_locked_in_constraints() and -add_locked_out_constraints() since they require binary -RasterStack objects as input arguments.

      -

      See also

      - -

      category_layer().

      +for preparing raster data for add_locked_in_constraints() and +add_locked_out_constraints() since they require binary +RasterStack objects as input arguments.

      +
      +
      +

      See also

      +

      category_layer().

      +
      -

      Examples

      - 
      # create raster with categorical identifers
-x <- raster(matrix(c(1, 2, 3, 1, NA, 1), nrow = 3))
-
-# convert to binary stack
-y <- binary_stack(x)
-
-# plot categorical raster and binary stack representation
-# \dontrun{
-plot(stack(x, y), main = c("x", "y[[1]]", "y[[2]]", "y[[3]]"), nr = 1)
-
-# }
+    
      
+    
      Examples
      
+    
      # create raster with categorical identifers
+x <- raster(matrix(c(1, 2, 3, 1, NA, 1), nrow = 3))
+
+# convert to binary stack
+y <- binary_stack(x)
+
+# plot categorical raster and binary stack representation
+# \dontrun{
+plot(stack(x, y), main = c("x", "y[[1]]", "y[[2]]", "y[[3]]"), nr = 1)
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/boundary_matrix.html b/docs/reference/boundary_matrix.html index d514677cb..9a8c06c99 100644 --- a/docs/reference/boundary_matrix.html +++ b/docs/reference/boundary_matrix.html @@ -1,103 +1,20 @@ - - - - - - - -Boundary matrix — boundary_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Boundary matrix — boundary_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Boundary matrix

      - Source: R/boundary_matrix.R + Source: R/boundary_matrix.R
      @@ -188,144 +105,137 @@

      Boundary matrix

      planning unit exhibits.

      - 
      boundary_matrix(x, str_tree)
+    
      Usage,
      boundary_matrix(x, str_tree)
 
-# S3 method for Raster
-boundary_matrix(x, str_tree = FALSE)
+# S3 method for Raster
+boundary_matrix(x, str_tree = FALSE)
 
-# S3 method for SpatialPolygons
-boundary_matrix(x, str_tree = FALSE)
+# S3 method for SpatialPolygons
+boundary_matrix(x, str_tree = FALSE)
 
-# S3 method for SpatialLines
-boundary_matrix(x, str_tree = FALSE)
+# S3 method for SpatialLines
+boundary_matrix(x, str_tree = FALSE)
 
-# S3 method for SpatialPoints
-boundary_matrix(x, str_tree = FALSE)
+# S3 method for SpatialPoints
+boundary_matrix(x, str_tree = FALSE)
 
-# S3 method for sf
-boundary_matrix(x, str_tree = FALSE)
+# S3 method for sf
+boundary_matrix(x, str_tree = FALSE)
 
-# S3 method for default
-boundary_matrix(x, str_tree = FALSE)
      
+# S3 method for default
+boundary_matrix(x, str_tree = FALSE)
      -

      Arguments

      - - - - - - - - - - -
      x

      Raster, -SpatialLines, -SpatialPolygons, -sf::sf() object representing planning units. If x is a -Raster object then it must have only one -layer.

      str_tree

      logical should a GEOS STRtree structure be used to +

      +

      Arguments

      +
      x
      +

      Raster, +SpatialLines, +SpatialPolygons, +sf::sf() object representing planning units. If x is a +Raster object then it must have only one +layer.

      +
      str_tree
      +

      logical should a GEOS STRtree structure be used to to pre-process data? If TRUE, then the experimental -rgeos::gUnarySTRtreeQuery() function +rgeos::gUnarySTRtreeQuery() function will be used to pre-compute which planning units are adjacent to each other and potentially reduce the processing time required to generate the boundary matrices. This argument is only used when -the planning unit data are vector-based polygons (i.e. -sp::SpatialPolygonsDataFrame() objects). Note that +the planning unit data are vector-based polygons (i.e., +sp::SpatialPolygonsDataFrame() objects). Note that using TRUE may crash Mac OSX systems. The default argument -is FALSE.

      - -

      Value

      - -

      dsCMatrix symmetric sparse matrix object. +is FALSE.

      +
      +
      +

      Value

      +

      dsCMatrix symmetric sparse matrix object. Each row and column represents a planning unit. Cells values indicate the shared boundary length between different pairs of planning units.

      -

      Details

      - -

      This function returns a dsCMatrix +

      +
      +

      Details

      +

      This function returns a dsCMatrix symmetric sparse matrix. Cells on the off-diagonal indicate the length of the shared boundary between two different planning units. Cells on the diagonal indicate length of a given planning unit's edges that have no -neighbors (e.g. for edges of planning units found along the +neighbors (e.g., for edges of planning units found along the coastline). This function assumes the data are in a coordinate system where Euclidean distances accurately describe the proximity between two points on the earth. Thus spatial data in a longitude/latitude -coordinate system (i.e. -WGS84) +coordinate system (i.e., +WGS84) should be reprojected to another coordinate system before using this -function. Note that for Raster objects +function. Note that for Raster objects boundaries are missing for cells that have NA values in all cells.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_polygons)
-
-# subset data to reduce processing time
-r <- crop(sim_pu_raster, c(0, 0.3, 0, 0.3))
-ply <- sim_pu_polygons[c(1:2, 10:12, 20:22), ]
-ply2 <- st_as_sf(ply)
-
-# create boundary matrix using raster data
-bm_raster <- boundary_matrix(r)
-
-# create boundary matrix using polygon (Spatial) data
-bm_ply1 <- boundary_matrix(ply)
-
-# create boundary matrix using polygon (sf) data
-bm_ply2 <- boundary_matrix(ply2)
-
-# create boundary matrix with polygon (Spatial) data and GEOS STR query trees
-# to speed up processing
-bm_ply3 <- boundary_matrix(ply, TRUE)
-
-# plot raster and boundary matrix
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(r, main = "raster", axes = FALSE, box = FALSE)
-plot(raster(as.matrix(bm_raster)), main = "boundary matrix",
-     axes = FALSE, box = FALSE)
-
-# }
-# plot polygons and boundary matrices
-# \dontrun{
-par(mfrow = c(1, 3))
-plot(r, main = "polygons (Spatial)", axes = FALSE, box = FALSE)
-plot(raster(as.matrix(bm_ply1)), main = "boundary matrix", axes = FALSE,
-     box = FALSE)
-plot(r, main = "polygons (sf)", axes = FALSE, box = FALSE)
-
-plot(raster(as.matrix(bm_ply2)), main = "boundary matrix", axes = FALSE,
-     box = FALSE)
-plot(raster(as.matrix(bm_ply3)), main = "boundary matrix (Spatial, STR)",
-            axes = FALSE, box = FALSE)
-# }
-
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_polygons)
+
+# subset data to reduce processing time
+r <- crop(sim_pu_raster, c(0, 0.3, 0, 0.3))
+ply <- sim_pu_polygons[c(1:2, 10:12, 20:22), ]
+ply2 <- st_as_sf(ply)
+
+# create boundary matrix using raster data
+bm_raster <- boundary_matrix(r)
+
+# create boundary matrix using polygon (Spatial) data
+bm_ply1 <- boundary_matrix(ply)
+
+# create boundary matrix using polygon (sf) data
+bm_ply2 <- boundary_matrix(ply2)
+
+# create boundary matrix with polygon (Spatial) data and GEOS STR query trees
+# to speed up processing
+bm_ply3 <- boundary_matrix(ply, TRUE)
+
+# plot raster and boundary matrix
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(r, main = "raster", axes = FALSE, box = FALSE)
+plot(raster(as.matrix(bm_raster)), main = "boundary matrix",
+     axes = FALSE, box = FALSE)
+
+# }
+# plot polygons and boundary matrices
+# \dontrun{
+par(mfrow = c(1, 3))
+plot(r, main = "polygons (Spatial)", axes = FALSE, box = FALSE)
+plot(raster(as.matrix(bm_ply1)), main = "boundary matrix", axes = FALSE,
+     box = FALSE)
+plot(r, main = "polygons (sf)", axes = FALSE, box = FALSE)
+
+plot(raster(as.matrix(bm_ply2)), main = "boundary matrix", axes = FALSE,
+     box = FALSE)
+plot(raster(as.matrix(bm_ply3)), main = "boundary matrix (Spatial, STR)",
+            axes = FALSE, box = FALSE)
+# }
+
 
      
+
      + - - - - - - - - - - - + diff --git a/docs/reference/branch_matrix.html b/docs/reference/branch_matrix.html index 309686cd4..eb3214782 100644 --- a/docs/reference/branch_matrix.html +++ b/docs/reference/branch_matrix.html @@ -1,107 +1,24 @@ - - - - - - - -Branch matrix — branch_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Branch matrix — branch_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Branch matrix

      - Source: R/branch_matrix.R + Source: R/branch_matrix.R
      @@ -196,69 +113,63 @@

      Branch matrix

      each species have experienced.

      - 
      branch_matrix(x)
-
-# S3 method for default
-branch_matrix(x)
-
-# S3 method for phylo
-branch_matrix(x)
      +
      Usage,
      branch_matrix(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      ape::phylo() tree object.
      
+# S3 method for default
+branch_matrix(x)
 
-    
      Value
      
+# S3 method for phylo
+branch_matrix(x)
      -

      dgCMatrix sparse matrix object. Each row +

      +

      Arguments

      +
      x
      +

      ape::phylo() tree object.

      +
      +
      +

      Value

      +

      dgCMatrix sparse matrix object. Each row corresponds to a different species. Each column corresponds to a different branch. Species that inherit from a given branch are denoted with a one.

      +
      -

      Examples

      - 
      # load data
-data(sim_phylogeny)
-
-# generate species by branch matrix
-m <- branch_matrix(sim_phylogeny)
-
-# plot data
-# \dontrun{
-par(mfrow = c(1,2))
-plot(sim_phylogeny, main = "phylogeny")
-plot(raster(as.matrix(m)), main = "branch matrix", axes = FALSE,
-     box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_phylogeny)
+
+# generate species by branch matrix
+m <- branch_matrix(sim_phylogeny)
+
+# plot data
+# \dontrun{
+par(mfrow = c(1,2))
+plot(sim_phylogeny, main = "phylogeny")
+plot(raster(as.matrix(m)), main = "branch matrix", axes = FALSE,
+     box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/category_layer.html b/docs/reference/category_layer.html index 90a40e98e..effd7e9f0 100644 --- a/docs/reference/category_layer.html +++ b/docs/reference/category_layer.html @@ -1,105 +1,22 @@ - - - - - - - -Category layer — category_layer • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Category layer — category_layer • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Category layer

      - Source: R/category_layer.R + Source: R/category_layer.R
      -

      Convert a RasterStack +

      Convert a RasterStack object where each layer corresponds to a different identifier and values indicate the presence/absence of that category into a -RasterLayer object containing categorical +RasterLayer object containing categorical identifiers.

      - 
      category_layer(x)
      - -

      Arguments

      - - - - - - -
      x

      Raster object containing a multiple -layers. Note that pixels must be 0, 1 or NA values.

      - -

      Value

      - -

      RasterLayer object.

      -

      Details

      - +
      Usage,
      category_layer(x)
      + +
      +

      Arguments

      +
      x
      +

      Raster object containing a multiple +layers. Note that pixels must be 0, 1 or NA values.

      +
      +
      +

      Value

      +

      RasterLayer object.

      +
      +
      +

      Details

      This function is provided to help manage data that encompass multiple management zones. For instance, this function may be helpful for interpreting solutions for problems associated with multiple zones that have binary decisions.

      -

      See also

      - -

      binary_stack().

      +
      +
      +

      See also

      +

      binary_stack().

      +
      -

      Examples

      - 
      # create a binary raster stack
-x <- stack(raster(matrix(c(1, 0, 0, 1, NA, 0), nrow = 3)),
-           raster(matrix(c(0, 1, 0, 0, NA, 0), nrow = 3)),
-           raster(matrix(c(0, 0, 1, 0, NA, 1), nrow = 3)))
-
-# convert to binary stack
-y <- category_layer(x)
-
-# plot categorical raster and binary stack representation
-# \dontrun{
-plot(stack(x, y), main = c("x[[1]]", "x[[2]]", "x[[3]]", "y"), nr = 1)
-
-# }
+    
      
+    
      Examples
      
+    
      # create a binary raster stack
+x <- stack(raster(matrix(c(1, 0, 0, 1, NA, 0), nrow = 3)),
+           raster(matrix(c(0, 1, 0, 0, NA, 0), nrow = 3)),
+           raster(matrix(c(0, 0, 1, 0, NA, 1), nrow = 3)))
+
+# convert to binary stack
+y <- category_layer(x)
+
+# plot categorical raster and binary stack representation
+# \dontrun{
+plot(stack(x, y), main = c("x[[1]]", "x[[2]]", "x[[3]]", "y"), nr = 1)
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/category_vector.html b/docs/reference/category_vector.html index 8406ea588..a6281900f 100644 --- a/docs/reference/category_vector.html +++ b/docs/reference/category_vector.html @@ -1,103 +1,20 @@ - - - - - - - -Category vector — category_vector • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Category vector — category_vector • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Category vector

      - Source: R/category_vector.R + Source: R/category_vector.R
      @@ -188,86 +105,82 @@

      Category vector

      1.

      - 
      category_vector(x)
-
-# S3 method for data.frame
-category_vector(x)
+    
      Usage,
      category_vector(x)
 
-# S3 method for sf
-category_vector(x)
+# S3 method for data.frame
+category_vector(x)
 
-# S3 method for Spatial
-category_vector(x)
+# S3 method for sf
+category_vector(x)
 
-# S3 method for matrix
-category_vector(x)
      
+# S3 method for Spatial
+category_vector(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      matrix, data.frame, Spatial,
-or sf::sf() object.
      
-
-    
      Value
      
+# S3 method for matrix
+category_vector(x)
      +
      +

      Arguments

      +
      x
      +

      matrix, data.frame, Spatial, +or sf::sf() object.

      +
      +
      +

      Value

      integer vector.

      -

      Details

      - -

      This function is conceptually similar to base::max.col() +

      +
      +

      Details

      +

      This function is conceptually similar to base::max.col() except that rows with no values equal to 1 values are assigned a value of zero. Also, note that in the argument to x, each row must contain only a single value equal to 1.

      -

      See also

      - -

      base::max.col()

      +
      +
      +

      See also

      +

      base::max.col()

      +
      -

      Examples

      - 
      # create matrix with logical fields
-x <- matrix(c(1, 0, 0, NA, 0, 1, 0, NA, 0, 0, 0, NA), ncol = 3)
-
-# print matrix
-print(x)
-#>      [,1] [,2] [,3]
-#> [1,]    1    0    0
-#> [2,]    0    1    0
-#> [3,]    0    0    0
-#> [4,]   NA   NA   NA
-
-# convert to category vector
-y <- category_vector(x)
-
-# print category vector
-print(y)
-#> [1]  1  2  0 NA
+    
      
+    
      Examples
      
+    
      # create matrix with logical fields
+x <- matrix(c(1, 0, 0, NA, 0, 1, 0, NA, 0, 0, 0, NA), ncol = 3)
+
+# print matrix
+print(x)
+#>      [,1] [,2] [,3]
+#> [1,]    1    0    0
+#> [2,]    0    1    0
+#> [3,]    0    0    0
+#> [4,]   NA   NA   NA
+
+# convert to category vector
+y <- category_vector(x)
+
+# print category vector
+print(y)
+#> [1]  1  2  0 NA
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/compile.html b/docs/reference/compile.html index 2eca18519..835f4f7bb 100644 --- a/docs/reference/compile.html +++ b/docs/reference/compile.html @@ -1,102 +1,19 @@ - - - - - - - -Compile a problem — compile • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Compile a problem — compile • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Compile a problem

      - Source: R/compile.R + Source: R/compile.R
      -

      Compile a conservation planning problem() into an +

      Compile a conservation planning problem() into an (potentially mixed) integer linear programming problem.

      - 
      compile(x, ...)
+    
      Usage,
      compile(x, ...)
 
-# S3 method for ConservationProblem
-compile(x, compressed_formulation = NA, ...)
      
+# S3 method for ConservationProblem
+compile(x, compressed_formulation = NA, ...)
      -

      Arguments

      - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      ...

      not used.

      compressed_formulation

      logical should the conservation problem +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      ...
      +

      not used.

      +
      compressed_formulation
      +

      logical should the conservation problem compiled into a compressed version of a planning problem? If TRUE then the problem is expressed using the compressed formulation. If FALSE then the problem is expressed using the expanded formulation. If NA, then the compressed is used unless one of the constraints requires the expanded formulation. This argument -defaults to NA.

      - -

      Value

      - -

      OptimizationProblem object.

      -

      Details

      - +defaults to NA.

      +
      +
      +

      Value

      +

      OptimizationProblem object.

      +
      +
      +

      Details

      This function might be useful for those interested in understanding -how their conservation planning problem() is expressed +how their conservation planning problem() is expressed as a mathematical problem. However, if the problem just needs to -be solved, then the solve() function should just be used.

      +be solved, then the solve() function should just be used.

      Please note that in nearly all cases, the default argument to formulation should be used. The only situation where manually setting the argument to formulation is desirable is during testing. @@ -230,48 +140,46 @@

      Details have no effect on the problem. At worst, it may result in an error, a misspecified problem, or unnecessarily long solve times.

      +

      -

      Examples

      - 
      # build minimal conservation problem
-p <- problem(sim_pu_raster, sim_features) %>%
-  add_min_set_objective() %>%
-  add_relative_targets(0.1)
-
-# compile the conservation problem into an optimization problem
-o <- compile(p)
-
-# print the optimization problem
-print(o)
-#> optimization problem
-#>   model sense: min
-#>   dimensions:  5, 90, 450 (nrow, ncol, ncell)
-#>   variables:   90 (B)
-
+    
      
+    
      Examples
      
+    
      # build minimal conservation problem
+p <- problem(sim_pu_raster, sim_features) %>%
+  add_min_set_objective() %>%
+  add_relative_targets(0.1)
+
+# compile the conservation problem into an optimization problem
+o <- compile(p)
+
+# print the optimization problem
+print(o)
+#> optimization problem
+#>   model sense: min
+#>   dimensions:  5, 90, 450 (nrow, ncol, ncell)
+#>   variables:   90 (B)
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/connectivity_matrix.html b/docs/reference/connectivity_matrix.html index b01fa0d8c..7230dd897 100644 --- a/docs/reference/connectivity_matrix.html +++ b/docs/reference/connectivity_matrix.html @@ -1,105 +1,22 @@ - - - - - - - -Connectivity matrix — connectivity_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Connectivity matrix — connectivity_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Connectivity matrix

      - Source: R/connectivity_matrix.R + Source: R/connectivity_matrix.R
      @@ -192,248 +109,238 @@

      Connectivity matrix

      boundary are associated with greater connectivity.

      - 
      connectivity_matrix(x, y, ...)
+    
      Usage,
      connectivity_matrix(x, y, ...)
 
-# S4 method for Spatial,Raster
-connectivity_matrix(x, y, ...)
+# S4 method for Spatial,Raster
+connectivity_matrix(x, y, ...)
 
-# S4 method for Spatial,character
-connectivity_matrix(x, y, ...)
+# S4 method for Spatial,character
+connectivity_matrix(x, y, ...)
 
-# S4 method for sf,character
-connectivity_matrix(x, y, ...)
+# S4 method for sf,character
+connectivity_matrix(x, y, ...)
 
-# S4 method for sf,Raster
-connectivity_matrix(x, y, ...)
+# S4 method for sf,Raster
+connectivity_matrix(x, y, ...)
 
-# S4 method for Raster,Raster
-connectivity_matrix(x, y, ...)
      
+# S4 method for Raster,Raster
+connectivity_matrix(x, y, ...)
      -

      Arguments

      - - - - - - - - - - - - - - -
      x

      Raster, -SpatialPolygonsDataFrame, -SpatialLinesDataFrame, -or sf::sf() object +

      +

      Arguments

      +
      x
      +

      Raster, +SpatialPolygonsDataFrame, +SpatialLinesDataFrame, +or sf::sf() object representing planning units. -If x is a Raster object then it must -contain a single layer.

      y

      Raster object showing the conductance +If x is a Raster object then it must +contain a single layer.

      +
      y
      +

      Raster object showing the conductance of different areas across the study area, or a character object denoting a column name in the attribute table of x that contains the conductance values. Note that argument to y can only be a character object if the argument to x is a -Spatial or sf::sf() object. +Spatial or sf::sf() object. Also, note that if the argument to x is a -Raster object then +Raster object then argument to y must have the same spatial properties as it -(i.e. coordinate system, extent, resolution).

      ...

      additional arguments passed to fast_extract() for +(i.e., coordinate system, extent, resolution).

      +
      ...
      +

      additional arguments passed to fast_extract() for extracting and calculating the conductance values for each planning unit. These arguments are only used if argument to x is a -link[sp]{Spatial-class} or sf::sf() object and argument -to y is a Raster object.

      - -

      Value

      - -

      dsCMatrix symmetric sparse matrix object. +link[sp]{Spatial-class} or sf::sf() object and argument +to y is a Raster object.

      +
      +
      +

      Value

      +

      dsCMatrix symmetric sparse matrix object. Each row and column represents a planning unit. Cells values indicate the connectivity between different pairs of planning units. To reduce computational burden, cells among the matrix diagonal are set to zero. Furthermore, if the argument to x is a -Raster object, then cells with NA -values are set to zero too.

      -

      Details

      - +Raster object, then cells with NAvalues are set to zero too.

      +
      +
      +

      Details

      Shared boundary calculations are performed using -boundary_matrix().

      +boundary_matrix().

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_sf, sim_features)
-
-# create connectivity matrix using raster planning unit data using
-# the raster cost values to represent conductance
-## extract 9 planning units
-r <- crop(sim_pu_raster, c(0, 0.3, 0, 0.3))
-
-## extract conductance data for the 9 planning units
-cd <- crop(sim_features, r)
-
-## make connectivity matrix using the habitat suitability data for the
-## second feature to represent the planning unit conductance data
-cm_raster <- connectivity_matrix(r, cd[[2]])
-
-## plot data and matrix
-# \dontrun{
-par(mfrow = c(1,3))
-plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
-plot(cd[[2]], main = "conductivity", axes = FALSE, box = FALSE)
-plot(clamp(raster(as.matrix(cm_raster)), lower = 1e-5, useValues = FALSE),
-     main = "connectivity", axes = FALSE, box = FALSE)
-
-# }
-# create connectivity matrix using polygon planning unit data using
-# the habitat suitability data for the second feature to represent
-# planning unit conductances
-## subset data to 9 polygons
-ply <- sim_pu_sf[c(1:2, 10:12, 20:22), ]
-
-## make connectivity matrix
-cm_ply <- connectivity_matrix(ply, sim_features[[2]])
-
-## plot data and matrix
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(st_geometry(ply), main = "planning units (sf)")
-plot(clamp(raster(as.matrix(cm_ply)), lower = 1e-5, useValues = FALSE),
-     main = "connectivity", axes = FALSE, box = FALSE)
-
-# }
-
-# create connectivity matrix using habitat suitability data for each feature,
-# this could be useful if prioritisations should spatially clump
-# together adjacent planning units that have suitable habitat
-# for the same species (e.g. to maintain functional connectivity)
-
-## let's use the raster data for this example, and we can generate the
-## connectivity matrix that we would use in the prioritization by
-## (1) generating a connectivity matrix for each feature separately, and
-## and then (2) then summing the values together
-cm_sum <- lapply(as.list(cd), connectivity_matrix, x = r) # make matrices
-cm_sum <- Reduce("+", cm_sum) # sum matrices together
-
-## plot data and matrix
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
-plot(clamp(raster(as.matrix(cm_sum)), lower = 1e-5, useValues = FALSE),
-     main = "connectivity", axes = FALSE, box = FALSE)
-
-# }
-
-## we could take this example one step further, and use weights to indicate
-## relative importance of maintaining functional connectivity
-## for each feature (i.e. use the weighted sum instead of the sum)
-
-## let's pretend that the first feature is 20 times more important
-## than all the other species
-weights <- c(20, 1, 1, 1, 1)
-
-## calculate connectivity matrix using weighted sum
-cm_wsum <- lapply(as.list(cd), connectivity_matrix, x = r) # make matrices
-cm_wsum <- Map("*", cm_wsum, weights) # multiply by weights
-cm_wsum <- Reduce("+", cm_wsum) # sum matrices together
-
-## plot data and matrix
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
-plot(clamp(raster(as.matrix(cm_wsum)), lower = 1e-5, useValues = FALSE),
-     main = "connectivity", axes = FALSE, box = FALSE)
-
-# }
-
-## since the statistical distribution of the connectivity values
-## for each feature (e.g. the mean and standard deviation of the
-## connectivity values) are different, it might make sense -- depending
-## on the goal of the conservation planning exercise and the underlying
-## data -- to first normalize the conductance values before applying the
-## weights and summing the data for feature together
-
-## one approach would be to linearly rescale the values between 0.01 and 1
-## note that we wouldn't want to rescale them between 0 and 1 since
-## a value of zero means that there is no connectivity at all (and
-## and not a relatively small amount of connectivity)
-# \dontrun{
-### define helper function
-library(scales) # load scales library for rescale
-rescale_matrix <- function(x) {x@x <- rescale(x@x, c(0.01, 1)); x}
-
-### calculate functional connectivity matrix using the weighted sum of
-### connectivity values that have been normalized by linearly re-scaling
-### values
-cm_lwsum <- lapply(as.list(cd), connectivity_matrix, x = r) # make matrices
-cm_lwsum <- lapply(cm_lwsum, rescale_matrix) # rescale matrices to [0.01, 1]
-cm_lwsum <- Map("*", cm_lwsum, weights) # multiply by weights
-cm_lwsum <- Reduce("+", cm_lwsum) # sum matrices together
-# }
-
-## plot data and matrix
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
-plot(clamp(raster(as.matrix(cm_lwsum)), lower = 1e-5, useValues = FALSE),
-     main = "connectivity", axes = FALSE, box = FALSE)
-
-# }
-
-## another approach for normalizing the data could be using z-scores
-## note that after normalizing the data we would need to add a constant
-## value so that none of the connectivity values are negative
-
-### define helper functions
-zscore <- function(x) {x@x <- (x@x - mean(x@x)) / sd(x@x); x}
-min_non_zero_value <- function(x) min(x@x)
-add_non_zero_value <- function(x, y) {x@x <- x@x + y; x}
-
-### calculate functional connectivity matrix using the weighted sum of
-### connectivity values that have been normalized using z-scores,
-### and transformed to account for negative values
-cm_zwsum <- lapply(as.list(cd), connectivity_matrix, x = r) # make matrices
-cm_zwsum <- lapply(cm_zwsum, zscore) # normalize using z-scores
-min_value <- min(sapply(cm_zwsum, min_non_zero_value)) # find min value
-min_value <- abs(min_value) + 0.01 # prepare constant for adding to matrices
-cm_zwsum <- lapply(cm_zwsum, add_non_zero_value, min_value) # add constant
-cm_zwsum <- Map("*", cm_zwsum, weights) # multiply by weights
-cm_zwsum <- Reduce("+", cm_zwsum) # sum matrices together
-
-## plot data and matrix
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
-plot(clamp(raster(as.matrix(cm_zwsum)), lower = 1e-5, useValues = FALSE),
-     main = "connectivity", axes = FALSE, box = FALSE)
-
-# }
-
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_sf, sim_features)
+
+# create connectivity matrix using raster planning unit data using
+# the raster cost values to represent conductance
+## extract 9 planning units
+r <- crop(sim_pu_raster, c(0, 0.3, 0, 0.3))
+
+## extract conductance data for the 9 planning units
+cd <- crop(sim_features, r)
+
+## make connectivity matrix using the habitat suitability data for the
+## second feature to represent the planning unit conductance data
+cm_raster <- connectivity_matrix(r, cd[[2]])
+
+## plot data and matrix
+# \dontrun{
+par(mfrow = c(1,3))
+plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
+plot(cd[[2]], main = "conductivity", axes = FALSE, box = FALSE)
+plot(clamp(raster(as.matrix(cm_raster)), lower = 1e-5, useValues = FALSE),
+     main = "connectivity", axes = FALSE, box = FALSE)
+
+# }
+# create connectivity matrix using polygon planning unit data using
+# the habitat suitability data for the second feature to represent
+# planning unit conductances
+## subset data to 9 polygons
+ply <- sim_pu_sf[c(1:2, 10:12, 20:22), ]
+
+## make connectivity matrix
+cm_ply <- connectivity_matrix(ply, sim_features[[2]])
+
+## plot data and matrix
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(st_geometry(ply), main = "planning units (sf)")
+plot(clamp(raster(as.matrix(cm_ply)), lower = 1e-5, useValues = FALSE),
+     main = "connectivity", axes = FALSE, box = FALSE)
+
+# }
+
+# create connectivity matrix using habitat suitability data for each feature,
+# this could be useful if prioritisations should spatially clump
+# together adjacent planning units that have suitable habitat
+# for the same species (e.g., to maintain functional connectivity)
+
+## let's use the raster data for this example, and we can generate the
+## connectivity matrix that we would use in the prioritization by
+## (1) generating a connectivity matrix for each feature separately, and
+## and then (2) then summing the values together
+cm_sum <- lapply(as.list(cd), connectivity_matrix, x = r) # make matrices
+cm_sum <- Reduce("+", cm_sum) # sum matrices together
+
+## plot data and matrix
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
+plot(clamp(raster(as.matrix(cm_sum)), lower = 1e-5, useValues = FALSE),
+     main = "connectivity", axes = FALSE, box = FALSE)
+
+# }
+
+## we could take this example one step further, and use weights to indicate
+## relative importance of maintaining functional connectivity
+## for each feature (i.e., use the weighted sum instead of the sum)
+
+## let's pretend that the first feature is 20 times more important
+## than all the other species
+weights <- c(20, 1, 1, 1, 1)
+
+## calculate connectivity matrix using weighted sum
+cm_wsum <- lapply(as.list(cd), connectivity_matrix, x = r) # make matrices
+cm_wsum <- Map("*", cm_wsum, weights) # multiply by weights
+cm_wsum <- Reduce("+", cm_wsum) # sum matrices together
+
+## plot data and matrix
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
+plot(clamp(raster(as.matrix(cm_wsum)), lower = 1e-5, useValues = FALSE),
+     main = "connectivity", axes = FALSE, box = FALSE)
+
+# }
+
+## since the statistical distribution of the connectivity values
+## for each feature (e.g., the mean and standard deviation of the
+## connectivity values) are different, it might make sense -- depending
+## on the goal of the conservation planning exercise and the underlying
+## data -- to first normalize the conductance values before applying the
+## weights and summing the data for feature together
+
+## one approach would be to linearly rescale the values between 0.01 and 1
+## note that we wouldn't want to rescale them between 0 and 1 since
+## a value of zero means that there is no connectivity at all (and
+## and not a relatively small amount of connectivity)
+# \dontrun{
+### define helper function
+library(scales) # load scales library for rescale
+rescale_matrix <- function(x) {x@x <- rescale(x@x, c(0.01, 1)); x}
+
+### calculate functional connectivity matrix using the weighted sum of
+### connectivity values that have been normalized by linearly re-scaling
+### values
+cm_lwsum <- lapply(as.list(cd), connectivity_matrix, x = r) # make matrices
+cm_lwsum <- lapply(cm_lwsum, rescale_matrix) # rescale matrices to [0.01, 1]
+cm_lwsum <- Map("*", cm_lwsum, weights) # multiply by weights
+cm_lwsum <- Reduce("+", cm_lwsum) # sum matrices together
+# }
+
+## plot data and matrix
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
+plot(clamp(raster(as.matrix(cm_lwsum)), lower = 1e-5, useValues = FALSE),
+     main = "connectivity", axes = FALSE, box = FALSE)
+
+# }
+
+## another approach for normalizing the data could be using z-scores
+## note that after normalizing the data we would need to add a constant
+## value so that none of the connectivity values are negative
+
+### define helper functions
+zscore <- function(x) {x@x <- (x@x - mean(x@x)) / sd(x@x); x}
+min_non_zero_value <- function(x) min(x@x)
+add_non_zero_value <- function(x, y) {x@x <- x@x + y; x}
+
+### calculate functional connectivity matrix using the weighted sum of
+### connectivity values that have been normalized using z-scores,
+### and transformed to account for negative values
+cm_zwsum <- lapply(as.list(cd), connectivity_matrix, x = r) # make matrices
+cm_zwsum <- lapply(cm_zwsum, zscore) # normalize using z-scores
+min_value <- min(sapply(cm_zwsum, min_non_zero_value)) # find min value
+min_value <- abs(min_value) + 0.01 # prepare constant for adding to matrices
+cm_zwsum <- lapply(cm_zwsum, add_non_zero_value, min_value) # add constant
+cm_zwsum <- Map("*", cm_zwsum, weights) # multiply by weights
+cm_zwsum <- Reduce("+", cm_zwsum) # sum matrices together
+
+## plot data and matrix
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(r, main = "planning units (raster)", axes = FALSE, box = FALSE)
+plot(clamp(raster(as.matrix(cm_zwsum)), lower = 1e-5, useValues = FALSE),
+     main = "connectivity", axes = FALSE, box = FALSE)
+
+# }
+
 
      
+
      + - - - - - - - - - - - + diff --git a/docs/reference/constraints.html b/docs/reference/constraints.html index 92eafcb4e..e88080bff 100644 --- a/docs/reference/constraints.html +++ b/docs/reference/constraints.html @@ -1,102 +1,19 @@ - - - - - - - -Conservation problem constraints — constraints • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Conservation problem constraints — constraints • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Conservation problem constraints

      - Source: R/constraints.R + Source: R/constraints.R
      -

      A constraint can be added to a conservation planning problem() +

      A constraint can be added to a conservation planning problem() to ensure that solutions exhibit a specific characteristic.

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      Constraints can be used to ensure that solutions exhibit a range of different characteristics. For instance, they can be used to lock in or lock out certain planning units from the solution, such as protected areas or degraded land (respectively). -Additionally, similar to the penalties functions, +Additionally, similar to the penalties functions, some of the constraint functions can be used to increase connectivity in a solution. The key difference between a penalty and a constraint, however, is that constraints work by invalidating solutions that do not exhibit @@ -203,117 +120,126 @@

      Details constraints do not affect the objective function. The following constraints are available.

      The following constraints can be added to a conservation planning -problem():

      -
      - -
      add_locked_in_constraints()

      Add constraints to ensure +problem():

      +
      add_locked_in_constraints()
      +

      Add constraints to ensure that certain planning units are selected in the solution.

      -
      add_locked_out_constraints()

      Add constraints to ensure + +

      add_locked_out_constraints()
      +

      Add constraints to ensure that certain planning units are not selected in the solution.

      -
      add_neighbor_constraints()

      Add constraints to + +

      add_neighbor_constraints()
      +

      Add constraints to ensure that all selected planning units have at least a certain number of neighbors.

      -
      add_contiguity_constraints()

      Add constraints to a + +

      add_contiguity_constraints()
      +

      Add constraints to a ensure that all selected planning units are spatially connected to each other and form a single contiguous unit.

      -
      add_feature_contiguity_constraints()

      Add constraints to + +

      add_feature_contiguity_constraints()
      +

      Add constraints to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of -those implemented in the add_contiguity_constraints() +those implemented in the add_contiguity_constraints() function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit.

      -
      add_linear_constraints()

      Add constraints to ensure that all selected planning units meet certain + +

      add_linear_constraints()
      +

      Add constraints to ensure that all selected planning units meet certain criteria. For example, they can be used to add multiple budgets, or limit the number of planning units selected in different administrative areas within a study -region (e.g. different countries).

      +region (e.g., different countries).

      -
      add_mandatory_allocation_constraints()

      Add constraints to ensure that every planning unit is allocated to a + +

      add_mandatory_allocation_constraints()
      +

      Add constraints to ensure that every planning unit is allocated to a management zone in the solution. This function can only be used with problems that contain multiple zones.

      -
      - -

      See also

      -

      Other overviews: -decisions, -importance, -objectives, -penalties, -portfolios, -solvers, -summaries, -targets

      +
      +
      +

      See also

      +

      Other overviews: +decisions, +importance, +objectives, +penalties, +portfolios, +solvers, +summaries, +targets

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features, sim_locked_in_raster,
-     sim_locked_out_raster)
-
-# create minimal problem with only targets and no additional constraints
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with locked in constraints
-p2 <- p1 %>% add_locked_in_constraints(sim_locked_in_raster)
-
-# create problem with locked in constraints
-p3 <- p1 %>% add_locked_out_constraints(sim_locked_out_raster)
-
-# create problem with neighbor constraints
-p4 <- p1 %>% add_neighbor_constraints(2)
-
-# create problem with contiguity constraints
-p5 <- p1 %>% add_contiguity_constraints()
-
-# create problem with feature contiguity constraints
-p6 <- p1 %>% add_feature_contiguity_constraints()
-# \dontrun{
-# solve problems
-s <- stack(lapply(list(p1, p2, p3, p4, p5, p6), solve))
-
-# plot solutions
-plot(s, box = FALSE, axes = FALSE, nr = 2,
-     main = c("minimal problem", "locked in", "locked out",
-              "neighbor", "contiguity", "feature contiguity"))
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features, sim_locked_in_raster,
+     sim_locked_out_raster)
+
+# create minimal problem with only targets and no additional constraints
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with locked in constraints
+p2 <- p1 %>% add_locked_in_constraints(sim_locked_in_raster)
+
+# create problem with locked in constraints
+p3 <- p1 %>% add_locked_out_constraints(sim_locked_out_raster)
+
+# create problem with neighbor constraints
+p4 <- p1 %>% add_neighbor_constraints(2)
+
+# create problem with contiguity constraints
+p5 <- p1 %>% add_contiguity_constraints()
+
+# create problem with feature contiguity constraints
+p6 <- p1 %>% add_feature_contiguity_constraints()
+# \dontrun{
+# solve problems
+s <- stack(lapply(list(p1, p2, p3, p4, p5, p6), solve))
+
+# plot solutions
+plot(s, box = FALSE, axes = FALSE, nr = 2,
+     main = c("minimal problem", "locked in", "locked out",
+              "neighbor", "contiguity", "feature contiguity"))
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/decisions.html b/docs/reference/decisions.html index a0f3a4cc3..4807838fe 100644 --- a/docs/reference/decisions.html +++ b/docs/reference/decisions.html @@ -1,106 +1,23 @@ - - - - - - - -Add decision types — decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add decision types — decisions • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add decision types

      - Source: R/decisions.R + Source: R/decisions.R
      @@ -191,113 +108,114 @@

      Add decision types

      turning an entire planning unit into a protected area, turning part of a planning unit into a protected area, or allocating a planning unit to a specific management zone. If no decision is explicitly added to a -problem(), then binary decisions will be used by default.

      +problem(), then binary decisions will be used by default.

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      Only a single type of decision can be added to a conservation -planning problem(). Note that if multiple decisions are added +planning problem(). Note that if multiple decisions are added to a problem, then the last one added will be used.

      The following decisions can be added to a conservation planning -problem():

      -
      - -
      add_binary_decisions()

      Add a binary decision to a +problem():

      +
      add_binary_decisions()
      +

      Add a binary decision to a conservation planning problem. This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem object then this decision class will be used by default.

      -
      add_proportion_decisions()

      Add a proportion decision to + +

      add_proportion_decisions()
      +

      Add a proportion decision to a conservation planning problem. This is a relaxed decision where a part of a planning unit can be prioritized, as opposed to the default of the entire planning unit. Typically, this decision has the assumed action of buying a fraction of a planning unit to include in a protected area network.

      -
      add_semicontinuous_decisions()

      Add a semi-continuous + +

      add_semicontinuous_decisions()
      +

      Add a semi-continuous decision to a conservation planning problem. This decision is similar to add_proportion_decision except that it has an upper bound parameter. By default, the decision can range from prioritizing none (0%) to all (100%) of a planning unit. However, a upper bound can be specified to ensure that at most only a fraction -(e.g. 80%) of a planning unit can be preserved. This type of +(e.g., 80%) of a planning unit can be preserved. This type of decision may be useful when it is not practical to conserve the entire area encompassed by any single planning unit.

      -
      -

      See also

      - -

      Other overviews: -constraints, -importance, -objectives, -penalties, -portfolios, -solvers, -summaries, -targets

      +
      +
      +

      See also

      +

      Other overviews: +constraints, +importance, +objectives, +penalties, +portfolios, +solvers, +summaries, +targets

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create basic problem and using the default decision types (binary)
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with manually specified binary decisions
-p2 <- p1 %>% add_binary_decisions()
-
-# create problem with proportion decisions
-p3 <- p1 %>% add_proportion_decisions()
-
-# create problem with semicontinuous decisions
-p4 <- p1 %>% add_semicontinuous_decisions(upper_limit = 0.5)
-
-# \dontrun{
-# solve problem
-s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
-
-# plot solutions
-plot(s, main = c("default (binary)", "binary", "proportion",
-                 "semicontinuous (upper = 0.5)"))
-
-# }
-
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create basic problem and using the default decision types (binary)
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with manually specified binary decisions
+p2 <- p1 %>% add_binary_decisions()
+
+# create problem with proportion decisions
+p3 <- p1 %>% add_proportion_decisions()
+
+# create problem with semicontinuous decisions
+p4 <- p1 %>% add_semicontinuous_decisions(upper_limit = 0.5)
+
+# \dontrun{
+# solve problem
+s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
+
+# plot solutions
+plot(s, main = c("default (binary)", "binary", "proportion",
+                 "semicontinuous (upper = 0.5)"))
+
+# }
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/distribute_load.html b/docs/reference/distribute_load.html index 64feeb949..d1c62e13b 100644 --- a/docs/reference/distribute_load.html +++ b/docs/reference/distribute_load.html @@ -1,102 +1,19 @@ - - - - - - - -Distribute load — distribute_load • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Distribute load — distribute_load • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Distribute load

      - Source: R/distribute_load.R + Source: R/distribute_load.R
      @@ -186,199 +103,192 @@

      Distribute load

      for parallel processing.

      - 
      distribute_load(x, n = 1)
      - -

      Arguments

      - - - - - - - - - - -
      x

      integer number of item to process.

      n

      integer number of threads.

      - -

      Value

      - +
      Usage,
      distribute_load(x, n = 1)
      + +
      +

      Arguments

      +
      x
      +

      integer number of item to process.

      +
      n
      +

      integer number of threads.

      +
      +
      +

      Value

      list object.

      -

      Details

      - +
      +
      +

      Details

      This function returns a list containing an element for each worker. Each element contains a integer vector specifying the indices that the worker should process.

      +
      -

      Examples

      - 
      # \dontrun{
-
-# imagine that we have 10 jobs that need processing. For simplicity,
-# our jobs will involve adding 1 to each element in 1:10.
-values <- 1:10
-
-# we could complete this processing using the following vectorized code
-result <- 1 + 1:10
-print(result)
-#>  [1]  2  3  4  5  6  7  8  9 10 11
-
-# however, if our jobs were complex then we would be better off using
-# functionals
-result <- lapply(1:10, function(x) x + 1)
-print(result)
-#> [[1]]
-#> [1] 2
-#> 
-#> [[2]]
-#> [1] 3
-#> 
-#> [[3]]
-#> [1] 4
-#> 
-#> [[4]]
-#> [1] 5
-#> 
-#> [[5]]
-#> [1] 6
-#> 
-#> [[6]]
-#> [1] 7
-#> 
-#> [[7]]
-#> [1] 8
-#> 
-#> [[8]]
-#> [1] 9
-#> 
-#> [[9]]
-#> [1] 10
-#> 
-#> [[10]]
-#> [1] 11
-#> 
-
-# we could do one better, and use the "plyr" package to handle the
-# processing
-result <- plyr::llply(1:10, function(x) x + 1)
-print(result)
-#> [[1]]
-#> [1] 2
-#> 
-#> [[2]]
-#> [1] 3
-#> 
-#> [[3]]
-#> [1] 4
-#> 
-#> [[4]]
-#> [1] 5
-#> 
-#> [[5]]
-#> [1] 6
-#> 
-#> [[6]]
-#> [1] 7
-#> 
-#> [[7]]
-#> [1] 8
-#> 
-#> [[8]]
-#> [1] 9
-#> 
-#> [[9]]
-#> [1] 10
-#> 
-#> [[10]]
-#> [1] 11
-#> 
-
-# we could also use the parallel processing options available through "plyr"
-# to use more computation resources to complete the jobs (note that since
-# these jobs are very quick to process this is actually slower).
-cl <- parallel::makeCluster(2, "PSOCK")
-doParallel::registerDoParallel(cl)
-result <- plyr::llply(1:10, function(x) x + 1, .parallel = TRUE)
-#> Warning: <anonymous>: ... may be used in an incorrect context: ‘.fun(piece, ...)’
-#> Warning: <anonymous>: ... may be used in an incorrect context: ‘.fun(piece, ...)’
-cl <- parallel::stopCluster(cl)
-print(result)
-#> [[1]]
-#> [1] 2
-#> 
-#> [[2]]
-#> [1] 3
-#> 
-#> [[3]]
-#> [1] 4
-#> 
-#> [[4]]
-#> [1] 5
-#> 
-#> [[5]]
-#> [1] 6
-#> 
-#> [[6]]
-#> [1] 7
-#> 
-#> [[7]]
-#> [1] 8
-#> 
-#> [[8]]
-#> [1] 9
-#> 
-#> [[9]]
-#> [1] 10
-#> 
-#> [[10]]
-#> [1] 11
-#> 
-
-# however this approach iterates over each element individually, we could
-# use the distribute_load function to split the N jobs up into K super
-# jobs, and evaluate each super job using vectorized code.
-x <- 1:10
-cl <- parallel::makeCluster(2, "PSOCK")
-parallel::clusterExport(cl, 'x', envir = environment())
-doParallel::registerDoParallel(cl)
-l <- distribute_load(length(x), n = 2)
-result <- plyr::llply(l, function(i) x[i] + 1, .parallel = TRUE)
-#> Warning: <anonymous>: ... may be used in an incorrect context: ‘.fun(piece, ...)’
-#> Warning: <anonymous>: ... may be used in an incorrect context: ‘.fun(piece, ...)’
-cl <- parallel::stopCluster(cl)
-print(result)
-#> [[1]]
-#> [1] 2 3 4 5 6
-#> 
-#> [[2]]
-#> [1]  7  8  9 10 11
-#> 
-# }
-
+    
      
+    
      Examples
      
+    
      # \dontrun{
+
+# imagine that we have 10 jobs that need processing. For simplicity,
+# our jobs will involve adding 1 to each element in 1:10.
+values <- 1:10
+
+# we could complete this processing using the following vectorized code
+result <- 1 + 1:10
+print(result)
+#>  [1]  2  3  4  5  6  7  8  9 10 11
+
+# however, if our jobs were complex then we would be better off using
+# functionals
+result <- lapply(1:10, function(x) x + 1)
+print(result)
+#> [[1]]
+#> [1] 2
+#> 
+#> [[2]]
+#> [1] 3
+#> 
+#> [[3]]
+#> [1] 4
+#> 
+#> [[4]]
+#> [1] 5
+#> 
+#> [[5]]
+#> [1] 6
+#> 
+#> [[6]]
+#> [1] 7
+#> 
+#> [[7]]
+#> [1] 8
+#> 
+#> [[8]]
+#> [1] 9
+#> 
+#> [[9]]
+#> [1] 10
+#> 
+#> [[10]]
+#> [1] 11
+#> 
+
+# we could do one better, and use the "plyr" package to handle the
+# processing
+result <- plyr::llply(1:10, function(x) x + 1)
+print(result)
+#> [[1]]
+#> [1] 2
+#> 
+#> [[2]]
+#> [1] 3
+#> 
+#> [[3]]
+#> [1] 4
+#> 
+#> [[4]]
+#> [1] 5
+#> 
+#> [[5]]
+#> [1] 6
+#> 
+#> [[6]]
+#> [1] 7
+#> 
+#> [[7]]
+#> [1] 8
+#> 
+#> [[8]]
+#> [1] 9
+#> 
+#> [[9]]
+#> [1] 10
+#> 
+#> [[10]]
+#> [1] 11
+#> 
+
+# we could also use the parallel processing options available through "plyr"
+# to use more computation resources to complete the jobs (note that since
+# these jobs are very quick to process this is actually slower).
+cl <- parallel::makeCluster(2, "PSOCK")
+doParallel::registerDoParallel(cl)
+result <- plyr::llply(1:10, function(x) x + 1, .parallel = TRUE)
+#> Warning: <anonymous>: ... may be used in an incorrect context: ‘.fun(piece, ...)’
+#> Warning: <anonymous>: ... may be used in an incorrect context: ‘.fun(piece, ...)’
+cl <- parallel::stopCluster(cl)
+print(result)
+#> [[1]]
+#> [1] 2
+#> 
+#> [[2]]
+#> [1] 3
+#> 
+#> [[3]]
+#> [1] 4
+#> 
+#> [[4]]
+#> [1] 5
+#> 
+#> [[5]]
+#> [1] 6
+#> 
+#> [[6]]
+#> [1] 7
+#> 
+#> [[7]]
+#> [1] 8
+#> 
+#> [[8]]
+#> [1] 9
+#> 
+#> [[9]]
+#> [1] 10
+#> 
+#> [[10]]
+#> [1] 11
+#> 
+
+# however this approach iterates over each element individually, we could
+# use the distribute_load function to split the N jobs up into K super
+# jobs, and evaluate each super job using vectorized code.
+x <- 1:10
+cl <- parallel::makeCluster(2, "PSOCK")
+parallel::clusterExport(cl, 'x', envir = environment())
+doParallel::registerDoParallel(cl)
+l <- distribute_load(length(x), n = 2)
+result <- plyr::llply(l, function(i) x[i] + 1, .parallel = TRUE)
+#> Warning: <anonymous>: ... may be used in an incorrect context: ‘.fun(piece, ...)’
+#> Warning: <anonymous>: ... may be used in an incorrect context: ‘.fun(piece, ...)’
+cl <- parallel::stopCluster(cl)
+print(result)
+#> [[1]]
+#> [1] 2 3 4 5 6
+#> 
+#> [[2]]
+#> [1]  7  8  9 10 11
+#> 
+# }
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/eval_boundary_summary.html b/docs/reference/eval_boundary_summary.html index f22163a1b..3f86ee603 100644 --- a/docs/reference/eval_boundary_summary.html +++ b/docs/reference/eval_boundary_summary.html @@ -1,104 +1,21 @@ - - - - - - - -Evaluate solution boundary length — eval_boundary_summary • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Evaluate solution boundary length — eval_boundary_summary • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Evaluate solution boundary length

      - Source: R/eval_boundary_summary.R + Source: R/eval_boundary_summary.R

      Calculate the exposed boundary length (perimeter) associated with a -solution to a conservation planning problem(). +solution to a conservation planning problem(). This summary statistic is useful for evaluating the spatial fragmentation of planning units selected within a solution.

      - 
      eval_boundary_summary(x, ...)
-
-# S3 method for default
-eval_boundary_summary(x, ...)
-
-# S3 method for ConservationProblem
-eval_boundary_summary(
-  x,
-  solution,
-  edge_factor = rep(0.5, number_of_zones(x)),
-  zones = diag(number_of_zones(x)),
-  data = NULL,
-  ...
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      ...

      not used.

      solution

      numeric, matrix, data.frame, -Raster, Spatial, -or sf::sf() object. +

      Usage,
      eval_boundary_summary(x, ...)
+
+# S3 method for default
+eval_boundary_summary(x, ...)
+
+# S3 method for ConservationProblem
+eval_boundary_summary(
+  x,
+  solution,
+  edge_factor = rep(0.5, number_of_zones(x)),
+  zones = diag(number_of_zones(x)),
+  data = NULL,
+  ...
+)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      ...
      +

      not used.

      +
      solution
      +

      numeric, matrix, data.frame, +Raster, Spatial, +or sf::sf() object. The argument should be in the same format as the planning unit cost data in the argument to x. -See the Solution format section for more information.

      edge_factor

      numeric proportion to scale +See the Solution format section for more information.

      +
      edge_factor
      +

      numeric proportion to scale planning unit edges (borders) that do not have any neighboring planning units. For example, an edge factor of 0.5 is commonly used to avoid overly penalizing planning units along a coastline. Note that this argument must have an element for each zone in the argument -to x.

      zones

      matrix or Matrix object describing the +to x.

      +
      zones
      +

      matrix or Matrix object describing the clumping scheme for different zones. Each row and column corresponds to a different zone in the argument to x, and cell values indicate the relative importance of clumping planning units that are allocated to @@ -245,33 +152,27 @@

      Arg allocated to the same zone. Cell values must range between 1 and -1, where negative values favor solutions that spread out planning units. The default argument to zones is an identity -matrix (i.e. a matrix with ones along the matrix diagonal and zeros +matrix (i.e., a matrix with ones along the matrix diagonal and zeros elsewhere), so that penalties are incurred when neighboring planning units are not assigned to the same zone. If the cells along the matrix diagonal contain markedly smaller values than those found elsewhere in the matrix, then solutions are preferred that surround planning units with those allocated to different zones -(i.e. greater spatial fragmentation).

      data

      NULL, data.frame, matrix, or Matrix +(i.e., greater spatial fragmentation).

      +
      data
      +

      NULL, data.frame, matrix, or Matrix object containing the boundary data. These data describe the total amount of boundary (perimeter) length for each planning unit, and the amount of boundary (perimeter) length shared between different -planning units (i.e. planning units that are adjacent to each other). -See the Data format section for more information.

      - -

      Value

      - -

      tibble::tibble() object containing the boundary length of the +planning units (i.e., planning units that are adjacent to each other). +See the Data format section for more information.

      +
      +
      +

      Value

      +

      tibble::tibble() object containing the boundary length of the solution. -It contains the following columns:

      -
      - -
      summary

      character description of the summary statistic. +It contains the following columns:

      summary
      +

      character description of the summary statistic. The statistic associated with the "overall" value in this column is calculated using the entire solution (including all management zones if there are multiple zones). @@ -279,78 +180,85 @@

      Value

      are also provided for each zone separately (indicated using zone names).

      -
      boundary

      numeric exposed boundary length value. + +

      boundary
      +

      numeric exposed boundary length value. Greater values correspond to solutions with greater boundary length and, in turn, greater spatial fragmentation. Thus conservation planning exercises typically prefer solutions with smaller values.

      -
      - -

      Details

      +
      +
      +

      Details

      This summary statistic is equivalent to the Connectivity_Edge metric -reported by the Marxan software +reported by the Marxan software (Ball et al. 2009). It is calculated using the same equations used to penalize solutions -according to their total exposed boundary (i.e. add_boundary_penalties()). +according to their total exposed boundary (i.e., add_boundary_penalties()). See the Examples section for examples on how differences zone arguments can be used to calculate boundaries for different combinations of zones.

      -

      Data format

      - +
      +
      +

      Data format

      The argument to data can be specified using the following formats. Note that boundary data must always describe symmetric relationships between planning units.

      -
      - -
      data as a NULL value

      indicating that the data should be -automatically calculated using the boundary_matrix() function. +

      data as a NULL value
      +

      indicating that the data should be +automatically calculated using the boundary_matrix() function. This argument is the default. Note that the boundary data must be supplied using one of the other formats below if the planning unit data in the argument to x do not explicitly contain spatial information -(e.g. planning unit data are a data.frame or numeric class).

      +(e.g., planning unit data are a data.frame or numeric class).

      -
      data as a matrix/Matrix object

      where rows and columns represent + +

      data as a matrix/Matrix object
      +

      where rows and columns represent different planning units and the value of each cell represents the amount of shared boundary length between two different planning units. Cells that occur along the matrix diagonal represent the amount of exposed boundary associated with each planning unit that has -no neighbor (e.g. these value might pertain to boundaries along a +no neighbor (e.g., these value might pertain to boundaries along a coastline).

      -
      data as a data.frame object

      with the columns "id1", + +

      data as a data.frame object
      +

      with the columns "id1", "id2", and "boundary". The "id1" and "id2" columns contain identifiers (indices) for a pair of planning units, and the "boundary" column contains the amount of shared boundary length between these two planning units. This format follows the the standard Marxan format for boundary -data (i.e. per the "bound.dat" file).

      +data (i.e., per the "bound.dat" file).

      -
      - -

      Solution format

      +
      +
      +

      Solution format

      Broadly speaking, the argument to solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to solution must be a +

      x has numeric planning units
      +

      The argument to solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to solution.

      -
      x has matrix planning units

      The argument to solution must be a + +

      x has matrix planning units
      +

      The argument to solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -358,8 +266,10 @@

      Raster planning units +

      The argument to solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -367,35 +277,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has Spatial planning units

      The argument to solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has sf::sf() planning units

      The argument to solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to solution must also have the same @@ -404,215 +320,214 @@

      References

      +

      +
      +

      References

      Ball IR, Possingham HP, and Watts M (2009) Marxan and relatives: Software for spatial conservation prioritisation in Spatial conservation prioritisation: Quantitative methods and computational tools. Eds Moilanen A, Wilson KA, and Possingham HP. Oxford University Press, Oxford, UK.

      -

      See also

      - -

      See summaries for an overview of all functions for summarizing solutions. -Also, see add_boundary_penalties() to penalize solutions with high +

      +
      +

      See also

      +

      See summaries for an overview of all functions for summarizing solutions. +Also, see add_boundary_penalties() to penalize solutions with high boundary length.

      Other summaries: -eval_connectivity_summary(), -eval_cost_summary(), -eval_feature_representation_summary(), -eval_n_summary(), -eval_target_coverage_summary()

      - -

      Examples

      - 
      # \dontrun{
-# set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_pu_sf, sim_features,
-     sim_pu_zones_sf, sim_features_zones)
-
-# build minimal conservation problem with raster data
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s1 <- solve(p1)
-
-# print solution
-print(s1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# calculate boundary associated with the solution
-r1 <- eval_boundary_summary(p1, s1)
-print(r1)
-#> # A tibble: 1 × 2
-#>   summary boundary
-#>   <chr>      <dbl>
-#> 1 overall     2.25
-
-# build minimal conservation problem with polygon (sf) data
-p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s2 <- solve(p2)
-
-# print first six rows of the attribute table
-print(head(s2))
-#> Simple feature collection with 6 features and 4 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>       cost locked_in locked_out solution_1                       geometry
-#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# plot solution
-plot(s2[, "solution_1"])
-
-
-# calculate boundary associated with the solution
-r2 <- eval_boundary_summary(p2, s2[, "solution_1"])
-print(r2)
-#> # A tibble: 1 × 2
-#>   summary boundary
-#>   <chr>      <dbl>
-#> 1 overall     2.05
-
-# build multi-zone conservation problem with polygon (sf) data
-p3 <- problem(sim_pu_zones_sf, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s3 <- solve(p3)
-
-# print first six rows of the attribute table
-print(head(s3))
-#> Simple feature collection with 6 features and 9 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
-#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
-#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
-#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
-#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
-#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
-#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
-#>   solution_1_zone_2 solution_1_zone_3                       geometry
-#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2                 0                 1 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4                 0                 1 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5                 0                 1 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s3$solution <- category_vector(
-  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-s3$solution <- factor(s3$solution)
-
-# plot solution
-plot(s3[, "solution"])
-
-
-# calculate boundary associated with the solution
-# here we will use the default argument for zones which treats each
-# zone as completely separate, meaning that the "overall"
-# boundary is just the sum of the boundaries for each zone
-r3 <- eval_boundary_summary(
-  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-print(r3)
-#> # A tibble: 4 × 2
-#>   summary boundary
-#>   <chr>      <dbl>
-#> 1 overall     14.2
-#> 2 zone_1       4.7
-#> 3 zone_2       4.9
-#> 4 zone_3       4.6
-
-# let's calculate the overall exposed boundary across the entire
-# solution, assuming that the shared boundaries between planning
-# units allocated to different zones "count" just as much
-# as those for planning units allocated to the same zone
-
-# in other words, let's calculate the overall exposed boundary
-# across the entire solution by "combining" all selected planning units
-# together (regardless of which zone they are allocated to in the solution)
-r3_combined <- eval_boundary_summary(
-  p3, zones = matrix(1, ncol = 3, nrow = 3),
-  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-print(r3_combined)
-#> # A tibble: 4 × 2
-#>   summary boundary
-#>   <chr>      <dbl>
-#> 1 overall     8.80
-#> 2 zone_1      4.7 
-#> 3 zone_2      4.9 
-#> 4 zone_3      4.6 
-
-# we can see that the "overall" boundary is now less than the
-# sum of the individual zone boundaries, because it does not
-# consider the shared boundary between two planning units allocated to
-# different zones as "exposed" when performing the calculations
-# }
+eval_connectivity_summary(),
+eval_cost_summary(),
+eval_feature_representation_summary(),
+eval_n_summary(),
+eval_target_coverage_summary()
      +
      + +
      +

      Examples

      + 
      # \dontrun{
+# set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_pu_sf, sim_features,
+     sim_pu_zones_sf, sim_features_zones)
+
+# build minimal conservation problem with raster data
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s1 <- solve(p1)
+
+# print solution
+print(s1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# calculate boundary associated with the solution
+r1 <- eval_boundary_summary(p1, s1)
+print(r1)
+#> # A tibble: 1 × 2
+#>   summary boundary
+#>   <chr>      <dbl>
+#> 1 overall     2.25
+
+# build minimal conservation problem with polygon (sf) data
+p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s2 <- solve(p2)
+
+# print first six rows of the attribute table
+print(head(s2))
+#> Simple feature collection with 6 features and 4 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>       cost locked_in locked_out solution_1                       geometry
+#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# plot solution
+plot(s2[, "solution_1"])
+
+
+# calculate boundary associated with the solution
+r2 <- eval_boundary_summary(p2, s2[, "solution_1"])
+print(r2)
+#> # A tibble: 1 × 2
+#>   summary boundary
+#>   <chr>      <dbl>
+#> 1 overall     2.05
+
+# build multi-zone conservation problem with polygon (sf) data
+p3 <- problem(sim_pu_zones_sf, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s3 <- solve(p3)
+
+# print first six rows of the attribute table
+print(head(s3))
+#> Simple feature collection with 6 features and 9 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
+#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
+#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
+#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
+#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
+#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
+#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
+#>   solution_1_zone_2 solution_1_zone_3                       geometry
+#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2                 0                 1 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4                 0                 1 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5                 0                 1 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s3$solution <- category_vector(
+  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+s3$solution <- factor(s3$solution)
+
+# plot solution
+plot(s3[, "solution"])
+
+
+# calculate boundary associated with the solution
+# here we will use the default argument for zones which treats each
+# zone as completely separate, meaning that the "overall"
+# boundary is just the sum of the boundaries for each zone
+r3 <- eval_boundary_summary(
+  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+print(r3)
+#> # A tibble: 4 × 2
+#>   summary boundary
+#>   <chr>      <dbl>
+#> 1 overall     14.2
+#> 2 zone_1       4.7
+#> 3 zone_2       4.9
+#> 4 zone_3       4.6
+
+# let's calculate the overall exposed boundary across the entire
+# solution, assuming that the shared boundaries between planning
+# units allocated to different zones "count" just as much
+# as those for planning units allocated to the same zone
+
+# in other words, let's calculate the overall exposed boundary
+# across the entire solution by "combining" all selected planning units
+# together (regardless of which zone they are allocated to in the solution)
+r3_combined <- eval_boundary_summary(
+  p3, zones = matrix(1, ncol = 3, nrow = 3),
+  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+print(r3_combined)
+#> # A tibble: 4 × 2
+#>   summary boundary
+#>   <chr>      <dbl>
+#> 1 overall     8.80
+#> 2 zone_1      4.7 
+#> 3 zone_2      4.9 
+#> 4 zone_3      4.6 
+
+# we can see that the "overall" boundary is now less than the
+# sum of the individual zone boundaries, because it does not
+# consider the shared boundary between two planning units allocated to
+# different zones as "exposed" when performing the calculations
+# }
      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/eval_connectivity_summary.html b/docs/reference/eval_connectivity_summary.html index a71f18236..5cee66282 100644 --- a/docs/reference/eval_connectivity_summary.html +++ b/docs/reference/eval_connectivity_summary.html @@ -1,104 +1,21 @@ - - - - - - - -Evaluate solution connectivity — eval_connectivity_summary • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Evaluate solution connectivity — eval_connectivity_summary • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Evaluate solution connectivity

      - Source: R/eval_connectivity_summary.R + Source: R/eval_connectivity_summary.R

      Calculate the connectivity held within a solution to a conservation -planning problem(). +planning problem(). This summary statistic evaluates the connectivity of a solution using pair-wise connectivity values between combinations of planning units.

      - 
      # S4 method for ConservationProblem,ANY,ANY,matrix
-eval_connectivity_summary(x, solution, zones, data)
-
-# S4 method for ConservationProblem,ANY,ANY,Matrix
-eval_connectivity_summary(x, solution, zones, data)
-
-# S4 method for ConservationProblem,ANY,ANY,data.frame
-eval_connectivity_summary(x, solution, zones, data)
-
-# S4 method for ConservationProblem,ANY,ANY,dgCMatrix
-eval_connectivity_summary(x, solution, zones, data)
-
-# S4 method for ConservationProblem,ANY,ANY,array
-eval_connectivity_summary(x, solution, zones, data)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      solution

      numeric, matrix, data.frame, -Raster, Spatial, -or sf::sf() object. +

      Usage,
      # S4 method for ConservationProblem,ANY,ANY,matrix
+eval_connectivity_summary(x, solution, zones, data)
+
+# S4 method for ConservationProblem,ANY,ANY,Matrix
+eval_connectivity_summary(x, solution, zones, data)
+
+# S4 method for ConservationProblem,ANY,ANY,data.frame
+eval_connectivity_summary(x, solution, zones, data)
+
+# S4 method for ConservationProblem,ANY,ANY,dgCMatrix
+eval_connectivity_summary(x, solution, zones, data)
+
+# S4 method for ConservationProblem,ANY,ANY,array
+eval_connectivity_summary(x, solution, zones, data)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      solution
      +

      numeric, matrix, data.frame, +Raster, Spatial, +or sf::sf() object. The argument should be in the same format as the planning unit cost data in the argument to x. -See the Solution format section for more information.

      zones

      matrix or Matrix object describing the +See the Solution format section for more information.

      +
      zones
      +

      matrix or Matrix object describing the level of connectivity between different zones. Each row and column corresponds to a different zone in the argument to x, and cell values indicate the level of connectivity between each combination @@ -231,33 +142,27 @@

      Arg the level of connectivity between planning units allocated to the same zone. Cell values must lay between 1 and -1, where negative values favor solutions with weak connectivity. The default argument to -zones is an identity matrix (i.e. a matrix with ones along the +zones is an identity matrix (i.e., a matrix with ones along the matrix diagonal and zeros elsewhere), so that planning units are only considered to be connected when they are allocated to the same zone. This argument is required when the argument to data is a matrix or Matrix object. If the argument to data is an array or data.frame with zone data, this argument -must explicitly be set to NULL otherwise an error will be thrown.

      data

      matrix, Matrix, data.frame, or +must explicitly be set to NULL otherwise an error will be thrown.

      +
      data
      +

      matrix, Matrix, data.frame, or array object containing connectivity data. The connectivity values correspond to the strength of connectivity between different planning units. Thus connections between planning units that are associated with higher values are more favorable in the solution. -See the Data format section for more information.

      - -

      Value

      - -

      tibble::tibble() object describing the connectivity of the +See the Data format section for more information.

      +
      +
      +

      Value

      +

      tibble::tibble() object describing the connectivity of the solution. -It contains the following columns:

      -
      - -
      summary

      character description of the summary statistic. +It contains the following columns:

      summary
      +

      character description of the summary statistic. The statistic associated with the "overall" value in this column is calculated using the entire solution (including all management zones if there are multiple zones). @@ -265,43 +170,47 @@

      Value

      are also provided for each zone separately (indicated using zone names).

      -
      connectivity

      numeric connectivity value. + +

      connectivity
      +

      numeric connectivity value. Greater values correspond to solutions associated with greater connectivity. Thus conservation planning exercises typically prefer solutions with greater values.

      -
      - -

      Details

      +
      +
      +

      Details

      This summary statistic is comparable to the Connectivity_In metric reported by the -Marxan software (Ball et al. 2009). +Marxan software (Ball et al. 2009). It is calculated using the same equations used to penalize solutions -with connectivity data (i.e. add_connectivity_penalties()). +with connectivity data (i.e., add_connectivity_penalties()). Specifically, it is calculated as the sum of the pair-wise connectivity values in the argument to data, weighted by the value of the planning units in the solution.

      -

      Solution format

      - +
      +
      +

      Solution format

      Broadly speaking, the argument to solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to solution must be a +

      x has numeric planning units
      +

      The argument to solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to solution.

      -
      x has matrix planning units

      The argument to solution must be a + +

      x has matrix planning units
      +

      The argument to solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -309,8 +218,10 @@

      Raster planning units +

      The argument to solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -318,35 +229,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has Spatial planning units

      The argument to solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has sf::sf() planning units

      The argument to solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to solution must also have the same @@ -355,18 +272,17 @@

      Data format

      +

      +
      +

      Data format

      The argument to data can be specified using several different formats. These formats can be used to describe symmetric or asymmetric relationships between planning units.

      -
      - -
      data as a matrix/Matrix object

      where rows and columns represent +

      data as a matrix/Matrix object
      +

      where rows and columns represent different planning units and the value of each cell represents the strength of connectivity between two different planning units. Cells that occur along the matrix diagonal are treated as weights which @@ -376,13 +292,15 @@

      zones is to treat planning units allocated to different zones as having zero connectivity.

      -
      data as a data.frame object

      containing the fields (columns) + +

      data as a data.frame object
      +

      containing the fields (columns) "id1", "id2", and "boundary". Here, each row denotes the connectivity between two planning units following the Marxan format. The data can be used to denote symmetric or asymmetric relationships between planning units. By default, input data is assumed to be symmetric unless asymmetric data is -also included (e.g. if data is present for planning units 2 and 3, then +also included (e.g., if data is present for planning units 2 and 3, then the same amount of connectivity is expected for planning units 3 and 2, unless connectivity data is also provided for planning units 3 and 2). If the argument to x contains multiple zones, then the columns @@ -392,10 +310,12 @@

      "zone2" are present, then the argument to zones must be NULL.

      -
      data as an array object

      containing four-dimensions where cell values + +

      data as an array object
      +

      containing four-dimensions where cell values indicate the strength of connectivity between planning units when they are assigned to specific management zones. The first two -dimensions (i.e. rows and columns) indicate the strength of +dimensions (i.e., rows and columns) indicate the strength of connectivity between different planning units and the second two dimensions indicate the different management zones. Thus the data[1, 2, 3, 4] indicates the strength of @@ -403,209 +323,208 @@

      -
      - -

      References

      +
      +
      +

      References

      Ball IR, Possingham HP, and Watts M (2009) Marxan and relatives: Software for spatial conservation prioritisation in Spatial conservation prioritisation: Quantitative methods and computational tools. Eds Moilanen A, Wilson KA, and Possingham HP. Oxford University Press, Oxford, UK.

      -

      See also

      - -

      See summaries for an overview of all functions for summarizing solutions. -Also, see add_connectivity_penalties() to penalize solutions with low +

      +
      +

      See also

      +

      See summaries for an overview of all functions for summarizing solutions. +Also, see add_connectivity_penalties() to penalize solutions with low connectivity.

      Other summaries: -eval_boundary_summary(), -eval_cost_summary(), -eval_feature_representation_summary(), -eval_n_summary(), -eval_target_coverage_summary()

      - -

      Examples

      - 
      # \dontrun{
-# set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_pu_sf, sim_features,
-     sim_pu_zones_sf, sim_features_zones)
-
-# build minimal conservation problem with raster data
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s1 <- solve(p1)
-
-# print solution
-print(s1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# simulate a connectivity matrix to describe the relative strength
-# of connectivity between different planning units
-# for brevity, we will use cost data here so that pairs
-# of adjacent planning units with higher cost values will have a
-# higher connectivity value
-# (but see ?connectivity_matrix for more information)
-cm1 <- connectivity_matrix(sim_pu_raster, sim_pu_raster)
-
-# calculate connectivity associated with the solution
-r1 <- eval_connectivity_summary(p1, s1, data = cm1)
-print(r1)
-#> # A tibble: 1 × 2
-#>   summary connectivity
-#>   <chr>          <dbl>
-#> 1 overall         198.
-
-# build minimal conservation problem with polygon (sf) data
-p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s2 <- solve(p2)
-
-# print first six rows of the attribute table
-print(head(s2))
-#> Simple feature collection with 6 features and 4 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>       cost locked_in locked_out solution_1                       geometry
-#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# plot solution
-plot(s2[, "solution_1"])
-
-
-# simulate connectivity matrix
-# here, we will generate connectivity values randomly
-# between all pairs of planning units
-cm2 <- matrix(runif(nrow(sim_pu_sf) ^ 2), nrow = nrow(sim_pu_sf))
-
-# calculate connectivity associated with the solution
-r2 <- eval_connectivity_summary(p2, s2[, "solution_1"], data = cm2)
-print(r2)
-#> # A tibble: 1 × 2
-#>   summary connectivity
-#>   <chr>          <dbl>
-#> 1 overall         36.8
-
-# build multi-zone conservation problem with polygon (sf) data
-p3 <- problem(sim_pu_zones_sf, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s3 <- solve(p3)
-
-# print first six rows of the attribute table
-print(head(s3))
-#> Simple feature collection with 6 features and 9 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
-#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
-#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
-#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
-#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
-#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
-#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
-#>   solution_1_zone_2 solution_1_zone_3                       geometry
-#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2                 0                 0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4                 0                 0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5                 0                 0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s3$solution <- category_vector(
-  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-s3$solution <- factor(s3$solution)
-
-# plot solution
-plot(s3[, "solution"])
-
-
-# simulate connectivity matrix
-# here, we will add a new column to sim_pu_zones_sf with
-# randomly simulated values and create a connectivity matrix
-# based on the average simulated values of adjacent planning units
-sim_pu_zones_sf$con <- runif(nrow(sim_pu_zones_sf))
-cm3 <- connectivity_matrix(sim_pu_zones_sf, "con")
-
-# calculate connectivity associated with the solution
-r3 <- eval_connectivity_summary(
-  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")],
-  data = cm3)
-print(r3)
-#> # A tibble: 4 × 2
-#>   summary connectivity
-#>   <chr>          <dbl>
-#> 1 overall        2.93 
-#> 2 zone_1         1.05 
-#> 3 zone_2         0.966
-#> 4 zone_3         0.912
-
-# }
+eval_boundary_summary(),
+eval_cost_summary(),
+eval_feature_representation_summary(),
+eval_n_summary(),
+eval_target_coverage_summary()
      +
      + +
      +

      Examples

      + 
      # \dontrun{
+# set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_pu_sf, sim_features,
+     sim_pu_zones_sf, sim_features_zones)
+
+# build minimal conservation problem with raster data
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s1 <- solve(p1)
+
+# print solution
+print(s1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# simulate a connectivity matrix to describe the relative strength
+# of connectivity between different planning units
+# for brevity, we will use cost data here so that pairs
+# of adjacent planning units with higher cost values will have a
+# higher connectivity value
+# (but see ?connectivity_matrix for more information)
+cm1 <- connectivity_matrix(sim_pu_raster, sim_pu_raster)
+
+# calculate connectivity associated with the solution
+r1 <- eval_connectivity_summary(p1, s1, data = cm1)
+print(r1)
+#> # A tibble: 1 × 2
+#>   summary connectivity
+#>   <chr>          <dbl>
+#> 1 overall         198.
+
+# build minimal conservation problem with polygon (sf) data
+p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s2 <- solve(p2)
+
+# print first six rows of the attribute table
+print(head(s2))
+#> Simple feature collection with 6 features and 4 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>       cost locked_in locked_out solution_1                       geometry
+#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# plot solution
+plot(s2[, "solution_1"])
+
+
+# simulate connectivity matrix
+# here, we will generate connectivity values randomly
+# between all pairs of planning units
+cm2 <- matrix(runif(nrow(sim_pu_sf) ^ 2), nrow = nrow(sim_pu_sf))
+
+# calculate connectivity associated with the solution
+r2 <- eval_connectivity_summary(p2, s2[, "solution_1"], data = cm2)
+print(r2)
+#> # A tibble: 1 × 2
+#>   summary connectivity
+#>   <chr>          <dbl>
+#> 1 overall         36.8
+
+# build multi-zone conservation problem with polygon (sf) data
+p3 <- problem(sim_pu_zones_sf, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s3 <- solve(p3)
+
+# print first six rows of the attribute table
+print(head(s3))
+#> Simple feature collection with 6 features and 9 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
+#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
+#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
+#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
+#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
+#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
+#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
+#>   solution_1_zone_2 solution_1_zone_3                       geometry
+#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2                 0                 0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4                 0                 0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5                 0                 0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s3$solution <- category_vector(
+  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+s3$solution <- factor(s3$solution)
+
+# plot solution
+plot(s3[, "solution"])
+
+
+# simulate connectivity matrix
+# here, we will add a new column to sim_pu_zones_sf with
+# randomly simulated values and create a connectivity matrix
+# based on the average simulated values of adjacent planning units
+sim_pu_zones_sf$con <- runif(nrow(sim_pu_zones_sf))
+cm3 <- connectivity_matrix(sim_pu_zones_sf, "con")
+
+# calculate connectivity associated with the solution
+r3 <- eval_connectivity_summary(
+  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")],
+  data = cm3)
+print(r3)
+#> # A tibble: 4 × 2
+#>   summary connectivity
+#>   <chr>          <dbl>
+#> 1 overall        2.93 
+#> 2 zone_1         1.05 
+#> 3 zone_2         0.966
+#> 4 zone_3         0.912
+
+# }
      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/eval_cost_summary.html b/docs/reference/eval_cost_summary.html index 3ad1590f1..4aa5b2e1a 100644 --- a/docs/reference/eval_cost_summary.html +++ b/docs/reference/eval_cost_summary.html @@ -1,105 +1,22 @@ - - - - - - - -Evaluate solution cost — eval_cost_summary • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Evaluate solution cost — eval_cost_summary • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Evaluate solution cost

      - Source: R/eval_cost_summary.R + Source: R/eval_cost_summary.R

      Calculate the total cost of a solution to a conservation planning -problem(). +problem(). For example, if the planning unit cost data describe land acquisition costs (USD), then the total cost would be net cost (USD) needed to acquire all planning units selected within the solution.

      - 
      eval_cost_summary(x, solution)
-
-# S3 method for default
-eval_cost_summary(x, solution)
-
-# S3 method for ConservationProblem
-eval_cost_summary(x, solution)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      solution

      numeric, matrix, data.frame, -Raster, Spatial, -or sf::sf() object. -The argument should be in the same format as the planning unit cost -data in the argument to x. -See the Solution format section for more information.

      +
      Usage,
      eval_cost_summary(x, solution)
 
-    
      Value
      
+# S3 method for default
+eval_cost_summary(x, solution)
 
-    
      tibble::tibble() object containing the solution cost.
-It contains the following columns:
      
-
      
+# S3 method for ConservationProblem
+eval_cost_summary(x, solution)
      -
      summary

      character description of the summary statistic. +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      solution
      +

      numeric, matrix, data.frame, +Raster, Spatial, +or sf::sf() object. +The argument should be in the same format as the planning unit cost +data in the argument to x. +See the Solution format section for more information.

      +
      +
      +

      Value

      +

      tibble::tibble() object containing the solution cost. +It contains the following columns:

      summary
      +

      character description of the summary statistic. The statistic associated with the "overall" value in this column is calculated using the entire solution (including all management zones if there are multiple zones). @@ -232,7 +141,9 @@

      Value

      are also provided for each zone separately (indicated using zone names).

      -
      cost

      numeric cost value. + +

      cost
      +

      numeric cost value. Greater values correspond to solutions that are more costly to implement. Thus conservation planning exercises typically prefer solutions @@ -241,34 +152,36 @@

      Value

      are equal).

      -
      - -

      Details

      +
      +
      +

      Details

      This metric is equivalent to the Cost metric reported by the -Marxan software (Ball et al. 2009). +Marxan software (Ball et al. 2009). Specifically, the cost of a solution is defined as the sum of the cost -values, supplied when creating a problem() object -(e.g. using the cost_column argument), +values, supplied when creating a problem() object +(e.g., using the cost_column argument), weighted by the status of each planning unit in the solution.

      -

      Solution format

      - +
      +
      +

      Solution format

      Broadly speaking, the argument to solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to solution must be a +

      x has numeric planning units
      +

      The argument to solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to solution.

      -
      x has matrix planning units

      The argument to solution must be a + +

      x has matrix planning units
      +

      The argument to solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -276,8 +189,10 @@

      Raster planning units +

      The argument to solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -285,35 +200,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has Spatial planning units

      The argument to solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has sf::sf() planning units

      The argument to solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to solution must also have the same @@ -322,190 +243,189 @@

      References

      +

      +
      +

      References

      Ball IR, Possingham HP, and Watts M (2009) Marxan and relatives: Software for spatial conservation prioritisation in Spatial conservation prioritisation: Quantitative methods and computational tools. Eds Moilanen A, Wilson KA, and Possingham HP. Oxford University Press, Oxford, UK.

      -

      See also

      - -

      See summaries for an overview of all functions for summarizing solutions.

      +
      +
      +

      See also

      +

      See summaries for an overview of all functions for summarizing solutions.

      Other summaries: -eval_boundary_summary(), -eval_connectivity_summary(), -eval_feature_representation_summary(), -eval_n_summary(), -eval_target_coverage_summary()

      - -

      Examples

      - 
      # \dontrun{
-# set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_pu_sf, sim_features,
-     sim_pu_zones_sf, sim_features_zones)
-
-# build minimal conservation problem with raster data
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s1 <- solve(p1)
-
-# print solution
-print(s1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# calculate cost of the solution
-r1 <- eval_cost_summary(p1, s1)
-print(r1)
-#> # A tibble: 1 × 2
-#>   summary  cost
-#>   <chr>   <dbl>
-#> 1 overall 1987.
-
-# build minimal conservation problem with polygon (sf) data
-p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s2 <- solve(p2)
-
-# plot solution
-plot(s2[, "solution_1"])
-
-
-# print first six rows of the attribute table
-print(head(s2))
-#> Simple feature collection with 6 features and 4 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>       cost locked_in locked_out solution_1                       geometry
-#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# calculate cost of the solution
-r2 <- eval_cost_summary(p2, s2[, "solution_1"])
-print(r2)
-#> # A tibble: 1 × 2
-#>   summary  cost
-#>   <chr>   <dbl>
-#> 1 overall 1793.
-
-# manually calculate cost of the solution
-r2_manual <- sum(s2$solution * sim_pu_sf$cost, na.rm = TRUE)
-print(r2_manual)
-#> [1] 1792.535
-
-# build multi-zone conservation problem with polygon (sf) data
-p3 <- problem(sim_pu_zones_sf, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s3 <- solve(p3)
-
-# print first six rows of the attribute table
-print(head(s3))
-#> Simple feature collection with 6 features and 9 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
-#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
-#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
-#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
-#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
-#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
-#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
-#>   solution_1_zone_2 solution_1_zone_3                       geometry
-#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2                 0                 1 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4                 0                 1 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5                 0                 1 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s3$solution <- category_vector(
-  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-s3$solution <- factor(s3$solution)
-
-# plot solution
-plot(s3[, "solution"])
-
-
-# calculate cost of the solution
-r3 <- eval_cost_summary(
-  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-print(r3)
-#> # A tibble: 4 × 2
-#>   summary   cost
-#>   <chr>    <dbl>
-#> 1 overall 10559.
-#> 2 zone_1   3409.
-#> 3 zone_2   3513.
-#> 4 zone_3   3638.
-# }
+eval_boundary_summary(),
+eval_connectivity_summary(),
+eval_feature_representation_summary(),
+eval_n_summary(),
+eval_target_coverage_summary()
      +
      + +
      +

      Examples

      + 
      # \dontrun{
+# set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_pu_sf, sim_features,
+     sim_pu_zones_sf, sim_features_zones)
+
+# build minimal conservation problem with raster data
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s1 <- solve(p1)
+
+# print solution
+print(s1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# calculate cost of the solution
+r1 <- eval_cost_summary(p1, s1)
+print(r1)
+#> # A tibble: 1 × 2
+#>   summary  cost
+#>   <chr>   <dbl>
+#> 1 overall 1987.
+
+# build minimal conservation problem with polygon (sf) data
+p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s2 <- solve(p2)
+
+# plot solution
+plot(s2[, "solution_1"])
+
+
+# print first six rows of the attribute table
+print(head(s2))
+#> Simple feature collection with 6 features and 4 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>       cost locked_in locked_out solution_1                       geometry
+#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# calculate cost of the solution
+r2 <- eval_cost_summary(p2, s2[, "solution_1"])
+print(r2)
+#> # A tibble: 1 × 2
+#>   summary  cost
+#>   <chr>   <dbl>
+#> 1 overall 1793.
+
+# manually calculate cost of the solution
+r2_manual <- sum(s2$solution * sim_pu_sf$cost, na.rm = TRUE)
+print(r2_manual)
+#> [1] 1792.535
+
+# build multi-zone conservation problem with polygon (sf) data
+p3 <- problem(sim_pu_zones_sf, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s3 <- solve(p3)
+
+# print first six rows of the attribute table
+print(head(s3))
+#> Simple feature collection with 6 features and 9 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
+#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
+#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
+#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
+#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
+#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
+#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
+#>   solution_1_zone_2 solution_1_zone_3                       geometry
+#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2                 0                 1 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4                 0                 1 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5                 0                 1 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s3$solution <- category_vector(
+  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+s3$solution <- factor(s3$solution)
+
+# plot solution
+plot(s3[, "solution"])
+
+
+# calculate cost of the solution
+r3 <- eval_cost_summary(
+  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+print(r3)
+#> # A tibble: 4 × 2
+#>   summary   cost
+#>   <chr>    <dbl>
+#> 1 overall 10559.
+#> 2 zone_1   3409.
+#> 3 zone_2   3513.
+#> 4 zone_3   3638.
+# }
      +
      +
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      -
      -

      Evaluate solution importance using Ferrier scores

      - Source: R/eval_ferrier_importance.R + Source: R/eval_ferrier_importance.R
      @@ -186,55 +103,50 @@

      Evaluate solution importance using Ferrier scores

      a solution following Ferrier et al. (2000).

      - 
      eval_ferrier_importance(x, solution)
+    
      Usage,
      eval_ferrier_importance(x, solution)
 
-# S4 method for ConservationProblem,numeric
-eval_ferrier_importance(x, solution)
+# S4 method for ConservationProblem,numeric
+eval_ferrier_importance(x, solution)
 
-# S4 method for ConservationProblem,matrix
-eval_ferrier_importance(x, solution)
+# S4 method for ConservationProblem,matrix
+eval_ferrier_importance(x, solution)
 
-# S4 method for ConservationProblem,data.frame
-eval_ferrier_importance(x, solution)
+# S4 method for ConservationProblem,data.frame
+eval_ferrier_importance(x, solution)
 
-# S4 method for ConservationProblem,Spatial
-eval_ferrier_importance(x, solution)
+# S4 method for ConservationProblem,Spatial
+eval_ferrier_importance(x, solution)
 
-# S4 method for ConservationProblem,sf
-eval_ferrier_importance(x, solution)
+# S4 method for ConservationProblem,sf
+eval_ferrier_importance(x, solution)
 
-# S4 method for ConservationProblem,Raster
-eval_ferrier_importance(x, solution)
      
+# S4 method for ConservationProblem,Raster
+eval_ferrier_importance(x, solution)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      solution

      numeric, matrix, data.frame, -Raster, Spatial, -or sf::sf() object. +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      solution
      +

      numeric, matrix, data.frame, +Raster, Spatial, +or sf::sf() object. The argument should be in the same format as the planning unit cost data in the argument to x. -See the Solution format section for more information.

      - -

      Value

      - -

      A matrix, tibble::tibble(), -RasterLayer, or -Spatial object containing the scores for each +See the Solution format section for more information.

      +
      +
      +

      Value

      +

      A matrix, tibble::tibble(), +RasterLayer, or +Spatial object containing the scores for each planning unit selected in the solution. Specifically, the returned object is in the same format (except if the planning units are a numeric vector) as the planning unit data in the argument to x.

      -

      Details

      - +
      +
      +

      Details

      Importance scores are reported separately for each feature within each planning unit. Additionally, a total importance score is also calculated as the sum of the scores for each feature. @@ -245,8 +157,9 @@

      Details the mathematical formulation for computing these scores needs verification, and so this functionality should be considered experimental at this point in time.

      -

      Notes

      - +
      +
      +

      Notes

      In previous versions, the documentation for this function had a warning @@ -254,24 +167,26 @@

      Notes

      verification. The mathematical formulation for this function has since been corrected and verified, so now this function is recommended for general use.

      -

      Solution format

      - +
      +
      +

      Solution format

      Broadly speaking, the argument to solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to solution must be a +

      x has numeric planning units
      +

      The argument to solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to solution.

      -
      x has matrix planning units

      The argument to solution must be a + +

      x has matrix planning units
      +

      The argument to solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -279,8 +194,10 @@

      Raster planning units +

      The argument to solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -288,35 +205,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has Spatial planning units

      The argument to solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has sf::sf() planning units

      The argument to solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to solution must also have the same @@ -325,145 +248,144 @@

      References

      +

      +
      +

      References

      Ferrier S, Pressey RL, and Barrett TW (2000) A new predictor of the irreplaceability of areas for achieving a conservation goal, its application to real-world planning, and a research agenda for further refinement. Biological Conservation, 93: 303--325.

      -

      See also

      - -

      See importance for an overview of all functions for evaluating +

      +
      +

      See also

      +

      See importance for an overview of all functions for evaluating the importance of planning units selected in a solution.

      Other importances: -eval_rare_richness_importance(), -eval_replacement_importance()

      - -

      Examples

      - 
      # seed seed for reproducibility
-set.seed(600)
-
-# load data
-data(sim_pu_raster, sim_features)
-
-# create minimal problem with binary decisions
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# print solution
-print(s1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# calculate importance scores using Ferrier et al. 2000 method
-fs1 <- eval_ferrier_importance(p1, s1)
-
-# print importance scores,
-# each planning unit has an importance score for each feature
-# (as indicated by the column names) and each planning unit also
-# has an overall total importance score (in the "total" column)
-print(fs1)
-#> class      : RasterStack 
-#> dimensions : 10, 10, 100, 6  (nrow, ncol, ncell, nlayers)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> names      :     layer.1,     layer.2,     layer.3,     layer.4,     layer.5,       total 
-#> min values :           0,           0,           0,           0,           0,           0 
-#> max values : 0.003472042, 0.003596401, 0.003341572, 0.003768489, 0.003504223, 0.016417187 
-#> 
-
-# plot total importance scores
-plot(fs1, main = "Ferrier scores", axes = FALSE, box = FALSE)
-
-
-# create minimal problem with polygon (sf) planning units
-p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.05) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem
-s2 <- solve(p2)
-
-# print solution
-print(s2)
-#> Simple feature collection with 90 features and 4 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
-#> CRS:           NA
-#> First 10 features:
-#>        cost locked_in locked_out solution_1                       geometry
-#> 1  215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2  212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3  207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4  208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5  214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6  213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
-#> 7  210.4612     FALSE      FALSE          0 POLYGON ((0.6 1, 0.7 1, 0.7...
-#> 8  211.0424     FALSE       TRUE          0 POLYGON ((0.7 1, 0.8 1, 0.8...
-#> 9  210.3878     FALSE      FALSE          0 POLYGON ((0.8 1, 0.9 1, 0.9...
-#> 10 204.3971     FALSE      FALSE          0 POLYGON ((0.9 1, 1 1, 1 0.9...
-
-# plot solution
-plot(s2[, "solution_1"], main = "solution")
-
-
-# calculate importance scores
-fs2 <- eval_ferrier_importance(p2, s2[, "solution_1"])
-
-# plot importance scores
-plot(fs2, main = "Ferrier scores")
-
-
-# }
-
+eval_rare_richness_importance(),
+eval_replacement_importance()
      +
      + +
      +

      Examples

      + 
      # seed seed for reproducibility
+set.seed(600)
+
+# load data
+data(sim_pu_raster, sim_features)
+
+# create minimal problem with binary decisions
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# print solution
+print(s1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# calculate importance scores using Ferrier et al. 2000 method
+fs1 <- eval_ferrier_importance(p1, s1)
+
+# print importance scores,
+# each planning unit has an importance score for each feature
+# (as indicated by the column names) and each planning unit also
+# has an overall total importance score (in the "total" column)
+print(fs1)
+#> class      : RasterStack 
+#> dimensions : 10, 10, 100, 6  (nrow, ncol, ncell, nlayers)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> names      :     layer.1,     layer.2,     layer.3,     layer.4,     layer.5,       total 
+#> min values :           0,           0,           0,           0,           0,           0 
+#> max values : 0.003472042, 0.003596401, 0.003341572, 0.003768489, 0.003504223, 0.016417187 
+#> 
+
+# plot total importance scores
+plot(fs1, main = "Ferrier scores", axes = FALSE, box = FALSE)
+
+
+# create minimal problem with polygon (sf) planning units
+p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.05) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem
+s2 <- solve(p2)
+
+# print solution
+print(s2)
+#> Simple feature collection with 90 features and 4 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
+#> CRS:           NA
+#> First 10 features:
+#>        cost locked_in locked_out solution_1                       geometry
+#> 1  215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2  212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3  207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4  208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5  214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6  213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
+#> 7  210.4612     FALSE      FALSE          0 POLYGON ((0.6 1, 0.7 1, 0.7...
+#> 8  211.0424     FALSE       TRUE          0 POLYGON ((0.7 1, 0.8 1, 0.8...
+#> 9  210.3878     FALSE      FALSE          0 POLYGON ((0.8 1, 0.9 1, 0.9...
+#> 10 204.3971     FALSE      FALSE          0 POLYGON ((0.9 1, 1 1, 1 0.9...
+
+# plot solution
+plot(s2[, "solution_1"], main = "solution")
+
+
+# calculate importance scores
+fs2 <- eval_ferrier_importance(p2, s2[, "solution_1"])
+
+# plot importance scores
+plot(fs2, main = "Ferrier scores")
+
+
+# }
+
      +
      + - - - - - - - - - - - + diff --git a/docs/reference/eval_n_summary.html b/docs/reference/eval_n_summary.html index 0fa02a224..7d590c6c1 100644 --- a/docs/reference/eval_n_summary.html +++ b/docs/reference/eval_n_summary.html @@ -1,102 +1,19 @@ - - - - - - - -Evaluate number of planning units selected — eval_n_summary • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Evaluate number of planning units selected — eval_n_summary • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Evaluate number of planning units selected

      - Source: R/eval_n_summary.R + Source: R/eval_n_summary.R

      Calculate the number of planning units selected within a solution -to a conservation planning problem().

      +to a conservation planning problem().

      - 
      eval_n_summary(x, solution)
-
-# S3 method for default
-eval_n_summary(x, solution)
-
-# S3 method for ConservationProblem
-eval_n_summary(x, solution)
      - -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      solution

      numeric, matrix, data.frame, -Raster, Spatial, -or sf::sf() object. -The argument should be in the same format as the planning unit cost -data in the argument to x. -See the Solution format section for more information.

      +
      Usage,
      eval_n_summary(x, solution)
 
-    
      Value
      
+# S3 method for default
+eval_n_summary(x, solution)
 
-    
      tibble::tibble() object containing the number of planning
-units selected within a solution.
-It contains the following columns:
      
-
      
+# S3 method for ConservationProblem
+eval_n_summary(x, solution)
      -
      summary

      character description of the summary statistic. +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      solution
      +

      numeric, matrix, data.frame, +Raster, Spatial, +or sf::sf() object. +The argument should be in the same format as the planning unit cost +data in the argument to x. +See the Solution format section for more information.

      +
      +
      +

      Value

      +

      tibble::tibble() object containing the number of planning +units selected within a solution. +It contains the following columns:

      summary
      +

      character description of the summary statistic. The statistic associated with the "overall" value in this column is calculated using the entire solution (including all management zones if there are multiple zones). @@ -227,36 +136,40 @@

      Value

      are also provided for each zone separately (indicated using zone names).

      -
      n

      numeric number of selected planning units.

      +
      n
      +

      numeric number of selected planning units.

      -
      -

      Details

      +
      +
      +

      Details

      This summary statistic is calculated as the sum of the values in the solution. As a consequence, this metric can produce a -non-integer value (e.g. 4.3) for solutions containing proportion values -(e.g. generated by solving a problem() built using the -add_proportion_decisions() function).

      -

      Solution format

      - +non-integer value (e.g., 4.3) for solutions containing proportion values +(e.g., generated by solving a problem() built using the +add_proportion_decisions() function).

      +
      +
      +

      Solution format

      Broadly speaking, the argument to solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to solution must be a +

      x has numeric planning units
      +

      The argument to solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to solution.

      -
      x has matrix planning units

      The argument to solution must be a + +

      x has matrix planning units
      +

      The argument to solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -264,8 +177,10 @@

      Raster planning units +

      The argument to solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -273,35 +188,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has Spatial planning units

      The argument to solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has sf::sf() planning units

      The argument to solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to solution must also have the same @@ -310,184 +231,182 @@

      See also

      -

      See summaries for an overview of all functions for summarizing solutions.

      +

      +
      +

      See also

      +

      See summaries for an overview of all functions for summarizing solutions.

      Other summaries: -eval_boundary_summary(), -eval_connectivity_summary(), -eval_cost_summary(), -eval_feature_representation_summary(), -eval_target_coverage_summary()

      - -

      Examples

      - 
      # \dontrun{
-# set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_pu_sf, sim_features,
-     sim_pu_zones_sf, sim_features_zones)
-
-# build minimal conservation problem with raster data
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s1 <- solve(p1)
-
-# print solution
-print(s1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# calculate number of selected planning units within solution
-r1 <- eval_n_summary(p1, s1)
-print(r1)
-#> # A tibble: 1 × 2
-#>   summary  cost
-#>   <chr>   <dbl>
-#> 1 overall    10
-
-# build minimal conservation problem with polygon (sf) data
-p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s2 <- solve(p2)
-
-# plot solution
-plot(s2[, "solution_1"])
-
-
-# print first six rows of the attribute table
-print(head(s2))
-#> Simple feature collection with 6 features and 4 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>       cost locked_in locked_out solution_1                       geometry
-#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# calculate number of selected planning units within solution
-r2 <- eval_n_summary(p2, s2[, "solution_1"])
-print(r2)
-#> # A tibble: 1 × 2
-#>   summary  cost
-#>   <chr>   <dbl>
-#> 1 overall     9
-
-# manually calculate number of selected planning units
-r2_manual <- sum(s2$solution, na.rm = TRUE)
-print(r2_manual)
-#> [1] 9
-
-# build multi-zone conservation problem with polygon (sf) data
-p3 <- problem(sim_pu_zones_sf, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s3 <- solve(p3)
-
-# print first six rows of the attribute table
-print(head(s3))
-#> Simple feature collection with 6 features and 9 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
-#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
-#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
-#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
-#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
-#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
-#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
-#>   solution_1_zone_2 solution_1_zone_3                       geometry
-#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2                 0                 1 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4                 0                 1 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5                 0                 1 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s3$solution <- category_vector(
-  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-s3$solution <- factor(s3$solution)
-
-# plot solution
-plot(s3[, "solution"])
-
-
-# calculate number of selected planning units within solution
-r3 <- eval_n_summary(
-  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-print(r3)
-#> # A tibble: 4 × 2
-#>   summary  cost
-#>   <chr>   <dbl>
-#> 1 overall    52
-#> 2 zone_1     17
-#> 3 zone_2     18
-#> 4 zone_3     17
-# }
+eval_boundary_summary(),
+eval_connectivity_summary(),
+eval_cost_summary(),
+eval_feature_representation_summary(),
+eval_target_coverage_summary()
      +
      + +
      +

      Examples

      + 
      # \dontrun{
+# set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_pu_sf, sim_features,
+     sim_pu_zones_sf, sim_features_zones)
+
+# build minimal conservation problem with raster data
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s1 <- solve(p1)
+
+# print solution
+print(s1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# calculate number of selected planning units within solution
+r1 <- eval_n_summary(p1, s1)
+print(r1)
+#> # A tibble: 1 × 2
+#>   summary  cost
+#>   <chr>   <dbl>
+#> 1 overall    10
+
+# build minimal conservation problem with polygon (sf) data
+p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s2 <- solve(p2)
+
+# plot solution
+plot(s2[, "solution_1"])
+
+
+# print first six rows of the attribute table
+print(head(s2))
+#> Simple feature collection with 6 features and 4 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>       cost locked_in locked_out solution_1                       geometry
+#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# calculate number of selected planning units within solution
+r2 <- eval_n_summary(p2, s2[, "solution_1"])
+print(r2)
+#> # A tibble: 1 × 2
+#>   summary  cost
+#>   <chr>   <dbl>
+#> 1 overall     9
+
+# manually calculate number of selected planning units
+r2_manual <- sum(s2$solution, na.rm = TRUE)
+print(r2_manual)
+#> [1] 9
+
+# build multi-zone conservation problem with polygon (sf) data
+p3 <- problem(sim_pu_zones_sf, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s3 <- solve(p3)
+
+# print first six rows of the attribute table
+print(head(s3))
+#> Simple feature collection with 6 features and 9 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
+#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
+#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
+#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
+#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
+#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
+#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
+#>   solution_1_zone_2 solution_1_zone_3                       geometry
+#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2                 0                 1 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4                 0                 1 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5                 0                 1 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s3$solution <- category_vector(
+  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+s3$solution <- factor(s3$solution)
+
+# plot solution
+plot(s3[, "solution"])
+
+
+# calculate number of selected planning units within solution
+r3 <- eval_n_summary(
+  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+print(r3)
+#> # A tibble: 4 × 2
+#>   summary  cost
+#>   <chr>   <dbl>
+#> 1 overall    52
+#> 2 zone_1     17
+#> 3 zone_2     18
+#> 4 zone_3     17
+# }
      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/eval_rare_richness_importance.html b/docs/reference/eval_rare_richness_importance.html index 483c70b25..2fc8a1962 100644 --- a/docs/reference/eval_rare_richness_importance.html +++ b/docs/reference/eval_rare_richness_importance.html @@ -1,110 +1,27 @@ - - - - - - - -Evaluate solution importance using rarity weighted richness scores — eval_rare_richness_importance • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Evaluate solution importance using rarity weighted richness scores — eval_rare_richness_importance • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Evaluate solution importance using rarity weighted richness scores

      - Source: R/eval_rare_richness_importance.R + Source: R/eval_rare_richness_importance.R
      @@ -193,7 +110,7 @@

      Evaluate solution importance using rarity weighted richness scores

      Calculate importance scores for planning units selected in a solution using rarity weighted richness scores (based on Williams et al. 1996). This method is only recommended for large-scaled conservation -planning exercises (i.e. more than 100,000 planning units) where +planning exercises (i.e., more than 100,000 planning units) where importance scores cannot be calculated using other methods in a feasible period of time. This is because rarity weighted richness scores cannot (i) account for the cost of different planning units, (ii) account for multiple @@ -202,63 +119,53 @@

      Evaluate solution importance using rarity weighted richness scores

      limitations.

      - 
      eval_rare_richness_importance(x, solution, ...)
+    
      Usage,
      eval_rare_richness_importance(x, solution, ...)
 
-# S4 method for ConservationProblem,numeric
-eval_rare_richness_importance(x, solution, rescale, ...)
+# S4 method for ConservationProblem,numeric
+eval_rare_richness_importance(x, solution, rescale, ...)
 
-# S4 method for ConservationProblem,matrix
-eval_rare_richness_importance(x, solution, rescale, ...)
+# S4 method for ConservationProblem,matrix
+eval_rare_richness_importance(x, solution, rescale, ...)
 
-# S4 method for ConservationProblem,data.frame
-eval_rare_richness_importance(x, solution, rescale, ...)
+# S4 method for ConservationProblem,data.frame
+eval_rare_richness_importance(x, solution, rescale, ...)
 
-# S4 method for ConservationProblem,Spatial
-eval_rare_richness_importance(x, solution, rescale, ...)
+# S4 method for ConservationProblem,Spatial
+eval_rare_richness_importance(x, solution, rescale, ...)
 
-# S4 method for ConservationProblem,sf
-eval_rare_richness_importance(x, solution, rescale, ...)
+# S4 method for ConservationProblem,sf
+eval_rare_richness_importance(x, solution, rescale, ...)
 
-# S4 method for ConservationProblem,Raster
-eval_rare_richness_importance(x, solution, rescale, ...)
      
+# S4 method for ConservationProblem,Raster
+eval_rare_richness_importance(x, solution, rescale, ...)
      -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      solution

      numeric, matrix, data.frame, -Raster, Spatial, -or sf::sf() object. +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      solution
      +

      numeric, matrix, data.frame, +Raster, Spatial, +or sf::sf() object. The argument should be in the same format as the planning unit cost data in the argument to x. -See the Solution format section for more information.

      ...

      not used.

      rescale

      logical flag indicating if replacement cost +See the Solution format section for more information.

      +
      ...
      +

      not used.

      +
      rescale
      +

      logical flag indicating if replacement cost values---excepting infinite (Inf) and zero values---should be -rescaled to range between 0.01 and 1. Defaults to TRUE.

      - -

      Value

      - -

      A numeric, matrix, data.frame -RasterLayer, Spatial, -or sf::sf() object containing the importance scores for each planning +rescaled to range between 0.01 and 1. Defaults to TRUE.

      +
      +
      +

      Value

      +

      A numeric, matrix, data.frameRasterLayer, Spatial, +or sf::sf() object containing the importance scores for each planning unit in the solution. Specifically, the returned object is in the same format as the planning unit data in the argument to x.

      -

      Details

      - +
      +
      +

      Details

      Rarity weighted richness scores are calculated using the following terms. Let \(I\) denote the set of planning units (indexed by \(i\)), let \(J\) denote the set of conservation features (indexed by @@ -271,24 +178,26 @@

      Details \mathit{RWR}_{k} = \sum_{j}^{J} \frac{ \frac{r_{ik}}{m_j} }{ \sum_{i}^{I}r_{ij}} $$

      -

      Solution format

      - +
      +
      +

      Solution format

      Broadly speaking, the argument to solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to solution must be a +

      x has numeric planning units
      +

      The argument to solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to solution.

      -
      x has matrix planning units

      The argument to solution must be a + +

      x has matrix planning units
      +

      The argument to solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -296,8 +205,10 @@

      Raster planning units +

      The argument to solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -305,35 +216,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has Spatial planning units

      The argument to solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has sf::sf() planning units

      The argument to solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to solution must also have the same @@ -342,142 +259,141 @@

      References

      +

      +
      +

      References

      Williams P, Gibbons D, Margules C, Rebelo A, Humphries C, and Pressey RL (1996) A comparison of richness hotspots, rarity hotspots and complementary areas for conserving diversity using British birds. Conservation Biology, 10: 155--174.

      -

      See also

      - -

      See importance for an overview of all functions for evaluating +

      +
      +

      See also

      +

      See importance for an overview of all functions for evaluating the importance of planning units selected in a solution.

      Other importances: -eval_ferrier_importance(), -eval_replacement_importance()

      - -

      Examples

      - 
      # \dontrun{
-# seed seed for reproducibility
-set.seed(600)
-
-# load data
-data(sim_pu_raster, sim_pu_sf, sim_features)
-
-# create minimal problem with raster planning units
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem
-s1 <- solve(p1)
-
-# print solution
-print(s1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# calculate importance scores
-rwr1 <- eval_rare_richness_importance(p1, s1)
-
-# print importance scores
-print(rwr1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : rwr 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot importance scores
-plot(rwr1, main = "rarity weighted richness", axes = FALSE, box = FALSE)
-
-
-# create minimal problem with polygon (sf) planning units
-p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.05) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem
-s2 <- solve(p2)
-
-# print solution
-print(s2)
-#> Simple feature collection with 90 features and 4 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
-#> CRS:           NA
-#> First 10 features:
-#>        cost locked_in locked_out solution_1                       geometry
-#> 1  215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2  212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3  207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4  208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5  214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6  213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
-#> 7  210.4612     FALSE      FALSE          0 POLYGON ((0.6 1, 0.7 1, 0.7...
-#> 8  211.0424     FALSE       TRUE          0 POLYGON ((0.7 1, 0.8 1, 0.8...
-#> 9  210.3878     FALSE      FALSE          0 POLYGON ((0.8 1, 0.9 1, 0.9...
-#> 10 204.3971     FALSE      FALSE          0 POLYGON ((0.9 1, 1 1, 1 0.9...
-
-# plot solution
-plot(s2[, "solution_1"], main = "solution")
-
-
-# calculate importance scores
-rwr2 <- eval_rare_richness_importance(p2, s2[, "solution_1"])
-
-# plot importance scores
-plot(rwr2, main = "rarity weighted richness")
-
-# }
-
+eval_ferrier_importance(),
+eval_replacement_importance()
      +
      + +
      +

      Examples

      + 
      # \dontrun{
+# seed seed for reproducibility
+set.seed(600)
+
+# load data
+data(sim_pu_raster, sim_pu_sf, sim_features)
+
+# create minimal problem with raster planning units
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem
+s1 <- solve(p1)
+
+# print solution
+print(s1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# calculate importance scores
+rwr1 <- eval_rare_richness_importance(p1, s1)
+
+# print importance scores
+print(rwr1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : rwr 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot importance scores
+plot(rwr1, main = "rarity weighted richness", axes = FALSE, box = FALSE)
+
+
+# create minimal problem with polygon (sf) planning units
+p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.05) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem
+s2 <- solve(p2)
+
+# print solution
+print(s2)
+#> Simple feature collection with 90 features and 4 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
+#> CRS:           NA
+#> First 10 features:
+#>        cost locked_in locked_out solution_1                       geometry
+#> 1  215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2  212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3  207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4  208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5  214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6  213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
+#> 7  210.4612     FALSE      FALSE          0 POLYGON ((0.6 1, 0.7 1, 0.7...
+#> 8  211.0424     FALSE       TRUE          0 POLYGON ((0.7 1, 0.8 1, 0.8...
+#> 9  210.3878     FALSE      FALSE          0 POLYGON ((0.8 1, 0.9 1, 0.9...
+#> 10 204.3971     FALSE      FALSE          0 POLYGON ((0.9 1, 1 1, 1 0.9...
+
+# plot solution
+plot(s2[, "solution_1"], main = "solution")
+
+
+# calculate importance scores
+rwr2 <- eval_rare_richness_importance(p2, s2[, "solution_1"])
+
+# plot importance scores
+plot(rwr2, main = "rarity weighted richness")
+
+# }
+
      +
      + - - - - - - - - - - - + diff --git a/docs/reference/eval_replacement_importance.html b/docs/reference/eval_replacement_importance.html index cdb90d16b..96cb51a9e 100644 --- a/docs/reference/eval_replacement_importance.html +++ b/docs/reference/eval_replacement_importance.html @@ -1,102 +1,19 @@ - - - - - - - -Evaluate solution importance using replacement cost scores — eval_replacement_importance • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Evaluate solution importance using replacement cost scores — eval_replacement_importance • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Evaluate solution importance using replacement cost scores

      - Source: R/eval_replacement_importance.R + Source: R/eval_replacement_importance.R
      @@ -186,82 +103,66 @@

      Evaluate solution importance using replacement cost scores

      based on the replacement cost method (Cabeza and Moilanen 2006).

      - 
      eval_replacement_importance(x, solution, ...)
+    
      Usage,
      eval_replacement_importance(x, solution, ...)
 
-# S4 method for ConservationProblem,numeric
-eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
+# S4 method for ConservationProblem,numeric
+eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
 
-# S4 method for ConservationProblem,matrix
-eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
+# S4 method for ConservationProblem,matrix
+eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
 
-# S4 method for ConservationProblem,data.frame
-eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
+# S4 method for ConservationProblem,data.frame
+eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
 
-# S4 method for ConservationProblem,Spatial
-eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
+# S4 method for ConservationProblem,Spatial
+eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
 
-# S4 method for ConservationProblem,sf
-eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
+# S4 method for ConservationProblem,sf
+eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
 
-# S4 method for ConservationProblem,Raster
-eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
      
+# S4 method for ConservationProblem,Raster
+eval_replacement_importance(x, solution, rescale, run_checks, force, threads, ...)
      -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      solution

      numeric, matrix, data.frame, -Raster, Spatial, -or sf::sf() object. +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      solution
      +

      numeric, matrix, data.frame, +Raster, Spatial, +or sf::sf() object. The argument should be in the same format as the planning unit cost data in the argument to x. -See the Solution format section for more information.

      ...

      not used.

      rescale

      logical flag indicating if replacement cost +See the Solution format section for more information.

      +
      ...
      +

      not used.

      +
      rescale
      +

      logical flag indicating if replacement cost values---excepting infinite (Inf) and zero values---should be -rescaled to range between 0.01 and 1. Defaults to TRUE.

      run_checks

      logical flag indicating whether presolve checks +rescaled to range between 0.01 and 1. Defaults to TRUE.

      +
      run_checks
      +

      logical flag indicating whether presolve checks should be run prior solving the problem. These checks are performed using -the presolve_check() function. Defaults to TRUE. -Skipping these checks may reduce run time for large problems.

      force

      logical flag indicating if an attempt to should be +the presolve_check() function. Defaults to TRUE. +Skipping these checks may reduce run time for large problems.

      +
      force
      +

      logical flag indicating if an attempt to should be made to solve the problem even if potential issues were detected during -the presolve checks. Defaults to FALSE.

      threads

      integer number of threads to use for the +the presolve checks. Defaults to FALSE.

      +
      threads
      +

      integer number of threads to use for the optimization algorithm. Defaults to 1 such that only a single -thread is used.

      - -

      Value

      - -

      A numeric, matrix, data.frame -RasterLayer, Spatial, -or sf::sf() object containing the importance scores for each planning +thread is used.

      +
      +
      +

      Value

      +

      A numeric, matrix, data.frameRasterLayer, Spatial, +or sf::sf() object containing the importance scores for each planning unit in the solution. Specifically, the returned object is in the same format as the planning unit data in the argument to x.

      -

      Details

      - +
      +
      +

      Details

      This function implements a modified version of the replacement cost method (Cabeza and Moilanen 2006). Specifically, the score for each planning unit is calculated @@ -274,46 +175,48 @@

      Details considered instead. Thus planning units with a higher score are more important (and irreplaceable). For example, when using the minimum set objective function -(add_min_set_objective()), the replacement cost scores +(add_min_set_objective()), the replacement cost scores correspond to the additional costs needed to meet targets when each planning unit is locked out. When using the maximum utility -objective function (add_max_utility_objective(), the +objective function (add_max_utility_objective(), the replacement cost scores correspond to the reduction in the utility when each planning unit is locked out. Infinite values mean that no feasible solution exists when planning units are locked out---they are -absolutely essential for obtaining a solution (e.g. they contain rare +absolutely essential for obtaining a solution (e.g., they contain rare species that are not found in any other planning units or were locked in). Zeros values mean that planning units can swapped with other planning units and this will have no effect on the performance of the solution at all -(e.g. because they were only selected due to spatial fragmentation +(e.g., because they were only selected due to spatial fragmentation penalties).

      These calculations can take a long time to complete for large or complex conservation planning problems. As such, we using this method for small or moderate-sized conservation planning problems -(e.g. < 30,000 planning units). To reduce run time, we -recommend calculating these scores without additional penalties (e.g. -add_boundary_penalties()) or spatial constraints (e.g. -add_contiguity_constraints()). To further reduce run time, +(e.g., < 30,000 planning units). To reduce run time, we +recommend calculating these scores without additional penalties (e.g., +add_boundary_penalties()) or spatial constraints (e.g., +add_contiguity_constraints()). To further reduce run time, we recommend using proportion-type decisions when calculating the scores (see below for an example).

      -

      Solution format

      - +
      +
      +

      Solution format

      Broadly speaking, the argument to solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to solution must be a +

      x has numeric planning units
      +

      The argument to solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to solution.

      -
      x has matrix planning units

      The argument to solution must be a + +

      x has matrix planning units
      +

      The argument to solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -321,8 +224,10 @@

      Raster planning units +

      The argument to solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -330,35 +235,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has Spatial planning units

      The argument to solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has sf::sf() planning units

      The argument to solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to solution must also have the same @@ -367,213 +278,212 @@

      References

      +

      +
      +

      References

      Cabeza M and Moilanen A (2006) Replacement cost: A practical measure of site value for cost-effective reserve planning. Biological Conservation, 132: 336--342.

      -

      See also

      - -

      See importance for an overview of all functions for evaluating +

      +
      +

      See also

      +

      See importance for an overview of all functions for evaluating the importance of planning units selected in a solution.

      Other importances: -eval_ferrier_importance(), -eval_rare_richness_importance()

      - -

      Examples

      - 
      # \dontrun{
-# seed seed for reproducibility
-set.seed(600)
-
-# load data
-data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
-
-# create minimal problem with binary decisions
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-# solve problem
-s1 <- solve(p1)
-
-# print solution
-print(s1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# calculate importance scores
-rc1 <- eval_replacement_importance(p1, s1)
-
-# print importance scores
-print(rc1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : rc 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot importance scores
-plot(rc1, main = "replacement cost", axes = FALSE, box = FALSE)
-
-
-# since replacement cost scores can take a long time to calculate with
-# binary decisions, we can calculate them using proportion-type
-# decision variables. Note we are still calculating the scores for our
-# previous solution (s1), we are just using a different optimization
-# problem when calculating the scores.
-p2 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_proportion_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# calculate importance scores using proportion type decisions
-rc2 <- eval_replacement_importance(p2, s1)
-
-# print importance scores based on proportion type decisions
-print(rc2)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : rc 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot importance scores based on proportion type decisions
-# we can see that the importance values in rc1 and rc2 are similar,
-# and this confirms that the proportion type decisions are a good
-# approximation
-plot(rc2, main = "replacement cost", axes = FALSE, box = FALSE)
-
-
-# create minimal problem with polygon (sf) planning units
-p3 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.05) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve problem
-s3 <- solve(p3)
-
-# print solution
-print(s3)
-#> Simple feature collection with 90 features and 4 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
-#> CRS:           NA
-#> First 10 features:
-#>        cost locked_in locked_out solution_1                       geometry
-#> 1  215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2  212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3  207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4  208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5  214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6  213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
-#> 7  210.4612     FALSE      FALSE          0 POLYGON ((0.6 1, 0.7 1, 0.7...
-#> 8  211.0424     FALSE       TRUE          0 POLYGON ((0.7 1, 0.8 1, 0.8...
-#> 9  210.3878     FALSE      FALSE          0 POLYGON ((0.8 1, 0.9 1, 0.9...
-#> 10 204.3971     FALSE      FALSE          0 POLYGON ((0.9 1, 1 1, 1 0.9...
-
-# plot solution
-plot(s3[, "solution_1"], main = "solution")
-
-
-# calculate importance scores
-rc3 <- eval_rare_richness_importance(p3, s3[, "solution_1"])
-
-# plot importance scores
-plot(rc3, main = "replacement cost")
-
-
-# build multi-zone conservation problem with raster data
-p4 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve the problem
-s4 <- solve(p4)
-
-# print solution
-print(s4)
-#> class      : RasterStack 
-#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> names      : zone_1, zone_2, zone_3 
-#> min values :      0,      0,      0 
-#> max values :      1,      1,      1 
-#> 
-
-# plot solution
-# each panel corresponds to a different zone, and data show the
-# status of each planning unit in a given zone
-plot(s4, main = paste0("zone ", seq_len(nlayers(s4))), axes = FALSE,
-     box = FALSE)
-
-
-# calculate importance scores
-rc4 <- eval_replacement_importance(p4, s4)
-
-# plot importance
-# each panel corresponds to a different zone, and data show the
-# importance of each planning unit in a given zone
-plot(rc4, main = paste0("zone ", seq_len(nlayers(s4))), axes = FALSE,
-     box = FALSE)
-
-# }
-
+eval_ferrier_importance(),
+eval_rare_richness_importance()
      +
      + +
      +

      Examples

      + 
      # \dontrun{
+# seed seed for reproducibility
+set.seed(600)
+
+# load data
+data(sim_pu_raster, sim_features, sim_pu_zones_stack, sim_features_zones)
+
+# create minimal problem with binary decisions
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+# solve problem
+s1 <- solve(p1)
+
+# print solution
+print(s1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# calculate importance scores
+rc1 <- eval_replacement_importance(p1, s1)
+
+# print importance scores
+print(rc1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : rc 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot importance scores
+plot(rc1, main = "replacement cost", axes = FALSE, box = FALSE)
+
+
+# since replacement cost scores can take a long time to calculate with
+# binary decisions, we can calculate them using proportion-type
+# decision variables. Note we are still calculating the scores for our
+# previous solution (s1), we are just using a different optimization
+# problem when calculating the scores.
+p2 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_proportion_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# calculate importance scores using proportion type decisions
+rc2 <- eval_replacement_importance(p2, s1)
+
+# print importance scores based on proportion type decisions
+print(rc2)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : rc 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot importance scores based on proportion type decisions
+# we can see that the importance values in rc1 and rc2 are similar,
+# and this confirms that the proportion type decisions are a good
+# approximation
+plot(rc2, main = "replacement cost", axes = FALSE, box = FALSE)
+
+
+# create minimal problem with polygon (sf) planning units
+p3 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.05) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve problem
+s3 <- solve(p3)
+
+# print solution
+print(s3)
+#> Simple feature collection with 90 features and 4 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
+#> CRS:           NA
+#> First 10 features:
+#>        cost locked_in locked_out solution_1                       geometry
+#> 1  215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2  212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3  207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4  208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5  214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6  213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
+#> 7  210.4612     FALSE      FALSE          0 POLYGON ((0.6 1, 0.7 1, 0.7...
+#> 8  211.0424     FALSE       TRUE          0 POLYGON ((0.7 1, 0.8 1, 0.8...
+#> 9  210.3878     FALSE      FALSE          0 POLYGON ((0.8 1, 0.9 1, 0.9...
+#> 10 204.3971     FALSE      FALSE          0 POLYGON ((0.9 1, 1 1, 1 0.9...
+
+# plot solution
+plot(s3[, "solution_1"], main = "solution")
+
+
+# calculate importance scores
+rc3 <- eval_rare_richness_importance(p3, s3[, "solution_1"])
+
+# plot importance scores
+plot(rc3, main = "replacement cost")
+
+
+# build multi-zone conservation problem with raster data
+p4 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve the problem
+s4 <- solve(p4)
+
+# print solution
+print(s4)
+#> class      : RasterStack 
+#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> names      : zone_1, zone_2, zone_3 
+#> min values :      0,      0,      0 
+#> max values :      1,      1,      1 
+#> 
+
+# plot solution
+# each panel corresponds to a different zone, and data show the
+# status of each planning unit in a given zone
+plot(s4, main = paste0("zone ", seq_len(nlayers(s4))), axes = FALSE,
+     box = FALSE)
+
+
+# calculate importance scores
+rc4 <- eval_replacement_importance(p4, s4)
+
+# plot importance
+# each panel corresponds to a different zone, and data show the
+# importance of each planning unit in a given zone
+plot(rc4, main = paste0("zone ", seq_len(nlayers(s4))), axes = FALSE,
+     box = FALSE)
+
+# }
+
      +
      + - - - - - - - - - - - + diff --git a/docs/reference/eval_target_coverage_summary.html b/docs/reference/eval_target_coverage_summary.html index bcf7d45be..59ecb5bae 100644 --- a/docs/reference/eval_target_coverage_summary.html +++ b/docs/reference/eval_target_coverage_summary.html @@ -1,106 +1,23 @@ - - - - - - - -Evaluate target coverage — eval_target_coverage_summary • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Evaluate target coverage — eval_target_coverage_summary • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Evaluate target coverage

      - Source: R/eval_target_coverage_summary.R + Source: R/eval_target_coverage_summary.R
      -

      Calculate how well feature representation targets are met by a solution to -a conservation planning problem(). +

      Calculate how well feature representation targets are met by a solution to +a conservation planning problem(). It is useful for understanding if features are adequately represented by a solution. Note that this function can only be used with problems that contain -targets.

      +targets.

      - 
      eval_target_coverage_summary(x, solution, include_zone, include_sense)
-
-# S3 method for default
-eval_target_coverage_summary(x, solution, include_zone, include_sense)
-
-# S3 method for ConservationProblem
-eval_target_coverage_summary(
-  x,
-  solution,
-  include_zone = number_of_zones(x) > 1,
-  include_sense = number_of_zones(x) > 1
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      solution

      numeric, matrix, data.frame, -Raster, Spatial, -or sf::sf() object. +

      Usage,
      eval_target_coverage_summary(x, solution, include_zone, include_sense)
+
+# S3 method for default
+eval_target_coverage_summary(x, solution, include_zone, include_sense)
+
+# S3 method for ConservationProblem
+eval_target_coverage_summary(
+  x,
+  solution,
+  include_zone = number_of_zones(x) > 1,
+  include_sense = number_of_zones(x) > 1
+)
      + +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      solution
      +

      numeric, matrix, data.frame, +Raster, Spatial, +or sf::sf() object. The argument should be in the same format as the planning unit cost data in the argument to x. -See the Solution format section for more information.

      include_zone

      logical include the zone column in the output? -Defaults to TRUE for problems that contain multiple zones.

      include_sense

      logical include the sense column in the output? -Defaults to TRUE for problems that contain multiple zones.

      - -

      Value

      - -

      tibble::tibble() object. +See the Solution format section for more information.

      +
      include_zone
      +

      logical include the zone column in the output? +Defaults to TRUE for problems that contain multiple zones.

      +
      include_sense
      +

      logical include the sense column in the output? +Defaults to TRUE for problems that contain multiple zones.

      +
      +
      +

      Value

      +

      tibble::tibble() object. Here, each row describes information for a different target. -It contains the following columns:

      -
      - -
      feature

      character name of the feature associated with each +It contains the following columns:

      feature
      +

      character name of the feature associated with each target.

      -
      zone

      list of character zone names associated with each target. + +

      zone
      +

      list of character zone names associated with each target. This column is in a list-column format because a single target can -correspond to multiple zones (see add_manual_targets() for details +correspond to multiple zones (see add_manual_targets() for details and examples). For an example of converting the list-column format to a standard character column format, please see the Examples section. This column is only included if the argument to include_zones is TRUE.

      -
      sense

      character sense associated with each target. + +

      sense
      +

      character sense associated with each target. Sense values specify the nature of the target. -Typically (e.g. when using the add_absolute_targets() or -add_relative_targets() functions), targets are specified using sense +Typically (e.g., when using the add_absolute_targets() or +add_relative_targets() functions), targets are specified using sense values indicating that the total amount of a feature held within a solution (ideally) be greater than or equal to a threshold amount -(i.e. a sense value of ">="). -Additionally, targets (i.e. using the add_manual_targets() function) +(i.e., a sense value of ">="). +Additionally, targets (i.e., using the add_manual_targets() function) can also be specified using sense values indicating that the total amount of a feature held within a solution must be equal to a -threshold amount (i.e. a sense value of "=") or smaller than or equal -to a threshold amount (i.e. a sense value of "<="). +threshold amount (i.e., a sense value of "=") or smaller than or equal +to a threshold amount (i.e., a sense value of "<="). This column is only included if the argument to include_sense is TRUE.

      -
      total_amount

      numeric total amount of the feature available across + +

      total_amount
      +

      numeric total amount of the feature available across the entire conservation planning problem for meeting each target (not just planning units selected within the solution). For problems involving a single zone, this column is calculated as the sum of all of the values for a given feature (similar to values in the total_amount column produced by the -eval_feature_representation_summary() function). +eval_feature_representation_summary() function). For problems involving multiple zones, this column is calculated as the sum of the values for the feature associated with target (per the "feature" column), across the zones associated with the target (per the "zone" column).

      -
      absolute_target

      numeric total threshold amount associated with + +

      absolute_target
      +

      numeric total threshold amount associated with each target.

      -
      absolute_held

      numeric total amount held within the solution for + +

      absolute_held
      +

      numeric total amount held within the solution for the feature and (if relevant) zones associated with each target (per the "feature" and "zone" columns, respectively). This column is calculated as the sum of the feature data, -supplied when creating a problem() object -(e.g. presence/absence values), weighted by the status of each -planning unit in the solution (e.g. selected or not for prioritization).

      +supplied when creating a problem() object +(e.g., presence/absence values), weighted by the status of each +planning unit in the solution (e.g., selected or not for +prioritization).

      -
      absolute_shortfall

      numeric total amount by which the solution + +

      absolute_shortfall
      +

      numeric total amount by which the solution fails to meet each target. This column is calculated as the difference between the total amount held within the solution for the feature and (if relevant) zones -associated with the target (i.e. "absolute_held" column) and the -target total threshold amount (i.e. "absolute_target" column), with +associated with the target (i.e., "absolute_held" column) and the +target total threshold amount (i.e., "absolute_target" column), with values set to zero depending on the sense specified for the target -(e.g. if the target sense is >= then the difference is +(e.g., if the target sense is >= then the difference is set to zero if the value in the "absolute_held" is smaller than that in the "absolute_target" column).

      -
      relative_target

      numeric proportion threshold amount associated + +

      relative_target
      +

      numeric proportion threshold amount associated with each target. This column is calculated by dividing the total threshold amount -associated with each target (i.e. "absolute_target" column) by +associated with each target (i.e., "absolute_target" column) by the total amount associated with each target -(i.e. "total_amount" column).

      +(i.e., "total_amount" column).

      -
      relative_held

      numeric proportion held within the solution for the + +

      relative_held
      +

      numeric proportion held within the solution for the feature and (if relevant) zones associated with each target (per the "feature" and "zone" columns, respectively). This column is calculated by dividing the total amount held -for each target (i.e. "absolute_held" column) by the +for each target (i.e., "absolute_held" column) by the total amount for with each target -(i.e. "total_amount" column).

      +(i.e., "total_amount" column).

      + -
      relative_shortfall

      numeric proportion by which the solution fails +

      relative_shortfall
      +

      numeric proportion by which the solution fails to meet each target. This column is calculated by dividing the total shortfall for -each target (i.e. "absolute_shortfall" column) by the -total amount for each target (i.e. "total_amount" column).

      +each target (i.e., "absolute_shortfall" column) by the +total amount for each target (i.e., "total_amount" column).

      -
      met

      logical indicating if each target is met by the solution. This + +

      met
      +

      logical indicating if each target is met by the solution. This column is calculated by checking if the total shortfall associated -with each target (i.e. "absolute_shortfall" column) is equal to +with each target (i.e., "absolute_shortfall" column) is equal to zero.

      -
      - -

      Solution format

      +
      +
      +

      Solution format

      Broadly speaking, the argument to solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to solution must be a +

      x has numeric planning units
      +

      The argument to solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to solution.

      -
      x has matrix planning units

      The argument to solution must be a + +

      x has matrix planning units
      +

      The argument to solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -357,8 +284,10 @@

      Raster planning units +

      The argument to solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -366,35 +295,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has Spatial planning units

      The argument to solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has sf::sf() planning units

      The argument to solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to solution must also have the same @@ -403,272 +338,270 @@

      See also

      -

      See summaries for an overview of all functions for summarizing solutions.

      +

      +
      +

      See also

      +

      See summaries for an overview of all functions for summarizing solutions.

      Other summaries: -eval_boundary_summary(), -eval_connectivity_summary(), -eval_cost_summary(), -eval_feature_representation_summary(), -eval_n_summary()

      - -

      Examples

      - 
      # \dontrun{
-# set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_pu_sf, sim_features,
-     sim_pu_zones_sf, sim_features_zones)
-
-# build minimal conservation problem with raster data
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s1 <- solve(p1)
-
-# print solution
-print(s1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# calculate target coverage by the solution
-r1 <- eval_target_coverage_summary(p1, s1)
-print(r1, width = Inf) # note: `width = Inf` tells R to print all columns
-#> # A tibble: 5 × 9
-#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
-#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
-#> 1 layer.1 TRUE          83.3            8.33          8.91                  0
-#> 2 layer.2 TRUE          31.2            3.12          3.13                  0
-#> 3 layer.3 TRUE          72.0            7.20          7.34                  0
-#> 4 layer.4 TRUE          42.7            4.27          4.35                  0
-#> 5 layer.5 TRUE          56.7            5.67          6.01                  0
-#>   relative_target relative_held relative_shortfall
-#>             <dbl>         <dbl>              <dbl>
-#> 1             0.1         0.107                  0
-#> 2             0.1         0.100                  0
-#> 3             0.1         0.102                  0
-#> 4             0.1         0.102                  0
-#> 5             0.1         0.106                  0
-
-# build minimal conservation problem with polygon (sf) data
-p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s2 <- solve(p2)
-
-# print first six rows of the attribute table
-print(head(s2))
-#> Simple feature collection with 6 features and 4 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>       cost locked_in locked_out solution_1                       geometry
-#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# plot solution
-plot(s2[, "solution_1"])
-
-
-# calculate target coverage by the solution
-r2 <- eval_target_coverage_summary(p2, s2[, "solution_1"])
-print(r2, width = Inf)
-#> # A tibble: 5 × 9
-#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
-#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
-#> 1 layer.1 TRUE          74.5            7.45          8.05                  0
-#> 2 layer.2 TRUE          28.1            2.81          2.83                  0
-#> 3 layer.3 TRUE          64.9            6.49          6.65                  0
-#> 4 layer.4 TRUE          38.2            3.82          3.87                  0
-#> 5 layer.5 TRUE          50.7            5.07          5.41                  0
-#>   relative_target relative_held relative_shortfall
-#>             <dbl>         <dbl>              <dbl>
-#> 1             0.1         0.108                  0
-#> 2             0.1         0.101                  0
-#> 3             0.1         0.103                  0
-#> 4             0.1         0.101                  0
-#> 5             0.1         0.107                  0
-
-# build multi-zone conservation problem with polygon (sf) data
-p3 <- problem(sim_pu_zones_sf, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s3 <- solve(p3)
-
-# print first six rows of the attribute table
-print(head(s3))
-#> Simple feature collection with 6 features and 9 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
-#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
-#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
-#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
-#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
-#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
-#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
-#>   solution_1_zone_2 solution_1_zone_3                       geometry
-#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2                 0                 1 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4                 0                 1 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5                 0                 1 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s3$solution <- category_vector(
-  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-s3$solution <- factor(s3$solution)
-
-# plot solution
-plot(s3[, "solution"])
-
-
-# calculate target coverage by the solution
-r3 <- eval_target_coverage_summary(
-  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-print(r3, width = Inf)
-#> # A tibble: 15 × 11
-#>    feature   zone      sense met   total_amount absolute_target absolute_held
-#>    <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
-#>  1 feature_1 <chr [1]> >=    TRUE          75.1           13.8          14.9 
-#>  2 feature_2 <chr [1]> >=    TRUE          28.0            4.82          5.14
-#>  3 feature_3 <chr [1]> >=    TRUE          65.0           12.8          12.8 
-#>  4 feature_4 <chr [1]> >=    TRUE          38.0            5.58          6.64
-#>  5 feature_5 <chr [1]> >=    TRUE          51.2            9.27          9.96
-#>  6 feature_1 <chr [1]> >=    TRUE          75.1            9.06         15.0 
-#>  7 feature_2 <chr [1]> >=    TRUE          28.0            4.23          5.58
-#>  8 feature_3 <chr [1]> >=    TRUE          65.0           12.5          13.6 
-#>  9 feature_4 <chr [1]> >=    TRUE          38.0            6.96          7.14
-#> 10 feature_5 <chr [1]> >=    TRUE          51.2            8.76          9.96
-#> 11 feature_1 <chr [1]> >=    TRUE          75.1            9.63         13.3 
-#> 12 feature_2 <chr [1]> >=    TRUE          28.0            5.29          5.65
-#> 13 feature_3 <chr [1]> >=    TRUE          65.0           11.5          11.8 
-#> 14 feature_4 <chr [1]> >=    TRUE          38.0            4.43          7.71
-#> 15 feature_5 <chr [1]> >=    TRUE          51.2            8.86          9.04
-#>    absolute_shortfall relative_target relative_held relative_shortfall
-#>                 <dbl>           <dbl>         <dbl>              <dbl>
-#>  1                  0           0.183         0.198                  0
-#>  2                  0           0.173         0.184                  0
-#>  3                  0           0.198         0.198                  0
-#>  4                  0           0.147         0.175                  0
-#>  5                  0           0.181         0.195                  0
-#>  6                  0           0.121         0.200                  0
-#>  7                  0           0.151         0.200                  0
-#>  8                  0           0.193         0.210                  0
-#>  9                  0           0.183         0.188                  0
-#> 10                  0           0.171         0.195                  0
-#> 11                  0           0.128         0.177                  0
-#> 12                  0           0.189         0.202                  0
-#> 13                  0           0.176         0.181                  0
-#> 14                  0           0.116         0.203                  0
-#> 15                  0           0.173         0.177                  0
-
-# create a new column with character values containing the zone names,
-# by extracting these data out of the zone column
-# (which is in list-column format)
-r3$zone2 <- vapply(r3$zone, FUN.VALUE = character(1), paste, sep = " & ")
-
-# print r3 again to show the new column
-print(r3, width = Inf)
-#> # A tibble: 15 × 12
-#>    feature   zone      sense met   total_amount absolute_target absolute_held
-#>    <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
-#>  1 feature_1 <chr [1]> >=    TRUE          75.1           13.8          14.9 
-#>  2 feature_2 <chr [1]> >=    TRUE          28.0            4.82          5.14
-#>  3 feature_3 <chr [1]> >=    TRUE          65.0           12.8          12.8 
-#>  4 feature_4 <chr [1]> >=    TRUE          38.0            5.58          6.64
-#>  5 feature_5 <chr [1]> >=    TRUE          51.2            9.27          9.96
-#>  6 feature_1 <chr [1]> >=    TRUE          75.1            9.06         15.0 
-#>  7 feature_2 <chr [1]> >=    TRUE          28.0            4.23          5.58
-#>  8 feature_3 <chr [1]> >=    TRUE          65.0           12.5          13.6 
-#>  9 feature_4 <chr [1]> >=    TRUE          38.0            6.96          7.14
-#> 10 feature_5 <chr [1]> >=    TRUE          51.2            8.76          9.96
-#> 11 feature_1 <chr [1]> >=    TRUE          75.1            9.63         13.3 
-#> 12 feature_2 <chr [1]> >=    TRUE          28.0            5.29          5.65
-#> 13 feature_3 <chr [1]> >=    TRUE          65.0           11.5          11.8 
-#> 14 feature_4 <chr [1]> >=    TRUE          38.0            4.43          7.71
-#> 15 feature_5 <chr [1]> >=    TRUE          51.2            8.86          9.04
-#>    absolute_shortfall relative_target relative_held relative_shortfall zone2 
-#>                 <dbl>           <dbl>         <dbl>              <dbl> <chr> 
-#>  1                  0           0.183         0.198                  0 zone_1
-#>  2                  0           0.173         0.184                  0 zone_1
-#>  3                  0           0.198         0.198                  0 zone_1
-#>  4                  0           0.147         0.175                  0 zone_1
-#>  5                  0           0.181         0.195                  0 zone_1
-#>  6                  0           0.121         0.200                  0 zone_2
-#>  7                  0           0.151         0.200                  0 zone_2
-#>  8                  0           0.193         0.210                  0 zone_2
-#>  9                  0           0.183         0.188                  0 zone_2
-#> 10                  0           0.171         0.195                  0 zone_2
-#> 11                  0           0.128         0.177                  0 zone_3
-#> 12                  0           0.189         0.202                  0 zone_3
-#> 13                  0           0.176         0.181                  0 zone_3
-#> 14                  0           0.116         0.203                  0 zone_3
-#> 15                  0           0.173         0.177                  0 zone_3
-# }
+eval_boundary_summary(),
+eval_connectivity_summary(),
+eval_cost_summary(),
+eval_feature_representation_summary(),
+eval_n_summary()
      +
      + +
      +

      Examples

      + 
      # \dontrun{
+# set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_pu_sf, sim_features,
+     sim_pu_zones_sf, sim_features_zones)
+
+# build minimal conservation problem with raster data
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s1 <- solve(p1)
+
+# print solution
+print(s1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# calculate target coverage by the solution
+r1 <- eval_target_coverage_summary(p1, s1)
+print(r1, width = Inf) # note: `width = Inf` tells R to print all columns
+#> # A tibble: 5 × 9
+#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
+#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
+#> 1 layer.1 TRUE          83.3            8.33          8.91                  0
+#> 2 layer.2 TRUE          31.2            3.12          3.13                  0
+#> 3 layer.3 TRUE          72.0            7.20          7.34                  0
+#> 4 layer.4 TRUE          42.7            4.27          4.35                  0
+#> 5 layer.5 TRUE          56.7            5.67          6.01                  0
+#>   relative_target relative_held relative_shortfall
+#>             <dbl>         <dbl>              <dbl>
+#> 1             0.1         0.107                  0
+#> 2             0.1         0.100                  0
+#> 3             0.1         0.102                  0
+#> 4             0.1         0.102                  0
+#> 5             0.1         0.106                  0
+
+# build minimal conservation problem with polygon (sf) data
+p2 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s2 <- solve(p2)
+
+# print first six rows of the attribute table
+print(head(s2))
+#> Simple feature collection with 6 features and 4 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>       cost locked_in locked_out solution_1                       geometry
+#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# plot solution
+plot(s2[, "solution_1"])
+
+
+# calculate target coverage by the solution
+r2 <- eval_target_coverage_summary(p2, s2[, "solution_1"])
+print(r2, width = Inf)
+#> # A tibble: 5 × 9
+#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
+#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
+#> 1 layer.1 TRUE          74.5            7.45          8.05                  0
+#> 2 layer.2 TRUE          28.1            2.81          2.83                  0
+#> 3 layer.3 TRUE          64.9            6.49          6.65                  0
+#> 4 layer.4 TRUE          38.2            3.82          3.87                  0
+#> 5 layer.5 TRUE          50.7            5.07          5.41                  0
+#>   relative_target relative_held relative_shortfall
+#>             <dbl>         <dbl>              <dbl>
+#> 1             0.1         0.108                  0
+#> 2             0.1         0.101                  0
+#> 3             0.1         0.103                  0
+#> 4             0.1         0.101                  0
+#> 5             0.1         0.107                  0
+
+# build multi-zone conservation problem with polygon (sf) data
+p3 <- problem(sim_pu_zones_sf, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s3 <- solve(p3)
+
+# print first six rows of the attribute table
+print(head(s3))
+#> Simple feature collection with 6 features and 9 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
+#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
+#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
+#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
+#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
+#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
+#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
+#>   solution_1_zone_2 solution_1_zone_3                       geometry
+#> 1                 0                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2                 0                 1 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4                 0                 1 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5                 0                 1 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s3$solution <- category_vector(
+  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+s3$solution <- factor(s3$solution)
+
+# plot solution
+plot(s3[, "solution"])
+
+
+# calculate target coverage by the solution
+r3 <- eval_target_coverage_summary(
+  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+print(r3, width = Inf)
+#> # A tibble: 15 × 11
+#>    feature   zone      sense met   total_amount absolute_target absolute_held
+#>    <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
+#>  1 feature_1 <chr [1]> >=    TRUE          75.1           13.8          14.9 
+#>  2 feature_2 <chr [1]> >=    TRUE          28.0            4.82          5.14
+#>  3 feature_3 <chr [1]> >=    TRUE          65.0           12.8          12.8 
+#>  4 feature_4 <chr [1]> >=    TRUE          38.0            5.58          6.64
+#>  5 feature_5 <chr [1]> >=    TRUE          51.2            9.27          9.96
+#>  6 feature_1 <chr [1]> >=    TRUE          75.1            9.06         15.0 
+#>  7 feature_2 <chr [1]> >=    TRUE          28.0            4.23          5.58
+#>  8 feature_3 <chr [1]> >=    TRUE          65.0           12.5          13.6 
+#>  9 feature_4 <chr [1]> >=    TRUE          38.0            6.96          7.14
+#> 10 feature_5 <chr [1]> >=    TRUE          51.2            8.76          9.96
+#> 11 feature_1 <chr [1]> >=    TRUE          75.1            9.63         13.3 
+#> 12 feature_2 <chr [1]> >=    TRUE          28.0            5.29          5.65
+#> 13 feature_3 <chr [1]> >=    TRUE          65.0           11.5          11.8 
+#> 14 feature_4 <chr [1]> >=    TRUE          38.0            4.43          7.71
+#> 15 feature_5 <chr [1]> >=    TRUE          51.2            8.86          9.04
+#>    absolute_shortfall relative_target relative_held relative_shortfall
+#>                 <dbl>           <dbl>         <dbl>              <dbl>
+#>  1                  0           0.183         0.198                  0
+#>  2                  0           0.173         0.184                  0
+#>  3                  0           0.198         0.198                  0
+#>  4                  0           0.147         0.175                  0
+#>  5                  0           0.181         0.195                  0
+#>  6                  0           0.121         0.200                  0
+#>  7                  0           0.151         0.200                  0
+#>  8                  0           0.193         0.210                  0
+#>  9                  0           0.183         0.188                  0
+#> 10                  0           0.171         0.195                  0
+#> 11                  0           0.128         0.177                  0
+#> 12                  0           0.189         0.202                  0
+#> 13                  0           0.176         0.181                  0
+#> 14                  0           0.116         0.203                  0
+#> 15                  0           0.173         0.177                  0
+
+# create a new column with character values containing the zone names,
+# by extracting these data out of the zone column
+# (which is in list-column format)
+r3$zone2 <- vapply(r3$zone, FUN.VALUE = character(1), paste, sep = " & ")
+
+# print r3 again to show the new column
+print(r3, width = Inf)
+#> # A tibble: 15 × 12
+#>    feature   zone      sense met   total_amount absolute_target absolute_held
+#>    <chr>     <list>    <chr> <lgl>        <dbl>           <dbl>         <dbl>
+#>  1 feature_1 <chr [1]> >=    TRUE          75.1           13.8          14.9 
+#>  2 feature_2 <chr [1]> >=    TRUE          28.0            4.82          5.14
+#>  3 feature_3 <chr [1]> >=    TRUE          65.0           12.8          12.8 
+#>  4 feature_4 <chr [1]> >=    TRUE          38.0            5.58          6.64
+#>  5 feature_5 <chr [1]> >=    TRUE          51.2            9.27          9.96
+#>  6 feature_1 <chr [1]> >=    TRUE          75.1            9.06         15.0 
+#>  7 feature_2 <chr [1]> >=    TRUE          28.0            4.23          5.58
+#>  8 feature_3 <chr [1]> >=    TRUE          65.0           12.5          13.6 
+#>  9 feature_4 <chr [1]> >=    TRUE          38.0            6.96          7.14
+#> 10 feature_5 <chr [1]> >=    TRUE          51.2            8.76          9.96
+#> 11 feature_1 <chr [1]> >=    TRUE          75.1            9.63         13.3 
+#> 12 feature_2 <chr [1]> >=    TRUE          28.0            5.29          5.65
+#> 13 feature_3 <chr [1]> >=    TRUE          65.0           11.5          11.8 
+#> 14 feature_4 <chr [1]> >=    TRUE          38.0            4.43          7.71
+#> 15 feature_5 <chr [1]> >=    TRUE          51.2            8.86          9.04
+#>    absolute_shortfall relative_target relative_held relative_shortfall zone2 
+#>                 <dbl>           <dbl>         <dbl>              <dbl> <chr> 
+#>  1                  0           0.183         0.198                  0 zone_1
+#>  2                  0           0.173         0.184                  0 zone_1
+#>  3                  0           0.198         0.198                  0 zone_1
+#>  4                  0           0.147         0.175                  0 zone_1
+#>  5                  0           0.181         0.195                  0 zone_1
+#>  6                  0           0.121         0.200                  0 zone_2
+#>  7                  0           0.151         0.200                  0 zone_2
+#>  8                  0           0.193         0.210                  0 zone_2
+#>  9                  0           0.183         0.188                  0 zone_2
+#> 10                  0           0.171         0.195                  0 zone_2
+#> 11                  0           0.128         0.177                  0 zone_3
+#> 12                  0           0.189         0.202                  0 zone_3
+#> 13                  0           0.176         0.181                  0 zone_3
+#> 14                  0           0.116         0.203                  0 zone_3
+#> 15                  0           0.173         0.177                  0 zone_3
+# }
      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/fast_extract.html b/docs/reference/fast_extract.html index a18cc266a..26b0e7881 100644 --- a/docs/reference/fast_extract.html +++ b/docs/reference/fast_extract.html @@ -1,101 +1,18 @@ - - - - - - - -Fast extract — fast_extract • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Fast extract — fast_extract • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Fast extract

      - Source: R/fast_extract.R + Source: R/fast_extract.R
      -

      Extract data from a Raster object.

      +

      Extract data from a Raster object.

      - 
      fast_extract(x, y, ...)
+    
      Usage,
      fast_extract(x, y, ...)
 
-# S4 method for Raster,SpatialPolygons
-fast_extract(x, y, fun = "mean", ...)
+# S4 method for Raster,SpatialPolygons
+fast_extract(x, y, fun = "mean", ...)
 
-# S4 method for Raster,SpatialPoints
-fast_extract(x, y, fun = "mean", ...)
+# S4 method for Raster,SpatialPoints
+fast_extract(x, y, fun = "mean", ...)
 
-# S4 method for Raster,SpatialLines
-fast_extract(x, y, fun = "mean", ...)
+# S4 method for Raster,SpatialLines
+fast_extract(x, y, fun = "mean", ...)
 
-# S4 method for Raster,sfc
-fast_extract(x, y, fun = "mean", ...)
+# S4 method for Raster,sfc
+fast_extract(x, y, fun = "mean", ...)
 
-# S4 method for Raster,sf
-fast_extract(x, y, fun = "mean", ...)
      
+# S4 method for Raster,sf
+fast_extract(x, y, fun = "mean", ...)
      -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      x

      Raster object.

      y

      Spatial or -sf::sf() object.

      ...

      not used.

      fun

      character name of statistic to summarize data. Defaults +

      +

      Arguments

      +
      x
      +

      Raster object.

      +
      y
      +

      Spatial or +sf::sf() object.

      +
      ...
      +

      not used.

      +
      fun
      +

      character name of statistic to summarize data. Defaults to "mean". Available options include "sum" or "mean". -Defaults to "mean".

      - -

      Value

      - +Defaults to "mean".

      +
      +
      +

      Value

      matrix containing the summary amount of each feature within each planning unit. Rows correspond to different spatial features in the argument to y and columns correspond to different raster layers in the argument to x.

      -

      Details

      - +
      +
      +

      Details

      This function is simply a wrapper that uses -raster::extract() to extract data for -SpatialPoints and -SpatialLines and -non-polygonal sf::sf() data, and -exactextractr::exact_extract() for -SpatialPolygons and -polygonal sf::sf() data.

      -

      See also

      - -

      raster::extract(), -exactextractr::exact_extract().

      +raster::extract() to extract data for +SpatialPoints and +SpatialLines and +non-polygonal sf::sf() data, and +exactextractr::exact_extract() for +SpatialPolygons and +polygonal sf::sf() data.

      +
      + -

      Examples

      - 
      # load data
-data(sim_pu_sf, sim_features)
-
-# extract data
-result <- fast_extract(sim_features, sim_pu_sf)
-
-# show result
-print(head(result))
-#>           [,1]      [,2]      [,3]      [,4]      [,5]
-#> [1,] 0.7150548 0.2900901 0.8178213 0.2199663 0.4533809
-#> [2,] 0.6990429 0.3052216 0.8064534 0.2713800 0.4413639
-#> [3,] 0.6859317 0.3266036 0.7852441 0.3296247 0.4343547
-#> [4,] 0.6783193 0.3510977 0.7541320 0.3900085 0.4355628
-#> [5,] 0.6782107 0.3750470 0.7131559 0.4468281 0.4474871
-#> [6,] 0.6863252 0.3950113 0.6628435 0.4946333 0.4714105
-
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_sf, sim_features)
+
+# extract data
+result <- fast_extract(sim_features, sim_pu_sf)
+
+# show result
+print(head(result))
+#>           [,1]      [,2]      [,3]      [,4]      [,5]
+#> [1,] 0.7150548 0.2900901 0.8178213 0.2199663 0.4533809
+#> [2,] 0.6990429 0.3052216 0.8064534 0.2713800 0.4413639
+#> [3,] 0.6859317 0.3266036 0.7852441 0.3296247 0.4343547
+#> [4,] 0.6783193 0.3510977 0.7541320 0.3900085 0.4355628
+#> [5,] 0.6782107 0.3750470 0.7131559 0.4468281 0.4474871
+#> [6,] 0.6863252 0.3950113 0.6628435 0.4946333 0.4714105
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/feature_abundances.html b/docs/reference/feature_abundances.html index 0ff84d554..353e3d6cd 100644 --- a/docs/reference/feature_abundances.html +++ b/docs/reference/feature_abundances.html @@ -1,102 +1,19 @@ - - - - - - - -Feature abundances — feature_abundances • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Feature abundances — feature_abundances • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Feature abundances

      - Source: R/feature_abundances.R + Source: R/feature_abundances.R
      @@ -186,47 +103,45 @@

      Feature abundances

      of a conservation planning problem.

      - 
      feature_abundances(x, na.rm)
+    
      Usage,
      feature_abundances(x, na.rm)
 
-# S3 method for ConservationProblem
-feature_abundances(x, na.rm = FALSE)
      
+# S3 method for ConservationProblem
+feature_abundances(x, na.rm = FALSE)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      na.rm

      logical should planning units with NA cost +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      na.rm
      +

      logical should planning units with NA cost data be excluded from the abundance calculations? The default argument -is FALSE.

      - -

      Value

      - -

      tibble::tibble() object containing the total amount +is FALSE.

      +
      +
      +

      Value

      +

      tibble::tibble() object containing the total amount ("absolute_abundance") and proportion ("relative_abundance") of the distribution of each feature in the planning units. Here, each row contains data that pertain to a specific feature in a specific management zone (if multiple zones are present). This object -contains the following columns:

      -
      +contains the following columns:

      feature
      +

      character name of the feature.

      -
      feature

      character name of the feature.

      -
      zone

      character name of the zone (not included when the +

      zone
      +

      character name of the zone (not included when the argument to x contains only one management zone).

      -
      absolute_abundance

      numeric amount of each feature in the + +

      absolute_abundance
      +

      numeric amount of each feature in the planning units. If the problem contains multiple zones, then this column shows how well each feature is represented in a each zone.

      -
      relative_abundance

      numeric proportion of the feature's + +

      relative_abundance
      +

      numeric proportion of the feature's distribution in the planning units. If the argument to na.rm is FALSE, then this column will only contain values equal to one. Otherwise, if the argument to na.rm is TRUE and planning @@ -234,15 +149,15 @@

      Value

      then this column will contain values between zero and one.

      -
      - -

      Details

      +
      +
      +

      Details

      Planning units can have cost data with finite values -(e.g. 0.1, 3, 100) and NA values. This functionality is provided so +(e.g., 0.1, 3, 100) and NA values. This functionality is provided so that locations which are not available for protected area acquisition can be included when calculating targets for conservation features -(e.g. when targets are specified using add_relative_targets()). +(e.g., when targets are specified using add_relative_targets()). If the total amount of each feature in all the planning units is required---including the planning units with NA cost data---then the the na.rm argument should be set to FALSE. However, if @@ -250,146 +165,145 @@

      Details excluded---for instance, to calculate the highest feasible targets for each feature---then the na.rm argument should be set to TRUE.

      -

      See also

      - -

      problem(), eval_feature_representation_summary().

      +
      + -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create a simple conservation planning dataset so we can see exactly
-# how the feature abundances are calculated
-pu <- data.frame(id = seq_len(10), cost = c(0.2, NA, runif(8)),
-                 spp1 = runif(10), spp2 = c(rpois(9, 4), NA))
-
-# create problem
-p1 <- problem(pu, c("spp1", "spp2"), cost_column = "cost")
-
-# calculate feature abundances; including planning units with NA costs
-a1 <- feature_abundances(p1, na.rm = FALSE) # (default)
-print(a1)
-#> # A tibble: 2 × 3
-#>   feature absolute_abundance relative_abundance
-#>   <chr>                <dbl>              <dbl>
-#> 1 spp1                  4.10                  1
-#> 2 spp2                 31                     1
-
-# calculate feature abundances; excluding planning units with NA costs
-a2 <- feature_abundances(p1, na.rm = TRUE)
-print(a2)
-#> # A tibble: 2 × 3
-#>   feature absolute_abundance relative_abundance
-#>   <chr>                <dbl>              <dbl>
-#> 1 spp1                  3.84              0.935
-#> 2 spp2                 28                 0.903
-
-# verify correctness of feature abundance calculations
-all.equal(a1$absolute_abundance,
-          c(sum(pu$spp1), sum(pu$spp2, na.rm = TRUE)))
-#> [1] TRUE
-
-all.equal(a1$relative_abundance,
-          c(sum(pu$spp1) / sum(pu$spp1),
-            sum(pu$spp2, na.rm = TRUE) / sum(pu$spp2, na.rm = TRUE)))
-#> [1] TRUE
-
-all.equal(a2$absolute_abundance,
-          c(sum(pu$spp1[!is.na(pu$cost)]),
-            sum(pu$spp2[!is.na(pu$cost)], na.rm = TRUE)))
-#> [1] TRUE
-
-all.equal(a2$relative_abundance,
-          c(sum(pu$spp1[!is.na(pu$cost)]) / sum(pu$spp1, na.rm = TRUE),
-            sum(pu$spp2[!is.na(pu$cost)], na.rm = TRUE) / sum(pu$spp2,
-                                                              na.rm = TRUE)))
-#> [1] TRUE
-
-# initialize conservation problem with raster data
-p3 <- problem(sim_pu_raster, sim_features)
-
-# calculate feature abundances; including planning units with NA costs
-a3 <- feature_abundances(p3, na.rm = FALSE) # (default)
-print(a3)
-#> # A tibble: 5 × 3
-#>   feature absolute_abundance relative_abundance
-#>   <chr>                <dbl>              <dbl>
-#> 1 layer.1               83.3                  1
-#> 2 layer.2               31.2                  1
-#> 3 layer.3               72.0                  1
-#> 4 layer.4               42.7                  1
-#> 5 layer.5               56.7                  1
-
-# create problem using total amounts of features in all the planning units
-# (including units with NA cost data)
-p4 <- p3 %>%
-      add_min_set_objective() %>%
-      add_relative_targets(a3$relative_abundance) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# attempt to solve the problem, but we will see that this problem is
-# infeasible because the targets cannot be met using only the planning units
-# with finite cost data
-# \dontrun{
-s4 <- try(solve(p4))
-#> Error in .local(a, b = b, ...) : 
-#>   no solution found (e.g. due to problem infeasibility or time limits)
-# }
-# calculate feature abundances; excluding planning units with NA costs
-a5 <- feature_abundances(p3, na.rm = TRUE)
-print(a5)
-#> # A tibble: 5 × 3
-#>   feature absolute_abundance relative_abundance
-#>   <chr>                <dbl>              <dbl>
-#> 1 layer.1               74.5              0.895
-#> 2 layer.2               28.1              0.900
-#> 3 layer.3               64.9              0.902
-#> 4 layer.4               38.2              0.895
-#> 5 layer.5               50.7              0.893
-
-# create problem using total amounts of features in the planning units with
-# finite cost data
-p5 <- p3 %>%
-      add_min_set_objective() %>%
-      add_relative_targets(a5$relative_abundance) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s5 <- solve(p5)
-
-# plot the solution
-# this solution contains all the planning units with finite cost data (i.e.
-# cost data that do not have NA values)
-plot(s5)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create a simple conservation planning dataset so we can see exactly
+# how the feature abundances are calculated
+pu <- data.frame(id = seq_len(10), cost = c(0.2, NA, runif(8)),
+                 spp1 = runif(10), spp2 = c(rpois(9, 4), NA))
+
+# create problem
+p1 <- problem(pu, c("spp1", "spp2"), cost_column = "cost")
+
+# calculate feature abundances; including planning units with NA costs
+a1 <- feature_abundances(p1, na.rm = FALSE) # (default)
+print(a1)
+#> # A tibble: 2 × 3
+#>   feature absolute_abundance relative_abundance
+#>   <chr>                <dbl>              <dbl>
+#> 1 spp1                  4.10                  1
+#> 2 spp2                 31                     1
+
+# calculate feature abundances; excluding planning units with NA costs
+a2 <- feature_abundances(p1, na.rm = TRUE)
+print(a2)
+#> # A tibble: 2 × 3
+#>   feature absolute_abundance relative_abundance
+#>   <chr>                <dbl>              <dbl>
+#> 1 spp1                  3.84              0.935
+#> 2 spp2                 28                 0.903
+
+# verify correctness of feature abundance calculations
+all.equal(a1$absolute_abundance,
+          c(sum(pu$spp1), sum(pu$spp2, na.rm = TRUE)))
+#> [1] TRUE
+
+all.equal(a1$relative_abundance,
+          c(sum(pu$spp1) / sum(pu$spp1),
+            sum(pu$spp2, na.rm = TRUE) / sum(pu$spp2, na.rm = TRUE)))
+#> [1] TRUE
+
+all.equal(a2$absolute_abundance,
+          c(sum(pu$spp1[!is.na(pu$cost)]),
+            sum(pu$spp2[!is.na(pu$cost)], na.rm = TRUE)))
+#> [1] TRUE
+
+all.equal(a2$relative_abundance,
+          c(sum(pu$spp1[!is.na(pu$cost)]) / sum(pu$spp1, na.rm = TRUE),
+            sum(pu$spp2[!is.na(pu$cost)], na.rm = TRUE) / sum(pu$spp2,
+                                                              na.rm = TRUE)))
+#> [1] TRUE
+
+# initialize conservation problem with raster data
+p3 <- problem(sim_pu_raster, sim_features)
+
+# calculate feature abundances; including planning units with NA costs
+a3 <- feature_abundances(p3, na.rm = FALSE) # (default)
+print(a3)
+#> # A tibble: 5 × 3
+#>   feature absolute_abundance relative_abundance
+#>   <chr>                <dbl>              <dbl>
+#> 1 layer.1               83.3                  1
+#> 2 layer.2               31.2                  1
+#> 3 layer.3               72.0                  1
+#> 4 layer.4               42.7                  1
+#> 5 layer.5               56.7                  1
+
+# create problem using total amounts of features in all the planning units
+# (including units with NA cost data)
+p4 <- p3 %>%
+      add_min_set_objective() %>%
+      add_relative_targets(a3$relative_abundance) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# attempt to solve the problem, but we will see that this problem is
+# infeasible because the targets cannot be met using only the planning units
+# with finite cost data
+# \dontrun{
+s4 <- try(solve(p4))
+#> Error in .local(a, b = b, ...) : 
+#>   no solution found (e.g., due to problem infeasibility or time limits)
+# }
+# calculate feature abundances; excluding planning units with NA costs
+a5 <- feature_abundances(p3, na.rm = TRUE)
+print(a5)
+#> # A tibble: 5 × 3
+#>   feature absolute_abundance relative_abundance
+#>   <chr>                <dbl>              <dbl>
+#> 1 layer.1               74.5              0.895
+#> 2 layer.2               28.1              0.900
+#> 3 layer.3               64.9              0.902
+#> 4 layer.4               38.2              0.895
+#> 5 layer.5               50.7              0.893
+
+# create problem using total amounts of features in the planning units with
+# finite cost data
+p5 <- p3 %>%
+      add_min_set_objective() %>%
+      add_relative_targets(a5$relative_abundance) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s5 <- solve(p5)
+
+# plot the solution
+# this solution contains all the planning units with finite cost data
+# (i.e., cost data that do not have NA values)
+plot(s5)
+
+# }
 
      
+
      + - - - - - - - - - - - + diff --git a/docs/reference/feature_names.html b/docs/reference/feature_names.html index 0e44a6225..89866267f 100644 --- a/docs/reference/feature_names.html +++ b/docs/reference/feature_names.html @@ -1,101 +1,18 @@ - - - - - - - -Feature names — feature_names • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Feature names — feature_names • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Feature names

      - Source: R/feature_names.R + Source: R/feature_names.R
      @@ -184,69 +101,63 @@

      Feature names

      Extract the names of the features in an object.

      - 
      feature_names(x)
-
-# S4 method for ConservationProblem
-feature_names(x)
-
-# S4 method for ZonesRaster
-feature_names(x)
+    
      Usage,
      feature_names(x)
 
-# S4 method for ZonesCharacter
-feature_names(x)
      
+# S4 method for ConservationProblem
+feature_names(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      problem() (i.e. ConservationProblem) or Zones()
-object.
      
+# S4 method for ZonesRaster
+feature_names(x)
 
-    
      Value
      
+# S4 method for ZonesCharacter
+feature_names(x)
      +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) or Zones() +object.

      +
      +
      +

      Value

      character feature names.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.2) %>%
-     add_binary_decisions()
-
-# print feature names
-print(feature_names(p))
-#> [1] "layer.1" "layer.2" "layer.3" "layer.4" "layer.5"
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.2) %>%
+     add_binary_decisions()
+
+# print feature names
+print(feature_names(p))
+#> [1] "layer.1" "layer.2" "layer.3" "layer.4" "layer.5"
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/importance.html b/docs/reference/importance.html index 1e88cd297..5f8d384b6 100644 --- a/docs/reference/importance.html +++ b/docs/reference/importance.html @@ -1,103 +1,20 @@ - - - - - - - -Evaluate solution importance — importance • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Evaluate solution importance — importance • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Evaluate solution importance

      - Source: R/importance.R + Source: R/importance.R

      Importance scores (also known as irreplaceability scores) can be used to assess the relative importance of planning units selected in a solution to a -conservation planning problem().

      +conservation planning problem().

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      The following methods are available for calculating importance scores:

      -
      - -
      eval_replacement_importance()

      Calculate importance scores using replacement costs (based +

      eval_replacement_importance()
      +

      Calculate importance scores using replacement costs (based on Cabeza and Moilanen 2006). These scores quantify the change in the objective -function (e.g. additional costs required to meet feature targets) of the +function (e.g., additional costs required to meet feature targets) of the optimal solution if a given planning unit in a solution cannot be acquired. They can (i) account for the cost of different planning units, (ii) account for multiple management zones, (iii) apply to any objective function, and (iv) identify truly irreplaceable planning units (denoted with infinite values).

      -
      eval_ferrier_importance()

      Calculate importance scores following Ferrier et al. (2000). + +

      eval_ferrier_importance()
      +

      Calculate importance scores following Ferrier et al. (2000). These scores measure importance based on how critical planning units are for meeting targets. They can only be applied to -conservation problems with a minimum set objective and a single zone (i.e. +conservation problems with a minimum set objective and a single zone (i.e., the classic Marxan-type problem). Furthermore---unlike the replacement cost scores---these scores provide a score for each feature within each planning unit, providing insight into why certain planning units are more important than other planning units.

      -
      eval_rare_richness_importance()

      Calculate importance scores using the rarity weighted richness metric + +

      eval_rare_richness_importance()
      +

      Calculate importance scores using the rarity weighted richness metric (based on Williams et al. 1996). These score are simply a measure of biodiversity. They do not account for planning costs, multiple management zones, objective @@ -224,24 +144,24 @@

      Details the importance of a planning unit for achieving conservation goals.

      -
      -

      Broadly speaking, we recommend using replacement cost scores where +

      Broadly speaking, we recommend using replacement cost scores where possible. This is because they can be applied to any type of conservation planning problem -- regardless of the objective function or number of zones considered in the problem -- and measure planning unit importance based on degradation of the prioritization. Although the replacement cost scores can be calculated for small and -moderate sized problems (e.g. less than 30,000 planning units), they may not -be feasible for particularly large problems (e.g. more than 100,000 planning +moderate sized problems (e.g., less than 30,000 planning units), they may not +be feasible for particularly large problems (e.g., more than 100,000 planning units). In such cases, we recommend calculating importance scores using the Ferrier method. This is because the Ferrier method can be calculated relatively quickly for large-sized problems and it explicitly accounts for representation targets. We only recommend using the rarity weighted richness metric when neither of the other two methods can be used.

      -

      References

      - +
      +
      +

      References

      Cabeza M and Moilanen A (2006) Replacement cost: A practical measure of site value for cost-effective reserve planning. Biological Conservation, 132: 336--342.

      @@ -253,78 +173,77 @@

      R (1996) A comparison of richness hotspots, rarity hotspots and complementary areas for conserving diversity using British birds. Conservation Biology, 10: 155--174.

      -

      See also

      - -

      Other overviews: -constraints, -decisions, -objectives, -penalties, -portfolios, -solvers, -summaries, -targets

      +
      +
      +

      See also

      +

      Other overviews: +constraints, +decisions, +objectives, +penalties, +portfolios, +solvers, +summaries, +targets

      +
      -

      Examples

      - 
      # \dontrun{
-# load data
-data(sim_pu_raster, sim_pu_polygons, sim_features)
-
-# build minimal conservation problem with raster data
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(gap = 0, verbose = FALSE)
-
-# solve the problem
-s1 <- solve(p1)
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-
-# calculate importance scores using replacement cost scores
-ir1 <- eval_replacement_importance(p1, s1)
-
-# calculate importance scores using Ferrier et al 2000 method,
-# and extract the total importance scores
-ir2 <- eval_ferrier_importance(p1, s1)[["total"]]
-
-# calculate importance scores using rarity weighted richness scores
-ir3 <- eval_rare_richness_importance(p1, s1)
-
-# plot importance scores
-plot(stack(ir1, ir2, ir3), axes = FALSE, box = FALSE,
-     main = c("replacement cost", "Ferrier score",
-              "rarity weighted richness"))
-
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# load data
+data(sim_pu_raster, sim_pu_polygons, sim_features)
+
+# build minimal conservation problem with raster data
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0, verbose = FALSE)
+
+# solve the problem
+s1 <- solve(p1)
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+
+# calculate importance scores using replacement cost scores
+ir1 <- eval_replacement_importance(p1, s1)
+
+# calculate importance scores using Ferrier et al 2000 method,
+# and extract the total importance scores
+ir2 <- eval_ferrier_importance(p1, s1)[["total"]]
+
+# calculate importance scores using rarity weighted richness scores
+ir3 <- eval_rare_richness_importance(p1, s1)
+
+# plot importance scores
+plot(stack(ir1, ir2, ir3), axes = FALSE, box = FALSE,
+     main = c("replacement cost", "Ferrier score",
+              "rarity weighted richness"))
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/index.html b/docs/reference/index.html index 4f875f4de..ddf973f0f 100644 --- a/docs/reference/index.html +++ b/docs/reference/index.html @@ -1,100 +1,18 @@ - - - - - - - -Function reference • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Function reference • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Reference

      - - - - - - - - - - -
      -

      Overview

      -

      Overview of the package

      + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - + - - - - + - - - - - - - - - - - - - - + - - - - + - - - + + + + + + + + + + - - - + + + + + + - - - + + - - - - - - + + + + - - - - - - - - - - - - - - - - - - - - - - - + - - - - + - - - - + - - - - + - - - - + - - - - - - - - - - - - - - + - - - - + - - - - + - - - - + + + - - - + + + + - - - - - - - - - - - - - - - - - + - - - - + - - - - + - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - + - - - - + - - - - - - - - - - - - - - + - - - - + - - - - + - - - - + - - - - + - - - - + - - - - - - - - - - - - - - + - - - - + - - - - - - - - - - - - + + - - - + + + + - - - - - - - - - - - - - + + + + + + - - - - - - - + - - - - + - - - - - - - - - - - - - - + - - - - + - - - - + - - - - - - - - - - - - - - + - - - - + - - - - - - - - - - - - - - + - - - - + - - - - + - - - - - - - - - - - - - - + - - - - + - - - - + - - - - + - - - - + - - - - + + + + + + + + + + + + + + + + + + + - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      +

      Overview

      +

      Overview of the package

      +

      prioritizr

      prioritizr: Systematic Conservation Prioritization in R

      -

      Create and solve problems

      -

      Functions for creating new problems and solving them

      +
      +

      Create and solve problems

      +

      Functions for creating new problems and solving them

      +

      problem()

      Conservation planning problem

      +

      marxan_problem()

      Marxan conservation problem

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      Solve

      -

      Data

      -

      Simulated datasets distributed with the package

      +
      +

      Data

      +

      Simulated datasets distributed with the package

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      Simulated conservation planning data

      -

      Objectives

      -

      Functions for adding an objective to a problem

      +
      +

      Objectives

      +

      Functions for adding an objective to a problem

      +

      objectives

      Add an objective

      +

      add_max_cover_objective()

      Add maximum coverage objective

      +

      add_max_features_objective()

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      Add minimum set objective

      +

      add_min_shortfall_objective()

      Add minimum shortfall objective

      -

      Targets

      -

      Functions for adding targets to a problem

      -
      -

      targets

      +
      +

      ArrayParameter-class

      Add representation targets

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      add_absolute_targets()

      Add absolute targets

      -

      add_loglinear_targets()

      +
      +

      add_binary_decisions()

      Add targets using log-linear scaling

      -

      add_manual_targets()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      Add manual targets

      -

      add_relative_targets()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      Add relative targets

      -

      Constraints

      -

      Functions for adding constraints to a problem

      -
      -

      constraints

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      Conservation problem constraints

      +

      Add connectivity penalties

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      Add contiguity constraints

      +
      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      Add feature contiguity constraints

      +
      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      Add linear constraints

      +
      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      add_locked_in_constraints()

      Add locked in constraints

      +

      add_locked_out_constraints()

      Add locked out constraints

      +
      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      add_mandatory_allocation_constraints(<ConservationProblem>)

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      Add manually specified locked constraints

      -

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +
      +

      add_manual_targets()

      Add neighbor constraints

      -

      Penalties

      -

      Functions for adding penalties to a problem

      -
      -

      penalties

      +

      Add manual targets

      +

      add_max_cover_objective()

      Add a penalty

      -

      add_boundary_penalties()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      Add boundary penalties

      -

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      Add connectivity penalties

      -

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      Add linear penalties

      -

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      Add feature weights

      -

      Decisions

      -

      Functions for specifying the type of decisions in a problem

      -
      -

      decisions

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      Add decision types

      -

      add_binary_decisions()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      Add binary decisions

      -

      add_default_decisions()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      Add default decisions

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      add_proportion_decisions()

      Add proportion decisions

      +
      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      add_semicontinuous_decisions()

      Add semi-continuous decisions

      -

      Solvers

      -

      Functions for specifying how a problem should be solved

      -
      -

      solvers

      +
      +

      add_shuffle_portfolio()

      Problem solvers

      -

      add_cbc_solver()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      Add a CBC solver

      -

      add_cplex_solver()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      Add a CPLEX solver

      -

      add_default_solver()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      Add a default solver

      -

      add_gurobi_solver()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Targets

      +

      Functions for adding targets to a problem

      +
      +

      targets

      +

      Add representation targets

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_relative_targets()

      +

      Add relative targets

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Constraints

      +

      Functions for adding constraints to a problem

      +
      +

      constraints

      +

      Conservation problem constraints

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_connected_constraints() add_corridor_constraints() set_number_of_threads() get_number_of_threads() is.parallel() add_pool_portfolio() connected_matrix() feature_representation() replacement_cost() rarity_weighted_richness() ferrier_score()

      +

      Deprecation notice

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Penalties

      +

      Functions for adding penalties to a problem

      +
      +

      penalties

      +

      Add a penalty

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Decisions

      +

      Functions for specifying the type of decisions in a problem

      +
      +

      decisions

      +

      Add decision types

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Solvers

      +

      Functions for specifying how a problem should be solved

      +
      +

      solvers

      +

      Problem solvers

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Portfolios

      +

      Functions for generating a portfolio of solutions

      +
      +

      portfolios

      +

      Solution portfolios

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      add_connected_constraints() add_corridor_constraints() set_number_of_threads() get_number_of_threads() is.parallel() add_pool_portfolio() connected_matrix() feature_representation() replacement_cost() rarity_weighted_richness() ferrier_score()

      +

      Deprecation notice

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Summary statistics

      +

      Functions for summarizing the performance of solutions

      +
      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Importance

      +

      Functions for calculating importance scores for a solution

      +
      +

      importance

      +

      Evaluate solution importance

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Data simulation

      +

      Functions for simulating new datasets

      +
      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      +

      Binary stack

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      compile()

      +

      Compile a problem

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      constraints

      +

      Conservation problem constraints

      +

      decisions

      +

      Add decision types

      +

      distribute_load()

      +

      Distribute load

      +

      eval_boundary_summary()

      +

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Evaluate solution connectivity

      +

      eval_cost_summary()

      +

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      +

      Evaluate feature representation

      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      +

      eval_n_summary()

      +

      Evaluate number of planning units selected

      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      +

      eval_target_coverage_summary()

      +

      Evaluate target coverage

      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      +

      importance

      +

      Evaluate solution importance

      +

      intersecting_units()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      +

      Is it?

      +

      loglinear_interpolation()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      +

      Matrix parameters

      +

      misc_parameter()

      +

      Miscellaneous parameter

      +

      new_id()

      +

      Identifier

      +

      new_optimization_problem()

      +

      Optimization problem

      +

      new_waiver()

      +

      Waiver

      +

      number_of_features()

      +

      Number of features

      +

      number_of_planning_units()

      +

      Number of planning units

      +

      number_of_total_units()

      +

      Number of total units

      +

      number_of_zones()

      +

      Number of zones

      +

      objectives

      +

      Add an objective

      +

      parameters()

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Geoprocessing

      +

      Functions for manipulating spatial datasets

      +
      +

      fast_extract()

      +

      Fast extract

      +

      intersecting_units()

      +

      Find intersecting units

      +

      Processing multi-zone data

      +

      Functions for manipulating data that pertain to multiple zones

      +
      +

      category_layer()

      +

      Category layer

      +

      category_vector()

      +

      Category vector

      +

      binary_stack()

      +

      Binary stack

      +

      Matrix functions

      +

      Functions for creating matrices that are used in conservation planning problems for use in planning problems

      +
      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      boundary_matrix()

      +

      Boundary matrix

      +

      branch_matrix()

      +

      Branch matrix

      +

      connectivity_matrix()

      +

      Connectivity matrix

      +

      marxan_boundary_data_to_matrix()

      +

      Convert Marxan boundary data to a matrix format

      +

      add_connected_constraints() add_corridor_constraints() set_number_of_threads() get_number_of_threads() is.parallel() add_pool_portfolio() connected_matrix() feature_representation() replacement_cost() rarity_weighted_richness() ferrier_score()

      +

      Deprecation notice

      +

      proximity_matrix()

      +

      Proximity matrix

      +

      rij_matrix()

      +

      Feature by planning unit matrix

      +

      ArrayParameter-class

      +

      Array parameter prototype

      +

      Collection-class

      +

      Collection prototype

      +

      ConservationModifier-class

      +

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      +

      Conservation problem class

      +

      Constraint-class

      +

      Constraint prototype

      +

      Decision-class

      +

      Decision prototype

      +

      MiscParameter-class

      +

      Miscellaneous parameter prototype

      +

      Objective-class

      +

      Objective prototype

      +

      OptimizationProblem-class

      +

      Optimization problem class

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      +

      Optimization problem methods

      +

      Parameter-class

      +

      Parameter class

      +

      Parameters-class

      +

      Parameters class

      +

      Penalty-class

      +

      Penalty prototype

      +

      Portfolio-class

      +

      Portfolio prototype

      +

      ScalarParameter-class

      +

      Scalar parameter prototype

      +

      Solver-class

      +

      Solver prototype

      +

      Target-class

      +

      Target prototype

      +

      add_absolute_targets()

      +

      Add absolute targets

      +

      add_binary_decisions()

      +

      Add binary decisions

      +

      add_boundary_penalties()

      +

      Add boundary penalties

      +

      add_cbc_solver()

      +

      Add a CBC solver

      +

      add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) add_connectivity_penalties(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add connectivity penalties

      +

      add_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>)

      +

      Add contiguity constraints

      +

      add_cplex_solver()

      +

      Add a CPLEX solver

      +

      add_cuts_portfolio()

      +

      Add Bender's cuts portfolio

      +

      add_default_decisions()

      +

      Add default decisions

      +

      add_default_solver()

      +

      Add a default solver

      +

      add_extra_portfolio()

      +

      Add an extra portfolio

      +

      add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<Matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<data.frame>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<matrix>) add_feature_contiguity_constraints(<ConservationProblem>,<ANY>,<ANY>)

      +

      Add feature contiguity constraints

      +

      add_feature_weights(<ConservationProblem>,<numeric>) add_feature_weights(<ConservationProblem>,<matrix>)

      +

      Add feature weights

      +

      add_gap_portfolio()

      +

      Add a gap portfolio

      +

      add_gurobi_solver()

      +

      Add a Gurobi solver

      +

      add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<character>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<numeric>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<Raster>) add_linear_constraints(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>)

      +

      Add linear constraints

      +

      add_linear_penalties(<ConservationProblem>,<ANY>,<character>) add_linear_penalties(<ConservationProblem>,<ANY>,<numeric>) add_linear_penalties(<ConservationProblem>,<ANY>,<matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Matrix>) add_linear_penalties(<ConservationProblem>,<ANY>,<Raster>) add_linear_penalties(<ConservationProblem>,<ANY>,<dgCMatrix>)

      +

      Add linear penalties

      +

      add_locked_in_constraints()

      +

      Add locked in constraints

      +

      add_locked_out_constraints()

      +

      Add locked out constraints

      +

      add_loglinear_targets()

      +

      Add targets using log-linear scaling

      +

      add_lpsymphony_solver()

      +

      Add a SYMPHONY solver with lpsymphony

      +

      add_mandatory_allocation_constraints(<ConservationProblem>)

      +

      Add mandatory allocation constraints

      +

      add_manual_bounded_constraints()

      +

      Add manually specified bound constraints

      +

      add_manual_locked_constraints()

      +

      Add manually specified locked constraints

      +

      add_manual_targets()

      +

      Add manual targets

      +

      add_max_cover_objective()

      +

      Add maximum coverage objective

      +

      add_max_features_objective()

      +

      Add maximum feature representation objective

      +

      add_max_phylo_div_objective()

      +

      Add maximum phylogenetic diversity objective

      +

      add_max_phylo_end_objective()

      +

      Add maximum phylogenetic endemism objective

      +

      add_max_utility_objective()

      +

      Add maximum utility objective

      +

      add_min_largest_shortfall_objective()

      +

      Add minimum largest shortfall objective

      +

      add_min_set_objective()

      +

      Add minimum set objective

      +

      add_min_shortfall_objective()

      +

      Add minimum shortfall objective

      +

      add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<ANY>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<matrix>) add_neighbor_constraints(<ConservationProblem>,<ANY>,<ANY>,<array>)

      +

      Add neighbor constraints

      +

      add_proportion_decisions()

      +

      Add proportion decisions

      +

      add_relative_targets()

      +

      Add relative targets

      +

      add_rsymphony_solver()

      +

      Add a SYMPHONY solver with Rsymphony

      +

      add_semicontinuous_decisions()

      +

      Add semi-continuous decisions

      +

      add_shuffle_portfolio()

      +

      Add a shuffle portfolio

      +

      add_top_portfolio()

      +

      Add a top portfolio

      +

      adjacency_matrix()

      +

      Adjacency matrix

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      +

      Array parameters

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      +

      Coerce object to another object

      +

      as.list(<OptimizationProblem>)

      +

      Convert OptimizationProblem to list

      +

      binary_stack()

      Add a Gurobi solver

      -

      add_lpsymphony_solver()

      +

      Binary stack

      +

      boundary_matrix()

      Add a SYMPHONY solver with lpsymphony

      -

      add_rsymphony_solver()

      +

      Boundary matrix

      +

      branch_matrix()

      Add a SYMPHONY solver with Rsymphony

      -

      Portfolios

      -

      Functions for generating a portfolio of solutions

      -
      -

      portfolios

      +

      Branch matrix

      +

      category_layer()

      Solution portfolios

      -

      add_cuts_portfolio()

      +

      Category layer

      +

      category_vector()

      Add Bender's cuts portfolio

      -

      add_extra_portfolio()

      +

      Category vector

      +

      compile()

      Add an extra portfolio

      -

      add_gap_portfolio()

      +

      Compile a problem

      +

      connectivity_matrix()

      Add a gap portfolio

      -

      add_shuffle_portfolio()

      +

      Connectivity matrix

      +

      constraints

      Add a shuffle portfolio

      -

      add_top_portfolio()

      +

      Conservation problem constraints

      +

      decisions

      Add a top portfolio

      -

      Summary statistics

      -

      Functions for summarizing the performance of solutions

      -
      -

      summaries

      +

      Add decision types

      +

      distribute_load()

      Evaluate solutions using summary statistics

      +

      Distribute load

      eval_boundary_summary()

      Evaluate solution boundary length

      +

      eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<Matrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<data.frame>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<dgCMatrix>) eval_connectivity_summary(<ConservationProblem>,<ANY>,<ANY>,<array>)

      Evaluate solution connectivity

      +

      eval_cost_summary()

      Evaluate solution cost

      +

      eval_feature_representation_summary()

      Evaluate feature representation

      +
      +

      eval_ferrier_importance()

      +

      Evaluate solution importance using Ferrier scores

      eval_n_summary()

      Evaluate number of planning units selected

      +
      +

      eval_rare_richness_importance()

      +

      Evaluate solution importance using rarity weighted richness scores

      +

      eval_replacement_importance()

      +

      Evaluate solution importance using replacement cost scores

      eval_target_coverage_summary()

      Evaluate target coverage

      -

      Importance

      -

      Functions for calculating importance scores for a solution

      -
      +
      +

      fast_extract()

      +

      Fast extract

      +

      feature_abundances()

      +

      Feature abundances

      +

      feature_names()

      +

      Feature names

      importance

      Evaluate solution importance

      -

      eval_ferrier_importance()

      +
      +

      intersecting_units()

      Evaluate solution importance using Ferrier scores

      -

      eval_rare_richness_importance()

      +

      Find intersecting units

      +

      is.Id() is.Waiver()

      Evaluate solution importance using rarity weighted richness scores

      -

      eval_replacement_importance()

      +

      Is it?

      +

      loglinear_interpolation()

      Evaluate solution importance using replacement cost scores

      -

      Data simulation

      -

      Functions for simulating new datasets

      -
      -

      simulate_cost()

      +

      Log-linear interpolation

      +

      marxan_boundary_data_to_matrix()

      Simulate cost data

      -

      simulate_data()

      +

      Convert Marxan boundary data to a matrix format

      +

      marxan_problem()

      Simulate data

      -

      simulate_species()

      +

      Marxan conservation problem

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      Simulate species habitat suitability data

      -

      Geoprocessing

      -

      Functions for manipulating spatial datasets

      -
      -

      fast_extract()

      +

      Matrix parameters

      +

      misc_parameter()

      Fast extract

      -

      intersecting_units()

      +

      Miscellaneous parameter

      +

      new_id()

      Find intersecting units

      -

      Processing multi-zone data

      -

      Functions for manipulating data that pertain to multiple zones

      -
      -

      category_layer()

      +

      Identifier

      +

      new_optimization_problem()

      Category layer

      -

      category_vector()

      +

      Optimization problem

      +

      new_waiver()

      Category vector

      -

      binary_stack()

      +

      Waiver

      +

      number_of_features()

      Binary stack

      -

      Matrix functions

      -

      Functions for creating matrices that are used in conservation planning problems for use in planning problems

      -
      -

      adjacency_matrix()

      +

      Number of features

      +

      number_of_planning_units()

      Adjacency matrix

      -

      boundary_matrix()

      +

      Number of planning units

      +

      number_of_total_units()

      Boundary matrix

      -

      branch_matrix()

      +

      Number of total units

      +

      number_of_zones()

      Branch matrix

      -

      connectivity_matrix()

      +

      Number of zones

      +

      objectives

      Connectivity matrix

      -

      marxan_boundary_data_to_matrix()

      +

      Add an objective

      +

      parameters()

      Convert Marxan boundary data to a matrix format

      +

      Parameters

      +

      penalties

      +

      Add a penalty

      +

      %>%

      +

      Pipe operator

      +

      portfolios

      +

      Solution portfolios

      +

      pproto()

      +

      Create a new pproto object

      +

      predefined_optimization_problem()

      +

      Predefined optimization problem

      +

      presolve_check()

      +

      Presolve check

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      +

      Print

      +

      prioritizr

      +

      prioritizr: Systematic Conservation Prioritization in R

      +

      problem()

      +

      Conservation planning problem

      proximity_matrix()

      Proximity matrix

      +

      rij_matrix()

      Feature by planning unit matrix

      -

      Problem manipulation functions

      -

      Functions for extracting information from problems

      +
      +

      run_calculations()

      +

      Run calculations

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      +

      Scalar parameters

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      +

      Show

      +

      sim_pu_polygons sim_pu_zones_polygons sim_pu_points sim_pu_lines sim_pu_sf sim_pu_zones_sf sim_pu_raster sim_locked_in_raster sim_locked_out_raster sim_pu_zones_stack sim_features sim_features_zones sim_phylogeny

      +

      Simulated conservation planning data

      +

      simulate_cost()

      +

      Simulate cost data

      +

      simulate_data()

      +

      Simulate data

      +

      simulate_species()

      +

      Simulate species habitat suitability data

      +

      solve(<OptimizationProblem>,<Solver>) solve(<ConservationProblem>,<missing>)

      +

      Solve

      +

      solvers

      +

      Problem solvers

      +

      summaries

      +

      Evaluate solutions using summary statistics

      +

      targets

      +

      Add representation targets

      +

      %T>%

      +

      Tee operator

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      +

      Manipulate tibbles

      +

      write_problem()

      +

      Write problem

      +

      zone_names()

      +

      Zone names

      +

      zones()

      +

      Management zones

      +

      Problem manipulation functions

      +

      Functions for extracting information from problems

      +

      number_of_features()

      Number of features

      +

      number_of_planning_units()

      Number of planning units

      +

      number_of_total_units()

      Number of total units

      +

      number_of_zones()

      Number of zones

      +

      feature_names()

      Feature names

      +

      feature_abundances()

      Feature abundances

      +

      zone_names()

      Zone names

      -

      Miscellaneous functions

      -

      Assorted functions distributed with the package

      +
      +

      Miscellaneous functions

      +

      Assorted functions distributed with the package

      +

      print(<ConservationProblem>) print(<ConservationModifier>) print(<Id>) print(<Id>) print(<OptimizationProblem>) print(<ScalarParameter>) print(<ArrayParameter>) print(<Solver>) print(<Zones>) print(<tbl_df>)

      Print

      +

      show(<ConservationModifier>) show(<ConservationProblem>) show(<Id>) show(<OptimizationProblem>) show(<Parameter>) show(<Solver>)

      Show

      -

      %>%

      +
      +

      %>%

      Pipe operator

      -

      %T>%

      +
      +

      %T>%

      Tee operator

      +

      is.Id() is.Waiver()

      Is it?

      +

      as.Id() as.list(<Parameters>) as.list(<Zones>)

      Coerce object to another object

      +

      compile()

      Compile a problem

      +

      presolve_check()

      Presolve check

      +

      loglinear_interpolation()

      Log-linear interpolation

      +

      run_calculations()

      Run calculations

      +

      distribute_load()

      Distribute load

      +

      write_problem()

      Write problem

      -

      Class definitions and methods

      -

      These pages document the package’s internal data structures and functions for manipulating them—they contain information that is really only useful when adding new functionality to the package

      +
      +

      Class definitions and methods

      +

      These pages document the package’s internal data structures and functions for manipulating them—they contain information that is really only useful when adding new functionality to the package

      +

      new_id()

      Identifier

      +

      new_waiver()

      Waiver

      +

      pproto()

      Create a new pproto object

      +

      new_optimization_problem()

      Optimization problem

      +

      predefined_optimization_problem()

      Predefined optimization problem

      +

      as.list(<OptimizationProblem>)

      Convert OptimizationProblem to list

      +

      ArrayParameter-class

      Array parameter prototype

      +

      Collection-class

      Collection prototype

      +

      ConservationModifier-class

      Conservation problem modifier prototype

      +

      ConservationProblem-class

      Conservation problem class

      +

      Constraint-class

      Constraint prototype

      +

      Decision-class

      Decision prototype

      +

      MiscParameter-class

      Miscellaneous parameter prototype

      +

      Objective-class

      Objective prototype

      +

      OptimizationProblem-class

      Optimization problem class

      +

      Parameter-class

      Parameter class

      +

      Parameters-class

      Parameters class

      +

      Penalty-class

      Penalty prototype

      +

      Portfolio-class

      Portfolio prototype

      +

      ScalarParameter-class

      Scalar parameter prototype

      +

      Solver-class

      Solver prototype

      +

      Target-class

      Target prototype

      +

      zones()

      Management zones

      +

      nrow() ncol() ncell() modelsense() vtype() obj() A() rhs() sense() lb() ub() col_ids() row_ids() compressed_formulation()

      Optimization problem methods

      +

      nrow(<tbl_df>) ncol(<tbl_df>) as.list(<tbl_df>)

      Manipulate tibbles

      -

      Parameter definitions

      -

      These pages document the package’s internal data structures for representing different types of variables—they contain information that is really only useful when adding new functionality to the package

      +
      +

      Parameter definitions

      +

      These pages document the package’s internal data structures for representing different types of variables—they contain information that is really only useful when adding new functionality to the package

      +

      proportion_parameter_array() binary_parameter_array() integer_parameter_array() numeric_parameter_array()

      Array parameters

      +

      numeric_matrix_parameter() binary_matrix_parameter()

      Matrix parameters

      +

      misc_parameter()

      Miscellaneous parameter

      +

      proportion_parameter() binary_parameter() integer_parameter() numeric_parameter()

      Scalar parameters

      +

      parameters()

      Parameters

      -

      Deprecated functions

      +
      +

      Deprecated functions

      +

      add_connected_constraints() add_corridor_constraints() set_number_of_threads() get_number_of_threads() is.parallel() add_pool_portfolio() connected_matrix() feature_representation() replacement_cost() rarity_weighted_richness() ferrier_score()

      Deprecation notice

      - +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/intersecting_units.html b/docs/reference/intersecting_units.html index c2dacf2dc..088f7c14f 100644 --- a/docs/reference/intersecting_units.html +++ b/docs/reference/intersecting_units.html @@ -1,102 +1,19 @@ - - - - - - - -Find intersecting units — intersecting_units • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Find intersecting units — intersecting_units • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Find intersecting units

      - Source: R/intersecting_units.R + Source: R/intersecting_units.R
      @@ -186,132 +103,125 @@

      Find intersecting units

      with the units in another spatial data object.

      - 
      intersecting_units(x, y)
+    
      Usage,
      intersecting_units(x, y)
 
-# S4 method for Raster,Raster
-intersecting_units(x, y)
+# S4 method for Raster,Raster
+intersecting_units(x, y)
 
-# S4 method for Spatial,Spatial
-intersecting_units(x, y)
+# S4 method for Spatial,Spatial
+intersecting_units(x, y)
 
-# S4 method for sf,Spatial
-intersecting_units(x, y)
+# S4 method for sf,Spatial
+intersecting_units(x, y)
 
-# S4 method for Spatial,Raster
-intersecting_units(x, y)
+# S4 method for Spatial,Raster
+intersecting_units(x, y)
 
-# S4 method for Spatial,sf
-intersecting_units(x, y)
+# S4 method for Spatial,sf
+intersecting_units(x, y)
 
-# S4 method for Raster,Spatial
-intersecting_units(x, y)
+# S4 method for Raster,Spatial
+intersecting_units(x, y)
 
-# S4 method for sf,sf
-intersecting_units(x, y)
+# S4 method for sf,sf
+intersecting_units(x, y)
 
-# S4 method for Raster,sf
-intersecting_units(x, y)
+# S4 method for Raster,sf
+intersecting_units(x, y)
 
-# S4 method for sf,Raster
-intersecting_units(x, y)
+# S4 method for sf,Raster
+intersecting_units(x, y)
 
-# S4 method for data.frame,ANY
-intersecting_units(x, y)
      
-
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
      x
      Spatial or Raster object.
      y
      Spatial or Raster object.
      
-
-    
      Value
      
+# S4 method for data.frame,ANY
+intersecting_units(x, y)
      +
      +

      Arguments

      +
      x
      +

      Spatial or Raster object.

      +
      y
      +

      Spatial or Raster object.

      +
      +
      +

      Value

      integer indices of the units in x that intersect with y.

      -

      See also

      - -

      fast_extract().

      +
      +
      +

      See also

      +

      fast_extract().

      +
      -

      Examples

      - 
      # create data
-r <- raster(matrix(1:9, byrow = TRUE, ncol=3))
-r_with_holes <- r
-r_with_holes[c(1, 5, 9)] <- NA
-ply <- rasterToPolygons(r)
-ply_with_holes <- st_as_sf(rasterToPolygons(r_with_holes))
-
-# intersect raster with raster
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(r, main = "x=Raster")
-plot(r_with_holes, main = "y=Raster")
-
-# }
-print(intersecting_units(r, r_with_holes))
-#> [1] 2 3 4 6 7 8
-
-# intersect raster with polygons (sf)
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(r, main = "x=Raster")
-plot(ply_with_holes, main = "y=sf", key.pos = NULL, reset = FALSE)
-
-# }
-print(intersecting_units(r, ply_with_holes))
-#> [1] 2 3 4 6 7 8
-
-# intersect polygons (Spatial) with raster
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(ply, main = "x=Spatial")
-plot(r_with_holes, main = "y=Raster")
-
-# }
-print(intersecting_units(ply, r_with_holes))
-#> [1] 2 3 4 5 6 7 8
-
-# intersect polygons (Spatial) with polygons (sf)
-# \dontrun{
-par(mfrow = c(1, 2))
-plot(ply, main = "x=Spatial")
-plot(ply_with_holes, main = "y=sf", key.pos = NULL, reset = FALSE)
-
-# }
-print(intersecting_units(ply, ply_with_holes))
-#> [1] 2 3 4 6 7 8
-
+    
      
+    
      Examples
      
+    
      # create data
+r <- raster(matrix(1:9, byrow = TRUE, ncol=3))
+r_with_holes <- r
+r_with_holes[c(1, 5, 9)] <- NA
+ply <- rasterToPolygons(r)
+ply_with_holes <- st_as_sf(rasterToPolygons(r_with_holes))
+
+# intersect raster with raster
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(r, main = "x=Raster")
+plot(r_with_holes, main = "y=Raster")
+
+# }
+print(intersecting_units(r, r_with_holes))
+#> [1] 2 3 4 6 7 8
+
+# intersect raster with polygons (sf)
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(r, main = "x=Raster")
+plot(ply_with_holes, main = "y=sf", key.pos = NULL, reset = FALSE)
+
+# }
+print(intersecting_units(r, ply_with_holes))
+#> [1] 2 3 4 6 7 8
+
+# intersect polygons (Spatial) with raster
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(ply, main = "x=Spatial")
+plot(r_with_holes, main = "y=Raster")
+
+# }
+print(intersecting_units(ply, r_with_holes))
+#> [1] 2 3 4 5 6 7 8
+
+# intersect polygons (Spatial) with polygons (sf)
+# \dontrun{
+par(mfrow = c(1, 2))
+plot(ply, main = "x=Spatial")
+plot(ply_with_holes, main = "y=sf", key.pos = NULL, reset = FALSE)
+
+# }
+print(intersecting_units(ply, ply_with_holes))
+#> [1] 2 3 4 6 7 8
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/is.html b/docs/reference/is.html index 350b69040..27a418ab7 100644 --- a/docs/reference/is.html +++ b/docs/reference/is.html @@ -1,101 +1,18 @@ - - - - - - - -Is it? — is.Id • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Is it? — is.Id • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Is it?

      - Source: R/Id.R, R/misc.R + Source: R/Id.R, R/misc.R
      @@ -184,47 +101,39 @@

      Is it?

      Test if an object inherits from a class.

      - 
      is.Id(x)
-
-is.Waiver(x)
      +
      Usage,
      is.Id(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      Object.
      
-
-    
      Value
      
+is.Waiver(x)
      +
      +

      Arguments

      +
      x
      +

      Object.

      +
      +
      +

      Value

      logical indicating if it inherits from the class.

      +
      +
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- +
      -
      -

      Log-linear interpolation

      - Source: R/loglinear_interpolation.R + Source: R/loglinear_interpolation.R
      @@ -184,129 +101,116 @@

      Log-linear interpolation

      Log-linearly interpolate values between two thresholds.

      - 
      loglinear_interpolation(
-  x,
-  coordinate_one_x,
-  coordinate_one_y,
-  coordinate_two_x,
-  coordinate_two_y
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - -
      x

      numeric x values for which interpolate y -values.

      coordinate_one_x

      numeric value for lower x-coordinate.

      coordinate_one_y

      numeric value for lower y-coordinate.

      coordinate_two_x

      numeric value for upper x-coordinate.

      coordinate_two_y

      numeric value for upper y-coordinate.

      - -

      Value

      - +
      Usage,
      loglinear_interpolation(
+  x,
+  coordinate_one_x,
+  coordinate_one_y,
+  coordinate_two_x,
+  coordinate_two_y
+)
      + +
      +

      Arguments

      +
      x
      +

      numeric x values for which interpolate y +values.

      +
      coordinate_one_x
      +

      numeric value for lower x-coordinate.

      +
      coordinate_one_y
      +

      numeric value for lower y-coordinate.

      +
      coordinate_two_x
      +

      numeric value for upper x-coordinate.

      +
      coordinate_two_y
      +

      numeric value for upper y-coordinate.

      +
      +
      +

      Value

      numeric values.

      -

      Details

      - +
      +
      +

      Details

      Values are log-linearly interpolated at the x-coordinates specified in x using the lower and upper coordinate arguments to define the line. Values lesser or greater than these numbers are assigned the minimum and maximum y coordinates.

      +
      -

      Examples

      - 
      # create series of x-values
-x <- seq(0, 1000)
-
-# interpolate y-values for the x-values given the two reference points:
-# (200, 100) and (900, 15)
-y <- loglinear_interpolation(x, 200, 100, 900, 15)
-
-# plot the interpolated values
-# \dontrun{
-plot(y ~ x)
-
-# add the reference points to the plot (shown in red)
-points(x = c(200, 900), y = c(100, 15), pch = 18, col = "red", cex = 2)
-
-# }
-
-# this function can also be used to calculate representation targets
-# following Rodrigues et al. (2014). For example, let's say that
-# we had a set of species we were interested in calculating representation
-# targets for and we had information on their range sizes (in km^2).
-spp_range_size_km2 <- seq(0.01, 15000000, by = 100)
-
-# we can now use this function to calculate representation targets
-# (expressed as a percentage of the species' range sizes) using
-# the thresholds and cap sizes reported by Rodrigues et al. 2014
-spp_target_percentage_rodrigues <-
-  loglinear_interpolation(
-    x = spp_range_size_km2,
-    coordinate_one_x = 1000,
-    coordinate_one_y = 1,
-    coordinate_two_x = 250000,
-    coordinate_two_y = 0.1) * 100
-
-# it is also common to apply a cap to the representation targets,
-# so let's apply the cap these targets following Butchart et al. (2015)
-spp_target_percentage_butchart <- ifelse(
-  spp_range_size_km2 >= 10000000,
-  (1000000 / spp_range_size_km2) * 100,
-  spp_target_percentage_rodrigues)
-
-# plot species range sizes and representation targets
-plot(spp_target_percentage_butchart ~ spp_range_size_km2,
-  xlab = "Range size km^2" , ylab = "Representation target (%)", type = "l")
-
-
-# plot species range sizes and representation targets on a log10 scale
-plot(spp_target_percentage_butchart ~ log10(spp_range_size_km2),
-  xlab = "Range size km^2" , ylab = "Representation target (%)",
-  type = "l", xaxt = "n")
-axis(1, pretty(log10(spp_range_size_km2)),
-     10^pretty(log10(spp_range_size_km2))) 
-
-
+    
      
+    
      Examples
      
+    
      # create series of x-values
+x <- seq(0, 1000)
+
+# interpolate y-values for the x-values given the two reference points:
+# (200, 100) and (900, 15)
+y <- loglinear_interpolation(x, 200, 100, 900, 15)
+
+# plot the interpolated values
+# \dontrun{
+plot(y ~ x)
+
+# add the reference points to the plot (shown in red)
+points(x = c(200, 900), y = c(100, 15), pch = 18, col = "red", cex = 2)
+
+# }
+
+# this function can also be used to calculate representation targets
+# following Rodrigues et al. (2014). For example, let's say that
+# we had a set of species we were interested in calculating representation
+# targets for and we had information on their range sizes (in km^2).
+spp_range_size_km2 <- seq(0.01, 15000000, by = 100)
+
+# we can now use this function to calculate representation targets
+# (expressed as a percentage of the species' range sizes) using
+# the thresholds and cap sizes reported by Rodrigues et al. 2014
+spp_target_percentage_rodrigues <-
+  loglinear_interpolation(
+    x = spp_range_size_km2,
+    coordinate_one_x = 1000,
+    coordinate_one_y = 1,
+    coordinate_two_x = 250000,
+    coordinate_two_y = 0.1) * 100
+
+# it is also common to apply a cap to the representation targets,
+# so let's apply the cap these targets following Butchart et al. (2015)
+spp_target_percentage_butchart <- ifelse(
+  spp_range_size_km2 >= 10000000,
+  (1000000 / spp_range_size_km2) * 100,
+  spp_target_percentage_rodrigues)
+
+# plot species range sizes and representation targets
+plot(spp_target_percentage_butchart ~ spp_range_size_km2,
+  xlab = "Range size km^2" , ylab = "Representation target (%)", type = "l")
+
+
+# plot species range sizes and representation targets on a log10 scale
+plot(spp_target_percentage_butchart ~ log10(spp_range_size_km2),
+  xlab = "Range size km^2" , ylab = "Representation target (%)",
+  type = "l", xaxt = "n")
+axis(1, pretty(log10(spp_range_size_km2)),
+     10^pretty(log10(spp_range_size_km2))) 
+
+
 
      
+
      +
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zK)IHXTSnB46!?6S*e(rx?7Nh(x+^!iF!3_`+`03tlxzd(L0=62dTftKW8bGf3O@HL zbj)F%8A8Zy9M1k5@~+mOo^AxW=+r%RS8!#iSnUQ2fGfIH5Zwb}f6=Ckz+$2!ecMiS;!LZ)%EooNGbh<@V`?kM5ltG)a%fxe zjD^_*j#o=0sHlt*hut^pgH4=H->2;C9HE2r4C(BrO|8K!M$~o}QR>p=r4VK3Eo2LQ z(qS> - - - - - - -Convert Marxan boundary data to a matrix format — marxan_boundary_data_to_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Convert Marxan boundary data to a matrix format — marxan_boundary_data_to_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Convert Marxan boundary data to a matrix format

      - Source: R/marxan_boundary_data_to_matrix.R + Source: R/marxan_boundary_data_to_matrix.R
      @@ -190,116 +107,108 @@

      Convert Marxan boundary data to a matrix format

      Convert a data.frame object that follows the Marxan format to a matrix format. This function is useful for converting data.frame objects to matrix or array objects that -are used by the various penalties and -constraints functions. If the boundary data contains data for +are used by the various penalties and +constraints functions. If the boundary data contains data for a single zone, then a matrix object is returned. Otherwise if the boundary data contains data for multiple zones, then an array is returned.

      - 
      marxan_boundary_data_to_matrix(x, data)
      +
      Usage,
      marxan_boundary_data_to_matrix(x, data)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object that +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object that contains planning unit and zone data to ensure that the argument to data is converted correctly. This argument can be set to -NULL if checks are not required (not recommended).

      data

      data.frame object with the columns "id1", +NULL if checks are not required (not recommended).

      +
      data
      +

      data.frame object with the columns "id1", "id2", and "boundary". The columns "zone1" and -"zone2" can also be provided to indicate zone data.

      - -

      Value

      - -

      array or dgCMatrix sparse matrix object.

      +"zone2" can also be provided to indicate zone data.

      +
      +
      +

      Value

      +

      array or dgCMatrix sparse matrix object.

      +
      -

      Examples

      - 
      # create marxan boundary with four planning units and one zone
-bldf1 <- expand.grid(id1 = seq_len(4), id2 = seq_len(4))
-bldf1$boundary <- 1
-bldf1$boundary[bldf1$id1 == bldf1$id2] <- 0.5
-
-# convert to matrix
-m1 <- marxan_boundary_data_to_matrix(NULL, bldf1)
-
-# visualize matrix
-# \dontrun{
-image(m1)
-
-# }
-# create marxan boundary with three planning units and two zones
-bldf2 <- expand.grid(id1 = seq_len(3), id2 = seq_len(3),
-                     zone1 = c("z1", "z2"),
-                     zone2 = c("z1", "z2"))
-bldf2$boundary <- 1
-bldf2$boundary[bldf2$id1 == bldf2$id2 & bldf2$zone1 == bldf2$zone2] <- 0.5
-bldf2$boundary[bldf2$id1 == bldf2$id2 & bldf2$zone1 != bldf2$zone2] <- 0
-
-# convert to array
-m2 <- marxan_boundary_data_to_matrix(NULL, bldf2)
-
-# print array
-print(m2)
-#> , , 1, 1
-#> 
-#>      [,1] [,2] [,3]
-#> [1,]  0.5  1.0  1.0
-#> [2,]  1.0  0.5  1.0
-#> [3,]  1.0  1.0  0.5
-#> 
-#> , , 2, 1
-#> 
-#>      [,1] [,2] [,3]
-#> [1,]    0    1    1
-#> [2,]    1    0    1
-#> [3,]    1    1    0
-#> 
-#> , , 1, 2
-#> 
-#>      [,1] [,2] [,3]
-#> [1,]    0    1    1
-#> [2,]    1    0    1
-#> [3,]    1    1    0
-#> 
-#> , , 2, 2
-#> 
-#>      [,1] [,2] [,3]
-#> [1,]  0.5  1.0  1.0
-#> [2,]  1.0  0.5  1.0
-#> [3,]  1.0  1.0  0.5
-#> 
+    
      
+    
      Examples
      
+    
      # create marxan boundary with four planning units and one zone
+bldf1 <- expand.grid(id1 = seq_len(4), id2 = seq_len(4))
+bldf1$boundary <- 1
+bldf1$boundary[bldf1$id1 == bldf1$id2] <- 0.5
+
+# convert to matrix
+m1 <- marxan_boundary_data_to_matrix(NULL, bldf1)
+
+# visualize matrix
+# \dontrun{
+image(m1)
+
+# }
+# create marxan boundary with three planning units and two zones
+bldf2 <- expand.grid(id1 = seq_len(3), id2 = seq_len(3),
+                     zone1 = c("z1", "z2"),
+                     zone2 = c("z1", "z2"))
+bldf2$boundary <- 1
+bldf2$boundary[bldf2$id1 == bldf2$id2 & bldf2$zone1 == bldf2$zone2] <- 0.5
+bldf2$boundary[bldf2$id1 == bldf2$id2 & bldf2$zone1 != bldf2$zone2] <- 0
+
+# convert to array
+m2 <- marxan_boundary_data_to_matrix(NULL, bldf2)
+
+# print array
+print(m2)
+#> , , 1, 1
+#> 
+#>      [,1] [,2] [,3]
+#> [1,]  0.5  1.0  1.0
+#> [2,]  1.0  0.5  1.0
+#> [3,]  1.0  1.0  0.5
+#> 
+#> , , 2, 1
+#> 
+#>      [,1] [,2] [,3]
+#> [1,]    0    1    1
+#> [2,]    1    0    1
+#> [3,]    1    1    0
+#> 
+#> , , 1, 2
+#> 
+#>      [,1] [,2] [,3]
+#> [1,]    0    1    1
+#> [2,]    1    0    1
+#> [3,]    1    1    0
+#> 
+#> , , 2, 2
+#> 
+#>      [,1] [,2] [,3]
+#> [1,]  0.5  1.0  1.0
+#> [2,]  1.0  0.5  1.0
+#> [3,]  1.0  1.0  0.5
+#> 
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/marxan_problem.html b/docs/reference/marxan_problem.html index 9c7d754e7..bb7f7cac1 100644 --- a/docs/reference/marxan_problem.html +++ b/docs/reference/marxan_problem.html @@ -1,104 +1,21 @@ - - - - - - - -Marxan conservation problem — marxan_problem • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Marxan conservation problem — marxan_problem • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Marxan conservation problem

      - Source: R/marxan_problem.R + Source: R/marxan_problem.R
      -

      Create a conservation planning problem() following the +

      Create a conservation planning problem() following the mathematical formulations used in Marxan (detailed in Beyer et al. 2016). Note that these problems are solved using -exact algorithms and not simulated annealing (i.e. the Marxan software).

      +exact algorithms and not simulated annealing (i.e., the Marxan software).

      - 
      marxan_problem(x, ...)
+    
      Usage,
      marxan_problem(x, ...)
 
-# S3 method for default
-marxan_problem(x, ...)
+# S3 method for default
+marxan_problem(x, ...)
 
-# S3 method for data.frame
-marxan_problem(x, spec, puvspr, bound = NULL, blm = 0, ...)
+# S3 method for data.frame
+marxan_problem(x, spec, puvspr, bound = NULL, blm = 0, ...)
 
-# S3 method for character
-marxan_problem(x, ...)
      
+# S3 method for character
+marxan_problem(x, ...)
      -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - - - - - -
      x

      character file path for a Marxan input file (typically +

      +

      Arguments

      +
      x
      +

      character file path for a Marxan input file (typically called "input.dat"), or data.frame containing planning unit data (typically called "pu.dat"). If the argument to x is a data.frame, then each row corresponds to a different planning unit, and it must have the following columns:

      -
      - -
      id

      integer unique identifier for each planning unit. +

      id
      +

      integer unique identifier for each planning unit. These identifiers are used in the argument to puvspr.

      -
      cost

      numeric cost of each planning unit.

      -
      status

      integer indicating if each planning unit +

      cost
      +

      numeric cost of each planning unit.

      + + +
      status
      +

      integer indicating if each planning unit should not be locked in the solution (0) or if it should be locked in (2) or locked out (3) of the solution. Although Marxan allows planning units to be selected in the initial solution (using values of 1), these values have no effect here. This column is optional.

      -
      ...

      not used.

      spec

      data.frame containing information on the features. + + +

      ...
      +

      not used.

      +
      spec
      +

      data.frame containing information on the features. The argument to spec must follow the conventions used by Marxan for the species data file (conventionally called "spec.dat"). Each row corresponds to a different feature and @@ -242,85 +157,94 @@

      Arg spec must contain at least one column named "prop" or "amount"---but not both columns with both of these names---to specify the target for each feature.

      -
      - -
      id

      integer unique identifier for each feature +

      id
      +

      integer unique identifier for each feature These identifiers are used in the argument to puvspr.

      -
      name

      character name for each feature.

      -
      prop

      numeric relative target for each feature -(optional).

      ' +
      name
      +

      character name for each feature.

      + + +
      prop
      +

      numeric relative target for each feature +(optional).

      +' -
      amount

      numeric absolute target for each +

      amount
      +

      numeric absolute target for each feature (optional).

      -

      puvspr

      data.frame containing information on the amount of + + +

      puvspr
      +

      data.frame containing information on the amount of each feature in each planning unit. The argument to puvspr must follow the conventions used in the Marxan input data file (conventionally called "puvspr.dat"). It must contain the following columns:

      -
      +
      pu
      +

      integer planning unit identifier.

      + -
      pu

      integer planning unit identifier.

      +
      species
      +

      integer feature identifier.

      -
      species

      integer feature identifier.

      -
      amount

      numeric amount of the feature in the +

      amount
      +

      numeric amount of the feature in the planning unit.

      -
      bound

      NULL object indicating that no boundary data + + +

      bound
      +

      NULL object indicating that no boundary data is required for the conservation planning problem, or a data.frame containing information on the planning units' boundaries. The argument to bound must follow the conventions used in the Marxan input data file (conventionally called "bound.dat"). It must contain the following columns:

      -
      - -
      id1

      integer planning unit identifier.

      +
      id1
      +

      integer planning unit identifier.

      -
      id2

      integer planning unit identifier.

      -
      boundary

      numeric length of shared boundary -between the planning units identified in the previous two columns.

      +
      id2
      +

      integer planning unit identifier.

      -
      blm

      numeric boundary length modifier. This argument only -has an effect when argument to x is a data.frame. The -default argument is zero.

      +
      boundary
      +

      numeric length of shared boundary +between the planning units identified in the previous two columns.

      -

      Value

      -

      problem() (i.e. ConservationProblem) object.

      -

      Details

      + +
      blm
      +

      numeric boundary length modifier. This argument only +has an effect when argument to x is a data.frame. The +default argument is zero.

      +
      +
      +

      Value

      +

      problem() (i.e., ConservationProblem) object.

      +
      +
      +

      Details

      This function is provided as a convenient wrapper for solving Marxan problems using prioritizr.

      -

      Notes

      - +
      +
      +

      Notes

      In early versions, this function could accommodate asymmetric connectivity data. This functionality is no longer supported. To specify asymmetric -connectivity, please see the add_connectivity_penalties() function.

      -

      References

      - +connectivity, please see the add_connectivity_penalties() function.

      +
      +
      +

      References

      Ball IR, Possingham HP, and Watts M (2009) Marxan and relatives: Software for spatial conservation prioritisation in Spatial conservation prioritisation: Quantitative methods and computational tools. Eds Moilanen @@ -328,142 +252,141 @@

      R

      Beyer HL, Dujardin Y, Watts ME, and Possingham HP (2016) Solving conservation planning problems with integer linear programming. Ecological Modelling, 228: 14--22.

      -

      See also

      - -

      For more information on the correct format for +

      +
      +

      See also

      +

      For more information on the correct format for for Marxan input data, see the -official Marxan website and Ball +official Marxan website and Ball et al. (2009).

      +
      -

      Examples

      - 
      # create Marxan problem using Marxan input file
-input_file <- system.file("extdata/input.dat", package = "prioritizr")
-p1 <- marxan_problem(input_file) %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s1 <- solve(p1)
-
-# print solution
-head(s1)
-#>   id       cost status    xloc     yloc locked_in locked_out solution_1
-#> 1  3        0.0      0 1116623 -4493479     FALSE      FALSE          0
-#> 2 30   752727.5      3 1110623 -4496943     FALSE       TRUE          0
-#> 3 56  3734907.5      0 1092623 -4500408     FALSE      FALSE          0
-#> 4 58  1695902.1      0 1116623 -4500408     FALSE      FALSE          0
-#> 5 84  3422025.6      0 1098623 -4503872     FALSE      FALSE          0
-#> 6 85 17890758.4      0 1110623 -4503872     FALSE      FALSE          0
-# }
-# create Marxan problem using data.frames that have been loaded into R
-## load in planning unit data
-pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr")
-pu_dat <- data.table::fread(pu_path, data.table = FALSE)
-head(pu_dat)
-#>   id       cost status    xloc     yloc
-#> 1  3        0.0      0 1116623 -4493479
-#> 2 30   752727.5      3 1110623 -4496943
-#> 3 56  3734907.5      0 1092623 -4500408
-#> 4 58  1695902.1      0 1116623 -4500408
-#> 5 84  3422025.6      0 1098623 -4503872
-#> 6 85 17890758.4      0 1110623 -4503872
-
-## load in feature data
-spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr")
-spec_dat <- data.table::fread(spec_path, data.table = FALSE)
-head(spec_dat)
-#>   id prop spf   name
-#> 1 10  0.3   1  bird1
-#> 2 11  0.3   1  nvis2
-#> 3 12  0.3   1  nvis8
-#> 4 13  0.3   1  nvis9
-#> 5 14  0.3   1 nvis14
-#> 6 15  0.3   1 nvis20
-
-## load in planning unit vs feature data
-puvspr_path <- system.file("extdata/input/puvspr.dat",
-                           package = "prioritizr")
-puvspr_dat <- data.table::fread(puvspr_path, data.table = FALSE)
-head(puvspr_dat)
-#>   species  pu     amount
-#> 1      26  56 1203448.84
-#> 2      26  58  451670.10
-#> 3      26  84  680473.75
-#> 4      26  85   97356.24
-#> 5      26  86   78034.76
-#> 6      26 111 4783274.17
-
-## load in the boundary data
-bound_path <- system.file("extdata/input/bound.dat", package = "prioritizr")
-bound_dat <- data.table::fread(bound_path, data.table = FALSE)
-head(bound_dat)
-#>   id1 id2 boundary
-#> 1   3   3    16000
-#> 2   3  30     4000
-#> 3   3  58     4000
-#> 4  30  30    12000
-#> 5  30  58     4000
-#> 6  30  85     4000
-
-# create problem without the boundary data
-p2 <- marxan_problem(pu_dat, spec_dat, puvspr_dat) %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s2 <- solve(p2)
-
-# print solution
-head(s2)
-#>   id       cost status    xloc     yloc locked_in locked_out solution_1
-#> 1  3        0.0      0 1116623 -4493479     FALSE      FALSE          0
-#> 2 30   752727.5      3 1110623 -4496943     FALSE       TRUE          0
-#> 3 56  3734907.5      0 1092623 -4500408     FALSE      FALSE          0
-#> 4 58  1695902.1      0 1116623 -4500408     FALSE      FALSE          0
-#> 5 84  3422025.6      0 1098623 -4503872     FALSE      FALSE          0
-#> 6 85 17890758.4      0 1110623 -4503872     FALSE      FALSE          0
-# }
-# create problem with the boundary data and a boundary length modifier
-# set to 5
-p3 <- marxan_problem(pu_dat, spec_dat, puvspr_dat, bound_dat, 5) %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s3 <- solve(p3)
-
-# print solution
-head(s3)
-#>   id       cost status    xloc     yloc locked_in locked_out solution_1
-#> 1  3        0.0      0 1116623 -4493479     FALSE      FALSE          0
-#> 2 30   752727.5      3 1110623 -4496943     FALSE       TRUE          0
-#> 3 56  3734907.5      0 1092623 -4500408     FALSE      FALSE          0
-#> 4 58  1695902.1      0 1116623 -4500408     FALSE      FALSE          0
-#> 5 84  3422025.6      0 1098623 -4503872     FALSE      FALSE          0
-#> 6 85 17890758.4      0 1110623 -4503872     FALSE      FALSE          0
-# }
+    
      
+    
      Examples
      
+    
      # create Marxan problem using Marxan input file
+input_file <- system.file("extdata/input.dat", package = "prioritizr")
+p1 <- marxan_problem(input_file) %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s1 <- solve(p1)
+
+# print solution
+head(s1)
+#>   id       cost status    xloc     yloc locked_in locked_out solution_1
+#> 1  3        0.0      0 1116623 -4493479     FALSE      FALSE          0
+#> 2 30   752727.5      3 1110623 -4496943     FALSE       TRUE          0
+#> 3 56  3734907.5      0 1092623 -4500408     FALSE      FALSE          0
+#> 4 58  1695902.1      0 1116623 -4500408     FALSE      FALSE          0
+#> 5 84  3422025.6      0 1098623 -4503872     FALSE      FALSE          0
+#> 6 85 17890758.4      0 1110623 -4503872     FALSE      FALSE          0
+# }
+# create Marxan problem using data.frames that have been loaded into R
+## load in planning unit data
+pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr")
+pu_dat <- data.table::fread(pu_path, data.table = FALSE)
+head(pu_dat)
+#>   id       cost status    xloc     yloc
+#> 1  3        0.0      0 1116623 -4493479
+#> 2 30   752727.5      3 1110623 -4496943
+#> 3 56  3734907.5      0 1092623 -4500408
+#> 4 58  1695902.1      0 1116623 -4500408
+#> 5 84  3422025.6      0 1098623 -4503872
+#> 6 85 17890758.4      0 1110623 -4503872
+
+## load in feature data
+spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr")
+spec_dat <- data.table::fread(spec_path, data.table = FALSE)
+head(spec_dat)
+#>   id prop spf   name
+#> 1 10  0.3   1  bird1
+#> 2 11  0.3   1  nvis2
+#> 3 12  0.3   1  nvis8
+#> 4 13  0.3   1  nvis9
+#> 5 14  0.3   1 nvis14
+#> 6 15  0.3   1 nvis20
+
+## load in planning unit vs feature data
+puvspr_path <- system.file("extdata/input/puvspr.dat",
+                           package = "prioritizr")
+puvspr_dat <- data.table::fread(puvspr_path, data.table = FALSE)
+head(puvspr_dat)
+#>   species  pu     amount
+#> 1      26  56 1203448.84
+#> 2      26  58  451670.10
+#> 3      26  84  680473.75
+#> 4      26  85   97356.24
+#> 5      26  86   78034.76
+#> 6      26 111 4783274.17
+
+## load in the boundary data
+bound_path <- system.file("extdata/input/bound.dat", package = "prioritizr")
+bound_dat <- data.table::fread(bound_path, data.table = FALSE)
+head(bound_dat)
+#>   id1 id2 boundary
+#> 1   3   3    16000
+#> 2   3  30     4000
+#> 3   3  58     4000
+#> 4  30  30    12000
+#> 5  30  58     4000
+#> 6  30  85     4000
+
+# create problem without the boundary data
+p2 <- marxan_problem(pu_dat, spec_dat, puvspr_dat) %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s2 <- solve(p2)
+
+# print solution
+head(s2)
+#>   id       cost status    xloc     yloc locked_in locked_out solution_1
+#> 1  3        0.0      0 1116623 -4493479     FALSE      FALSE          0
+#> 2 30   752727.5      3 1110623 -4496943     FALSE       TRUE          0
+#> 3 56  3734907.5      0 1092623 -4500408     FALSE      FALSE          0
+#> 4 58  1695902.1      0 1116623 -4500408     FALSE      FALSE          0
+#> 5 84  3422025.6      0 1098623 -4503872     FALSE      FALSE          0
+#> 6 85 17890758.4      0 1110623 -4503872     FALSE      FALSE          0
+# }
+# create problem with the boundary data and a boundary length modifier
+# set to 5
+p3 <- marxan_problem(pu_dat, spec_dat, puvspr_dat, bound_dat, 5) %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s3 <- solve(p3)
+
+# print solution
+head(s3)
+#>   id       cost status    xloc     yloc locked_in locked_out solution_1
+#> 1  3        0.0      0 1116623 -4493479     FALSE      FALSE          0
+#> 2 30   752727.5      3 1110623 -4496943     FALSE       TRUE          0
+#> 3 56  3734907.5      0 1092623 -4500408     FALSE      FALSE          0
+#> 4 58  1695902.1      0 1116623 -4500408     FALSE      FALSE          0
+#> 5 84  3422025.6      0 1098623 -4503872     FALSE      FALSE          0
+#> 6 85 17890758.4      0 1110623 -4503872     FALSE      FALSE          0
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/matrix_parameters.html b/docs/reference/matrix_parameters.html index 296325d93..eee89720b 100644 --- a/docs/reference/matrix_parameters.html +++ b/docs/reference/matrix_parameters.html @@ -1,101 +1,18 @@ - - - - - - - -Matrix parameters — matrix_parameters • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Matrix parameters — matrix_parameters • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Matrix parameters

      - Source: R/parameters.R + Source: R/parameters.R
      @@ -184,129 +101,115 @@

      Matrix parameters

      Create a parameter that represents a matrix object.

      - 
      numeric_matrix_parameter(
-  name,
-  value,
-  lower_limit = .Machine$double.xmin,
-  upper_limit = .Machine$double.xmax,
-  symmetric = FALSE
-)
-
-binary_matrix_parameter(name, value, symmetric = FALSE)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - -
      name

      character name of parameter.

      value

      matrix object.

      lower_limit

      numeric values denoting the minimum acceptable +

      Usage,
      numeric_matrix_parameter(
+  name,
+  value,
+  lower_limit = .Machine$double.xmin,
+  upper_limit = .Machine$double.xmax,
+  symmetric = FALSE
+)
+
+binary_matrix_parameter(name, value, symmetric = FALSE)
      + +
      +

      Arguments

      +
      name
      +

      character name of parameter.

      +
      value
      +

      matrix object.

      +
      lower_limit
      +

      numeric values denoting the minimum acceptable value in the matrix. Defaults to the smallest possible number on the -system.

      upper_limit

      numeric values denoting the maximum acceptable +system.

      +
      upper_limit
      +

      numeric values denoting the maximum acceptable value in the matrix. Defaults to the smallest possible number on the -system.

      symmetric

      logical must the must be matrix be symmetric? -Defaults to FALSE.

      - -

      Value

      - -

      MiscParameter object.

      +system.

      +
      symmetric
      +

      logical must the must be matrix be symmetric? +Defaults to FALSE.

      +
      +
      +

      Value

      +

      MiscParameter object.

      +
      -

      Examples

      - 
      # create matrix
-m <- matrix(runif(9), ncol = 3)
-colnames(m) <- letters[1:3]
-rownames(m) <- letters[1:3]
-
-# create a numeric matrix parameter
-p1 <- numeric_matrix_parameter("m", m)
-print(p1) # print it
-#> <environment: 0x56421961e978>
-#> attr(,"class")
-#> [1] "MiscParameter" "MiscParameter" "Parameter"     "pproto"       
-#> [5] "proto"         "environment"  
-p1$get() # get value
-#>           a         b         c
-#> a 0.8334376 0.5892456 0.2387031
-#> b 0.4846932 0.5758689 0.2372128
-#> c 0.8543447 0.4674843 0.2312509
-p1$id # get id
-#> id: 2248e95f-421a-435d-8db1-c600ca82cc25
-p1$validate(m[, -1]) # check if parameter can be updated
-#> [1] FALSE
-#> attr(,"msg")
-#> [1] "ncol(m) not equal to ncol(value)"
-p1$set(m + 1) # set parameter to new values
-p1$print() # print it again
-#> [1] "m"
-
-# create a binary matrix parameter
-m <- matrix(round(runif(9)), ncol = 3)
-colnames(m) <- letters[1:3]
-rownames(m) <- letters[1:3]
-
-# create a binary matrix parameter
-p2 <- binary_matrix_parameter("m", m)
-print(p2) # print it
-#> <environment: 0x5642173f7e50>
-#> attr(,"class")
-#> [1] "MiscParameter" "MiscParameter" "Parameter"     "pproto"       
-#> [5] "proto"         "environment"  
-p2$get() # get value
-#>   a b c
-#> a 1 0 1
-#> b 0 1 1
-#> c 0 0 1
-p2$id # get id
-#> id: dba810e0-8f3a-4645-bf60-aba12ac1db20
-p2$validate(m[, -1]) # check if parameter can be updated
-#> [1] FALSE
-#> attr(,"msg")
-#> [1] "ncol(m) not equal to ncol(value)"
-p2$set(m + 1) # set parameter to new values
-p2$print() # print it again
-#> [1] "m"
+    
      
+    
      Examples
      
+    
      # create matrix
+m <- matrix(runif(9), ncol = 3)
+colnames(m) <- letters[1:3]
+rownames(m) <- letters[1:3]
+
+# create a numeric matrix parameter
+p1 <- numeric_matrix_parameter("m", m)
+print(p1) # print it
+#> <environment: 0x55f268cc53e8>
+#> attr(,"class")
+#> [1] "MiscParameter" "MiscParameter" "Parameter"     "pproto"       
+#> [5] "proto"         "environment"  
+p1$get() # get value
+#>           a         b         c
+#> a 0.8334376 0.5892456 0.2387031
+#> b 0.4846932 0.5758689 0.2372128
+#> c 0.8543447 0.4674843 0.2312509
+p1$id # get id
+#> id: 13f9d51f-08c9-4f23-b46a-c63798e6e9d8
+p1$validate(m[, -1]) # check if parameter can be updated
+#> [1] FALSE
+#> attr(,"msg")
+#> [1] "ncol(m) not equal to ncol(value)"
+p1$set(m + 1) # set parameter to new values
+p1$print() # print it again
+#> [1] "m"
+
+# create a binary matrix parameter
+m <- matrix(round(runif(9)), ncol = 3)
+colnames(m) <- letters[1:3]
+rownames(m) <- letters[1:3]
+
+# create a binary matrix parameter
+p2 <- binary_matrix_parameter("m", m)
+print(p2) # print it
+#> <environment: 0x55f2684deee0>
+#> attr(,"class")
+#> [1] "MiscParameter" "MiscParameter" "Parameter"     "pproto"       
+#> [5] "proto"         "environment"  
+p2$get() # get value
+#>   a b c
+#> a 1 0 1
+#> b 0 1 1
+#> c 0 0 1
+p2$id # get id
+#> id: a6f935ec-bc06-4421-9875-522a7f1ad24d
+p2$validate(m[, -1]) # check if parameter can be updated
+#> [1] FALSE
+#> attr(,"msg")
+#> [1] "ncol(m) not equal to ncol(value)"
+p2$set(m + 1) # set parameter to new values
+p2$print() # print it again
+#> [1] "m"
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/misc_parameter.html b/docs/reference/misc_parameter.html index 457770fc9..b1f55c333 100644 --- a/docs/reference/misc_parameter.html +++ b/docs/reference/misc_parameter.html @@ -1,101 +1,18 @@ - - - - - - - -Miscellaneous parameter — misc_parameter • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Miscellaneous parameter — misc_parameter • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Miscellaneous parameter

      - Source: R/parameters.R + Source: R/parameters.R
      @@ -184,403 +101,393 @@

      Miscellaneous parameter

      Create a parameter that consists of a miscellaneous object.

      - 
      misc_parameter(name, value, validator)
      +
      Usage,
      misc_parameter(name, value, validator)
      -

      Arguments

      - - - - - - - - - - - - - - -
      name

      character name of parameter.

      value

      object.

      validator

      function to validate changes to the parameter. This +

      +

      Arguments

      +
      name
      +

      character name of parameter.

      +
      value
      +

      object.

      +
      validator
      +

      function to validate changes to the parameter. This function must have a single argument and return either TRUE or FALSE depending on if the argument is valid candidate for the -parameter.

      - -

      Value

      - -

      MiscParameter object.

      +parameter.

      +
      +
      +

      Value

      +

      MiscParameter object.

      +
      -

      Examples

      - 
      # load data
-data(iris, mtcars)
-
-# create table parameter can that can be updated to any other object
-p1 <- misc_parameter("tbl", iris, function(x) TRUE)
-print(p1) # print it
-#> <environment: 0x564226189508>
-#> attr(,"class")
-#> [1] "MiscParameter" "MiscParameter" "Parameter"     "pproto"       
-#> [5] "proto"         "environment"  
-p1$get() # get value
-#>     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
-#> 1            5.1         3.5          1.4         0.2     setosa
-#> 2            4.9         3.0          1.4         0.2     setosa
-#> 3            4.7         3.2          1.3         0.2     setosa
-#> 4            4.6         3.1          1.5         0.2     setosa
-#> 5            5.0         3.6          1.4         0.2     setosa
-#> 6            5.4         3.9          1.7         0.4     setosa
-#> 7            4.6         3.4          1.4         0.3     setosa
-#> 8            5.0         3.4          1.5         0.2     setosa
-#> 9            4.4         2.9          1.4         0.2     setosa
-#> 10           4.9         3.1          1.5         0.1     setosa
-#> 11           5.4         3.7          1.5         0.2     setosa
-#> 12           4.8         3.4          1.6         0.2     setosa
-#> 13           4.8         3.0          1.4         0.1     setosa
-#> 14           4.3         3.0          1.1         0.1     setosa
-#> 15           5.8         4.0          1.2         0.2     setosa
-#> 16           5.7         4.4          1.5         0.4     setosa
-#> 17           5.4         3.9          1.3         0.4     setosa
-#> 18           5.1         3.5          1.4         0.3     setosa
-#> 19           5.7         3.8          1.7         0.3     setosa
-#> 20           5.1         3.8          1.5         0.3     setosa
-#> 21           5.4         3.4          1.7         0.2     setosa
-#> 22           5.1         3.7          1.5         0.4     setosa
-#> 23           4.6         3.6          1.0         0.2     setosa
-#> 24           5.1         3.3          1.7         0.5     setosa
-#> 25           4.8         3.4          1.9         0.2     setosa
-#> 26           5.0         3.0          1.6         0.2     setosa
-#> 27           5.0         3.4          1.6         0.4     setosa
-#> 28           5.2         3.5          1.5         0.2     setosa
-#> 29           5.2         3.4          1.4         0.2     setosa
-#> 30           4.7         3.2          1.6         0.2     setosa
-#> 31           4.8         3.1          1.6         0.2     setosa
-#> 32           5.4         3.4          1.5         0.4     setosa
-#> 33           5.2         4.1          1.5         0.1     setosa
-#> 34           5.5         4.2          1.4         0.2     setosa
-#> 35           4.9         3.1          1.5         0.2     setosa
-#> 36           5.0         3.2          1.2         0.2     setosa
-#> 37           5.5         3.5          1.3         0.2     setosa
-#> 38           4.9         3.6          1.4         0.1     setosa
-#> 39           4.4         3.0          1.3         0.2     setosa
-#> 40           5.1         3.4          1.5         0.2     setosa
-#> 41           5.0         3.5          1.3         0.3     setosa
-#> 42           4.5         2.3          1.3         0.3     setosa
-#> 43           4.4         3.2          1.3         0.2     setosa
-#> 44           5.0         3.5          1.6         0.6     setosa
-#> 45           5.1         3.8          1.9         0.4     setosa
-#> 46           4.8         3.0          1.4         0.3     setosa
-#> 47           5.1         3.8          1.6         0.2     setosa
-#> 48           4.6         3.2          1.4         0.2     setosa
-#> 49           5.3         3.7          1.5         0.2     setosa
-#> 50           5.0         3.3          1.4         0.2     setosa
-#> 51           7.0         3.2          4.7         1.4 versicolor
-#> 52           6.4         3.2          4.5         1.5 versicolor
-#> 53           6.9         3.1          4.9         1.5 versicolor
-#> 54           5.5         2.3          4.0         1.3 versicolor
-#> 55           6.5         2.8          4.6         1.5 versicolor
-#> 56           5.7         2.8          4.5         1.3 versicolor
-#> 57           6.3         3.3          4.7         1.6 versicolor
-#> 58           4.9         2.4          3.3         1.0 versicolor
-#> 59           6.6         2.9          4.6         1.3 versicolor
-#> 60           5.2         2.7          3.9         1.4 versicolor
-#> 61           5.0         2.0          3.5         1.0 versicolor
-#> 62           5.9         3.0          4.2         1.5 versicolor
-#> 63           6.0         2.2          4.0         1.0 versicolor
-#> 64           6.1         2.9          4.7         1.4 versicolor
-#> 65           5.6         2.9          3.6         1.3 versicolor
-#> 66           6.7         3.1          4.4         1.4 versicolor
-#> 67           5.6         3.0          4.5         1.5 versicolor
-#> 68           5.8         2.7          4.1         1.0 versicolor
-#> 69           6.2         2.2          4.5         1.5 versicolor
-#> 70           5.6         2.5          3.9         1.1 versicolor
-#> 71           5.9         3.2          4.8         1.8 versicolor
-#> 72           6.1         2.8          4.0         1.3 versicolor
-#> 73           6.3         2.5          4.9         1.5 versicolor
-#> 74           6.1         2.8          4.7         1.2 versicolor
-#> 75           6.4         2.9          4.3         1.3 versicolor
-#> 76           6.6         3.0          4.4         1.4 versicolor
-#> 77           6.8         2.8          4.8         1.4 versicolor
-#> 78           6.7         3.0          5.0         1.7 versicolor
-#> 79           6.0         2.9          4.5         1.5 versicolor
-#> 80           5.7         2.6          3.5         1.0 versicolor
-#> 81           5.5         2.4          3.8         1.1 versicolor
-#> 82           5.5         2.4          3.7         1.0 versicolor
-#> 83           5.8         2.7          3.9         1.2 versicolor
-#> 84           6.0         2.7          5.1         1.6 versicolor
-#> 85           5.4         3.0          4.5         1.5 versicolor
-#> 86           6.0         3.4          4.5         1.6 versicolor
-#> 87           6.7         3.1          4.7         1.5 versicolor
-#> 88           6.3         2.3          4.4         1.3 versicolor
-#> 89           5.6         3.0          4.1         1.3 versicolor
-#> 90           5.5         2.5          4.0         1.3 versicolor
-#> 91           5.5         2.6          4.4         1.2 versicolor
-#> 92           6.1         3.0          4.6         1.4 versicolor
-#> 93           5.8         2.6          4.0         1.2 versicolor
-#> 94           5.0         2.3          3.3         1.0 versicolor
-#> 95           5.6         2.7          4.2         1.3 versicolor
-#> 96           5.7         3.0          4.2         1.2 versicolor
-#> 97           5.7         2.9          4.2         1.3 versicolor
-#> 98           6.2         2.9          4.3         1.3 versicolor
-#> 99           5.1         2.5          3.0         1.1 versicolor
-#> 100          5.7         2.8          4.1         1.3 versicolor
-#> 101          6.3         3.3          6.0         2.5  virginica
-#> 102          5.8         2.7          5.1         1.9  virginica
-#> 103          7.1         3.0          5.9         2.1  virginica
-#> 104          6.3         2.9          5.6         1.8  virginica
-#> 105          6.5         3.0          5.8         2.2  virginica
-#> 106          7.6         3.0          6.6         2.1  virginica
-#> 107          4.9         2.5          4.5         1.7  virginica
-#> 108          7.3         2.9          6.3         1.8  virginica
-#> 109          6.7         2.5          5.8         1.8  virginica
-#> 110          7.2         3.6          6.1         2.5  virginica
-#> 111          6.5         3.2          5.1         2.0  virginica
-#> 112          6.4         2.7          5.3         1.9  virginica
-#> 113          6.8         3.0          5.5         2.1  virginica
-#> 114          5.7         2.5          5.0         2.0  virginica
-#> 115          5.8         2.8          5.1         2.4  virginica
-#> 116          6.4         3.2          5.3         2.3  virginica
-#> 117          6.5         3.0          5.5         1.8  virginica
-#> 118          7.7         3.8          6.7         2.2  virginica
-#> 119          7.7         2.6          6.9         2.3  virginica
-#> 120          6.0         2.2          5.0         1.5  virginica
-#> 121          6.9         3.2          5.7         2.3  virginica
-#> 122          5.6         2.8          4.9         2.0  virginica
-#> 123          7.7         2.8          6.7         2.0  virginica
-#> 124          6.3         2.7          4.9         1.8  virginica
-#> 125          6.7         3.3          5.7         2.1  virginica
-#> 126          7.2         3.2          6.0         1.8  virginica
-#> 127          6.2         2.8          4.8         1.8  virginica
-#> 128          6.1         3.0          4.9         1.8  virginica
-#> 129          6.4         2.8          5.6         2.1  virginica
-#> 130          7.2         3.0          5.8         1.6  virginica
-#> 131          7.4         2.8          6.1         1.9  virginica
-#> 132          7.9         3.8          6.4         2.0  virginica
-#> 133          6.4         2.8          5.6         2.2  virginica
-#> 134          6.3         2.8          5.1         1.5  virginica
-#> 135          6.1         2.6          5.6         1.4  virginica
-#> 136          7.7         3.0          6.1         2.3  virginica
-#> 137          6.3         3.4          5.6         2.4  virginica
-#> 138          6.4         3.1          5.5         1.8  virginica
-#> 139          6.0         3.0          4.8         1.8  virginica
-#> 140          6.9         3.1          5.4         2.1  virginica
-#> 141          6.7         3.1          5.6         2.4  virginica
-#> 142          6.9         3.1          5.1         2.3  virginica
-#> 143          5.8         2.7          5.1         1.9  virginica
-#> 144          6.8         3.2          5.9         2.3  virginica
-#> 145          6.7         3.3          5.7         2.5  virginica
-#> 146          6.7         3.0          5.2         2.3  virginica
-#> 147          6.3         2.5          5.0         1.9  virginica
-#> 148          6.5         3.0          5.2         2.0  virginica
-#> 149          6.2         3.4          5.4         2.3  virginica
-#> 150          5.9         3.0          5.1         1.8  virginica
-p1$id # get id
-#> id: 63b54362-2dd2-4512-bb80-773bdce363f6
-p1$validate(mtcars) # check if parameter can be updated
-#> [1] TRUE
-p1$set(mtcars) # set parameter to mtcars
-p1$print() # print it again
-#> [1] "tbl"
-
-# create table parameter with validation function that requires
-# all values in the first column to be less then 200 and that the
-# parameter have the same column names as the iris dataset
-p2 <- misc_parameter("tbl2", iris,
-                     function(x) all(names(x) %in% names(iris)) &&
-                                 all(x[[1]] < 200))
-print(p2) # print it
-#> <environment: 0x56421aa597b0>
-#> attr(,"class")
-#> [1] "MiscParameter" "MiscParameter" "Parameter"     "pproto"       
-#> [5] "proto"         "environment"  
-p2$get() # get value
-#>     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
-#> 1            5.1         3.5          1.4         0.2     setosa
-#> 2            4.9         3.0          1.4         0.2     setosa
-#> 3            4.7         3.2          1.3         0.2     setosa
-#> 4            4.6         3.1          1.5         0.2     setosa
-#> 5            5.0         3.6          1.4         0.2     setosa
-#> 6            5.4         3.9          1.7         0.4     setosa
-#> 7            4.6         3.4          1.4         0.3     setosa
-#> 8            5.0         3.4          1.5         0.2     setosa
-#> 9            4.4         2.9          1.4         0.2     setosa
-#> 10           4.9         3.1          1.5         0.1     setosa
-#> 11           5.4         3.7          1.5         0.2     setosa
-#> 12           4.8         3.4          1.6         0.2     setosa
-#> 13           4.8         3.0          1.4         0.1     setosa
-#> 14           4.3         3.0          1.1         0.1     setosa
-#> 15           5.8         4.0          1.2         0.2     setosa
-#> 16           5.7         4.4          1.5         0.4     setosa
-#> 17           5.4         3.9          1.3         0.4     setosa
-#> 18           5.1         3.5          1.4         0.3     setosa
-#> 19           5.7         3.8          1.7         0.3     setosa
-#> 20           5.1         3.8          1.5         0.3     setosa
-#> 21           5.4         3.4          1.7         0.2     setosa
-#> 22           5.1         3.7          1.5         0.4     setosa
-#> 23           4.6         3.6          1.0         0.2     setosa
-#> 24           5.1         3.3          1.7         0.5     setosa
-#> 25           4.8         3.4          1.9         0.2     setosa
-#> 26           5.0         3.0          1.6         0.2     setosa
-#> 27           5.0         3.4          1.6         0.4     setosa
-#> 28           5.2         3.5          1.5         0.2     setosa
-#> 29           5.2         3.4          1.4         0.2     setosa
-#> 30           4.7         3.2          1.6         0.2     setosa
-#> 31           4.8         3.1          1.6         0.2     setosa
-#> 32           5.4         3.4          1.5         0.4     setosa
-#> 33           5.2         4.1          1.5         0.1     setosa
-#> 34           5.5         4.2          1.4         0.2     setosa
-#> 35           4.9         3.1          1.5         0.2     setosa
-#> 36           5.0         3.2          1.2         0.2     setosa
-#> 37           5.5         3.5          1.3         0.2     setosa
-#> 38           4.9         3.6          1.4         0.1     setosa
-#> 39           4.4         3.0          1.3         0.2     setosa
-#> 40           5.1         3.4          1.5         0.2     setosa
-#> 41           5.0         3.5          1.3         0.3     setosa
-#> 42           4.5         2.3          1.3         0.3     setosa
-#> 43           4.4         3.2          1.3         0.2     setosa
-#> 44           5.0         3.5          1.6         0.6     setosa
-#> 45           5.1         3.8          1.9         0.4     setosa
-#> 46           4.8         3.0          1.4         0.3     setosa
-#> 47           5.1         3.8          1.6         0.2     setosa
-#> 48           4.6         3.2          1.4         0.2     setosa
-#> 49           5.3         3.7          1.5         0.2     setosa
-#> 50           5.0         3.3          1.4         0.2     setosa
-#> 51           7.0         3.2          4.7         1.4 versicolor
-#> 52           6.4         3.2          4.5         1.5 versicolor
-#> 53           6.9         3.1          4.9         1.5 versicolor
-#> 54           5.5         2.3          4.0         1.3 versicolor
-#> 55           6.5         2.8          4.6         1.5 versicolor
-#> 56           5.7         2.8          4.5         1.3 versicolor
-#> 57           6.3         3.3          4.7         1.6 versicolor
-#> 58           4.9         2.4          3.3         1.0 versicolor
-#> 59           6.6         2.9          4.6         1.3 versicolor
-#> 60           5.2         2.7          3.9         1.4 versicolor
-#> 61           5.0         2.0          3.5         1.0 versicolor
-#> 62           5.9         3.0          4.2         1.5 versicolor
-#> 63           6.0         2.2          4.0         1.0 versicolor
-#> 64           6.1         2.9          4.7         1.4 versicolor
-#> 65           5.6         2.9          3.6         1.3 versicolor
-#> 66           6.7         3.1          4.4         1.4 versicolor
-#> 67           5.6         3.0          4.5         1.5 versicolor
-#> 68           5.8         2.7          4.1         1.0 versicolor
-#> 69           6.2         2.2          4.5         1.5 versicolor
-#> 70           5.6         2.5          3.9         1.1 versicolor
-#> 71           5.9         3.2          4.8         1.8 versicolor
-#> 72           6.1         2.8          4.0         1.3 versicolor
-#> 73           6.3         2.5          4.9         1.5 versicolor
-#> 74           6.1         2.8          4.7         1.2 versicolor
-#> 75           6.4         2.9          4.3         1.3 versicolor
-#> 76           6.6         3.0          4.4         1.4 versicolor
-#> 77           6.8         2.8          4.8         1.4 versicolor
-#> 78           6.7         3.0          5.0         1.7 versicolor
-#> 79           6.0         2.9          4.5         1.5 versicolor
-#> 80           5.7         2.6          3.5         1.0 versicolor
-#> 81           5.5         2.4          3.8         1.1 versicolor
-#> 82           5.5         2.4          3.7         1.0 versicolor
-#> 83           5.8         2.7          3.9         1.2 versicolor
-#> 84           6.0         2.7          5.1         1.6 versicolor
-#> 85           5.4         3.0          4.5         1.5 versicolor
-#> 86           6.0         3.4          4.5         1.6 versicolor
-#> 87           6.7         3.1          4.7         1.5 versicolor
-#> 88           6.3         2.3          4.4         1.3 versicolor
-#> 89           5.6         3.0          4.1         1.3 versicolor
-#> 90           5.5         2.5          4.0         1.3 versicolor
-#> 91           5.5         2.6          4.4         1.2 versicolor
-#> 92           6.1         3.0          4.6         1.4 versicolor
-#> 93           5.8         2.6          4.0         1.2 versicolor
-#> 94           5.0         2.3          3.3         1.0 versicolor
-#> 95           5.6         2.7          4.2         1.3 versicolor
-#> 96           5.7         3.0          4.2         1.2 versicolor
-#> 97           5.7         2.9          4.2         1.3 versicolor
-#> 98           6.2         2.9          4.3         1.3 versicolor
-#> 99           5.1         2.5          3.0         1.1 versicolor
-#> 100          5.7         2.8          4.1         1.3 versicolor
-#> 101          6.3         3.3          6.0         2.5  virginica
-#> 102          5.8         2.7          5.1         1.9  virginica
-#> 103          7.1         3.0          5.9         2.1  virginica
-#> 104          6.3         2.9          5.6         1.8  virginica
-#> 105          6.5         3.0          5.8         2.2  virginica
-#> 106          7.6         3.0          6.6         2.1  virginica
-#> 107          4.9         2.5          4.5         1.7  virginica
-#> 108          7.3         2.9          6.3         1.8  virginica
-#> 109          6.7         2.5          5.8         1.8  virginica
-#> 110          7.2         3.6          6.1         2.5  virginica
-#> 111          6.5         3.2          5.1         2.0  virginica
-#> 112          6.4         2.7          5.3         1.9  virginica
-#> 113          6.8         3.0          5.5         2.1  virginica
-#> 114          5.7         2.5          5.0         2.0  virginica
-#> 115          5.8         2.8          5.1         2.4  virginica
-#> 116          6.4         3.2          5.3         2.3  virginica
-#> 117          6.5         3.0          5.5         1.8  virginica
-#> 118          7.7         3.8          6.7         2.2  virginica
-#> 119          7.7         2.6          6.9         2.3  virginica
-#> 120          6.0         2.2          5.0         1.5  virginica
-#> 121          6.9         3.2          5.7         2.3  virginica
-#> 122          5.6         2.8          4.9         2.0  virginica
-#> 123          7.7         2.8          6.7         2.0  virginica
-#> 124          6.3         2.7          4.9         1.8  virginica
-#> 125          6.7         3.3          5.7         2.1  virginica
-#> 126          7.2         3.2          6.0         1.8  virginica
-#> 127          6.2         2.8          4.8         1.8  virginica
-#> 128          6.1         3.0          4.9         1.8  virginica
-#> 129          6.4         2.8          5.6         2.1  virginica
-#> 130          7.2         3.0          5.8         1.6  virginica
-#> 131          7.4         2.8          6.1         1.9  virginica
-#> 132          7.9         3.8          6.4         2.0  virginica
-#> 133          6.4         2.8          5.6         2.2  virginica
-#> 134          6.3         2.8          5.1         1.5  virginica
-#> 135          6.1         2.6          5.6         1.4  virginica
-#> 136          7.7         3.0          6.1         2.3  virginica
-#> 137          6.3         3.4          5.6         2.4  virginica
-#> 138          6.4         3.1          5.5         1.8  virginica
-#> 139          6.0         3.0          4.8         1.8  virginica
-#> 140          6.9         3.1          5.4         2.1  virginica
-#> 141          6.7         3.1          5.6         2.4  virginica
-#> 142          6.9         3.1          5.1         2.3  virginica
-#> 143          5.8         2.7          5.1         1.9  virginica
-#> 144          6.8         3.2          5.9         2.3  virginica
-#> 145          6.7         3.3          5.7         2.5  virginica
-#> 146          6.7         3.0          5.2         2.3  virginica
-#> 147          6.3         2.5          5.0         1.9  virginica
-#> 148          6.5         3.0          5.2         2.0  virginica
-#> 149          6.2         3.4          5.4         2.3  virginica
-#> 150          5.9         3.0          5.1         1.8  virginica
-p2$id # get id
-#> id: e50355ed-fb0a-46e8-abbe-51e5b7af1617
-p2$validate(mtcars) # check if parameter can be updated
-#> [1] FALSE
-iris2 <- iris; iris2[1,1] <- 300 # create updated iris dataset
-p2$validate(iris2) # check if parameter can be updated
-#> [1] FALSE
-iris3 <- iris; iris2[1,1] <- 100 # create updated iris dataset
-p2$set(iris3) # set parameter to iris3
-p2$print() # print it again
-#> [1] "tbl2"
-
+    
      
+    
      Examples
      
+    
      # load data
+data(iris, mtcars)
+
+# create table parameter can that can be updated to any other object
+p1 <- misc_parameter("tbl", iris, function(x) TRUE)
+print(p1) # print it
+#> <environment: 0x55f2795ce6b0>
+#> attr(,"class")
+#> [1] "MiscParameter" "MiscParameter" "Parameter"     "pproto"       
+#> [5] "proto"         "environment"  
+p1$get() # get value
+#>     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
+#> 1            5.1         3.5          1.4         0.2     setosa
+#> 2            4.9         3.0          1.4         0.2     setosa
+#> 3            4.7         3.2          1.3         0.2     setosa
+#> 4            4.6         3.1          1.5         0.2     setosa
+#> 5            5.0         3.6          1.4         0.2     setosa
+#> 6            5.4         3.9          1.7         0.4     setosa
+#> 7            4.6         3.4          1.4         0.3     setosa
+#> 8            5.0         3.4          1.5         0.2     setosa
+#> 9            4.4         2.9          1.4         0.2     setosa
+#> 10           4.9         3.1          1.5         0.1     setosa
+#> 11           5.4         3.7          1.5         0.2     setosa
+#> 12           4.8         3.4          1.6         0.2     setosa
+#> 13           4.8         3.0          1.4         0.1     setosa
+#> 14           4.3         3.0          1.1         0.1     setosa
+#> 15           5.8         4.0          1.2         0.2     setosa
+#> 16           5.7         4.4          1.5         0.4     setosa
+#> 17           5.4         3.9          1.3         0.4     setosa
+#> 18           5.1         3.5          1.4         0.3     setosa
+#> 19           5.7         3.8          1.7         0.3     setosa
+#> 20           5.1         3.8          1.5         0.3     setosa
+#> 21           5.4         3.4          1.7         0.2     setosa
+#> 22           5.1         3.7          1.5         0.4     setosa
+#> 23           4.6         3.6          1.0         0.2     setosa
+#> 24           5.1         3.3          1.7         0.5     setosa
+#> 25           4.8         3.4          1.9         0.2     setosa
+#> 26           5.0         3.0          1.6         0.2     setosa
+#> 27           5.0         3.4          1.6         0.4     setosa
+#> 28           5.2         3.5          1.5         0.2     setosa
+#> 29           5.2         3.4          1.4         0.2     setosa
+#> 30           4.7         3.2          1.6         0.2     setosa
+#> 31           4.8         3.1          1.6         0.2     setosa
+#> 32           5.4         3.4          1.5         0.4     setosa
+#> 33           5.2         4.1          1.5         0.1     setosa
+#> 34           5.5         4.2          1.4         0.2     setosa
+#> 35           4.9         3.1          1.5         0.2     setosa
+#> 36           5.0         3.2          1.2         0.2     setosa
+#> 37           5.5         3.5          1.3         0.2     setosa
+#> 38           4.9         3.6          1.4         0.1     setosa
+#> 39           4.4         3.0          1.3         0.2     setosa
+#> 40           5.1         3.4          1.5         0.2     setosa
+#> 41           5.0         3.5          1.3         0.3     setosa
+#> 42           4.5         2.3          1.3         0.3     setosa
+#> 43           4.4         3.2          1.3         0.2     setosa
+#> 44           5.0         3.5          1.6         0.6     setosa
+#> 45           5.1         3.8          1.9         0.4     setosa
+#> 46           4.8         3.0          1.4         0.3     setosa
+#> 47           5.1         3.8          1.6         0.2     setosa
+#> 48           4.6         3.2          1.4         0.2     setosa
+#> 49           5.3         3.7          1.5         0.2     setosa
+#> 50           5.0         3.3          1.4         0.2     setosa
+#> 51           7.0         3.2          4.7         1.4 versicolor
+#> 52           6.4         3.2          4.5         1.5 versicolor
+#> 53           6.9         3.1          4.9         1.5 versicolor
+#> 54           5.5         2.3          4.0         1.3 versicolor
+#> 55           6.5         2.8          4.6         1.5 versicolor
+#> 56           5.7         2.8          4.5         1.3 versicolor
+#> 57           6.3         3.3          4.7         1.6 versicolor
+#> 58           4.9         2.4          3.3         1.0 versicolor
+#> 59           6.6         2.9          4.6         1.3 versicolor
+#> 60           5.2         2.7          3.9         1.4 versicolor
+#> 61           5.0         2.0          3.5         1.0 versicolor
+#> 62           5.9         3.0          4.2         1.5 versicolor
+#> 63           6.0         2.2          4.0         1.0 versicolor
+#> 64           6.1         2.9          4.7         1.4 versicolor
+#> 65           5.6         2.9          3.6         1.3 versicolor
+#> 66           6.7         3.1          4.4         1.4 versicolor
+#> 67           5.6         3.0          4.5         1.5 versicolor
+#> 68           5.8         2.7          4.1         1.0 versicolor
+#> 69           6.2         2.2          4.5         1.5 versicolor
+#> 70           5.6         2.5          3.9         1.1 versicolor
+#> 71           5.9         3.2          4.8         1.8 versicolor
+#> 72           6.1         2.8          4.0         1.3 versicolor
+#> 73           6.3         2.5          4.9         1.5 versicolor
+#> 74           6.1         2.8          4.7         1.2 versicolor
+#> 75           6.4         2.9          4.3         1.3 versicolor
+#> 76           6.6         3.0          4.4         1.4 versicolor
+#> 77           6.8         2.8          4.8         1.4 versicolor
+#> 78           6.7         3.0          5.0         1.7 versicolor
+#> 79           6.0         2.9          4.5         1.5 versicolor
+#> 80           5.7         2.6          3.5         1.0 versicolor
+#> 81           5.5         2.4          3.8         1.1 versicolor
+#> 82           5.5         2.4          3.7         1.0 versicolor
+#> 83           5.8         2.7          3.9         1.2 versicolor
+#> 84           6.0         2.7          5.1         1.6 versicolor
+#> 85           5.4         3.0          4.5         1.5 versicolor
+#> 86           6.0         3.4          4.5         1.6 versicolor
+#> 87           6.7         3.1          4.7         1.5 versicolor
+#> 88           6.3         2.3          4.4         1.3 versicolor
+#> 89           5.6         3.0          4.1         1.3 versicolor
+#> 90           5.5         2.5          4.0         1.3 versicolor
+#> 91           5.5         2.6          4.4         1.2 versicolor
+#> 92           6.1         3.0          4.6         1.4 versicolor
+#> 93           5.8         2.6          4.0         1.2 versicolor
+#> 94           5.0         2.3          3.3         1.0 versicolor
+#> 95           5.6         2.7          4.2         1.3 versicolor
+#> 96           5.7         3.0          4.2         1.2 versicolor
+#> 97           5.7         2.9          4.2         1.3 versicolor
+#> 98           6.2         2.9          4.3         1.3 versicolor
+#> 99           5.1         2.5          3.0         1.1 versicolor
+#> 100          5.7         2.8          4.1         1.3 versicolor
+#> 101          6.3         3.3          6.0         2.5  virginica
+#> 102          5.8         2.7          5.1         1.9  virginica
+#> 103          7.1         3.0          5.9         2.1  virginica
+#> 104          6.3         2.9          5.6         1.8  virginica
+#> 105          6.5         3.0          5.8         2.2  virginica
+#> 106          7.6         3.0          6.6         2.1  virginica
+#> 107          4.9         2.5          4.5         1.7  virginica
+#> 108          7.3         2.9          6.3         1.8  virginica
+#> 109          6.7         2.5          5.8         1.8  virginica
+#> 110          7.2         3.6          6.1         2.5  virginica
+#> 111          6.5         3.2          5.1         2.0  virginica
+#> 112          6.4         2.7          5.3         1.9  virginica
+#> 113          6.8         3.0          5.5         2.1  virginica
+#> 114          5.7         2.5          5.0         2.0  virginica
+#> 115          5.8         2.8          5.1         2.4  virginica
+#> 116          6.4         3.2          5.3         2.3  virginica
+#> 117          6.5         3.0          5.5         1.8  virginica
+#> 118          7.7         3.8          6.7         2.2  virginica
+#> 119          7.7         2.6          6.9         2.3  virginica
+#> 120          6.0         2.2          5.0         1.5  virginica
+#> 121          6.9         3.2          5.7         2.3  virginica
+#> 122          5.6         2.8          4.9         2.0  virginica
+#> 123          7.7         2.8          6.7         2.0  virginica
+#> 124          6.3         2.7          4.9         1.8  virginica
+#> 125          6.7         3.3          5.7         2.1  virginica
+#> 126          7.2         3.2          6.0         1.8  virginica
+#> 127          6.2         2.8          4.8         1.8  virginica
+#> 128          6.1         3.0          4.9         1.8  virginica
+#> 129          6.4         2.8          5.6         2.1  virginica
+#> 130          7.2         3.0          5.8         1.6  virginica
+#> 131          7.4         2.8          6.1         1.9  virginica
+#> 132          7.9         3.8          6.4         2.0  virginica
+#> 133          6.4         2.8          5.6         2.2  virginica
+#> 134          6.3         2.8          5.1         1.5  virginica
+#> 135          6.1         2.6          5.6         1.4  virginica
+#> 136          7.7         3.0          6.1         2.3  virginica
+#> 137          6.3         3.4          5.6         2.4  virginica
+#> 138          6.4         3.1          5.5         1.8  virginica
+#> 139          6.0         3.0          4.8         1.8  virginica
+#> 140          6.9         3.1          5.4         2.1  virginica
+#> 141          6.7         3.1          5.6         2.4  virginica
+#> 142          6.9         3.1          5.1         2.3  virginica
+#> 143          5.8         2.7          5.1         1.9  virginica
+#> 144          6.8         3.2          5.9         2.3  virginica
+#> 145          6.7         3.3          5.7         2.5  virginica
+#> 146          6.7         3.0          5.2         2.3  virginica
+#> 147          6.3         2.5          5.0         1.9  virginica
+#> 148          6.5         3.0          5.2         2.0  virginica
+#> 149          6.2         3.4          5.4         2.3  virginica
+#> 150          5.9         3.0          5.1         1.8  virginica
+p1$id # get id
+#> id: 040b7e90-039b-4388-ac59-1eeee8f7c100
+p1$validate(mtcars) # check if parameter can be updated
+#> [1] TRUE
+p1$set(mtcars) # set parameter to mtcars
+p1$print() # print it again
+#> [1] "tbl"
+
+# create table parameter with validation function that requires
+# all values in the first column to be less then 200 and that the
+# parameter have the same column names as the iris dataset
+p2 <- misc_parameter("tbl2", iris,
+                     function(x) all(names(x) %in% names(iris)) &&
+                                 all(x[[1]] < 200))
+print(p2) # print it
+#> <environment: 0x55f2791d5880>
+#> attr(,"class")
+#> [1] "MiscParameter" "MiscParameter" "Parameter"     "pproto"       
+#> [5] "proto"         "environment"  
+p2$get() # get value
+#>     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
+#> 1            5.1         3.5          1.4         0.2     setosa
+#> 2            4.9         3.0          1.4         0.2     setosa
+#> 3            4.7         3.2          1.3         0.2     setosa
+#> 4            4.6         3.1          1.5         0.2     setosa
+#> 5            5.0         3.6          1.4         0.2     setosa
+#> 6            5.4         3.9          1.7         0.4     setosa
+#> 7            4.6         3.4          1.4         0.3     setosa
+#> 8            5.0         3.4          1.5         0.2     setosa
+#> 9            4.4         2.9          1.4         0.2     setosa
+#> 10           4.9         3.1          1.5         0.1     setosa
+#> 11           5.4         3.7          1.5         0.2     setosa
+#> 12           4.8         3.4          1.6         0.2     setosa
+#> 13           4.8         3.0          1.4         0.1     setosa
+#> 14           4.3         3.0          1.1         0.1     setosa
+#> 15           5.8         4.0          1.2         0.2     setosa
+#> 16           5.7         4.4          1.5         0.4     setosa
+#> 17           5.4         3.9          1.3         0.4     setosa
+#> 18           5.1         3.5          1.4         0.3     setosa
+#> 19           5.7         3.8          1.7         0.3     setosa
+#> 20           5.1         3.8          1.5         0.3     setosa
+#> 21           5.4         3.4          1.7         0.2     setosa
+#> 22           5.1         3.7          1.5         0.4     setosa
+#> 23           4.6         3.6          1.0         0.2     setosa
+#> 24           5.1         3.3          1.7         0.5     setosa
+#> 25           4.8         3.4          1.9         0.2     setosa
+#> 26           5.0         3.0          1.6         0.2     setosa
+#> 27           5.0         3.4          1.6         0.4     setosa
+#> 28           5.2         3.5          1.5         0.2     setosa
+#> 29           5.2         3.4          1.4         0.2     setosa
+#> 30           4.7         3.2          1.6         0.2     setosa
+#> 31           4.8         3.1          1.6         0.2     setosa
+#> 32           5.4         3.4          1.5         0.4     setosa
+#> 33           5.2         4.1          1.5         0.1     setosa
+#> 34           5.5         4.2          1.4         0.2     setosa
+#> 35           4.9         3.1          1.5         0.2     setosa
+#> 36           5.0         3.2          1.2         0.2     setosa
+#> 37           5.5         3.5          1.3         0.2     setosa
+#> 38           4.9         3.6          1.4         0.1     setosa
+#> 39           4.4         3.0          1.3         0.2     setosa
+#> 40           5.1         3.4          1.5         0.2     setosa
+#> 41           5.0         3.5          1.3         0.3     setosa
+#> 42           4.5         2.3          1.3         0.3     setosa
+#> 43           4.4         3.2          1.3         0.2     setosa
+#> 44           5.0         3.5          1.6         0.6     setosa
+#> 45           5.1         3.8          1.9         0.4     setosa
+#> 46           4.8         3.0          1.4         0.3     setosa
+#> 47           5.1         3.8          1.6         0.2     setosa
+#> 48           4.6         3.2          1.4         0.2     setosa
+#> 49           5.3         3.7          1.5         0.2     setosa
+#> 50           5.0         3.3          1.4         0.2     setosa
+#> 51           7.0         3.2          4.7         1.4 versicolor
+#> 52           6.4         3.2          4.5         1.5 versicolor
+#> 53           6.9         3.1          4.9         1.5 versicolor
+#> 54           5.5         2.3          4.0         1.3 versicolor
+#> 55           6.5         2.8          4.6         1.5 versicolor
+#> 56           5.7         2.8          4.5         1.3 versicolor
+#> 57           6.3         3.3          4.7         1.6 versicolor
+#> 58           4.9         2.4          3.3         1.0 versicolor
+#> 59           6.6         2.9          4.6         1.3 versicolor
+#> 60           5.2         2.7          3.9         1.4 versicolor
+#> 61           5.0         2.0          3.5         1.0 versicolor
+#> 62           5.9         3.0          4.2         1.5 versicolor
+#> 63           6.0         2.2          4.0         1.0 versicolor
+#> 64           6.1         2.9          4.7         1.4 versicolor
+#> 65           5.6         2.9          3.6         1.3 versicolor
+#> 66           6.7         3.1          4.4         1.4 versicolor
+#> 67           5.6         3.0          4.5         1.5 versicolor
+#> 68           5.8         2.7          4.1         1.0 versicolor
+#> 69           6.2         2.2          4.5         1.5 versicolor
+#> 70           5.6         2.5          3.9         1.1 versicolor
+#> 71           5.9         3.2          4.8         1.8 versicolor
+#> 72           6.1         2.8          4.0         1.3 versicolor
+#> 73           6.3         2.5          4.9         1.5 versicolor
+#> 74           6.1         2.8          4.7         1.2 versicolor
+#> 75           6.4         2.9          4.3         1.3 versicolor
+#> 76           6.6         3.0          4.4         1.4 versicolor
+#> 77           6.8         2.8          4.8         1.4 versicolor
+#> 78           6.7         3.0          5.0         1.7 versicolor
+#> 79           6.0         2.9          4.5         1.5 versicolor
+#> 80           5.7         2.6          3.5         1.0 versicolor
+#> 81           5.5         2.4          3.8         1.1 versicolor
+#> 82           5.5         2.4          3.7         1.0 versicolor
+#> 83           5.8         2.7          3.9         1.2 versicolor
+#> 84           6.0         2.7          5.1         1.6 versicolor
+#> 85           5.4         3.0          4.5         1.5 versicolor
+#> 86           6.0         3.4          4.5         1.6 versicolor
+#> 87           6.7         3.1          4.7         1.5 versicolor
+#> 88           6.3         2.3          4.4         1.3 versicolor
+#> 89           5.6         3.0          4.1         1.3 versicolor
+#> 90           5.5         2.5          4.0         1.3 versicolor
+#> 91           5.5         2.6          4.4         1.2 versicolor
+#> 92           6.1         3.0          4.6         1.4 versicolor
+#> 93           5.8         2.6          4.0         1.2 versicolor
+#> 94           5.0         2.3          3.3         1.0 versicolor
+#> 95           5.6         2.7          4.2         1.3 versicolor
+#> 96           5.7         3.0          4.2         1.2 versicolor
+#> 97           5.7         2.9          4.2         1.3 versicolor
+#> 98           6.2         2.9          4.3         1.3 versicolor
+#> 99           5.1         2.5          3.0         1.1 versicolor
+#> 100          5.7         2.8          4.1         1.3 versicolor
+#> 101          6.3         3.3          6.0         2.5  virginica
+#> 102          5.8         2.7          5.1         1.9  virginica
+#> 103          7.1         3.0          5.9         2.1  virginica
+#> 104          6.3         2.9          5.6         1.8  virginica
+#> 105          6.5         3.0          5.8         2.2  virginica
+#> 106          7.6         3.0          6.6         2.1  virginica
+#> 107          4.9         2.5          4.5         1.7  virginica
+#> 108          7.3         2.9          6.3         1.8  virginica
+#> 109          6.7         2.5          5.8         1.8  virginica
+#> 110          7.2         3.6          6.1         2.5  virginica
+#> 111          6.5         3.2          5.1         2.0  virginica
+#> 112          6.4         2.7          5.3         1.9  virginica
+#> 113          6.8         3.0          5.5         2.1  virginica
+#> 114          5.7         2.5          5.0         2.0  virginica
+#> 115          5.8         2.8          5.1         2.4  virginica
+#> 116          6.4         3.2          5.3         2.3  virginica
+#> 117          6.5         3.0          5.5         1.8  virginica
+#> 118          7.7         3.8          6.7         2.2  virginica
+#> 119          7.7         2.6          6.9         2.3  virginica
+#> 120          6.0         2.2          5.0         1.5  virginica
+#> 121          6.9         3.2          5.7         2.3  virginica
+#> 122          5.6         2.8          4.9         2.0  virginica
+#> 123          7.7         2.8          6.7         2.0  virginica
+#> 124          6.3         2.7          4.9         1.8  virginica
+#> 125          6.7         3.3          5.7         2.1  virginica
+#> 126          7.2         3.2          6.0         1.8  virginica
+#> 127          6.2         2.8          4.8         1.8  virginica
+#> 128          6.1         3.0          4.9         1.8  virginica
+#> 129          6.4         2.8          5.6         2.1  virginica
+#> 130          7.2         3.0          5.8         1.6  virginica
+#> 131          7.4         2.8          6.1         1.9  virginica
+#> 132          7.9         3.8          6.4         2.0  virginica
+#> 133          6.4         2.8          5.6         2.2  virginica
+#> 134          6.3         2.8          5.1         1.5  virginica
+#> 135          6.1         2.6          5.6         1.4  virginica
+#> 136          7.7         3.0          6.1         2.3  virginica
+#> 137          6.3         3.4          5.6         2.4  virginica
+#> 138          6.4         3.1          5.5         1.8  virginica
+#> 139          6.0         3.0          4.8         1.8  virginica
+#> 140          6.9         3.1          5.4         2.1  virginica
+#> 141          6.7         3.1          5.6         2.4  virginica
+#> 142          6.9         3.1          5.1         2.3  virginica
+#> 143          5.8         2.7          5.1         1.9  virginica
+#> 144          6.8         3.2          5.9         2.3  virginica
+#> 145          6.7         3.3          5.7         2.5  virginica
+#> 146          6.7         3.0          5.2         2.3  virginica
+#> 147          6.3         2.5          5.0         1.9  virginica
+#> 148          6.5         3.0          5.2         2.0  virginica
+#> 149          6.2         3.4          5.4         2.3  virginica
+#> 150          5.9         3.0          5.1         1.8  virginica
+p2$id # get id
+#> id: 14b3e9a0-0615-40ab-a93b-7c4044df4025
+p2$validate(mtcars) # check if parameter can be updated
+#> [1] FALSE
+iris2 <- iris; iris2[1,1] <- 300 # create updated iris dataset
+p2$validate(iris2) # check if parameter can be updated
+#> [1] FALSE
+iris3 <- iris; iris2[1,1] <- 100 # create updated iris dataset
+p2$set(iris3) # set parameter to iris3
+p2$print() # print it again
+#> [1] "tbl2"
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/new_id.html b/docs/reference/new_id.html index 03704eec7..47674f574 100644 --- a/docs/reference/new_id.html +++ b/docs/reference/new_id.html @@ -1,101 +1,18 @@ - - - - - - - -Identifier — new_id • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Identifier — new_id • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Identifier

      - Source: R/Id.R + Source: R/Id.R
      @@ -184,60 +101,59 @@

      Identifier

      Generate a new unique identifier.

      - 
      new_id()
      - - -

      Value

      +
      Usage,
      new_id()
      +
      +

      Value

      Id object.

      -

      Details

      - -

      Identifiers are made using the uuid::UUIDgenerate().

      -

      See also

      - -

      uuid::UUIDgenerate().

      +
      +
      +

      Details

      +

      Identifiers are made using the uuid::UUIDgenerate().

      +
      +
      +

      See also

      +

      uuid::UUIDgenerate().

      +
      -

      Examples

      - 
      # create new id
-i <- new_id()
-
-# print id
-print(i)
-#> id: 43a158b3-35cc-4e7a-972f-6694d5f49029
-
-# convert to character
-as.character(i)
-#> [1] "43a158b3-35cc-4e7a-972f-6694d5f49029"
-
-# check if it is an Id object
-is.Id(i)
-#> [1] TRUE
-
+    
      
+    
      Examples
      
+    
      # create new id
+i <- new_id()
+
+# print id
+print(i)
+#> id: cadf51e9-ebce-425a-a5b7-d25c37c10b4e
+
+# convert to character
+as.character(i)
+#> [1] "cadf51e9-ebce-425a-a5b7-d25c37c10b4e"
+
+# check if it is an Id object
+is.Id(i)
+#> [1] TRUE
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/new_optimization_problem.html b/docs/reference/new_optimization_problem.html index 195dc76ab..cdc17fb33 100644 --- a/docs/reference/new_optimization_problem.html +++ b/docs/reference/new_optimization_problem.html @@ -1,101 +1,18 @@ - - - - - - - -Optimization problem — new_optimization_problem • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Optimization problem — new_optimization_problem • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Optimization problem

      - Source: R/new_optimization_problem.R + Source: R/new_optimization_problem.R
      -

      Generate a new empty OptimizationProblem object.

      +

      Generate a new empty OptimizationProblem object.

      - 
      new_optimization_problem()
      +
      Usage,
      new_optimization_problem()
      +
      +

      Value

      +

      OptimizationProblem object.

      +
      + -

      Value

      - -

      OptimizationProblem object.

      -

      See also

      - -

      OptimizationProblem-methods

      - -

      Examples

      - 
      # create empty OptimizationProblem object
-x <- new_optimization_problem()
-
-# print new object
-print(x)
-#> optimization problem (empty)
+    
      
+    
      Examples
      
+    
      # create empty OptimizationProblem object
+x <- new_optimization_problem()
+
+# print new object
+print(x)
+#> optimization problem (empty)
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/new_waiver.html b/docs/reference/new_waiver.html index 7bada84fd..304e96e5f 100644 --- a/docs/reference/new_waiver.html +++ b/docs/reference/new_waiver.html @@ -1,101 +1,18 @@ - - - - - - - -Waiver — new_waiver • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Waiver — new_waiver • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Waiver

      - Source: R/waiver.R + Source: R/waiver.R
      @@ -184,59 +101,57 @@

      Waiver

      Create a waiver object.

      - 
      new_waiver()
      - - -

      Value

      +
      Usage,
      new_waiver()
      +
      +

      Value

      Object of class Waiver.

      -

      Details

      - +
      +
      +

      Details

      This object is used to represent that the user has not manually specified a setting, and so defaults should be used. By explicitly using a new_waiver(), this means that NULL objects can be a valid setting. The use of a "waiver" object was inspired by the ggplot2 package.

      +
      -

      Examples

      - 
      # create new waiver object
-w <- new_waiver()
-
-# print object
-print(w)
-#> list()
-#> attr(,"class")
-#> [1] "Waiver"
-
-# is it a waiver object?
-is.Waiver(w)
-#> [1] TRUE
-
+    
      
+    
      Examples
      
+    
      # create new waiver object
+w <- new_waiver()
+
+# print object
+print(w)
+#> list()
+#> attr(,"class")
+#> [1] "Waiver"
+
+# is it a waiver object?
+is.Waiver(w)
+#> [1] TRUE
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/number_of_features.html b/docs/reference/number_of_features.html index f3cd964b8..30d9495c3 100644 --- a/docs/reference/number_of_features.html +++ b/docs/reference/number_of_features.html @@ -1,101 +1,18 @@ - - - - - - - -Number of features — number_of_features • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Number of features — number_of_features • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Number of features

      - Source: R/number_of_features.R + Source: R/number_of_features.R
      @@ -184,72 +101,66 @@

      Number of features

      Extract the number of features in an object.

      - 
      number_of_features(x)
-
-# S4 method for ConservationProblem
-number_of_features(x)
-
-# S4 method for OptimizationProblem
-number_of_features(x)
+    
      Usage,
      number_of_features(x)
 
-# S4 method for ZonesRaster
-number_of_features(x)
+# S4 method for ConservationProblem
+number_of_features(x)
 
-# S4 method for ZonesCharacter
-number_of_features(x)
      
+# S4 method for OptimizationProblem
+number_of_features(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      problem() (i.e. ConservationProblem),
-OptimizationProblem, or Zones() object.
      
+# S4 method for ZonesRaster
+number_of_features(x)
 
-    
      Value
      
+# S4 method for ZonesCharacter
+number_of_features(x)
      +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem), +OptimizationProblem, or Zones() object.

      +
      +
      +

      Value

      integer number of features.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.2) %>%
-     add_binary_decisions()
-
-# print number of features
-print(number_of_features(p))
-#> [1] 5
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.2) %>%
+     add_binary_decisions()
+
+# print number of features
+print(number_of_features(p))
+#> [1] 5
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/number_of_planning_units.html b/docs/reference/number_of_planning_units.html index 7e15f5915..348bc7403 100644 --- a/docs/reference/number_of_planning_units.html +++ b/docs/reference/number_of_planning_units.html @@ -1,101 +1,18 @@ - - - - - - - -Number of planning units — number_of_planning_units • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Number of planning units — number_of_planning_units • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Number of planning units

      - Source: R/number_of_planning_units.R + Source: R/number_of_planning_units.R
      @@ -184,66 +101,60 @@

      Number of planning units

      Extract the number of planning units in an object.

      - 
      number_of_planning_units(x)
-
-# S4 method for ConservationProblem
-number_of_planning_units(x)
-
-# S4 method for OptimizationProblem
-number_of_planning_units(x)
      +
      Usage,
      number_of_planning_units(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      problem() (i.e. ConservationProblem),
-OptimizationProblem, or Zones() object.
      
+# S4 method for ConservationProblem
+number_of_planning_units(x)
 
-    
      Value
      
+# S4 method for OptimizationProblem
+number_of_planning_units(x)
      +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem), +OptimizationProblem, or Zones() object.

      +
      +
      +

      Value

      integer number of planning units.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.2) %>%
-     add_binary_decisions()
-
-# print number of planning units
-print(number_of_planning_units(p))
-#> [1] 90
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.2) %>%
+     add_binary_decisions()
+
+# print number of planning units
+print(number_of_planning_units(p))
+#> [1] 90
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/number_of_total_units.html b/docs/reference/number_of_total_units.html index 043f5baa7..629e333e3 100644 --- a/docs/reference/number_of_total_units.html +++ b/docs/reference/number_of_total_units.html @@ -1,101 +1,18 @@ - - - - - - - -Number of total units — number_of_total_units • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Number of total units — number_of_total_units • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Number of total units

      - Source: R/number_of_total_units.R + Source: R/number_of_total_units.R
      @@ -184,81 +101,75 @@

      Number of total units

      Extract the number of total units in an object.

      - 
      number_of_total_units(x)
-
-# S4 method for ConservationProblem
-number_of_total_units(x)
      - -

      Arguments

      - - - - - - -
      x

      problem() (i.e. ConservationProblem), -OptimizationProblem, or Zones() object.

      +
      Usage,
      number_of_total_units(x)
 
-    
      Value
      
+# S4 method for ConservationProblem
+number_of_total_units(x)
      +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem), +OptimizationProblem, or Zones() object.

      +
      +
      +

      Value

      integer number of total units.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
-
-# create problem with one zone
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions()
-
-# print number of planning units
-print(number_of_planning_units(p1))
-#> [1] 90
-
-# print number of total units
-print(number_of_total_units(p1))
-#> [1] 100
-
-# create problem with multiple zones
-p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(0.2, ncol = 3, nrow = 5)) %>%
-      add_binary_decisions()
-
-# print number of planning units
-print(number_of_planning_units(p2))
-#> [1] 90
-
-# print number of total units
-print(number_of_total_units(p2))
-#> [1] 100
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_zones_stack, sim_features, sim_features_zones)
+
+# create problem with one zone
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions()
+
+# print number of planning units
+print(number_of_planning_units(p1))
+#> [1] 90
+
+# print number of total units
+print(number_of_total_units(p1))
+#> [1] 100
+
+# create problem with multiple zones
+p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(0.2, ncol = 3, nrow = 5)) %>%
+      add_binary_decisions()
+
+# print number of planning units
+print(number_of_planning_units(p2))
+#> [1] 90
+
+# print number of total units
+print(number_of_total_units(p2))
+#> [1] 100
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/number_of_zones.html b/docs/reference/number_of_zones.html index 89f83ea26..0a6687bef 100644 --- a/docs/reference/number_of_zones.html +++ b/docs/reference/number_of_zones.html @@ -1,101 +1,18 @@ - - - - - - - -Number of zones — number_of_zones • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Number of zones — number_of_zones • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Number of zones

      - Source: R/number_of_zones.R + Source: R/number_of_zones.R
      @@ -184,75 +101,69 @@

      Number of zones

      Extract the number of zones in an object.

      - 
      number_of_zones(x)
-
-# S4 method for ConservationProblem
-number_of_zones(x)
-
-# S4 method for OptimizationProblem
-number_of_zones(x)
+    
      Usage,
      number_of_zones(x)
 
-# S4 method for ZonesRaster
-number_of_zones(x)
+# S4 method for ConservationProblem
+number_of_zones(x)
 
-# S4 method for ZonesCharacter
-number_of_zones(x)
      
+# S4 method for OptimizationProblem
+number_of_zones(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      problem() (i.e. ConservationProblem),
-OptimizationProblem, or Zones() object.
      
+# S4 method for ZonesRaster
+number_of_zones(x)
 
-    
      Value
      
+# S4 method for ZonesCharacter
+number_of_zones(x)
      +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem), +OptimizationProblem, or Zones() object.

      +
      +
      +

      Value

      integer number of zones.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_zones_stack, sim_features_zones)
-
-# print number of zones in a Zones object
-print(number_of_zones(sim_features_zones))
-#> [1] 3
-# create problem with multiple zones
-p <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(matrix(0.2, ncol = 3, nrow = 5)) %>%
-     add_binary_decisions()
-
-# print number of zones in the problem
-print(number_of_zones(p))
-#> [1] 3
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_zones_stack, sim_features_zones)
+
+# print number of zones in a Zones object
+print(number_of_zones(sim_features_zones))
+#> [1] 3
+# create problem with multiple zones
+p <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(matrix(0.2, ncol = 3, nrow = 5)) %>%
+     add_binary_decisions()
+
+# print number of zones in the problem
+print(number_of_zones(p))
+#> [1] 3
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/objectives.html b/docs/reference/objectives.html index 52d355f18..b6615553b 100644 --- a/docs/reference/objectives.html +++ b/docs/reference/objectives.html @@ -1,107 +1,24 @@ - - - - - - - -Add an objective — objectives • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add an objective — objectives • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add an objective

      - Source: R/objectives.R + Source: R/objectives.R

      An objective is used to specify the overall goal of a conservation planning -problem(). All conservation planning problems involve minimizing +problem(). All conservation planning problems involve minimizing or maximizing some kind of objective. For instance, the planner may require a solution that conserves enough habitat for each species while minimizing the overall cost of the reserve network. Alternatively, the planner may @@ -196,141 +113,152 @@

      Add an objective

      ensuring that the cost of the reserve network does not exceed the budget.

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      Please note that all conservation planning problems formulated using the prioritizr package require an objective function---failing to do so will return an error message when attempting to solve problem.

      The following objectives can be added to a conservation planning -problem():

      -
      - -
      add_min_set_objective()

      Minimize the cost of the +problem():

      +
      add_min_set_objective()
      +

      Minimize the cost of the solution whilst ensuring that all targets are met. This objective is similar to that used in Marxan.

      -
      add_max_cover_objective()

      Represent at least one + +

      add_max_cover_objective()
      +

      Represent at least one instance of as many features as possible within a given budget.

      -
      add_max_features_objective()

      Fulfill as many targets as + +

      add_max_features_objective()
      +

      Fulfill as many targets as possible while ensuring that the cost of the solution does not exceed a budget.

      -
      add_min_shortfall_objective()

      Minimize the overall + +

      add_min_shortfall_objective()
      +

      Minimize the overall (weighted sum) shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget.

      -
      add_min_largest_shortfall_objective()

      Minimize the + +

      add_min_largest_shortfall_objective()
      +

      Minimize the largest (maximum) shortfall among all targets while ensuring that the cost of the solution does not exceed a budget.

      -
      add_max_phylo_div_objective()

      Maximize the phylogenetic + +

      add_max_phylo_div_objective()
      +

      Maximize the phylogenetic diversity of the features represented in the solution subject to a budget.

      -
      add_max_phylo_end_objective()

      Maximize the phylogenetic + +

      add_max_phylo_end_objective()
      +

      Maximize the phylogenetic endemism of the features represented in the solution subject to a budget.

      -
      add_max_utility_objective()

      Secure as much of the + +

      add_max_utility_objective()
      +

      Secure as much of the features as possible without exceeding a budget.

      -
      - -

      See also

      - -

      Other overviews: -constraints, -decisions, -importance, -penalties, -portfolios, -solvers, -summaries, -targets

      - -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features, sim_phylogeny)
-
-# create base problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_relative_targets(0.1) %>%
-     add_binary_decisions() %>%
-     add_default_solver(verbose = FALSE)
-
- # create problem with added minimum set objective
-p1 <- p %>% add_min_set_objective()
-
-# create problem with added maximum coverage objective
-# note that this objective does not use targets
-p2 <- p %>% add_max_cover_objective(500)
-
-# create problem with added maximum feature representation objective
-p3 <- p %>% add_max_features_objective(1900)
-
-# create problem with added minimum shortfall objective
-p4 <- p %>% add_min_shortfall_objective(1900)
-
-# create problem with added minimum largest shortfall objective
-p5 <- p %>% add_min_largest_shortfall_objective(1900)
-
-# create problem with added maximum phylogenetic diversity objective
-p6 <- p %>% add_max_phylo_div_objective(1900, sim_phylogeny)
-
-# create problem with added maximum phylogenetic diversity objective
-p7 <- p %>% add_max_phylo_end_objective(1900, sim_phylogeny)
-
-# create problem with added maximum utility objective
-# note that this objective does not use targets
-p8 <- p %>% add_max_utility_objective(1900)
-
-# \dontrun{
-# solve problems
-s <- stack(solve(p1), solve(p2), solve(p3), solve(p4), solve(p5), solve(p6),
-           solve(p7), solve(p8))
-#> Warning: ignoring targets since the specified objective function doesn't use targets
-#> Warning: ignoring targets since the specified objective function doesn't use targets
-#> Warning: ignoring targets since the specified objective function doesn't use targets
-#> Warning: ignoring targets since the specified objective function doesn't use targets
-
-# plot solutions
-plot(s, axes = FALSE, box = FALSE,
-     main = c("min set", "max coverage", "max features",
-              "min shortfall", "min largest shortfall",
-              "max phylogenetic diversity",
-              "max phylogenetic endemism", "max utility"))
-
-# }
+
+
      +
      +

      See also

      +

      Other overviews: +constraints, +decisions, +importance, +penalties, +portfolios, +solvers, +summaries, +targets

      +
      + +
      +

      Examples

      + 
      # load data
+data(sim_pu_raster, sim_features, sim_phylogeny)
+
+# create base problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_relative_targets(0.1) %>%
+     add_binary_decisions() %>%
+     add_default_solver(verbose = FALSE)
+
+ # create problem with added minimum set objective
+p1 <- p %>% add_min_set_objective()
+
+# create problem with added maximum coverage objective
+# note that this objective does not use targets
+p2 <- p %>% add_max_cover_objective(500)
+
+# create problem with added maximum feature representation objective
+p3 <- p %>% add_max_features_objective(1900)
+
+# create problem with added minimum shortfall objective
+p4 <- p %>% add_min_shortfall_objective(1900)
+
+# create problem with added minimum largest shortfall objective
+p5 <- p %>% add_min_largest_shortfall_objective(1900)
+
+# create problem with added maximum phylogenetic diversity objective
+p6 <- p %>% add_max_phylo_div_objective(1900, sim_phylogeny)
+
+# create problem with added maximum phylogenetic diversity objective
+p7 <- p %>% add_max_phylo_end_objective(1900, sim_phylogeny)
+
+# create problem with added maximum utility objective
+# note that this objective does not use targets
+p8 <- p %>% add_max_utility_objective(1900)
+
+# \dontrun{
+# solve problems
+s <- stack(solve(p1), solve(p2), solve(p3), solve(p4), solve(p5), solve(p6),
+           solve(p7), solve(p8))
+#> Warning: ignoring targets since the specified objective function doesn't use targets
+#> Warning: ignoring targets since the specified objective function doesn't use targets
+#> Warning: ignoring targets since the specified objective function doesn't use targets
+#> Warning: ignoring targets since the specified objective function doesn't use targets
+
+# plot solutions
+plot(s, axes = FALSE, box = FALSE,
+     main = c("min set", "max coverage", "max features",
+              "min shortfall", "min largest shortfall",
+              "max phylogenetic diversity",
+              "max phylogenetic endemism", "max utility"))
+
+# }
      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/parameters.html b/docs/reference/parameters.html index 6a3bdfe11..bdd9d2aae 100644 --- a/docs/reference/parameters.html +++ b/docs/reference/parameters.html @@ -1,101 +1,18 @@ - - - - - - - -Parameters — parameters • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Parameters — parameters • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Parameters

      - Source: R/parameters.R + Source: R/parameters.R
      @@ -184,66 +101,61 @@

      Parameters

      Create a new collection of Parameter objects.

      - 
      parameters(...)
      +
      Usage,
      parameters(...)
      -

      Arguments

      - - - - - - -
      ...

      Parameter objects.

      - -

      Value

      - -

      Parameters object.

      -

      See also

      - -

      array_parameters(), scalar_parameters().

      +
      +

      Arguments

      +
      ...
      +

      Parameter objects.

      +
      +
      +

      Value

      +

      Parameters object.

      +
      + -

      Examples

      - 
      # create two Parameter objects
-p1 <- binary_parameter("parameter one", 1)
-print(p1)
-#> parameter one (1)
-
-p2 <- numeric_parameter("parameter two", 5)
-print(p2)
-#> parameter two (5)
-
-# store Parameter objects in a Parameters object
-p <- parameters(p1, p2)
-print(p)
-#> <environment: 0x5642197ee900>
-#> attr(,"class")
-#> [1] "Parameters"  "pproto"      "proto"       "environment"
-
+    
      
+    
      Examples
      
+    
      # create two Parameter objects
+p1 <- binary_parameter("parameter one", 1)
+print(p1)
+#> parameter one (1)
+
+p2 <- numeric_parameter("parameter two", 5)
+print(p2)
+#> parameter two (5)
+
+# store Parameter objects in a Parameters object
+p <- parameters(p1, p2)
+print(p)
+#> <environment: 0x55f26c2269d8>
+#> attr(,"class")
+#> [1] "Parameters"  "pproto"      "proto"       "environment"
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/penalties.html b/docs/reference/penalties.html index e0750733d..4737e9bf6 100644 --- a/docs/reference/penalties.html +++ b/docs/reference/penalties.html @@ -1,105 +1,22 @@ - - - - - - - -Add a penalty — penalties • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add a penalty — penalties • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Add a penalty

      - Source: R/penalties.R + Source: R/penalties.R
      -

      A penalty can be applied to a conservation planning problem() to +

      A penalty can be applied to a conservation planning problem() to penalize solutions according to a specific metric. Penalties---unlike -constraints---act as an explicit trade-off with the objective -being minimized or maximized (e.g. solution cost when used with -add_min_set_objective()).

      +constraints---act as an explicit trade-off with the objective +being minimized or maximized (e.g., solution cost when used with +add_min_set_objective()).

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      Both penalties and constraints can be used to modify a problem and identify solutions that exhibit specific characteristics. Constraints work by invalidating solutions that do not exhibit specific characteristics. On the other hand, penalties work by specifying trade-offs against the main problem objective and are mediated by a penalty factor.

      The following penalties can be added to a conservation planning -problem():

      -
      - -
      add_boundary_penalties()

      Add penalties to a +problem():

      +
      add_boundary_penalties()
      +

      Add penalties to a conservation problem to favor solutions that have planning units clumped together into contiguous areas.

      -
      add_connectivity_penalties()

      Add penalties to a + +

      add_connectivity_penalties()
      +

      Add penalties to a conservation problem to favor solutions that select planning units with high connectivity between them.

      -
      add_linear_penalties()

      Add penalties to a + +

      add_linear_penalties()
      +

      Add penalties to a conservation problem to favor solutions that avoid selecting planning units based on a certain variable -(e.g. anthropogenic pressure).

      - - -
      - -

      See also

      - -

      Other overviews: -constraints, -decisions, -importance, -objectives, -portfolios, -solvers, -summaries, -targets

      +(e.g., anthropogenic pressure).

      + + + +
      +
      +

      See also

      +

      Other overviews: +constraints, +decisions, +importance, +objectives, +portfolios, +solvers, +summaries, +targets

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create basic problem
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with boundary penalties
-p2 <- p1 %>% add_boundary_penalties(5, 1)
-
-# create connectivity matrix based on spatial proximity
- scm <- as.data.frame(sim_pu_raster, xy = TRUE, na.rm = FALSE)
- scm <- 1 / (as.matrix(dist(scm)) + 1)
-
-# remove weak and moderate connections between planning units to reduce
-# run time
-scm[scm < 0.85] <- 0
-
-# create problem with connectivity penalties
-p3 <- p1 %>% add_connectivity_penalties(25, data = scm)
-
-# create problem with linear penalties,
-# here the penalties will be based on random numbers to keep it simple
-# \dontrun{
-# simulate penalty data
-# (note this requires the RandomFields package to be installed)
-sim_penalty_raster <- simulate_cost(sim_pu_raster)
-
-# plot penalty data
-plot(sim_penalty_raster, main = "penalty data", axes = FALSE, box = FALSE)
-
-
-# create problem with linear penalties, with a penalty scaling factor of 100
-p4 <- p1 %>% add_linear_penalties(100, data = sim_penalty_raster)
-
-# solve problems
-s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
-
-# plot solutions
-plot(s, axes = FALSE, box = FALSE,
-     main = c("basic solution", "boundary penalties",
-              "connectivity penalties", "linear penalties"))
-
- # }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create basic problem
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with boundary penalties
+p2 <- p1 %>% add_boundary_penalties(5, 1)
+
+# create connectivity matrix based on spatial proximity
+ scm <- as.data.frame(sim_pu_raster, xy = TRUE, na.rm = FALSE)
+ scm <- 1 / (as.matrix(dist(scm)) + 1)
+
+# remove weak and moderate connections between planning units to reduce
+# run time
+scm[scm < 0.85] <- 0
+
+# create problem with connectivity penalties
+p3 <- p1 %>% add_connectivity_penalties(25, data = scm)
+
+# create problem with linear penalties,
+# here the penalties will be based on random numbers to keep it simple
+# \dontrun{
+# simulate penalty data
+# (note this requires the RandomFields package to be installed)
+sim_penalty_raster <- simulate_cost(sim_pu_raster)
+
+# plot penalty data
+plot(sim_penalty_raster, main = "penalty data", axes = FALSE, box = FALSE)
+
+
+# create problem with linear penalties, with a penalty scaling factor of 100
+p4 <- p1 %>% add_linear_penalties(100, data = sim_penalty_raster)
+
+# solve problems
+s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
+
+# plot solutions
+plot(s, axes = FALSE, box = FALSE,
+     main = c("basic solution", "boundary penalties",
+              "connectivity penalties", "linear penalties"))
+
+ # }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/pipe.html b/docs/reference/pipe.html index 2ff599fc3..140894358 100644 --- a/docs/reference/pipe.html +++ b/docs/reference/pipe.html @@ -1,102 +1,19 @@ - - - - - - - -Pipe operator — %>% • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Pipe operator — %>% • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Pipe operator

      - Source: R/magrittr-operators.R + Source: R/magrittr-operators.R
      @@ -186,64 +103,60 @@

      Pipe operator

      as a series of imperative procedures.

      +
      Usage,NULL
      -

      Arguments

      - - - - - - -
      lhs, rhs

      An object and a function.

      - -

      Value

      - +
      +

      Arguments

      +
      lhs, rhs
      +

      An object and a function.

      +
      +
      +

      Value

      An object.

      -

      See also

      - -

      magrittr::%>%(), tee().

      +
      +
      +

      See also

      +

      magrittr::%>%(), tee().

      +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# generate 100 random numbers and calculate the mean
-mean(runif(100))
-#> [1] 0.473179
-
-# reset the seed
-set.seed(500)
-
-# repeat the previous procedure but use the pipe operator instead of nesting
-# function calls inside each other.
-runif(100) %>% mean()
-#> [1] 0.473179
-
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# generate 100 random numbers and calculate the mean
+mean(runif(100))
+#> [1] 0.473179
+
+# reset the seed
+set.seed(500)
+
+# repeat the previous procedure but use the pipe operator instead of nesting
+# function calls inside each other.
+runif(100) %>% mean()
+#> [1] 0.473179
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/portfolios.html b/docs/reference/portfolios.html index e89300785..83e4f2c6e 100644 --- a/docs/reference/portfolios.html +++ b/docs/reference/portfolios.html @@ -1,109 +1,26 @@ - - - - - - - -Solution portfolios — portfolios • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Solution portfolios — portfolios • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Solution portfolios

      - Source: R/portfolios.R + Source: R/portfolios.R
      @@ -192,32 +109,33 @@

      Solution portfolios

      Conservation planning exercises rarely have access to all the data needed to identify the truly perfect solution. This is because available data may lack important details -(e.g. land acquisition costs may be unavailable), contain errors -(e.g. species presence/absence data may have false positives), +(e.g., land acquisition costs may be unavailable), contain errors +(e.g., species presence/absence data may have false positives), or key objectives may not be formally incorporated into the -prioritization process (e.g. future land use requirements). +prioritization process (e.g., future land use requirements). As such, conservation planners can help decision makers by providing them with a portfolio of solutions to inform their decision.

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      The following portfolios can be added to a conservation planning -problem(). +problem(). Note that all methods for generating portfolios return solutions that are within the specified optimality gap.

      -
      - -
      add_extra_portfolio()

      Generate a portfolio of solutions +

      add_extra_portfolio()
      +

      Generate a portfolio of solutions by storing feasible solutions found during the optimization process. This method is useful for quickly obtaining multiple solutions, but does not provide any guarantees on the number of solutions, or the quality of solutions. Note that it requires the Gurobi solver.

      -
      add_top_portfolio()

      Generate a portfolio of + +

      add_top_portfolio()
      +

      Generate a portfolio of solutions by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions). This is useful for examining differences among near-optimal solutions. @@ -225,113 +143,117 @@

      Details to calculate selection frequencies for small problems. Note that it requires the Gurobi solver.

      -
      add_gap_portfolio()

      Generate a portfolio of solutions + +

      add_gap_portfolio()
      +

      Generate a portfolio of solutions by finding a certain number of solutions that are all within a pre- specified optimality gap. This method is useful for generating multiple solutions that can be used to calculate selection frequencies for moderate and large-sized problems (similar to Marxan). Note that it requires the Gurobi solver.

      -
      add_cuts_portfolio()

      Generate a portfolio of distinct + +

      add_cuts_portfolio()
      +

      Generate a portfolio of distinct solutions within a pre-specified optimality gap using Bender's cuts. -This is recommended as a replacement for add_top_portfolio() +This is recommended as a replacement for add_top_portfolio() when the Gurobi software is not available.

      -
      add_shuffle_portfolio()

      Generate a portfolio of + +

      add_shuffle_portfolio()
      +

      Generate a portfolio of solutions by randomly reordering the data prior to attempting to solve the problem. -This is recommended as a replacement for add_gap_portfolio() +This is recommended as a replacement for add_gap_portfolio() when the Gurobi software is not available.

      -
      -

      See also

      - -

      Other overviews: -constraints, -decisions, -importance, -objectives, -penalties, -solvers, -summaries, -targets

      +
      +
      +

      See also

      +

      Other overviews: +constraints, +decisions, +importance, +objectives, +penalties, +solvers, +summaries, +targets

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.1) %>%
-     add_binary_decisions() %>%
-     add_default_solver(gap = 0.02, verbose = FALSE)
-
-# create problem with cuts portfolio with 4 solutions
-p1 <- p %>% add_cuts_portfolio(4)
-
-# create problem with shuffle portfolio with 4 solutions
-p2 <- p %>% add_shuffle_portfolio(4)
-# \dontrun{
-# create problem with extra portfolio
-p3 <- p %>% add_extra_portfolio()
-
-# create problem with top portfolio with 4 solutions
-p4 <- p %>% add_top_portfolio(4)
-
-# create problem with gap portfolio with 4 solutions within 50% of optimality
-p5 <- p %>% add_gap_portfolio(4, 0.5)
-
-# solve problems and create solution portfolios
-s <- list(solve(p1), solve(p2), solve(p3), solve(p4), solve(p5))
-
-# plot solutions from extra portfolio
-plot(stack(s[[1]]), axes = FALSE, box = FALSE)
-
-
-# plot solutions from top portfolio
-plot(stack(s[[2]]), axes = FALSE, box = FALSE)
-
-
-# plot solutions from gap portfolio
-plot(stack(s[[3]]), axes = FALSE, box = FALSE)
-
-
-# plot solutions from cuts portfolio
-plot(stack(s[[4]]), axes = FALSE, box = FALSE)
-
-
-# plot solutions from shuffle portfolio
-plot(stack(s[[5]]), axes = FALSE, box = FALSE)
-
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.1) %>%
+     add_binary_decisions() %>%
+     add_default_solver(gap = 0.02, verbose = FALSE)
+
+# create problem with cuts portfolio with 4 solutions
+p1 <- p %>% add_cuts_portfolio(4)
+
+# create problem with shuffle portfolio with 4 solutions
+p2 <- p %>% add_shuffle_portfolio(4)
+# \dontrun{
+# create problem with extra portfolio
+p3 <- p %>% add_extra_portfolio()
+
+# create problem with top portfolio with 4 solutions
+p4 <- p %>% add_top_portfolio(4)
+
+# create problem with gap portfolio with 4 solutions within 50% of optimality
+p5 <- p %>% add_gap_portfolio(4, 0.5)
+
+# solve problems and create solution portfolios
+s <- list(solve(p1), solve(p2), solve(p3), solve(p4), solve(p5))
+
+# plot solutions from extra portfolio
+plot(stack(s[[1]]), axes = FALSE, box = FALSE)
+
+
+# plot solutions from top portfolio
+plot(stack(s[[2]]), axes = FALSE, box = FALSE)
+
+
+# plot solutions from gap portfolio
+plot(stack(s[[3]]), axes = FALSE, box = FALSE)
+
+
+# plot solutions from cuts portfolio
+plot(stack(s[[4]]), axes = FALSE, box = FALSE)
+
+
+# plot solutions from shuffle portfolio
+plot(stack(s[[5]]), axes = FALSE, box = FALSE)
+
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/pproto.html b/docs/reference/pproto.html index 6f6831aa0..6f027b21a 100644 --- a/docs/reference/pproto.html +++ b/docs/reference/pproto.html @@ -1,102 +1,19 @@ - - - - - - - -Create a new pproto object — pproto • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Create a new pproto object — pproto • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Create a new pproto object

      - Source: R/pproto.R + Source: R/pproto.R
      @@ -186,79 +103,68 @@

      Create a new pproto object

      from the ggproto system used in the ggplot2 package.

      - 
      pproto(`_class` = NULL, `_inherit` = NULL, ...)
      +
      Usage,
      pproto(`_class` = NULL, `_inherit` = NULL, ...)
      -

      Arguments

      - - - - - - - - - - - - - - -
      _class

      Class name to assign to the object. This is stored as the class +

      +

      Arguments

      +
      _class
      +

      Class name to assign to the object. This is stored as the class attribute of the object. This is optional: if NULL (the default), -no class name will be added to the object.

      _inherit

      pproto object to inherit from. If NULL, don"t -inherit from any object.

      ...

      A list of members to add to the new pproto object.

      - - -

      Examples

      - 
      Adder <- pproto("Adder",
-  x = 0,
-  add = function(self, n) {
-    self$x <- self$x + n
-    self$x
-  }
-)
-
-Adder$add(10)
-#> [1] 10
-Adder$add(10)
-#> [1] 20
-
-Abacus <- pproto("Abacus", Adder,
-  subtract = function(self, n) {
-    self$x <- self$x - n
-    self$x
-  }
-)
-Abacus$add(10)
-#> [1] 30
-Abacus$subtract(10)
-#> [1] 20
-
+no class name will be added to the object.
      
+
      _inherit
      
+
      pproto object to inherit from. If NULL, don"t
+inherit from any object.
      
+
      ...
      
+
      A list of members to add to the new pproto object.
      
+
      + +
      +

      Examples

      + 
      Adder <- pproto("Adder",
+  x = 0,
+  add = function(self, n) {
+    self$x <- self$x + n
+    self$x
+  }
+)
+
+Adder$add(10)
+#> [1] 10
+Adder$add(10)
+#> [1] 20
+
+Abacus <- pproto("Abacus", Adder,
+  subtract = function(self, n) {
+    self$x <- self$x - n
+    self$x
+  }
+)
+Abacus$add(10)
+#> [1] 30
+Abacus$subtract(10)
+#> [1] 20
+
      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/predefined_optimization_problem.html b/docs/reference/predefined_optimization_problem.html index 7cd15ac98..10a84e51f 100644 --- a/docs/reference/predefined_optimization_problem.html +++ b/docs/reference/predefined_optimization_problem.html @@ -1,101 +1,18 @@ - - - - - - - -Predefined optimization problem — predefined_optimization_problem • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Predefined optimization problem — predefined_optimization_problem • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Predefined optimization problem

      - Source: R/predefined_optimization_problem.R + Source: R/predefined_optimization_problem.R
      -

      Create a new OptimizationProblem object.

      +

      Create a new OptimizationProblem object.

      - 
      predefined_optimization_problem(x)
      - -

      Arguments

      - - - - - - -
      x

      list object containing data to construct the problem.

      - -

      Details

      +
      Usage,
      predefined_optimization_problem(x)
      +
      +

      Arguments

      +
      x
      +

      list object containing data to construct the problem.

      +
      +
      +

      Details

      The argument to x must be a list that contains the following elements:

      -
      +
      modelsense
      +

      character model sense.

      + + +
      number_of_features
      +

      integer number of features in problem.

      + + +
      number_of_planning_units
      +

      integer number of planning units.

      + -
      modelsense

      character model sense.

      +
      A_i
      +

      integer row indices for problem matrix.

      -
      number_of_features

      integer number of features in problem.

      -
      number_of_planning_units

      integer number of planning units.

      +
      A_j
      +

      integer column indices for problem matrix.

      -
      A_i

      integer row indices for problem matrix.

      -
      A_j

      integer column indices for problem matrix.

      +
      A_x
      +

      numeric values for problem matrix.

      -
      A_x

      numeric values for problem matrix.

      -
      obj

      numeric objective function values.

      +
      obj
      +

      numeric objective function values.

      -
      lb

      numeric lower bound for decision values.

      -
      ub

      numeric upper bound for decision values.

      +
      lb
      +

      numeric lower bound for decision values.

      -
      rhs

      numeric right-hand side values.

      -
      sense

      numeric constraint senses.

      +
      ub
      +

      numeric upper bound for decision values.

      -
      vtype

      character variable types. These are used to specify + +

      rhs
      +

      numeric right-hand side values.

      + + +
      sense
      +

      numeric constraint senses.

      + + +
      vtype
      +

      character variable types. These are used to specify that the decision variables are binary ("B") or continuous ("C").

      -
      row_ids

      character identifiers for the rows in the problem + +

      row_ids
      +

      character identifiers for the rows in the problem matrix.

      -
      col_ids

      character identifiers for the columns in the problem + +

      col_ids
      +

      character identifiers for the columns in the problem matrix.

      -
      - - -

      Examples

      - 
      # create list with problem data
-l <- list(modelsense = "min", number_of_features = 2,
-          number_of_planning_units = 3, number_of_zones = 1,
-          A_i = c(0L, 1L, 0L, 1L, 0L, 1L), A_j = c(0L, 0L, 1L, 1L, 2L, 2L),
-          A_x = c(2, 10, 1, 10, 1, 10), obj = c(1, 2, 2), lb = c(0, 1, 0),
-          ub = c(0, 1, 1), rhs = c(2, 10), compressed_formulation = TRUE,
-          sense = c(">=", ">="), vtype = c("B", "B", "B"),
-          row_ids = c("spp_target", "spp_target"),
-          col_ids = c("pu", "pu", "pu"))
-
-# create OptimizationProblem object
-x <- predefined_optimization_problem(l)
-
-# print new object
-print(x)
-#> optimization problem
-#>   model sense: min
-#>   dimensions:  2, 3, 6 (nrow, ncol, ncell)
-#>   variables:   3 (B)
+
+
      + +
      +

      Examples

      + 
      # create list with problem data
+l <- list(modelsense = "min", number_of_features = 2,
+          number_of_planning_units = 3, number_of_zones = 1,
+          A_i = c(0L, 1L, 0L, 1L, 0L, 1L), A_j = c(0L, 0L, 1L, 1L, 2L, 2L),
+          A_x = c(2, 10, 1, 10, 1, 10), obj = c(1, 2, 2), lb = c(0, 1, 0),
+          ub = c(0, 1, 1), rhs = c(2, 10), compressed_formulation = TRUE,
+          sense = c(">=", ">="), vtype = c("B", "B", "B"),
+          row_ids = c("spp_target", "spp_target"),
+          col_ids = c("pu", "pu", "pu"))
+
+# create OptimizationProblem object
+x <- predefined_optimization_problem(l)
+
+# print new object
+print(x)
+#> optimization problem
+#>   model sense: min
+#>   dimensions:  2, 3, 6 (nrow, ncol, ncell)
+#>   variables:   3 (B)
      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/presolve_check.html b/docs/reference/presolve_check.html index 40b5ca9d3..6166e7d59 100644 --- a/docs/reference/presolve_check.html +++ b/docs/reference/presolve_check.html @@ -1,108 +1,25 @@ - - - - - - - -Presolve check — presolve_check • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Presolve check — presolve_check • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Presolve check

      - Source: R/presolve_check.R + Source: R/presolve_check.R
      -

      Check a conservation planning problem() for potential issues +

      Check a conservation planning problem() for potential issues before trying to solve it. Specifically, problems are checked for (i) values that are likely to result in "strange" solutions and (ii) values that are likely to cause numerical instability issues and lead to unreasonably long @@ -198,37 +115,34 @@

      Presolve check

      verify if a problem has a feasible solution or not.

      - 
      presolve_check(x)
-
-# S3 method for ConservationProblem
-presolve_check(x)
+    
      Usage,
      presolve_check(x)
 
-# S3 method for OptimizationProblem
-presolve_check(x)
      
+# S3 method for ConservationProblem
+presolve_check(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      problem() (i.e. ConservationProblem) or
-OptimizationProblem object.
      
-
-    
      Value
      
+# S3 method for OptimizationProblem
+presolve_check(x)
      +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) or +OptimizationProblem object.

      +
      +
      +

      Value

      logical value indicating if all checks are passed successfully.

      -

      Details

      - +
      +
      +

      Details

      This function checks for issues that are likely to result in "strange" solutions. Specifically, it checks if (i) all planning units are locked in, (ii) all planning units are locked out, and (iii) all planning units have negative cost values (after applying penalties if any were specified). Although such conservation planning problems are mathematically valid, they are generally the result of a coding mistake -when building the problem (e.g. using an absurdly high +when building the problem (e.g., using an absurdly high penalty value or using the wrong dataset to lock in planning units). Thus such issues, if they are indeed issues and not false positives, can be fixed by carefully checking the code, data, and parameters used to build @@ -236,22 +150,22 @@

      Details

      This function then checks for values that may lead to numerical instability issues when solving the problem. Specifically, it checks if the range of values in certain components of the optimization problem are over a -certain threshold (i.e. \(1 \times 10 ^9\)) or if the values +certain threshold (i.e., \(1 \times 10 ^9\)) or if the values themselves exceed a certain threshold -(i.e. \(1 \times 10^{10}\)). +(i.e., \(1 \times 10^{10}\)). In most cases, such issues will simply cause an exact algorithm solver to take a very long time to generate a solution. In rare cases, such issues can cause incorrect calculations which can lead to exact algorithm solvers returning infeasible solutions -(e.g. a solution to the minimum set problem where not all targets are met) -or solutions that exceed the specified optimality gap (e.g. a suboptimal +(e.g., a solution to the minimum set problem where not all targets are met) +or solutions that exceed the specified optimality gap (e.g., a suboptimal solution when a zero optimality gap is specified).

      What can you do if a conservation planning problem fails to pass these checks? Well, this function will have thrown some warning messages describing the source of these issues, so read them carefully. For instance, a common issue is when a relatively large penalty value is -specified for boundary (add_boundary_penalties()) or -connectivity penalties (add_connectivity_penalties()). This +specified for boundary (add_boundary_penalties()) or +connectivity penalties (add_connectivity_penalties()). This can be fixed by trying a smaller penalty value. In such cases, the original penalty value supplied was so high that the optimal solution would just have selected every single planning unit in the solution---and @@ -261,7 +175,7 @@

      Details costs of the planning units in terms of USD then you might have some planning units that cost over one billion dollars in large-scale planning exercises. This can be fixed by rescaling the values so that they -are smaller (e.g. multiplying the values by a number smaller than one, or +are smaller (e.g., multiplying the values by a number smaller than one, or expressing them as a fraction of the maximum cost). Let's consider another common issue, let's pretend that you used habitat suitability models to predict the amount of suitable habitat @@ -287,7 +201,7 @@

      Details solving the problem, you will need to manually recalculate the cost of the solutions but at least now you can be confident that you have the optimal solution. Now let's pretend that you are using the maximum features -objective (i.e. add_max_features_objective()) and assigned some +objective (i.e., add_max_features_objective()) and assigned some really high weights to the targets for some features to ensure that their targets were met in the optimal solution. If you set the weights for these features to one billion then you will probably run into numerical @@ -295,133 +209,132 @@

      Details guarantee that these features will be represented in the optimal solution and use this value instead of one billion. This minimum weight value can be calculated as the sum of the weight values for the other features -and adding a small number to it (e.g. 1). Finally, if you're running out +and adding a small number to it (e.g., 1). Finally, if you're running out of ideas for addressing numerical stability issues you have one remaining option: you can use the numeric_focus argument in the -add_gurobi_solver() function to tell the solver to pay extra +add_gurobi_solver() function to tell the solver to pay extra attention to numerical instability issues. This is not a free lunch, however, because telling the solver to pay extra attention to numerical issues can substantially increase run time. So, if you have problems that are already taking an unreasonable time to solve, then this will not help at all.

      -

      See also

      - -

      problem(), solve(), https://www.gurobi.com/documentation/9.1/refman/numerics_gurobi_guidelines.html.

      +
      + -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features)
-
-# create minimal problem with no issues
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions()
-
-# run presolve checks
-# note that no warning is thrown which suggests that we should not
-# encounter any numerical stability issues when trying to solve the problem
-print(presolve_check(p1))
-#> [1] TRUE
-
-# create a minimal problem, containing cost values that are really
-# high so that they could cause numerical instability issues when trying
-# to solve it
-sim_pu_raster2 <- sim_pu_raster
-sim_pu_raster2[1] <- 1e+15
-p2 <- problem(sim_pu_raster2, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions()
-
-# run presolve checks
-# note that a warning is thrown which suggests that we might encounter
-# some issues, such as long solve time or suboptimal solutions, when
-# trying to solve the problem
-print(presolve_check(p2))
-#> Warning: planning units with very high (> 1e+6) or very low (< 1e-6) non-zero cost values note this may be a false positive
-#> [1] FALSE
-
-# create a minimal problem with connectivity penalties values that have
-# a really high penalty value that is likely to cause numerical instability
-# issues when trying to solve the it
-cm <- adjacency_matrix(sim_pu_raster)
-p3 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_connectivity_penalties(1e+15, data = cm) %>%
-      add_binary_decisions()
-
-# run presolve checks
-# note that a warning is thrown which suggests that we might encounter
-# some numerical instability issues when trying to solve the problem
-print(presolve_check(p3))
-#> Warning: penalty multiplied connectivity values are very high
-#> [1] FALSE
-# \dontrun{
-# let's forcibly solve the problem using Gurobi and tell it to
-# be extra careful about numerical instability problems
-s3 <- p3 %>%
-      add_gurobi_solver(numeric_focus = TRUE) %>%
-      solve(force = TRUE)
-#> Warning: penalty multiplied connectivity values are very high
-#> Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-#> Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-#> Optimize a model with 581 rows, 378 columns and 1602 nonzeros
-#> Model fingerprint: 0xaaf590f0
-#> Variable types: 0 continuous, 378 integer (378 binary)
-#> Coefficient statistics:
-#>   Matrix range     [2e-01, 1e+00]
-#>   Objective range  [2e+02, 1e+15]
-#>   Bounds range     [1e+00, 1e+00]
-#>   RHS range        [3e+00, 8e+00]
-#> Warning: Model contains large objective coefficients
-#> Found heuristic solution: objective -2.88000e+17
-#> 
-#> Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
-#> Thread count was 1 (of 8 available processors)
-#> 
-#> Solution count 1: -2.88e+17 
-#> No other solutions better than -2.88e+17
-#> 
-#> Optimal solution found (tolerance 1.00e-01)
-#> Best objective -2.880000000000e+17, best bound -2.880000000000e+17, gap 0.0000%
-
-# plot solution
-# we can see that all planning units were selected because the connectivity
-# penalty is so high that cost becomes irrelevant, so we should try using
-# a much lower penalty value
-plot(s3, main = "solution", axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features)
+
+# create minimal problem with no issues
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions()
+
+# run presolve checks
+# note that no warning is thrown which suggests that we should not
+# encounter any numerical stability issues when trying to solve the problem
+print(presolve_check(p1))
+#> [1] TRUE
+
+# create a minimal problem, containing cost values that are really
+# high so that they could cause numerical instability issues when trying
+# to solve it
+sim_pu_raster2 <- sim_pu_raster
+sim_pu_raster2[1] <- 1e+15
+p2 <- problem(sim_pu_raster2, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions()
+
+# run presolve checks
+# note that a warning is thrown which suggests that we might encounter
+# some issues, such as long solve time or suboptimal solutions, when
+# trying to solve the problem
+print(presolve_check(p2))
+#> Warning: planning units with very high (> 1e+6) or very low (< 1e-6) non-zero cost values note this may be a false positive
+#> [1] FALSE
+
+# create a minimal problem with connectivity penalties values that have
+# a really high penalty value that is likely to cause numerical instability
+# issues when trying to solve the it
+cm <- adjacency_matrix(sim_pu_raster)
+p3 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_connectivity_penalties(1e+15, data = cm) %>%
+      add_binary_decisions()
+
+# run presolve checks
+# note that a warning is thrown which suggests that we might encounter
+# some numerical instability issues when trying to solve the problem
+print(presolve_check(p3))
+#> Warning: penalty multiplied connectivity values are very high
+#> [1] FALSE
+# \dontrun{
+# let's forcibly solve the problem using Gurobi and tell it to
+# be extra careful about numerical instability problems
+s3 <- p3 %>%
+      add_gurobi_solver(numeric_focus = TRUE) %>%
+      solve(force = TRUE)
+#> Warning: penalty multiplied connectivity values are very high
+#> Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+#> Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+#> Optimize a model with 581 rows, 378 columns and 1602 nonzeros
+#> Model fingerprint: 0xaaf590f0
+#> Variable types: 0 continuous, 378 integer (378 binary)
+#> Coefficient statistics:
+#>   Matrix range     [2e-01, 1e+00]
+#>   Objective range  [2e+02, 1e+15]
+#>   Bounds range     [1e+00, 1e+00]
+#>   RHS range        [3e+00, 8e+00]
+#> Warning: Model contains large objective coefficients
+#> Found heuristic solution: objective -2.88000e+17
+#> 
+#> Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
+#> Thread count was 1 (of 8 available processors)
+#> 
+#> Solution count 1: -2.88e+17 
+#> No other solutions better than -2.88e+17
+#> 
+#> Optimal solution found (tolerance 1.00e-01)
+#> Best objective -2.880000000000e+17, best bound -2.880000000000e+17, gap 0.0000%
+
+# plot solution
+# we can see that all planning units were selected because the connectivity
+# penalty is so high that cost becomes irrelevant, so we should try using
+# a much lower penalty value
+plot(s3, main = "solution", axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/print.html b/docs/reference/print.html index 9697dde62..5c4d3f511 100644 --- a/docs/reference/print.html +++ b/docs/reference/print.html @@ -1,101 +1,18 @@ - - - - - - - -Print — print • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Print — print • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Print

      - Source: R/print.R + Source: R/print.R
      @@ -184,85 +101,78 @@

      Print

      Display information about an object.

      - 
      # S3 method for ConservationProblem
-print(x, ...)
+    
      Usage,
      # S3 method for ConservationProblem
+print(x, ...)
 
-# S3 method for ConservationModifier
-print(x, ...)
+# S3 method for ConservationModifier
+print(x, ...)
 
-# S3 method for Id
-print(x, ...)
+# S3 method for Id
+print(x, ...)
 
-# S4 method for Id
-print(x)
+# S4 method for Id
+print(x)
 
-# S3 method for OptimizationProblem
-print(x, ...)
+# S3 method for OptimizationProblem
+print(x, ...)
 
-# S3 method for ScalarParameter
-print(x, ...)
+# S3 method for ScalarParameter
+print(x, ...)
 
-# S3 method for ArrayParameter
-print(x, ...)
+# S3 method for ArrayParameter
+print(x, ...)
 
-# S3 method for Solver
-print(x, ...)
+# S3 method for Solver
+print(x, ...)
 
-# S3 method for Zones
-print(x, ...)
+# S3 method for Zones
+print(x, ...)
 
-# S4 method for tbl_df
-print(x)
      
-
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
      x
      Any object.
      ...
      not used.
      
-
-    
      Value
      
+# S4 method for tbl_df
+print(x)
      +
      +

      Arguments

      +
      x
      +

      Any object.

      +
      ...
      +

      not used.

      +
      +
      +

      Value

      None.

      -

      See also

      - -

      base::print().

      +
      +
      +

      See also

      +

      base::print().

      +
      -

      Examples

      - 
      a <- 1:4
-print(a)
-#> [1] 1 2 3 4
+    
      
+    
      Examples
      
+    
      a <- 1:4
+print(a)
+#> [1] 1 2 3 4
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/prioritizr-deprecated.html b/docs/reference/prioritizr-deprecated.html index 656e5b995..4147df6fb 100644 --- a/docs/reference/prioritizr-deprecated.html +++ b/docs/reference/prioritizr-deprecated.html @@ -1,61 +1,5 @@ - - - - - - - -Deprecation notice — prioritizr-deprecated • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Deprecation notice — prioritizr-deprecated • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Deprecation notice

      - Source: R/deprecated.R + Source: R/deprecated.R
      @@ -201,110 +118,120 @@

      Deprecation notice

      (where applicable). If a function is described as being renamed, then this means that only the name of the function has changed -(i.e. the inputs, outputs, and underlying code remain the same).

      +(i.e., the inputs, outputs, and underlying code remain the same).

      - 
      add_connected_constraints(...)
+    
      Usage,
      add_connected_constraints(...)
 
-add_corridor_constraints(...)
+add_corridor_constraints(...)
 
-set_number_of_threads(...)
+set_number_of_threads(...)
 
-get_number_of_threads(...)
+get_number_of_threads(...)
 
-is.parallel(...)
+is.parallel(...)
 
-add_pool_portfolio(...)
+add_pool_portfolio(...)
 
-connected_matrix(...)
+connected_matrix(...)
 
-feature_representation(...)
+feature_representation(...)
 
-replacement_cost(...)
+replacement_cost(...)
 
-rarity_weighted_richness(...)
+rarity_weighted_richness(...)
 
-ferrier_score(...)
      
-
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      ...
      not used.
      
-
-    
      Details
      
+ferrier_score(...)
      +
      +

      Arguments

      +
      ...
      +

      not used.

      +
      +
      +

      Details

      The following functions have been deprecated:

      -
      +
      add_connected_constraints()
      +

      renamed +as the add_contiguity_constraints() function.

      + -
      add_connected_constraints()

      renamed -as the add_contiguity_constraints() function.

      +
      add_corridor_constraints()
      +

      replaced by the +add_feature_contiguity_constraints() function.

      -
      add_corridor_constraints()

      replaced by the -add_feature_contiguity_constraints() function.

      -
      set_number_of_threads()

      no longer needed used with the +

      set_number_of_threads()
      +

      no longer needed used with the implementation of superior data extraction.

      -
      get_number_of_threads()

      no longer needed used with the + +

      get_number_of_threads()
      +

      no longer needed used with the implementation of superior data extraction.

      -
      is.parallel()

      no longer needed used with the + +

      is.parallel()
      +

      no longer needed used with the implementation of superior data extraction.

      -
      add_pool_portfolio()

      replaced by the -add_extra_portfolio() and add_top_portfolio().

      -
      connected_matrix()

      renamed as -the adjacency_matrix() function.

      +
      add_pool_portfolio()
      +

      replaced by the +add_extra_portfolio() and add_top_portfolio().

      + + +
      connected_matrix()
      +

      renamed as +the adjacency_matrix() function.

      -
      feature_representation()

      replaced by -the eval_feature_representation_summary() function for consistency with + +

      feature_representation()
      +

      replaced by +the eval_feature_representation_summary() function for consistency with other functions.

      -
      replacement_cost()

      renamed as -the eval_replacement_importance() function for consistency with + +

      replacement_cost()
      +

      renamed as +the eval_replacement_importance() function for consistency with other functions for evaluating solutions.

      -
      rarity_weighted_richness()

      renamed as -the eval_rare_richness_importance() function for consistency with + +

      rarity_weighted_richness()
      +

      renamed as +the eval_rare_richness_importance() function for consistency with other functions for evaluating solutions.

      -
      ferrier_score()

      renamed as -the eval_ferrier_importance() function for consistency with + +

      ferrier_score()
      +

      renamed as +the eval_ferrier_importance() function for consistency with other functions for evaluating solutions.

      -
      +
      + - - - - - - - - - - - + diff --git a/docs/reference/prioritizr.html b/docs/reference/prioritizr.html index 58ed38bc1..1f6c9fedf 100644 --- a/docs/reference/prioritizr.html +++ b/docs/reference/prioritizr.html @@ -1,61 +1,5 @@ - - - - - - - -prioritizr: Systematic Conservation Prioritization in R — prioritizr • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -prioritizr: Systematic Conservation Prioritization in R — prioritizr • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      prioritizr: Systematic Conservation Prioritization in R

      - Source: R/package.R + Source: R/package.R
      @@ -218,49 +135,60 @@

      prioritizr: Systematic Conservation Prioritization in R

      conservation planning program (Ball et al. 2009), and find much cheaper solutions in a much shorter period of time than Marxan (Beyer et al. 2016). See the -online code repository +online code repository for more information.

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      This package contains several vignettes that are designed to showcase its functionality. To view them, please use the code vignette("name", package = "prioritizr") where "name" is the -name of the desired vignette (e.g. "gurobi_installation").

      -
      - -
      prioritizr

      Background information on systematic conservation +name of the desired vignette (e.g., "gurobi_installation").

      +
      prioritizr
      +

      Background information on systematic conservation planning and a comprehensive overview of the package and its usage.

      -
      tasmania

      Tutorial using Tasmania, Australia + +

      tasmania
      +

      Tutorial using Tasmania, Australia as a case-study. This tutorial uses vector-based planning unit data and is written for individuals familiar with the Marxan decision support tool.

      -
      saltspring

      Tutorial using Salt Spring Island, Canada as a + +

      saltspring
      +

      Tutorial using Salt Spring Island, Canada as a case-study. This tutorial uses raster-based planning unit data.

      -
      zones

      Tutorial on using multiple management actions or zones + +

      zones
      +

      Tutorial on using multiple management actions or zones to create detailed prioritizations.

      -
      gurobi_installation

      Instructions for installing and setting up + +

      gurobi_installation
      +

      Instructions for installing and setting up the Gurobi optimization software for use with the package.

      -
      solver_benchmark

      Reports run times for solving + +

      solver_benchmark
      +

      Reports run times for solving conservation planning problems of varying size and complexity using different solvers.

      -
      publication_record

      List of publications that have cited the -package.

      +
      publication_record
      +

      List of publications that have cited the +package.

      -
      -

      References

      +
      +
      +

      References

      Ball IR, Possingham HP, and Watts M (2009) Marxan and relatives: Software for spatial conservation prioritisation in Spatial conservation prioritisation: Quantitative methods and computational tools. Eds Moilanen @@ -274,31 +202,27 @@

      R

      Rodrigues AS, Cerdeira OJ, and Gaston KJ (2000) Flexibility, efficiency, and accountability: adapting reserve selection algorithms to more complex conservation problems. Ecography, 23: 565--574.

      +

      +
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zzklAb>z6h|u_0N`@aFk%rXap4Zf%G?mtw!Hspl4H01-DwcYzyyCkXg)nc@w6saMa_fZSyWKx;4LRdqJIjS$x|Qimmy0C%ByoUcQ$5W`Znu@75nGd!H>4 z&Hb(`%48|`({eXtgVR2eb0g-kG+Bkjh|C6A{7qJq7v~~9$+RSV9z!ZpTkIcgsr9sl zl;Br91(LjD@XEw{+&QlBKdtd+^3vQbu%cjr56@o}Vm9Cc>%uZ@F;iv{phBhD(v|DG z4fgykB6>niedP_&M~OAlyl-SY0B5B6)(ZY!R|=@NKxL5mTxKSy=X*0t_0ZH#kOz#- z48z<~gNTHqJS1I$?ZyKxARPBgGM;rCh`F?P38(|&D9adPt6b$z15$RM^+Y@W4+)%Z zMZ%}f^*PlP`|i7yWv1GLgbCOLSX`|vRxO*6uI%|Uw?-GOnGVFJyN7)Wy!%p>DAd$x zGqrTSaROdk60BFHinK*3u6fT81WDJnY)`z9}X1x954=ZmXs3f9w>DYAdav8 z%7mGh7BN0pg`%`yf>heuI()xp$ - - - - - - -Conservation planning problem — problem • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Conservation planning problem — problem • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Conservation planning problem

      - Source: R/problem.R + Source: R/problem.R
      @@ -194,99 +111,94 @@

      Conservation planning problem

      Create a systematic conservation planning problem. This function is used to specify the basic data used in a spatial prioritization problem: the spatial distribution of the planning units and their costs, as well as -the features (e.g. species, ecosystems) that need to be conserved. After +the features (e.g., species, ecosystems) that need to be conserved. After constructing this ConservationProblem-class object, it can be -customized to meet specific goals using objectives, -targets, constraints, and -penalties. After building the problem, the -solve() function can be used to identify solutions. +customized to meet specific goals using objectives, +targets, constraints, and +penalties. After building the problem, the +solve() function can be used to identify solutions. Note that problems require an objective, and failing to specify an an objective will throw an error when attempting to solve it.

      - 
      problem(x, features, ...)
+    
      Usage,
      problem(x, features, ...)
 
-# S4 method for Raster,Raster
-problem(x, features, run_checks, ...)
+# S4 method for Raster,Raster
+problem(x, features, run_checks, ...)
 
-# S4 method for Raster,ZonesRaster
-problem(x, features, run_checks, ...)
+# S4 method for Raster,ZonesRaster
+problem(x, features, run_checks, ...)
 
-# S4 method for Spatial,Raster
-problem(x, features, cost_column, run_checks, ...)
+# S4 method for Spatial,Raster
+problem(x, features, cost_column, run_checks, ...)
 
-# S4 method for Spatial,ZonesRaster
-problem(x, features, cost_column, run_checks, ...)
+# S4 method for Spatial,ZonesRaster
+problem(x, features, cost_column, run_checks, ...)
 
-# S4 method for Spatial,character
-problem(x, features, cost_column, ...)
+# S4 method for Spatial,character
+problem(x, features, cost_column, ...)
 
-# S4 method for Spatial,ZonesCharacter
-problem(x, features, cost_column, ...)
+# S4 method for Spatial,ZonesCharacter
+problem(x, features, cost_column, ...)
 
-# S4 method for data.frame,character
-problem(x, features, cost_column, ...)
+# S4 method for data.frame,character
+problem(x, features, cost_column, ...)
 
-# S4 method for data.frame,ZonesCharacter
-problem(x, features, cost_column, ...)
+# S4 method for data.frame,ZonesCharacter
+problem(x, features, cost_column, ...)
 
-# S4 method for data.frame,data.frame
-problem(x, features, rij, cost_column, zones, ...)
+# S4 method for data.frame,data.frame
+problem(x, features, rij, cost_column, zones, ...)
 
-# S4 method for numeric,data.frame
-problem(x, features, rij_matrix, ...)
+# S4 method for numeric,data.frame
+problem(x, features, rij_matrix, ...)
 
-# S4 method for matrix,data.frame
-problem(x, features, rij_matrix, ...)
+# S4 method for matrix,data.frame
+problem(x, features, rij_matrix, ...)
 
-# S4 method for sf,Raster
-problem(x, features, cost_column, run_checks, ...)
+# S4 method for sf,Raster
+problem(x, features, cost_column, run_checks, ...)
 
-# S4 method for sf,ZonesRaster
-problem(x, features, cost_column, run_checks, ...)
+# S4 method for sf,ZonesRaster
+problem(x, features, cost_column, run_checks, ...)
 
-# S4 method for sf,character
-problem(x, features, cost_column, ...)
+# S4 method for sf,character
+problem(x, features, cost_column, ...)
 
-# S4 method for sf,ZonesCharacter
-problem(x, features, cost_column, ...)
      
+# S4 method for sf,ZonesCharacter
+problem(x, features, cost_column, ...)
      -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      x

      Raster, -sf::st_sf(), -SpatialPolygonsDataFrame, -SpatialLinesDataFrame, -SpatialPointsDataFrame, -data.frame() object, -numeric() vector, or -matrix() specifying the planning units to use in the reserve +

      +

      Arguments

      +
      x
      +

      Raster, +sf::st_sf(), +SpatialPolygonsDataFrame, +SpatialLinesDataFrame, +SpatialPointsDataFrame, +data.frame() object, +numeric() vector, or +matrix() specifying the planning units to use in the reserve design exercise and their corresponding cost. It may be desirable to exclude some planning units from the analysis, for example those outside the study area. To exclude planning units, set the cost for those raster -cells to NA, or use the add_locked_out_constraint function.

      features

      The feature data can be specified in a variety of ways. -The specific formats that can be used depend on the cost data format (i.e. +cells to NA, or use the add_locked_out_constraint function.

      +
      features
      +

      The feature data can be specified in a variety of ways. +The specific formats that can be used depend on the cost data format (i.e., argument to x) and whether the problem should have a single zone or multiple zones. If the problem should have a single zone, then the feature -data can be specified following:

        -

      • x = RasterLayer-class, or -x = Spatial-class, or -x = sf::st_sf(): +data can be specified following:

        • x = RasterLayer-class, or +x = Spatial-class, or +x = sf::st_sf(): y = Raster-class object showing the distribution of conservation features. Missing -values (i.e. NA values) can be used to indicate the absence of +values (i.e., NA values) can be used to indicate the absence of a feature in a particular cell instead of explicitly setting these cells to zero. Note that this argument type for features can only be used to specify data for problems involving a single zone.

          • -

        • x = Spatial-class, or -x = sf::st_sf(), or +

        • x = Spatial-class, or +x = sf::st_sf(), or x = data.frame: y = character vector with column names that correspond to the abundance or occurrence of @@ -301,112 +213,113 @@

          Arg rij or rij_matrix must also be supplied. This type of argument should follow the conventions used by Marxan, wherein each row corresponds to a different feature. It must also contain the -following columns:

          -
          id

          integer unique identifier for each feature +following columns:

          id
          +

          integer unique identifier for each feature These identifiers are used in the argument to rij.

          -
          name

          character name for each feature.

          -
          prop

          numeric relative target for each feature + +

          name
          +

          character name for each feature.

          + +
          prop
          +

          numeric relative target for each feature (optional).

          -
          amount

          numeric absolute target for each + +

          amount
          +

          numeric absolute target for each feature (optional).

          -

          • -
        -

        If the problem should have multiple zones, then the feature -data can be specified following:

          -

        • x = RasterStack-class, or +

          • +

        If the problem should have multiple zones, then the feature +data can be specified following:

      ...

      not used.

      run_checks

      logical flag indicating whether checks should be + +

      ...
      +

      not used.

      +
      run_checks
      +

      logical flag indicating whether checks should be run to ensure the integrity of the input data. These checks are run by default; however, for large datasets they may increase run time. If it is taking a prohibitively long time to create the prioritization problem, it -is suggested to try setting run_checks to FALSE.

      cost_column

      character name or integer indicating the +is suggested to try setting run_checks to FALSE.

      +
      cost_column
      +

      character name or integer indicating the column(s) with the cost data. This argument must be supplied when the -argument to x is a Spatial or +argument to x is a Spatial or data.frame object. This argument should contain the name of each column containing cost data for each management zone when creating problems with multiple zones. To create a problem with a single zone, then -set the argument to cost_column as a single column name.

      rij

      data.frame containing information on the amount of +set the argument to cost_column as a single column name.

      +
      rij
      +

      data.frame containing information on the amount of each feature in each planning unit assuming each management zone. Similar to data.frame arguments for features, the data.frame objects must follow the conventions used by Marxan. Note that the "zone" column is not needed for problems involving a single management zone. Specifically, the argument should contain the following -columns:

      -
      pu

      integer planning unit identifier.

      -
      species

      integer feature identifier.

      -
      zone

      integer zone identifier (optional for +columns:

      pu
      +

      integer planning unit identifier.

      + +
      species
      +

      integer feature identifier.

      + +
      zone
      +

      integer zone identifier (optional for problems involving a single zone).

      -
      amount

      numeric amount of the feature in the + +

      amount
      +

      numeric amount of the feature in the planning unit.

      -
      zones

      data.frame containing information on the zones. This + + +

      zones
      +

      data.frame containing information on the zones. This argument is only used when argument to x and y are both data.frame objects and the problem being built contains multiple zones. Following conventions used in MarZone, this argument should contain the following columns: -columns:

      -
      id

      integer zone identifier.

      -
      name

      character zone name.

      - -
      rij_matrix

      list of matrix or -dgCMatrix +columns:

      id
      +

      integer zone identifier.

      + +
      name
      +

      character zone name.

      + + +
      +
      rij_matrix
      +

      list of matrix or +dgCMatrix objects specifying the amount of each feature (rows) within each planning unit (columns) for each zone. The list elements denote different zones, matrix rows denote features, and matrix columns denote planning units. For convenience, the argument to rij_matrix can be a single matrix or -dgCMatrix when specifying a problem with a +dgCMatrix when specifying a problem with a single management zone. This argument is only used when the argument -to x is a numeric or matrix object.

      - -

      Value

      - -

      ConservationProblem object containing +to x is a numeric or matrix object.

      +
      +
      +

      Value

      +

      ConservationProblem object containing data for a prioritization.

      -

      Details

      - +
      +
      +

      Details

      A systematic conservation planning exercise leverages data to help inform conservation decision making. To help ensure that the data -- and resulting prioritizations -- are relevant to the over-arching @@ -421,33 +334,33 @@

      Details (see the Management Zones vignette for details). After deciding on the management action(s), you can compile the following data.

      First, you will need to create a set of planning units -(i.e. discrete spatial areas) to inform decision making. +(i.e., discrete spatial areas) to inform decision making. Planning units are often created by subdividing a study region into a set square or hexagonal cells. They can also be created using -administrative boundaries (e.g. provinces), land management boundaries -(e.g. property boundaries derived from cadastral data), or -ecological boundaries (e.g. based on ecosystem classification data). -The size (i.e. spatial grain) of the planning units is often determined +administrative boundaries (e.g., provinces), land management boundaries +(e.g., property boundaries derived from cadastral data), or +ecological boundaries (e.g., based on ecosystem classification data). +The size (i.e., spatial grain) of the planning units is often determined based on a compromise between the scale needed to inform decision making, the spatial accuracy (resolution) of available datasets, and the computational resources available for generating prioritizations -(e.g. RAM and number of CPUs on your computer).

      +(e.g., RAM and number of CPUs on your computer).

      Second, you will need data to quantify the cost of implementing implementing each management action within each planning unit. Critically, the cost data should reflect the management action(s) considered in the exercise. For example, costs are often specified using data that reflect economic -expenditure (e.g. land acquisition cost), -socioeconomic conditions (e.g. human population density), +expenditure (e.g., land acquisition cost), +socioeconomic conditions (e.g., human population density), opportunity costs of foregone commercial activities -(e.g. logging or agriculture), or +(e.g., logging or agriculture), or opportunity costs of foregone recreational activities -(e.g. recreational fishing) activities, +(e.g., recreational fishing) activities, In some cases -- depending on the management action(s) considered -- it can make sense to use a constant cost value -(e.g. all planning units are assigned a cost value equal to one) +(e.g., all planning units are assigned a cost value equal to one) or use a cost value based on spatial extent -(e.g. each planning unit is assigned a cost value based on its total area). +(e.g., each planning unit is assigned a cost value based on its total area). Also, in most cases, you want to avoid negative cost values. This because a negative value means that a place is desirable for implementing a management action, and such places will almost @@ -457,13 +370,13 @@

      Details To achieve this, you will need to select a set of conservation features that relate to the over-arching goals of the exercise. For example, conservation features often include -species (e.g. Clouded Leopard), habitats (e.g. mangroves or +species (e.g., Clouded Leopard), habitats (e.g., mangroves or cloud forest), or ecosystems. The benefit that each feature derives from a planning unit -can take a variety of forms, but is typically occupancy (i.e. +can take a variety of forms, but is typically occupancy (i.e., presence or absence), area of occurrence within each planning unit -(e.g. based on species' geographic range data), or -a measure of habitat suitability (e.g. estimated using a statistical model). +(e.g., based on species' geographic range data), or +a measure of habitat suitability (e.g., estimated using a statistical model). After compiling these data, you have the minimal data need to generate a prioritization.

      A systematic conservation planning exercise involves prioritizing a set of @@ -479,20 +392,21 @@

      Details conservation plans. The decision variables are what we control, and usually there is one binary variable for each planning unit to specify whether that unit is selected or not (but other approaches are available, see -decisions). The constraints can be thought of as rules that must be +decisions). The constraints can be thought of as rules that must be followed. For example, constraints can be used to ensure a prioritization must stay within a certain budget. These constraints can also leverage additional data to help ensure that prioritizations meet the over-arching goals of the exercise. For example, to account for existing conservation efforts, you could obtain data delineating the extent of existing protected areas and use constraints to lock in planning units that are covered by them -(see add_locked_in_constraints).

      -

      Optimization

      - +(see add_locked_in_constraints).

      +
      +
      +

      Optimization

      The prioritizr package uses exact algorithms to solve reserve design -problems (see solvers for details). +problems (see solvers for details). To achieve this, it internally formulates mathematical optimization problems using mixed integer linear programming (MILP). The general form of such problems can be expressed in matrix notation using @@ -512,286 +426,285 @@

      < representation level of feature \(i\) in planning unit \(j\). If you wish to see exactly how a conservation planning problem is formulated as mixed integer linear programming problem, you can use -the write_problem() function to save the optimization problem +the write_problem() function to save the optimization problem to a plain-text file on your computer and then view it using a standard -text editor (e.g. Notepad).

      +text editor (e.g., Notepad).

      Please note that this function internally computes the amount of each feature in each planning unit when this data is not supplied (using the -rij_matrix function). As a consequence, it can take a while to +rij_matrix function). As a consequence, it can take a while to initialize large-scale conservation planning problems that involve millions of planning units.

      -

      See also

      - -

      See solve() for details on solving a problem to generate solutions. -Also, see objectives, penalties, targets, constraints, -decisions, portfolios, solvers for information on customizing problems. -Additionally, see summaries and importance for information on +

      +
      +

      See also

      +

      See solve() for details on solving a problem to generate solutions. +Also, see objectives, penalties, targets, constraints, +decisions, portfolios, solvers for information on customizing problems. +Additionally, see summaries and importance for information on evaluating solutions.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_polygons, sim_pu_lines, sim_pu_points,
-     sim_pu_sf, sim_features)
-
-# create problem using raster planning unit data
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# \dontrun{
-# create problem using polygon (Spatial) planning unit data
-p2 <- problem(sim_pu_polygons, sim_features, "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem using line (Spatial) planning unit data
-p3 <- problem(sim_pu_lines, sim_features, "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem using point (Spatial) planning unit data
-p4 <- problem(sim_pu_points, sim_features, "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem using polygon (sf) planning unit data
-p5 <- problem(sim_pu_sf, sim_features, "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# since geo-processing can be slow for large spatial vector datasets
-# (e.g. polygons, lines, points), it can be worthwhile to pre-process the
-# planning unit data so that it contains columns indicating the amount of
-# each feature inside each planning unit
-# (i.e. each column corresponds to a different feature)
-
-# calculate the amount of each species within each planning unit
-# (i.e. SpatialPolygonsDataFrame object)
-pre_proc_data <- rij_matrix(sim_pu_polygons, sim_features)
-
-# add extra columns to the polygon (Spatial) planning unit data
-# to indicate the amount of each species within each planning unit
-pre_proc_data <- as.data.frame(t(as.matrix(pre_proc_data)))
-names(pre_proc_data) <- names(sim_features)
-sim_pu_polygons@data <- cbind(sim_pu_polygons@data, pre_proc_data)
-
-# create problem using the polygon (Spatial) planning unit data
-# with the pre-processed columns
-p6 <- problem(sim_pu_polygons, features = names(pre_proc_data), "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# this strategy of pre-processing columns can be used for sf objects too
-pre_proc_data2 <- rij_matrix(sim_pu_sf, sim_features)
-pre_proc_data2 <- as.data.frame(t(as.matrix(pre_proc_data2)))
-names(pre_proc_data2) <- names(sim_features)
-sim_pu_sf <- cbind(sim_pu_sf, pre_proc_data2)
-
-# create problem using the polygon (sf) planning unit data
-# with pre-processed columns
-p7 <- problem(sim_pu_sf, features = names(pre_proc_data2), "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# in addition to spatially explicit data, pre-processed aspatial data
-# can also be used to create a problem
-# (e.g. data created using external spreadsheet software)
-costs <- sim_pu_polygons$cost
-features <- data.frame(id = seq_len(nlayers(sim_features)),
-                       name = names(sim_features))
-rij_mat <- rij_matrix(sim_pu_polygons, sim_features)
-p8 <- problem(costs, features, rij_matrix = rij_mat) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve problems
-s1 <- solve(p1)
-s2 <- solve(p2)
-s3 <- solve(p3)
-s4 <- solve(p4)
-s5 <- solve(p5)
-s6 <- solve(p6)
-s7 <- solve(p7)
-s8 <- solve(p8)
-
-# plot solutions for problems associated with spatial data
-par(mfrow = c(3, 2), mar = c(0, 0, 4.1, 0))
-plot(s1, main = "raster data", axes = FALSE, box = FALSE, legend = FALSE)
-
-plot(s2, main = "polygon data")
-plot(s2[s2$solution_1 > 0.5, ], col = "darkgreen", add = TRUE)
-
-plot(s3, main = "line data")
-lines(s3[s3$solution_1 > 0.5, ], col = "darkgreen", lwd = 2)
-
-plot(s4, main = "point data", pch = 19)
-points(s4[s4$solution_1 > 0.5, ], col = "darkgreen", cex = 2, pch = 19)
-
-# note that as_Spatial() is for convenience to plot all solutions together
-plot(as_Spatial(s5), main = "sf (polygon) data", pch = 19)
-plot(as_Spatial(s5[s5$solution_1 > 0.5, ]), col = "darkgreen", add = TRUE)
-
-plot(s6, main = "preprocessed data (polygon data)", pch = 19)
-plot(s6[s6$solution_1 > 0.5, ], col = "darkgreen", add = TRUE)
-
-
-# show solutions for problems associated with aspatial data
-str(s8)
-#>  num [1:90] 0 0 0 0 0 0 0 0 0 1 ...
-#>  - attr(*, "objective")= Named num 3586
-#>   ..- attr(*, "names")= chr "solution_1"
-#>  - attr(*, "status")= Named chr "OPTIMAL"
-#>   ..- attr(*, "names")= chr "solution_1"
-#>  - attr(*, "runtime")= Named num 0.003
-#>   ..- attr(*, "names")= chr "solution_1"
-# }
-# create some problems with multiple zones
-
-# first, create a matrix containing the targets for multi-zone problems
-# here each row corresponds to a different feature, each
-# column corresponds to a different zone, and values correspond
-# to the total (absolute) amount of a given feature that needs to be secured
-# in a given zone
-targets <- matrix(rpois(15, 1),
-                  nrow = number_of_features(sim_features_zones),
-                  ncol = number_of_zones(sim_features_zones),
-                  dimnames = list(feature_names(sim_features_zones),
-                                  zone_names(sim_features_zones)))
-
-# print targets
-print(targets)
-#>           zone_1 zone_2 zone_3
-#> feature_1      2      0      0
-#> feature_2      1      1      2
-#> feature_3      3      3      2
-#> feature_4      1      2      0
-#> feature_5      2      1      1
-
-# create a multi-zone problem with raster data
-p8 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_absolute_targets(targets) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve problem
-s8 <- solve(p8)
-
-# plot solution
-# here, each layer/panel corresponds to a different zone and pixel values
-# indicate if a given planning unit has been allocated to a given zone
-par(mfrow = c(1, 1))
-plot(s8, main = c("zone 1", "zone 2", "zone 3"), axes = FALSE, box = FALSE)
-
-
-# alternatively, the category_layer function can be used to create
-# a new raster object containing the zone ids for each planning unit
-# in the solution (note this only works for problems with binary decisions)
-par(mfrow = c(1, 1))
-plot(category_layer(s8), axes = FALSE, box = FALSE)
-
-
-# create a multi-zone problem with polygon data
-p9 <- problem(sim_pu_zones_polygons, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_absolute_targets(targets) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve problem
-s9 <- solve(p9)
-
-# create column containing the zone id for which each planning unit was
-# allocated to in the solution
-s9$solution <- category_vector(s9@data[, c("solution_1_zone_1",
-                                           "solution_1_zone_2",
-                                           "solution_1_zone_3")])
-s9$solution <- factor(s9$solution)
-
-# plot solution
-spplot(s9, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
-
-
-# create a multi-zone problem with polygon planning unit data
-# and where fields (columns) in the attribute table correspond
-# to feature abundances
-
-# first fields need to be added to the planning unit data
-# which indicate the amount of each feature in each zone
-# to do this, the fields will be populated with random counts
-sim_pu_zones_polygons$spp1_z1 <- rpois(nrow(sim_pu_zones_polygons), 1)
-sim_pu_zones_polygons$spp2_z1 <- rpois(nrow(sim_pu_zones_polygons), 1)
-sim_pu_zones_polygons$spp3_z1 <- rpois(nrow(sim_pu_zones_polygons), 1)
-sim_pu_zones_polygons$spp1_z2 <- rpois(nrow(sim_pu_zones_polygons), 1)
-sim_pu_zones_polygons$spp2_z2 <- rpois(nrow(sim_pu_zones_polygons), 1)
-sim_pu_zones_polygons$spp3_z2 <- rpois(nrow(sim_pu_zones_polygons), 1)
-
-# create problem with polygon planning unit data and use field names
-# to indicate feature data
-# additionally, to make this example slightly more interesting,
-# the problem will have prfoportion-type decisions such that
-# a proportion of each planning unit can be allocated to each of the
-# two management zones
-p10 <- problem(sim_pu_zones_polygons,
-               zones(c("spp1_z1", "spp2_z1", "spp3_z1"),
-                     c("spp1_z2", "spp2_z2", "spp3_z2"),
-                     zone_names = c("z1", "z2")),
-               cost_column = c("cost_1", "cost_2")) %>%
-       add_min_set_objective() %>%
-       add_absolute_targets(targets[1:3, 1:2]) %>%
-       add_proportion_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve problem
-s10 <- solve(p10)
-
-# plot solution
-spplot(s10, zcol = c("solution_1_z1", "solution_1_z2"), main = "solution",
-       axes = FALSE, box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_polygons, sim_pu_lines, sim_pu_points,
+     sim_pu_sf, sim_features)
+
+# create problem using raster planning unit data
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# \dontrun{
+# create problem using polygon (Spatial) planning unit data
+p2 <- problem(sim_pu_polygons, sim_features, "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem using line (Spatial) planning unit data
+p3 <- problem(sim_pu_lines, sim_features, "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem using point (Spatial) planning unit data
+p4 <- problem(sim_pu_points, sim_features, "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem using polygon (sf) planning unit data
+p5 <- problem(sim_pu_sf, sim_features, "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# since geo-processing can be slow for large spatial vector datasets
+# (e.g., polygons, lines, points), it can be worthwhile to pre-process the
+# planning unit data so that it contains columns indicating the amount of
+# each feature inside each planning unit
+# (i.e., each column corresponds to a different feature)
+
+# calculate the amount of each species within each planning unit
+# (i.e., SpatialPolygonsDataFrame object)
+pre_proc_data <- rij_matrix(sim_pu_polygons, sim_features)
+
+# add extra columns to the polygon (Spatial) planning unit data
+# to indicate the amount of each species within each planning unit
+pre_proc_data <- as.data.frame(t(as.matrix(pre_proc_data)))
+names(pre_proc_data) <- names(sim_features)
+sim_pu_polygons@data <- cbind(sim_pu_polygons@data, pre_proc_data)
+
+# create problem using the polygon (Spatial) planning unit data
+# with the pre-processed columns
+p6 <- problem(sim_pu_polygons, features = names(pre_proc_data), "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# this strategy of pre-processing columns can be used for sf objects too
+pre_proc_data2 <- rij_matrix(sim_pu_sf, sim_features)
+pre_proc_data2 <- as.data.frame(t(as.matrix(pre_proc_data2)))
+names(pre_proc_data2) <- names(sim_features)
+sim_pu_sf <- cbind(sim_pu_sf, pre_proc_data2)
+
+# create problem using the polygon (sf) planning unit data
+# with pre-processed columns
+p7 <- problem(sim_pu_sf, features = names(pre_proc_data2), "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# in addition to spatially explicit data, pre-processed aspatial data
+# can also be used to create a problem
+# (e.g., data created using external spreadsheet software)
+costs <- sim_pu_polygons$cost
+features <- data.frame(id = seq_len(nlayers(sim_features)),
+                       name = names(sim_features))
+rij_mat <- rij_matrix(sim_pu_polygons, sim_features)
+p8 <- problem(costs, features, rij_matrix = rij_mat) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve problems
+s1 <- solve(p1)
+s2 <- solve(p2)
+s3 <- solve(p3)
+s4 <- solve(p4)
+s5 <- solve(p5)
+s6 <- solve(p6)
+s7 <- solve(p7)
+s8 <- solve(p8)
+
+# plot solutions for problems associated with spatial data
+par(mfrow = c(3, 2), mar = c(0, 0, 4.1, 0))
+plot(s1, main = "raster data", axes = FALSE, box = FALSE, legend = FALSE)
+
+plot(s2, main = "polygon data")
+plot(s2[s2$solution_1 > 0.5, ], col = "darkgreen", add = TRUE)
+
+plot(s3, main = "line data")
+lines(s3[s3$solution_1 > 0.5, ], col = "darkgreen", lwd = 2)
+
+plot(s4, main = "point data", pch = 19)
+points(s4[s4$solution_1 > 0.5, ], col = "darkgreen", cex = 2, pch = 19)
+
+# note that as_Spatial() is for convenience to plot all solutions together
+plot(as_Spatial(s5), main = "sf (polygon) data", pch = 19)
+plot(as_Spatial(s5[s5$solution_1 > 0.5, ]), col = "darkgreen", add = TRUE)
+
+plot(s6, main = "preprocessed data (polygon data)", pch = 19)
+plot(s6[s6$solution_1 > 0.5, ], col = "darkgreen", add = TRUE)
+
+
+# show solutions for problems associated with aspatial data
+str(s8)
+#>  num [1:90] 0 0 0 0 0 0 0 0 0 1 ...
+#>  - attr(*, "objective")= Named num 3586
+#>   ..- attr(*, "names")= chr "solution_1"
+#>  - attr(*, "status")= Named chr "OPTIMAL"
+#>   ..- attr(*, "names")= chr "solution_1"
+#>  - attr(*, "runtime")= Named num 0.004
+#>   ..- attr(*, "names")= chr "solution_1"
+# }
+# create some problems with multiple zones
+
+# first, create a matrix containing the targets for multi-zone problems
+# here each row corresponds to a different feature, each
+# column corresponds to a different zone, and values correspond
+# to the total (absolute) amount of a given feature that needs to be secured
+# in a given zone
+targets <- matrix(rpois(15, 1),
+                  nrow = number_of_features(sim_features_zones),
+                  ncol = number_of_zones(sim_features_zones),
+                  dimnames = list(feature_names(sim_features_zones),
+                                  zone_names(sim_features_zones)))
+
+# print targets
+print(targets)
+#>           zone_1 zone_2 zone_3
+#> feature_1      2      0      0
+#> feature_2      1      1      2
+#> feature_3      3      3      2
+#> feature_4      1      2      0
+#> feature_5      2      1      1
+
+# create a multi-zone problem with raster data
+p8 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_absolute_targets(targets) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve problem
+s8 <- solve(p8)
+
+# plot solution
+# here, each layer/panel corresponds to a different zone and pixel values
+# indicate if a given planning unit has been allocated to a given zone
+par(mfrow = c(1, 1))
+plot(s8, main = c("zone 1", "zone 2", "zone 3"), axes = FALSE, box = FALSE)
+
+
+# alternatively, the category_layer function can be used to create
+# a new raster object containing the zone ids for each planning unit
+# in the solution (note this only works for problems with binary decisions)
+par(mfrow = c(1, 1))
+plot(category_layer(s8), axes = FALSE, box = FALSE)
+
+
+# create a multi-zone problem with polygon data
+p9 <- problem(sim_pu_zones_polygons, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_absolute_targets(targets) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve problem
+s9 <- solve(p9)
+
+# create column containing the zone id for which each planning unit was
+# allocated to in the solution
+s9$solution <- category_vector(s9@data[, c("solution_1_zone_1",
+                                           "solution_1_zone_2",
+                                           "solution_1_zone_3")])
+s9$solution <- factor(s9$solution)
+
+# plot solution
+spplot(s9, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
+
+
+# create a multi-zone problem with polygon planning unit data
+# and where fields (columns) in the attribute table correspond
+# to feature abundances
+
+# first fields need to be added to the planning unit data
+# which indicate the amount of each feature in each zone
+# to do this, the fields will be populated with random counts
+sim_pu_zones_polygons$spp1_z1 <- rpois(nrow(sim_pu_zones_polygons), 1)
+sim_pu_zones_polygons$spp2_z1 <- rpois(nrow(sim_pu_zones_polygons), 1)
+sim_pu_zones_polygons$spp3_z1 <- rpois(nrow(sim_pu_zones_polygons), 1)
+sim_pu_zones_polygons$spp1_z2 <- rpois(nrow(sim_pu_zones_polygons), 1)
+sim_pu_zones_polygons$spp2_z2 <- rpois(nrow(sim_pu_zones_polygons), 1)
+sim_pu_zones_polygons$spp3_z2 <- rpois(nrow(sim_pu_zones_polygons), 1)
+
+# create problem with polygon planning unit data and use field names
+# to indicate feature data
+# additionally, to make this example slightly more interesting,
+# the problem will have prfoportion-type decisions such that
+# a proportion of each planning unit can be allocated to each of the
+# two management zones
+p10 <- problem(sim_pu_zones_polygons,
+               zones(c("spp1_z1", "spp2_z1", "spp3_z1"),
+                     c("spp1_z2", "spp2_z2", "spp3_z2"),
+                     zone_names = c("z1", "z2")),
+               cost_column = c("cost_1", "cost_2")) %>%
+       add_min_set_objective() %>%
+       add_absolute_targets(targets[1:3, 1:2]) %>%
+       add_proportion_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve problem
+s10 <- solve(p10)
+
+# plot solution
+spplot(s10, zcol = c("solution_1_z1", "solution_1_z2"), main = "solution",
+       axes = FALSE, box = FALSE)
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/proximity_matrix.html b/docs/reference/proximity_matrix.html index db506954e..9bdd4900d 100644 --- a/docs/reference/proximity_matrix.html +++ b/docs/reference/proximity_matrix.html @@ -1,102 +1,19 @@ - - - - - - - -Proximity matrix — proximity_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Proximity matrix — proximity_matrix • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Proximity matrix

      - Source: R/proximity_matrix.R + Source: R/proximity_matrix.R
      @@ -186,143 +103,132 @@

      Proximity matrix

      spatial proximity to each other.

      - 
      proximity_matrix(x, distance)
+    
      Usage,
      proximity_matrix(x, distance)
 
-# S3 method for Raster
-proximity_matrix(x, distance)
+# S3 method for Raster
+proximity_matrix(x, distance)
 
-# S3 method for SpatialPolygons
-proximity_matrix(x, distance)
+# S3 method for SpatialPolygons
+proximity_matrix(x, distance)
 
-# S3 method for SpatialLines
-proximity_matrix(x, distance)
+# S3 method for SpatialLines
+proximity_matrix(x, distance)
 
-# S3 method for SpatialPoints
-proximity_matrix(x, distance)
+# S3 method for SpatialPoints
+proximity_matrix(x, distance)
 
-# S3 method for sf
-proximity_matrix(x, distance)
+# S3 method for sf
+proximity_matrix(x, distance)
 
-# S3 method for default
-proximity_matrix(x, distance)
      
+# S3 method for default
+proximity_matrix(x, distance)
      -

      Arguments

      - - - - - - - - - - -
      x

      Raster, -Spatial, or sf::sf() object -representing planning units.

      distance

      numeric distance threshold. Planning units +

      +

      Arguments

      +
      x
      +

      Raster, +Spatial, or sf::sf() object +representing planning units.

      +
      distance
      +

      numeric distance threshold. Planning units that are further apart from each other than this threshold are -not treated as being within proximity of each other.

      - -

      Value

      - - - - -

      dsCMatrix symmetric sparse matrix object. +not treated as being within proximity of each other.

      +
      +
      +

      Value

      +

      dsCMatrix symmetric sparse matrix object. Each row and column represents a planning unit. Cells values indicate if the pair-wise distances between different planning units are within the distance threshold or not (using ones and zeros). To reduce computational burden, cells among the matrix diagonal are set to zero. Furthermore, if the argument to x is a -Raster object, then cells with NA -values are set to zero too.

      -

      Details

      - +Raster object, then cells with NAvalues are set to zero too.

      +
      +
      +

      Details

      Proximity calculations are performed using -sf::st_is_within_distance().

      +sf::st_is_within_distance().

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_sf, sim_pu_lines, sim_pu_points)
-
-# create proximity matrix using raster data
-## crop raster to 9 cells to provide a small example
-r <- crop(sim_pu_raster, c(0, 0.3, 0, 0.3))
-
-## make proximity matrix using a distance threshold of 2
-cm_raster <- proximity_matrix(r, distance = 2)
-
-# create proximity matrix using polygon (sf) data
-## subset 9 polygons to provide a small example
-ply <- sim_pu_sf[c(1:2, 10:12, 20:22), ]
-
-## make proximity matrix using a distance threshold of 2
-cm_ply <- proximity_matrix(ply, distance = 2)
-
-# create proximity matrix using line (Spatial) data
-## subset 9 lines to provide a small example
-lns <- sim_pu_lines[c(1:2, 10:12, 20:22), ]
-
-## make proximity matrix
-cm_lns <- proximity_matrix(lns, distance = 2)
-
-## create proximity matrix using point (Spatial) data
-## subset 9 points to provide a small example
-pts <- sim_pu_points[c(1:2, 10:12, 20:22), ]
-
-# make proximity matrix
-cm_pts <- proximity_matrix(pts, distance = 2)
-
-# plot data and the proximity matrices
-# \dontrun{
-par(mfrow = c(4,2))
-
-## plot raster and proximity matrix
-plot(r, main = "raster", axes = FALSE, box = FALSE)
-plot(raster(as.matrix(cm_raster)), main = "proximity matrix", axes = FALSE,
-     box = FALSE)
-
-## plot polygons and proximity matrix
-plot(r, main = "polygons (sf)", axes = FALSE, box = FALSE)
-plot(raster(as.matrix(cm_ply)), main = "proximity matrix", axes = FALSE,
-    box = FALSE)
-
-## plot lines and proximity matrix
-plot(r, main = "lines (Spatial)", axes = FALSE, box = FALSE)
-plot(raster(as.matrix(cm_lns)), main = "proximity matrix", axes = FALSE,
-     box = FALSE)
-
-## plot points and proximity matrix
-plot(r, main = "points (Spatial)", axes = FALSE, box = FALSE)
-plot(raster(as.matrix(cm_pts)), main = "proximity matrix", axes = FALSE,
-     box = FALSE)
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_sf, sim_pu_lines, sim_pu_points)
+
+# create proximity matrix using raster data
+## crop raster to 9 cells to provide a small example
+r <- crop(sim_pu_raster, c(0, 0.3, 0, 0.3))
+
+## make proximity matrix using a distance threshold of 2
+cm_raster <- proximity_matrix(r, distance = 2)
+
+# create proximity matrix using polygon (sf) data
+## subset 9 polygons to provide a small example
+ply <- sim_pu_sf[c(1:2, 10:12, 20:22), ]
+
+## make proximity matrix using a distance threshold of 2
+cm_ply <- proximity_matrix(ply, distance = 2)
+
+# create proximity matrix using line (Spatial) data
+## subset 9 lines to provide a small example
+lns <- sim_pu_lines[c(1:2, 10:12, 20:22), ]
+
+## make proximity matrix
+cm_lns <- proximity_matrix(lns, distance = 2)
+
+## create proximity matrix using point (Spatial) data
+## subset 9 points to provide a small example
+pts <- sim_pu_points[c(1:2, 10:12, 20:22), ]
+
+# make proximity matrix
+cm_pts <- proximity_matrix(pts, distance = 2)
+
+# plot data and the proximity matrices
+# \dontrun{
+par(mfrow = c(4,2))
+
+## plot raster and proximity matrix
+plot(r, main = "raster", axes = FALSE, box = FALSE)
+plot(raster(as.matrix(cm_raster)), main = "proximity matrix", axes = FALSE,
+     box = FALSE)
+
+## plot polygons and proximity matrix
+plot(r, main = "polygons (sf)", axes = FALSE, box = FALSE)
+plot(raster(as.matrix(cm_ply)), main = "proximity matrix", axes = FALSE,
+    box = FALSE)
+
+## plot lines and proximity matrix
+plot(r, main = "lines (Spatial)", axes = FALSE, box = FALSE)
+plot(raster(as.matrix(cm_lns)), main = "proximity matrix", axes = FALSE,
+     box = FALSE)
+
+## plot points and proximity matrix
+plot(r, main = "points (Spatial)", axes = FALSE, box = FALSE)
+plot(raster(as.matrix(cm_pts)), main = "proximity matrix", axes = FALSE,
+     box = FALSE)
+
+# }
 
      
+
      + - - - - - - - - - - - + diff --git a/docs/reference/rij_matrix.html b/docs/reference/rij_matrix.html index 37696006b..d41bcb6b9 100644 --- a/docs/reference/rij_matrix.html +++ b/docs/reference/rij_matrix.html @@ -1,102 +1,19 @@ - - - - - - - -Feature by planning unit matrix — rij_matrix • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Feature by planning unit matrix — rij_matrix • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Feature by planning unit matrix

      - Source: R/rij_matrix.R + Source: R/rij_matrix.R
      @@ -186,421 +103,410 @@

      Feature by planning unit matrix

      unit (also known as an rij matrix).

      - 
      rij_matrix(x, y, ...)
-
-# S4 method for Raster,Raster
-rij_matrix(x, y, ...)
-
-# S4 method for Spatial,Raster
-rij_matrix(x, y, fun, ...)
-
-# S4 method for sf,Raster
-rij_matrix(x, y, fun, ...)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      x

      Raster, -Spatial, or sf::sf() object -representing the planning units.

      y

      Raster object representing the -features.

      ...

      not used.

      fun

      character for summarizing values inside each planning unit. +

      Usage,
      rij_matrix(x, y, ...)
+
+# S4 method for Raster,Raster
+rij_matrix(x, y, ...)
+
+# S4 method for Spatial,Raster
+rij_matrix(x, y, fun, ...)
+
+# S4 method for sf,Raster
+rij_matrix(x, y, fun, ...)
      + +
      +

      Arguments

      +
      x
      +

      Raster, +Spatial, or sf::sf() object +representing the planning units.

      +
      y
      +

      Raster object representing the +features.

      +
      ...
      +

      not used.

      +
      fun
      +

      character for summarizing values inside each planning unit. This parameter is only used when the argument to x is a -Spatial or sf::sf() object. -Defaults to "sum".

      - -

      Value

      - -

      dgCMatrix sparse matrix object. +Spatial or sf::sf() object. +Defaults to "sum".

      +
      +
      +

      Value

      +

      dgCMatrix sparse matrix object. The sparse matrix represents the spatial intersection between the planning units and the features. Rows correspond to features, and columns correspond to planning units. Values correspond to the amount (or presence/absence) of the feature in the planning unit. For example, the amount of the third species in the second planning unit would be stored in the third column and second row.

      -

      Details

      - -

      Generally, processing vector (i.e. Spatial or -sf::sf()) data takes much -longer to process then Raster data, -so it is recommended to use Raster data +

      +
      +

      Details

      +

      Generally, processing vector (i.e., Spatial or +sf::sf()) data takes much +longer to process then Raster data, +so it is recommended to use Raster data for planning units where possible.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_pu_polygons, sim_pu_sf, sim_pu_zones_stack)
-
-# create rij matrix using raster layer planning units
-rij_raster <- rij_matrix(sim_pu_raster, sim_features)
-print(rij_raster)
-#> 5 x 90 sparse Matrix of class "dgCMatrix"
-#>                                                                              
-#> layer.1 0.7150548 0.6990429 0.6859317 0.6783193 0.6782107 0.6863252 0.7017231
-#> layer.2 0.2900901 0.3052216 0.3266036 0.3510977 0.3750470 0.3950113 0.4084749
-#> layer.3 0.8178213 0.8064534 0.7852441 0.7541320 0.7131559 0.6628435 0.6046204
-#> layer.4 0.2199663 0.2713800 0.3296247 0.3900085 0.4468281 0.4946333 0.5292249
-#> layer.5 0.4533809 0.4413639 0.4343547 0.4355628 0.4474871 0.4714105 0.5068509
-#>                                                                              
-#> layer.1 0.7219284 0.7435505 0.7631509 0.7505900 0.7357791 0.7233151 0.7156627
-#> layer.2 0.4142271 0.4123446 0.4038949 0.2800841 0.2967547 0.3181723 0.3409791
-#> layer.3 0.5411391 0.4763017 0.4147364 0.8275983 0.8194545 0.8013062 0.7730503
-#> layer.4 0.5479991 0.5498153 0.5348758 0.2208512 0.2738525 0.3350935 0.3998241
-#> layer.5 0.5510725 0.5991256 0.6448475 0.4741697 0.4569167 0.4453572 0.4428185
-#>                                                                              
-#> layer.1 0.7147517 0.7212831 0.7343615 0.7516415 0.7699543 0.7897989 0.7772875
-#> layer.2 0.3615030 0.3765606 0.3841340 0.3836641 0.3759393 0.2716298 0.2901825
-#> layer.3 0.7345400 0.6860553 0.6288231 0.5654560 0.5000330 0.8346555 0.8298830
-#> layer.4 0.4618047 0.5148344 0.5541170 0.5767631 0.5815260 0.2249796 0.2776009
-#> layer.5 0.4517499 0.4732935 0.5068285 0.5495481 0.5965013 0.5022737 0.4802429
-#>                                                                              
-#> layer.1 0.7661407 0.7585159 0.7561971 0.7599327 0.7690602 0.7816119 0.7948577
-#> layer.2 0.3119889 0.3334326 0.3508138 0.3612252 0.3631965 0.3568911 0.3438730
-#> layer.3 0.8151305 0.7903745 0.7553823 0.7102172 0.6558247 0.5945687 0.5304188
-#> layer.4 0.3390011 0.4047008 0.4684589 0.5238040 0.5655910 0.5906737 0.5976491
-#> layer.5 0.4646212 0.4587578 0.4649525 0.4840959 0.5153215 0.5556964 0.6003282
-#>                                                                              
-#> layer.1 0.8059966 0.8286461 0.8189872 0.8095434 0.8020377 0.7980313 0.7983424
-#> layer.2 0.3265679 0.2650109 0.2854743 0.3077757 0.3280176 0.3424767 0.3485511
-#> layer.3 0.4684656 0.8381119 0.8367193 0.8254115 0.8043530 0.7733527 0.7323690
-#> layer.4 0.5863706 0.2330116 0.2831343 0.3416658 0.4047077 0.4665769 0.5210694
-#> layer.5 0.6432595 0.5353515 0.5095593 0.4907792 0.4822721 0.4860960 0.5028092
-#>                                                                              
-#> layer.1 0.8026563 0.8095316 0.8167839 0.8220091 0.8633036 0.8564520 0.8487799
-#> layer.2 0.3453627 0.3338433 0.3163452 0.2959188 0.2603208 0.2824472 0.3051395
-#> layer.3 0.6821137 0.6246373 0.5636095 0.5039577 0.8370439 0.8390267 0.8310691
-#> layer.4 0.5629582 0.5888172 0.5969403 0.5869119 0.2456164 0.2910969 0.3438600
-#> layer.5 0.5312405 0.5683321 0.6093528 0.6487382 0.5700379 0.5418938 0.5211593
-#>                                                                              
-#> layer.1 0.8415392 0.8360026 0.8325552 0.8337363 0.8339533 0.8912849 0.8867860
-#> layer.2 0.3242198 0.3359588 0.3303278 0.3143945 0.2708325 0.2575975 0.2809245
-#> layer.3 0.8136049 0.7866027 0.7045769 0.6519655 0.5398928 0.8305082 0.8359634
-#> layer.4 0.4008068 0.4572360 0.5471036 0.5718452 0.5700792 0.2632826 0.3020677
-#> layer.5 0.5108757 0.5127704 0.5521633 0.5850800 0.6559584 0.6024207 0.5734186
-#>                                                                              
-#> layer.1 0.8807106 0.8738915 0.8672825 0.8616340 0.8571536 0.8533099 0.8488533
-#> layer.2 0.3037493 0.3216412 0.3308881 0.3295497 0.3179543 0.2985197 0.2749763
-#> layer.3 0.8312740 0.8171942 0.7939453 0.7616869 0.7210738 0.6737960 0.6228802
-#> layer.4 0.3465595 0.3945501 0.4425012 0.4859430 0.5203217 0.5418532 0.5479865
-#> layer.5 0.5520171 0.5408934 0.5413574 0.5531961 0.5746993 0.6028225 0.6335755
-#>                                                                              
-#> layer.1 0.8419808 0.9117805 0.9090526 0.9042812 0.8979800 0.8833313 0.8758136
-#> layer.2 0.2512416 0.2570026 0.2809260 0.3035274 0.3201754 0.3229680 0.3083414
-#> layer.3 0.5724977 0.8175488 0.8267526 0.8253873 0.8145533 0.7665224 0.7305762
-#> layer.4 0.5375278 0.2860727 0.3163391 0.3506471 0.3876575 0.4590604 0.4860971
-#> layer.5 0.6626552 0.6287730 0.6001593 0.5792111 0.5681102 0.5773113 0.5951498
-#>                                                                              
-#> layer.1 0.8679237 0.8586633 0.8463772 0.9251764 0.9199524 0.9141710 0.9067838
-#> layer.2 0.2863445 0.2611997 0.2370352 0.2589605 0.3047683 0.3200938 0.3251705
-#> layer.3 0.6886562 0.6435894 0.5991429 0.7972733 0.8129275 0.8053968 0.7890073
-#> layer.4 0.5023710 0.5050812 0.4927354 0.3133764 0.3566663 0.3816158 0.4070643
-#> layer.5 0.6183284 0.6433893 0.6667633 0.6461805 0.5990580 0.5886663 0.5878728
-#>                                                                              
-#> layer.1 0.8981802 0.8643680 0.8473654 0.9322748 0.9317639 0.9287528 0.9159813
-#> layer.2 0.3186414 0.2521341 0.2280966 0.2641903 0.2872474 0.3081174 0.3253428
-#> layer.3 0.7645150 0.6570162 0.6186335 0.7690767 0.7873422 0.7936492 0.7768533
-#> layer.4 0.4304725 0.4559778 0.4408970 0.3437657 0.3535038 0.3646749 0.3908502
-#> layer.5 0.5957192 0.6486412 0.6667338 0.6528235 0.6269821 0.6089827 0.5991743
-#>                                                                              
-#> layer.1 0.9066665 0.8822224 0.8658993 0.8449602 0.9336696 0.9339562 0.9315392
-#> layer.2 0.3170430 0.2740393 0.2478477 0.2243090 0.2736019 0.2951441 0.3143908
-#> layer.3 0.7561399 0.6972504 0.6635963 0.6310227 0.7330271 0.7567352 0.7677462
-#> layer.4 0.4031866 0.4135759 0.4061247 0.3879679 0.3750617 0.3743479 0.3741982
-#> layer.5 0.6058227 0.6325923 0.6479832 0.6617020 0.6480034 0.6238690 0.6078230
-#>                                                                    
-#> layer.1 0.9265291 0.9190510 0.8968893 0.8817701 0.8629508 0.8388748
-#> layer.2 0.3265712 0.3282949 0.2992975 0.2742826 0.2483226 0.2255383
-#> layer.3 0.7679649 0.7589920 0.7195554 0.6927858 0.6644491 0.6371886
-#> layer.4 0.3753241 0.3774461 0.3785580 0.3729116 0.3601426 0.3391285
-#> layer.5 0.6002171 0.6002851 0.6166497 0.6288149 0.6410043 0.6515710
-
-# create rij matrix using polygon (Spatial) planning units
-rij_polygons <- rij_matrix(sim_pu_polygons, sim_features)
-print(rij_polygons)
-#> 5 x 90 sparse Matrix of class "dgCMatrix"
-#>                                                                              
-#> layer.1 0.7150548 0.6990429 0.6859317 0.6783193 0.6782107 0.6863252 0.7017231
-#> layer.2 0.2900901 0.3052216 0.3266036 0.3510977 0.3750470 0.3950113 0.4084749
-#> layer.3 0.8178213 0.8064534 0.7852441 0.7541320 0.7131559 0.6628435 0.6046204
-#> layer.4 0.2199663 0.2713800 0.3296247 0.3900085 0.4468281 0.4946333 0.5292249
-#> layer.5 0.4533809 0.4413639 0.4343547 0.4355628 0.4474871 0.4714105 0.5068509
-#>                                                                              
-#> layer.1 0.7219284 0.7435505 0.7631509 0.7505900 0.7357791 0.7233151 0.7156627
-#> layer.2 0.4142271 0.4123446 0.4038949 0.2800841 0.2967547 0.3181723 0.3409791
-#> layer.3 0.5411391 0.4763017 0.4147364 0.8275983 0.8194545 0.8013062 0.7730503
-#> layer.4 0.5479991 0.5498153 0.5348758 0.2208512 0.2738525 0.3350935 0.3998241
-#> layer.5 0.5510725 0.5991256 0.6448475 0.4741697 0.4569167 0.4453572 0.4428185
-#>                                                                              
-#> layer.1 0.7147517 0.7212831 0.7343615 0.7516415 0.7699543 0.7897989 0.7772875
-#> layer.2 0.3615030 0.3765606 0.3841340 0.3836641 0.3759393 0.2716298 0.2901825
-#> layer.3 0.7345400 0.6860553 0.6288231 0.5654560 0.5000330 0.8346555 0.8298830
-#> layer.4 0.4618047 0.5148344 0.5541170 0.5767631 0.5815260 0.2249796 0.2776009
-#> layer.5 0.4517499 0.4732935 0.5068285 0.5495481 0.5965013 0.5022737 0.4802429
-#>                                                                              
-#> layer.1 0.7661407 0.7585159 0.7561971 0.7599327 0.7690602 0.7816119 0.7948577
-#> layer.2 0.3119889 0.3334326 0.3508138 0.3612252 0.3631965 0.3568911 0.3438730
-#> layer.3 0.8151305 0.7903745 0.7553823 0.7102172 0.6558247 0.5945687 0.5304188
-#> layer.4 0.3390011 0.4047008 0.4684589 0.5238040 0.5655910 0.5906737 0.5976491
-#> layer.5 0.4646212 0.4587578 0.4649525 0.4840959 0.5153215 0.5556964 0.6003282
-#>                                                                              
-#> layer.1 0.8059966 0.8286461 0.8189872 0.8095434 0.8020377 0.7980313 0.7983424
-#> layer.2 0.3265679 0.2650109 0.2854743 0.3077757 0.3280176 0.3424767 0.3485511
-#> layer.3 0.4684656 0.8381119 0.8367193 0.8254115 0.8043530 0.7733527 0.7323690
-#> layer.4 0.5863706 0.2330116 0.2831343 0.3416658 0.4047077 0.4665769 0.5210694
-#> layer.5 0.6432595 0.5353515 0.5095593 0.4907792 0.4822721 0.4860960 0.5028092
-#>                                                                              
-#> layer.1 0.8026563 0.8095316 0.8167839 0.8220091 0.8633036 0.8564520 0.8487799
-#> layer.2 0.3453627 0.3338433 0.3163452 0.2959188 0.2603208 0.2824472 0.3051395
-#> layer.3 0.6821137 0.6246373 0.5636095 0.5039577 0.8370439 0.8390267 0.8310691
-#> layer.4 0.5629582 0.5888172 0.5969403 0.5869119 0.2456164 0.2910969 0.3438600
-#> layer.5 0.5312405 0.5683321 0.6093528 0.6487382 0.5700379 0.5418938 0.5211593
-#>                                                                              
-#> layer.1 0.8415392 0.8360026 0.8325552 0.8337363 0.8339533 0.8912849 0.8867860
-#> layer.2 0.3242198 0.3359588 0.3303278 0.3143945 0.2708325 0.2575975 0.2809245
-#> layer.3 0.8136049 0.7866027 0.7045769 0.6519655 0.5398928 0.8305082 0.8359634
-#> layer.4 0.4008068 0.4572360 0.5471036 0.5718452 0.5700792 0.2632826 0.3020677
-#> layer.5 0.5108757 0.5127704 0.5521633 0.5850800 0.6559584 0.6024207 0.5734186
-#>                                                                              
-#> layer.1 0.8807106 0.8738915 0.8672825 0.8616340 0.8571536 0.8533099 0.8488533
-#> layer.2 0.3037493 0.3216412 0.3308881 0.3295497 0.3179543 0.2985197 0.2749763
-#> layer.3 0.8312740 0.8171942 0.7939453 0.7616869 0.7210738 0.6737960 0.6228802
-#> layer.4 0.3465595 0.3945501 0.4425012 0.4859430 0.5203217 0.5418532 0.5479865
-#> layer.5 0.5520171 0.5408934 0.5413574 0.5531961 0.5746993 0.6028225 0.6335755
-#>                                                                              
-#> layer.1 0.8419808 0.9117805 0.9090526 0.9042812 0.8979800 0.8833313 0.8758136
-#> layer.2 0.2512416 0.2570026 0.2809260 0.3035274 0.3201754 0.3229680 0.3083414
-#> layer.3 0.5724977 0.8175488 0.8267526 0.8253873 0.8145533 0.7665224 0.7305762
-#> layer.4 0.5375278 0.2860727 0.3163391 0.3506471 0.3876575 0.4590604 0.4860971
-#> layer.5 0.6626552 0.6287730 0.6001593 0.5792111 0.5681102 0.5773113 0.5951498
-#>                                                                              
-#> layer.1 0.8679237 0.8586633 0.8463772 0.9251764 0.9199524 0.9141710 0.9067838
-#> layer.2 0.2863445 0.2611997 0.2370352 0.2589605 0.3047683 0.3200938 0.3251705
-#> layer.3 0.6886562 0.6435894 0.5991429 0.7972733 0.8129275 0.8053968 0.7890073
-#> layer.4 0.5023710 0.5050812 0.4927354 0.3133764 0.3566663 0.3816158 0.4070643
-#> layer.5 0.6183284 0.6433893 0.6667633 0.6461805 0.5990580 0.5886663 0.5878728
-#>                                                                              
-#> layer.1 0.8981802 0.8643680 0.8473654 0.9322748 0.9317639 0.9287528 0.9159813
-#> layer.2 0.3186414 0.2521341 0.2280966 0.2641903 0.2872474 0.3081174 0.3253428
-#> layer.3 0.7645150 0.6570162 0.6186335 0.7690767 0.7873422 0.7936492 0.7768533
-#> layer.4 0.4304725 0.4559778 0.4408970 0.3437657 0.3535038 0.3646749 0.3908502
-#> layer.5 0.5957192 0.6486412 0.6667338 0.6528235 0.6269821 0.6089827 0.5991743
-#>                                                                              
-#> layer.1 0.9066665 0.8822224 0.8658993 0.8449602 0.9336696 0.9339562 0.9315392
-#> layer.2 0.3170430 0.2740393 0.2478477 0.2243090 0.2736019 0.2951441 0.3143908
-#> layer.3 0.7561399 0.6972504 0.6635963 0.6310227 0.7330271 0.7567352 0.7677462
-#> layer.4 0.4031866 0.4135759 0.4061247 0.3879679 0.3750617 0.3743479 0.3741982
-#> layer.5 0.6058227 0.6325923 0.6479832 0.6617020 0.6480034 0.6238690 0.6078230
-#>                                                                    
-#> layer.1 0.9265291 0.9190510 0.8968893 0.8817701 0.8629508 0.8388748
-#> layer.2 0.3265712 0.3282949 0.2992975 0.2742826 0.2483226 0.2255383
-#> layer.3 0.7679649 0.7589920 0.7195554 0.6927858 0.6644491 0.6371886
-#> layer.4 0.3753241 0.3774461 0.3785580 0.3729116 0.3601426 0.3391285
-#> layer.5 0.6002171 0.6002851 0.6166497 0.6288149 0.6410043 0.6515710
-
-# create rij matrix using polygon (sf) planning units
-rij_sf <- rij_matrix(sim_pu_sf, sim_features)
-print(rij_sf)
-#> 5 x 90 sparse Matrix of class "dgCMatrix"
-#>                                                                              
-#> layer.1 0.7150548 0.6990429 0.6859317 0.6783193 0.6782107 0.6863252 0.7017231
-#> layer.2 0.2900901 0.3052216 0.3266036 0.3510977 0.3750470 0.3950113 0.4084749
-#> layer.3 0.8178213 0.8064534 0.7852441 0.7541320 0.7131559 0.6628435 0.6046204
-#> layer.4 0.2199663 0.2713800 0.3296247 0.3900085 0.4468281 0.4946333 0.5292249
-#> layer.5 0.4533809 0.4413639 0.4343547 0.4355628 0.4474871 0.4714105 0.5068509
-#>                                                                              
-#> layer.1 0.7219284 0.7435505 0.7631509 0.7505900 0.7357791 0.7233151 0.7156627
-#> layer.2 0.4142271 0.4123446 0.4038949 0.2800841 0.2967547 0.3181723 0.3409791
-#> layer.3 0.5411391 0.4763017 0.4147364 0.8275983 0.8194545 0.8013062 0.7730503
-#> layer.4 0.5479991 0.5498153 0.5348758 0.2208512 0.2738525 0.3350935 0.3998241
-#> layer.5 0.5510725 0.5991256 0.6448475 0.4741697 0.4569167 0.4453572 0.4428185
-#>                                                                              
-#> layer.1 0.7147517 0.7212831 0.7343615 0.7516415 0.7699543 0.7897989 0.7772875
-#> layer.2 0.3615030 0.3765606 0.3841340 0.3836641 0.3759393 0.2716298 0.2901825
-#> layer.3 0.7345400 0.6860553 0.6288231 0.5654560 0.5000330 0.8346555 0.8298830
-#> layer.4 0.4618047 0.5148344 0.5541170 0.5767631 0.5815260 0.2249796 0.2776009
-#> layer.5 0.4517499 0.4732935 0.5068285 0.5495481 0.5965013 0.5022737 0.4802429
-#>                                                                              
-#> layer.1 0.7661407 0.7585159 0.7561971 0.7599327 0.7690602 0.7816119 0.7948577
-#> layer.2 0.3119889 0.3334326 0.3508138 0.3612252 0.3631965 0.3568911 0.3438730
-#> layer.3 0.8151305 0.7903745 0.7553823 0.7102172 0.6558247 0.5945687 0.5304188
-#> layer.4 0.3390011 0.4047008 0.4684589 0.5238040 0.5655910 0.5906737 0.5976491
-#> layer.5 0.4646212 0.4587578 0.4649525 0.4840959 0.5153215 0.5556964 0.6003282
-#>                                                                              
-#> layer.1 0.8059966 0.8286461 0.8189872 0.8095434 0.8020377 0.7980313 0.7983424
-#> layer.2 0.3265679 0.2650109 0.2854743 0.3077757 0.3280176 0.3424767 0.3485511
-#> layer.3 0.4684656 0.8381119 0.8367193 0.8254115 0.8043530 0.7733527 0.7323690
-#> layer.4 0.5863706 0.2330116 0.2831343 0.3416658 0.4047077 0.4665769 0.5210694
-#> layer.5 0.6432595 0.5353515 0.5095593 0.4907792 0.4822721 0.4860960 0.5028092
-#>                                                                              
-#> layer.1 0.8026563 0.8095316 0.8167839 0.8220091 0.8633036 0.8564520 0.8487799
-#> layer.2 0.3453627 0.3338433 0.3163452 0.2959188 0.2603208 0.2824472 0.3051395
-#> layer.3 0.6821137 0.6246373 0.5636095 0.5039577 0.8370439 0.8390267 0.8310691
-#> layer.4 0.5629582 0.5888172 0.5969403 0.5869119 0.2456164 0.2910969 0.3438600
-#> layer.5 0.5312405 0.5683321 0.6093528 0.6487382 0.5700379 0.5418938 0.5211593
-#>                                                                              
-#> layer.1 0.8415392 0.8360026 0.8325552 0.8337363 0.8339533 0.8912849 0.8867860
-#> layer.2 0.3242198 0.3359588 0.3303278 0.3143945 0.2708325 0.2575975 0.2809245
-#> layer.3 0.8136049 0.7866027 0.7045769 0.6519655 0.5398928 0.8305082 0.8359634
-#> layer.4 0.4008068 0.4572360 0.5471036 0.5718452 0.5700792 0.2632826 0.3020677
-#> layer.5 0.5108757 0.5127704 0.5521633 0.5850800 0.6559584 0.6024207 0.5734186
-#>                                                                              
-#> layer.1 0.8807106 0.8738915 0.8672825 0.8616340 0.8571536 0.8533099 0.8488533
-#> layer.2 0.3037493 0.3216412 0.3308881 0.3295497 0.3179543 0.2985197 0.2749763
-#> layer.3 0.8312740 0.8171942 0.7939453 0.7616869 0.7210738 0.6737960 0.6228802
-#> layer.4 0.3465595 0.3945501 0.4425012 0.4859430 0.5203217 0.5418532 0.5479865
-#> layer.5 0.5520171 0.5408934 0.5413574 0.5531961 0.5746993 0.6028225 0.6335755
-#>                                                                              
-#> layer.1 0.8419808 0.9117805 0.9090526 0.9042812 0.8979800 0.8833313 0.8758136
-#> layer.2 0.2512416 0.2570026 0.2809260 0.3035274 0.3201754 0.3229680 0.3083414
-#> layer.3 0.5724977 0.8175488 0.8267526 0.8253873 0.8145533 0.7665224 0.7305762
-#> layer.4 0.5375278 0.2860727 0.3163391 0.3506471 0.3876575 0.4590604 0.4860971
-#> layer.5 0.6626552 0.6287730 0.6001593 0.5792111 0.5681102 0.5773113 0.5951498
-#>                                                                              
-#> layer.1 0.8679237 0.8586633 0.8463772 0.9251764 0.9199524 0.9141710 0.9067838
-#> layer.2 0.2863445 0.2611997 0.2370352 0.2589605 0.3047683 0.3200938 0.3251705
-#> layer.3 0.6886562 0.6435894 0.5991429 0.7972733 0.8129275 0.8053968 0.7890073
-#> layer.4 0.5023710 0.5050812 0.4927354 0.3133764 0.3566663 0.3816158 0.4070643
-#> layer.5 0.6183284 0.6433893 0.6667633 0.6461805 0.5990580 0.5886663 0.5878728
-#>                                                                              
-#> layer.1 0.8981802 0.8643680 0.8473654 0.9322748 0.9317639 0.9287528 0.9159813
-#> layer.2 0.3186414 0.2521341 0.2280966 0.2641903 0.2872474 0.3081174 0.3253428
-#> layer.3 0.7645150 0.6570162 0.6186335 0.7690767 0.7873422 0.7936492 0.7768533
-#> layer.4 0.4304725 0.4559778 0.4408970 0.3437657 0.3535038 0.3646749 0.3908502
-#> layer.5 0.5957192 0.6486412 0.6667338 0.6528235 0.6269821 0.6089827 0.5991743
-#>                                                                              
-#> layer.1 0.9066665 0.8822224 0.8658993 0.8449602 0.9336696 0.9339562 0.9315392
-#> layer.2 0.3170430 0.2740393 0.2478477 0.2243090 0.2736019 0.2951441 0.3143908
-#> layer.3 0.7561399 0.6972504 0.6635963 0.6310227 0.7330271 0.7567352 0.7677462
-#> layer.4 0.4031866 0.4135759 0.4061247 0.3879679 0.3750617 0.3743479 0.3741982
-#> layer.5 0.6058227 0.6325923 0.6479832 0.6617020 0.6480034 0.6238690 0.6078230
-#>                                                                    
-#> layer.1 0.9265291 0.9190510 0.8968893 0.8817701 0.8629508 0.8388748
-#> layer.2 0.3265712 0.3282949 0.2992975 0.2742826 0.2483226 0.2255383
-#> layer.3 0.7679649 0.7589920 0.7195554 0.6927858 0.6644491 0.6371886
-#> layer.4 0.3753241 0.3774461 0.3785580 0.3729116 0.3601426 0.3391285
-#> layer.5 0.6002171 0.6002851 0.6166497 0.6288149 0.6410043 0.6515710
-
-# create rij matrix using raster stack planning units
-rij_zones_raster <- rij_matrix(sim_pu_zones_stack, sim_features)
-print(rij_zones_raster)
-#> 5 x 90 sparse Matrix of class "dgCMatrix"
-#>                                                                              
-#> layer.1 0.7150548 0.6990429 0.6859317 0.6783193 0.6782107 0.6863252 0.7219284
-#> layer.2 0.2900901 0.3052216 0.3266036 0.3510977 0.3750470 0.3950113 0.4142271
-#> layer.3 0.8178213 0.8064534 0.7852441 0.7541320 0.7131559 0.6628435 0.5411391
-#> layer.4 0.2199663 0.2713800 0.3296247 0.3900085 0.4468281 0.4946333 0.5479991
-#> layer.5 0.4533809 0.4413639 0.4343547 0.4355628 0.4474871 0.4714105 0.5510725
-#>                                                                              
-#> layer.1 0.7435505 0.7631509 0.7505900 0.7357791 0.7233151 0.7156627 0.7147517
-#> layer.2 0.4123446 0.4038949 0.2800841 0.2967547 0.3181723 0.3409791 0.3615030
-#> layer.3 0.4763017 0.4147364 0.8275983 0.8194545 0.8013062 0.7730503 0.7345400
-#> layer.4 0.5498153 0.5348758 0.2208512 0.2738525 0.3350935 0.3998241 0.4618047
-#> layer.5 0.5991256 0.6448475 0.4741697 0.4569167 0.4453572 0.4428185 0.4517499
-#>                                                                              
-#> layer.1 0.7212831 0.7343615 0.7699543 0.7861227 0.7897989 0.7772875 0.7561971
-#> layer.2 0.3765606 0.3841340 0.3759393 0.3627013 0.2716298 0.2901825 0.3508138
-#> layer.3 0.6860553 0.6288231 0.5000330 0.4375452 0.8346555 0.8298830 0.7553823
-#> layer.4 0.5148344 0.5541170 0.5815260 0.5684388 0.2249796 0.2776009 0.4684589
-#> layer.5 0.4732935 0.5068285 0.5965013 0.6415349 0.5022737 0.4802429 0.4649525
-#>                                                                              
-#> layer.1 0.7599327 0.7690602 0.7816119 0.7948577 0.8059966 0.8286461 0.8189872
-#> layer.2 0.3612252 0.3631965 0.3568911 0.3438730 0.3265679 0.2650109 0.2854743
-#> layer.3 0.7102172 0.6558247 0.5945687 0.5304188 0.4684656 0.8381119 0.8367193
-#> layer.4 0.5238040 0.5655910 0.5906737 0.5976491 0.5863706 0.2330116 0.2831343
-#> layer.5 0.4840959 0.5153215 0.5556964 0.6003282 0.6432595 0.5353515 0.5095593
-#>                                                                              
-#> layer.1 0.8095434 0.8020377 0.7980313 0.7983424 0.8026563 0.8095316 0.8167839
-#> layer.2 0.3077757 0.3280176 0.3424767 0.3485511 0.3453627 0.3338433 0.3163452
-#> layer.3 0.8254115 0.8043530 0.7733527 0.7323690 0.6821137 0.6246373 0.5636095
-#> layer.4 0.3416658 0.4047077 0.4665769 0.5210694 0.5629582 0.5888172 0.5969403
-#> layer.5 0.4907792 0.4822721 0.4860960 0.5028092 0.5312405 0.5683321 0.6093528
-#>                                                                              
-#> layer.1 0.8220091 0.8633036 0.8564520 0.8487799 0.8360026 0.8330038 0.8337363
-#> layer.2 0.2959188 0.2603208 0.2824472 0.3051395 0.3359588 0.3380832 0.3143945
-#> layer.3 0.5039577 0.8370439 0.8390267 0.8310691 0.7866027 0.7500573 0.6519655
-#> layer.4 0.5869119 0.2456164 0.2910969 0.3438600 0.4572360 0.5076754 0.5718452
-#> layer.5 0.6487382 0.5700379 0.5418938 0.5211593 0.5127704 0.5270232 0.5850800
-#>                                                                              
-#> layer.1 0.8348882 0.8339533 0.8912849 0.8867860 0.8807106 0.8738915 0.8672825
-#> layer.2 0.2933767 0.2708325 0.2575975 0.2809245 0.3037493 0.3216412 0.3308881
-#> layer.3 0.5955431 0.5398928 0.8305082 0.8359634 0.8312740 0.8171942 0.7939453
-#> layer.4 0.5797670 0.5700792 0.2632826 0.3020677 0.3465595 0.3945501 0.4425012
-#> layer.5 0.6213430 0.6559584 0.6024207 0.5734186 0.5520171 0.5408934 0.5413574
-#>                                                                              
-#> layer.1 0.8616340 0.8571536 0.8488533 0.9117805 0.9090526 0.9042812 0.8979800
-#> layer.2 0.3295497 0.3179543 0.2749763 0.2570026 0.2809260 0.3035274 0.3201754
-#> layer.3 0.7616869 0.7210738 0.6228802 0.8175488 0.8267526 0.8253873 0.8145533
-#> layer.4 0.4859430 0.5203217 0.5479865 0.2860727 0.3163391 0.3506471 0.3876575
-#> layer.5 0.5531961 0.5746993 0.6335755 0.6287730 0.6001593 0.5792111 0.5681102
-#>                                                                              
-#> layer.1 0.8908018 0.8833313 0.8758136 0.8679237 0.8586633 0.8463772 0.9251764
-#> layer.2 0.3271982 0.3229680 0.3083414 0.2863445 0.2611997 0.2370352 0.2589605
-#> layer.3 0.7947903 0.7665224 0.7305762 0.6886562 0.6435894 0.5991429 0.7972733
-#> layer.4 0.4249398 0.4590604 0.4860971 0.5023710 0.5050812 0.4927354 0.3133764
-#> layer.5 0.5676758 0.5773113 0.5951498 0.6183284 0.6433893 0.6667633 0.6461805
-#>                                                                              
-#> layer.1 0.9237208 0.9199524 0.9141710 0.9067838 0.8981802 0.8885294 0.8775561
-#> layer.2 0.2828033 0.3047683 0.3200938 0.3251705 0.3186414 0.3017897 0.2781030
-#> layer.3 0.8107003 0.8129275 0.8053968 0.7890073 0.7645150 0.7330004 0.6962687
-#> layer.4 0.3337335 0.3566663 0.3816158 0.4070643 0.4304725 0.4485815 0.4580145
-#> layer.5 0.6187615 0.5990580 0.5886663 0.5878728 0.5957192 0.6102524 0.6288607
-#>                                                                              
-#> layer.1 0.8643680 0.8473654 0.9322748 0.9317639 0.9287528 0.9234146 0.9159813
-#> layer.2 0.2521341 0.2280966 0.2641903 0.2872474 0.3081174 0.3219892 0.3253428
-#> layer.3 0.6570162 0.6186335 0.7690767 0.7873422 0.7936492 0.7897301 0.7768533
-#> layer.4 0.4559778 0.4408970 0.3437657 0.3535038 0.3646749 0.3773969 0.3908502
-#> layer.5 0.6486412 0.6667338 0.6528235 0.6269821 0.6089827 0.5997976 0.5991743
-#>                                                                              
-#> layer.1 0.9066665 0.8955188 0.8822224 0.8658993 0.8449602 0.9336696 0.9339562
-#> layer.2 0.3170430 0.2986799 0.2740393 0.2478477 0.2243090 0.2736019 0.2951441
-#> layer.3 0.7561399 0.7289606 0.6972504 0.6635963 0.6310227 0.7330271 0.7567352
-#> layer.4 0.4031866 0.4117466 0.4135759 0.4061247 0.3879679 0.3750617 0.3743479
-#> layer.5 0.6058227 0.6177441 0.6325923 0.6479832 0.6617020 0.6480034 0.6238690
-#>                                                                    
-#> layer.1 0.9315392 0.9190510 0.9091912 0.8968893 0.8629508 0.8388748
-#> layer.2 0.3143908 0.3282949 0.3186099 0.2992975 0.2483226 0.2255383
-#> layer.3 0.7677462 0.7589920 0.7423054 0.7195554 0.6644491 0.6371886
-#> layer.4 0.3741982 0.3774461 0.3792402 0.3785580 0.3601426 0.3391285
-#> layer.5 0.6078230 0.6002851 0.6064383 0.6166497 0.6410043 0.6515710
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_pu_polygons, sim_pu_sf, sim_pu_zones_stack)
+
+# create rij matrix using raster layer planning units
+rij_raster <- rij_matrix(sim_pu_raster, sim_features)
+print(rij_raster)
+#> 5 x 90 sparse Matrix of class "dgCMatrix"
+#>                                                                              
+#> layer.1 0.7150548 0.6990429 0.6859317 0.6783193 0.6782107 0.6863252 0.7017231
+#> layer.2 0.2900901 0.3052216 0.3266036 0.3510977 0.3750470 0.3950113 0.4084749
+#> layer.3 0.8178213 0.8064534 0.7852441 0.7541320 0.7131559 0.6628435 0.6046204
+#> layer.4 0.2199663 0.2713800 0.3296247 0.3900085 0.4468281 0.4946333 0.5292249
+#> layer.5 0.4533809 0.4413639 0.4343547 0.4355628 0.4474871 0.4714105 0.5068509
+#>                                                                              
+#> layer.1 0.7219284 0.7435505 0.7631509 0.7505900 0.7357791 0.7233151 0.7156627
+#> layer.2 0.4142271 0.4123446 0.4038949 0.2800841 0.2967547 0.3181723 0.3409791
+#> layer.3 0.5411391 0.4763017 0.4147364 0.8275983 0.8194545 0.8013062 0.7730503
+#> layer.4 0.5479991 0.5498153 0.5348758 0.2208512 0.2738525 0.3350935 0.3998241
+#> layer.5 0.5510725 0.5991256 0.6448475 0.4741697 0.4569167 0.4453572 0.4428185
+#>                                                                              
+#> layer.1 0.7147517 0.7212831 0.7343615 0.7516415 0.7699543 0.7897989 0.7772875
+#> layer.2 0.3615030 0.3765606 0.3841340 0.3836641 0.3759393 0.2716298 0.2901825
+#> layer.3 0.7345400 0.6860553 0.6288231 0.5654560 0.5000330 0.8346555 0.8298830
+#> layer.4 0.4618047 0.5148344 0.5541170 0.5767631 0.5815260 0.2249796 0.2776009
+#> layer.5 0.4517499 0.4732935 0.5068285 0.5495481 0.5965013 0.5022737 0.4802429
+#>                                                                              
+#> layer.1 0.7661407 0.7585159 0.7561971 0.7599327 0.7690602 0.7816119 0.7948577
+#> layer.2 0.3119889 0.3334326 0.3508138 0.3612252 0.3631965 0.3568911 0.3438730
+#> layer.3 0.8151305 0.7903745 0.7553823 0.7102172 0.6558247 0.5945687 0.5304188
+#> layer.4 0.3390011 0.4047008 0.4684589 0.5238040 0.5655910 0.5906737 0.5976491
+#> layer.5 0.4646212 0.4587578 0.4649525 0.4840959 0.5153215 0.5556964 0.6003282
+#>                                                                              
+#> layer.1 0.8059966 0.8286461 0.8189872 0.8095434 0.8020377 0.7980313 0.7983424
+#> layer.2 0.3265679 0.2650109 0.2854743 0.3077757 0.3280176 0.3424767 0.3485511
+#> layer.3 0.4684656 0.8381119 0.8367193 0.8254115 0.8043530 0.7733527 0.7323690
+#> layer.4 0.5863706 0.2330116 0.2831343 0.3416658 0.4047077 0.4665769 0.5210694
+#> layer.5 0.6432595 0.5353515 0.5095593 0.4907792 0.4822721 0.4860960 0.5028092
+#>                                                                              
+#> layer.1 0.8026563 0.8095316 0.8167839 0.8220091 0.8633036 0.8564520 0.8487799
+#> layer.2 0.3453627 0.3338433 0.3163452 0.2959188 0.2603208 0.2824472 0.3051395
+#> layer.3 0.6821137 0.6246373 0.5636095 0.5039577 0.8370439 0.8390267 0.8310691
+#> layer.4 0.5629582 0.5888172 0.5969403 0.5869119 0.2456164 0.2910969 0.3438600
+#> layer.5 0.5312405 0.5683321 0.6093528 0.6487382 0.5700379 0.5418938 0.5211593
+#>                                                                              
+#> layer.1 0.8415392 0.8360026 0.8325552 0.8337363 0.8339533 0.8912849 0.8867860
+#> layer.2 0.3242198 0.3359588 0.3303278 0.3143945 0.2708325 0.2575975 0.2809245
+#> layer.3 0.8136049 0.7866027 0.7045769 0.6519655 0.5398928 0.8305082 0.8359634
+#> layer.4 0.4008068 0.4572360 0.5471036 0.5718452 0.5700792 0.2632826 0.3020677
+#> layer.5 0.5108757 0.5127704 0.5521633 0.5850800 0.6559584 0.6024207 0.5734186
+#>                                                                              
+#> layer.1 0.8807106 0.8738915 0.8672825 0.8616340 0.8571536 0.8533099 0.8488533
+#> layer.2 0.3037493 0.3216412 0.3308881 0.3295497 0.3179543 0.2985197 0.2749763
+#> layer.3 0.8312740 0.8171942 0.7939453 0.7616869 0.7210738 0.6737960 0.6228802
+#> layer.4 0.3465595 0.3945501 0.4425012 0.4859430 0.5203217 0.5418532 0.5479865
+#> layer.5 0.5520171 0.5408934 0.5413574 0.5531961 0.5746993 0.6028225 0.6335755
+#>                                                                              
+#> layer.1 0.8419808 0.9117805 0.9090526 0.9042812 0.8979800 0.8833313 0.8758136
+#> layer.2 0.2512416 0.2570026 0.2809260 0.3035274 0.3201754 0.3229680 0.3083414
+#> layer.3 0.5724977 0.8175488 0.8267526 0.8253873 0.8145533 0.7665224 0.7305762
+#> layer.4 0.5375278 0.2860727 0.3163391 0.3506471 0.3876575 0.4590604 0.4860971
+#> layer.5 0.6626552 0.6287730 0.6001593 0.5792111 0.5681102 0.5773113 0.5951498
+#>                                                                              
+#> layer.1 0.8679237 0.8586633 0.8463772 0.9251764 0.9199524 0.9141710 0.9067838
+#> layer.2 0.2863445 0.2611997 0.2370352 0.2589605 0.3047683 0.3200938 0.3251705
+#> layer.3 0.6886562 0.6435894 0.5991429 0.7972733 0.8129275 0.8053968 0.7890073
+#> layer.4 0.5023710 0.5050812 0.4927354 0.3133764 0.3566663 0.3816158 0.4070643
+#> layer.5 0.6183284 0.6433893 0.6667633 0.6461805 0.5990580 0.5886663 0.5878728
+#>                                                                              
+#> layer.1 0.8981802 0.8643680 0.8473654 0.9322748 0.9317639 0.9287528 0.9159813
+#> layer.2 0.3186414 0.2521341 0.2280966 0.2641903 0.2872474 0.3081174 0.3253428
+#> layer.3 0.7645150 0.6570162 0.6186335 0.7690767 0.7873422 0.7936492 0.7768533
+#> layer.4 0.4304725 0.4559778 0.4408970 0.3437657 0.3535038 0.3646749 0.3908502
+#> layer.5 0.5957192 0.6486412 0.6667338 0.6528235 0.6269821 0.6089827 0.5991743
+#>                                                                              
+#> layer.1 0.9066665 0.8822224 0.8658993 0.8449602 0.9336696 0.9339562 0.9315392
+#> layer.2 0.3170430 0.2740393 0.2478477 0.2243090 0.2736019 0.2951441 0.3143908
+#> layer.3 0.7561399 0.6972504 0.6635963 0.6310227 0.7330271 0.7567352 0.7677462
+#> layer.4 0.4031866 0.4135759 0.4061247 0.3879679 0.3750617 0.3743479 0.3741982
+#> layer.5 0.6058227 0.6325923 0.6479832 0.6617020 0.6480034 0.6238690 0.6078230
+#>                                                                    
+#> layer.1 0.9265291 0.9190510 0.8968893 0.8817701 0.8629508 0.8388748
+#> layer.2 0.3265712 0.3282949 0.2992975 0.2742826 0.2483226 0.2255383
+#> layer.3 0.7679649 0.7589920 0.7195554 0.6927858 0.6644491 0.6371886
+#> layer.4 0.3753241 0.3774461 0.3785580 0.3729116 0.3601426 0.3391285
+#> layer.5 0.6002171 0.6002851 0.6166497 0.6288149 0.6410043 0.6515710
+
+# create rij matrix using polygon (Spatial) planning units
+rij_polygons <- rij_matrix(sim_pu_polygons, sim_features)
+print(rij_polygons)
+#> 5 x 90 sparse Matrix of class "dgCMatrix"
+#>                                                                              
+#> layer.1 0.7150548 0.6990429 0.6859317 0.6783193 0.6782107 0.6863252 0.7017231
+#> layer.2 0.2900901 0.3052216 0.3266036 0.3510977 0.3750470 0.3950113 0.4084749
+#> layer.3 0.8178213 0.8064534 0.7852441 0.7541320 0.7131559 0.6628435 0.6046204
+#> layer.4 0.2199663 0.2713800 0.3296247 0.3900085 0.4468281 0.4946333 0.5292249
+#> layer.5 0.4533809 0.4413639 0.4343547 0.4355628 0.4474871 0.4714105 0.5068509
+#>                                                                              
+#> layer.1 0.7219284 0.7435505 0.7631509 0.7505900 0.7357791 0.7233151 0.7156627
+#> layer.2 0.4142271 0.4123446 0.4038949 0.2800841 0.2967547 0.3181723 0.3409791
+#> layer.3 0.5411391 0.4763017 0.4147364 0.8275983 0.8194545 0.8013062 0.7730503
+#> layer.4 0.5479991 0.5498153 0.5348758 0.2208512 0.2738525 0.3350935 0.3998241
+#> layer.5 0.5510725 0.5991256 0.6448475 0.4741697 0.4569167 0.4453572 0.4428185
+#>                                                                              
+#> layer.1 0.7147517 0.7212831 0.7343615 0.7516415 0.7699543 0.7897989 0.7772875
+#> layer.2 0.3615030 0.3765606 0.3841340 0.3836641 0.3759393 0.2716298 0.2901825
+#> layer.3 0.7345400 0.6860553 0.6288231 0.5654560 0.5000330 0.8346555 0.8298830
+#> layer.4 0.4618047 0.5148344 0.5541170 0.5767631 0.5815260 0.2249796 0.2776009
+#> layer.5 0.4517499 0.4732935 0.5068285 0.5495481 0.5965013 0.5022737 0.4802429
+#>                                                                              
+#> layer.1 0.7661407 0.7585159 0.7561971 0.7599327 0.7690602 0.7816119 0.7948577
+#> layer.2 0.3119889 0.3334326 0.3508138 0.3612252 0.3631965 0.3568911 0.3438730
+#> layer.3 0.8151305 0.7903745 0.7553823 0.7102172 0.6558247 0.5945687 0.5304188
+#> layer.4 0.3390011 0.4047008 0.4684589 0.5238040 0.5655910 0.5906737 0.5976491
+#> layer.5 0.4646212 0.4587578 0.4649525 0.4840959 0.5153215 0.5556964 0.6003282
+#>                                                                              
+#> layer.1 0.8059966 0.8286461 0.8189872 0.8095434 0.8020377 0.7980313 0.7983424
+#> layer.2 0.3265679 0.2650109 0.2854743 0.3077757 0.3280176 0.3424767 0.3485511
+#> layer.3 0.4684656 0.8381119 0.8367193 0.8254115 0.8043530 0.7733527 0.7323690
+#> layer.4 0.5863706 0.2330116 0.2831343 0.3416658 0.4047077 0.4665769 0.5210694
+#> layer.5 0.6432595 0.5353515 0.5095593 0.4907792 0.4822721 0.4860960 0.5028092
+#>                                                                              
+#> layer.1 0.8026563 0.8095316 0.8167839 0.8220091 0.8633036 0.8564520 0.8487799
+#> layer.2 0.3453627 0.3338433 0.3163452 0.2959188 0.2603208 0.2824472 0.3051395
+#> layer.3 0.6821137 0.6246373 0.5636095 0.5039577 0.8370439 0.8390267 0.8310691
+#> layer.4 0.5629582 0.5888172 0.5969403 0.5869119 0.2456164 0.2910969 0.3438600
+#> layer.5 0.5312405 0.5683321 0.6093528 0.6487382 0.5700379 0.5418938 0.5211593
+#>                                                                              
+#> layer.1 0.8415392 0.8360026 0.8325552 0.8337363 0.8339533 0.8912849 0.8867860
+#> layer.2 0.3242198 0.3359588 0.3303278 0.3143945 0.2708325 0.2575975 0.2809245
+#> layer.3 0.8136049 0.7866027 0.7045769 0.6519655 0.5398928 0.8305082 0.8359634
+#> layer.4 0.4008068 0.4572360 0.5471036 0.5718452 0.5700792 0.2632826 0.3020677
+#> layer.5 0.5108757 0.5127704 0.5521633 0.5850800 0.6559584 0.6024207 0.5734186
+#>                                                                              
+#> layer.1 0.8807106 0.8738915 0.8672825 0.8616340 0.8571536 0.8533099 0.8488533
+#> layer.2 0.3037493 0.3216412 0.3308881 0.3295497 0.3179543 0.2985197 0.2749763
+#> layer.3 0.8312740 0.8171942 0.7939453 0.7616869 0.7210738 0.6737960 0.6228802
+#> layer.4 0.3465595 0.3945501 0.4425012 0.4859430 0.5203217 0.5418532 0.5479865
+#> layer.5 0.5520171 0.5408934 0.5413574 0.5531961 0.5746993 0.6028225 0.6335755
+#>                                                                              
+#> layer.1 0.8419808 0.9117805 0.9090526 0.9042812 0.8979800 0.8833313 0.8758136
+#> layer.2 0.2512416 0.2570026 0.2809260 0.3035274 0.3201754 0.3229680 0.3083414
+#> layer.3 0.5724977 0.8175488 0.8267526 0.8253873 0.8145533 0.7665224 0.7305762
+#> layer.4 0.5375278 0.2860727 0.3163391 0.3506471 0.3876575 0.4590604 0.4860971
+#> layer.5 0.6626552 0.6287730 0.6001593 0.5792111 0.5681102 0.5773113 0.5951498
+#>                                                                              
+#> layer.1 0.8679237 0.8586633 0.8463772 0.9251764 0.9199524 0.9141710 0.9067838
+#> layer.2 0.2863445 0.2611997 0.2370352 0.2589605 0.3047683 0.3200938 0.3251705
+#> layer.3 0.6886562 0.6435894 0.5991429 0.7972733 0.8129275 0.8053968 0.7890073
+#> layer.4 0.5023710 0.5050812 0.4927354 0.3133764 0.3566663 0.3816158 0.4070643
+#> layer.5 0.6183284 0.6433893 0.6667633 0.6461805 0.5990580 0.5886663 0.5878728
+#>                                                                              
+#> layer.1 0.8981802 0.8643680 0.8473654 0.9322748 0.9317639 0.9287528 0.9159813
+#> layer.2 0.3186414 0.2521341 0.2280966 0.2641903 0.2872474 0.3081174 0.3253428
+#> layer.3 0.7645150 0.6570162 0.6186335 0.7690767 0.7873422 0.7936492 0.7768533
+#> layer.4 0.4304725 0.4559778 0.4408970 0.3437657 0.3535038 0.3646749 0.3908502
+#> layer.5 0.5957192 0.6486412 0.6667338 0.6528235 0.6269821 0.6089827 0.5991743
+#>                                                                              
+#> layer.1 0.9066665 0.8822224 0.8658993 0.8449602 0.9336696 0.9339562 0.9315392
+#> layer.2 0.3170430 0.2740393 0.2478477 0.2243090 0.2736019 0.2951441 0.3143908
+#> layer.3 0.7561399 0.6972504 0.6635963 0.6310227 0.7330271 0.7567352 0.7677462
+#> layer.4 0.4031866 0.4135759 0.4061247 0.3879679 0.3750617 0.3743479 0.3741982
+#> layer.5 0.6058227 0.6325923 0.6479832 0.6617020 0.6480034 0.6238690 0.6078230
+#>                                                                    
+#> layer.1 0.9265291 0.9190510 0.8968893 0.8817701 0.8629508 0.8388748
+#> layer.2 0.3265712 0.3282949 0.2992975 0.2742826 0.2483226 0.2255383
+#> layer.3 0.7679649 0.7589920 0.7195554 0.6927858 0.6644491 0.6371886
+#> layer.4 0.3753241 0.3774461 0.3785580 0.3729116 0.3601426 0.3391285
+#> layer.5 0.6002171 0.6002851 0.6166497 0.6288149 0.6410043 0.6515710
+
+# create rij matrix using polygon (sf) planning units
+rij_sf <- rij_matrix(sim_pu_sf, sim_features)
+print(rij_sf)
+#> 5 x 90 sparse Matrix of class "dgCMatrix"
+#>                                                                              
+#> layer.1 0.7150548 0.6990429 0.6859317 0.6783193 0.6782107 0.6863252 0.7017231
+#> layer.2 0.2900901 0.3052216 0.3266036 0.3510977 0.3750470 0.3950113 0.4084749
+#> layer.3 0.8178213 0.8064534 0.7852441 0.7541320 0.7131559 0.6628435 0.6046204
+#> layer.4 0.2199663 0.2713800 0.3296247 0.3900085 0.4468281 0.4946333 0.5292249
+#> layer.5 0.4533809 0.4413639 0.4343547 0.4355628 0.4474871 0.4714105 0.5068509
+#>                                                                              
+#> layer.1 0.7219284 0.7435505 0.7631509 0.7505900 0.7357791 0.7233151 0.7156627
+#> layer.2 0.4142271 0.4123446 0.4038949 0.2800841 0.2967547 0.3181723 0.3409791
+#> layer.3 0.5411391 0.4763017 0.4147364 0.8275983 0.8194545 0.8013062 0.7730503
+#> layer.4 0.5479991 0.5498153 0.5348758 0.2208512 0.2738525 0.3350935 0.3998241
+#> layer.5 0.5510725 0.5991256 0.6448475 0.4741697 0.4569167 0.4453572 0.4428185
+#>                                                                              
+#> layer.1 0.7147517 0.7212831 0.7343615 0.7516415 0.7699543 0.7897989 0.7772875
+#> layer.2 0.3615030 0.3765606 0.3841340 0.3836641 0.3759393 0.2716298 0.2901825
+#> layer.3 0.7345400 0.6860553 0.6288231 0.5654560 0.5000330 0.8346555 0.8298830
+#> layer.4 0.4618047 0.5148344 0.5541170 0.5767631 0.5815260 0.2249796 0.2776009
+#> layer.5 0.4517499 0.4732935 0.5068285 0.5495481 0.5965013 0.5022737 0.4802429
+#>                                                                              
+#> layer.1 0.7661407 0.7585159 0.7561971 0.7599327 0.7690602 0.7816119 0.7948577
+#> layer.2 0.3119889 0.3334326 0.3508138 0.3612252 0.3631965 0.3568911 0.3438730
+#> layer.3 0.8151305 0.7903745 0.7553823 0.7102172 0.6558247 0.5945687 0.5304188
+#> layer.4 0.3390011 0.4047008 0.4684589 0.5238040 0.5655910 0.5906737 0.5976491
+#> layer.5 0.4646212 0.4587578 0.4649525 0.4840959 0.5153215 0.5556964 0.6003282
+#>                                                                              
+#> layer.1 0.8059966 0.8286461 0.8189872 0.8095434 0.8020377 0.7980313 0.7983424
+#> layer.2 0.3265679 0.2650109 0.2854743 0.3077757 0.3280176 0.3424767 0.3485511
+#> layer.3 0.4684656 0.8381119 0.8367193 0.8254115 0.8043530 0.7733527 0.7323690
+#> layer.4 0.5863706 0.2330116 0.2831343 0.3416658 0.4047077 0.4665769 0.5210694
+#> layer.5 0.6432595 0.5353515 0.5095593 0.4907792 0.4822721 0.4860960 0.5028092
+#>                                                                              
+#> layer.1 0.8026563 0.8095316 0.8167839 0.8220091 0.8633036 0.8564520 0.8487799
+#> layer.2 0.3453627 0.3338433 0.3163452 0.2959188 0.2603208 0.2824472 0.3051395
+#> layer.3 0.6821137 0.6246373 0.5636095 0.5039577 0.8370439 0.8390267 0.8310691
+#> layer.4 0.5629582 0.5888172 0.5969403 0.5869119 0.2456164 0.2910969 0.3438600
+#> layer.5 0.5312405 0.5683321 0.6093528 0.6487382 0.5700379 0.5418938 0.5211593
+#>                                                                              
+#> layer.1 0.8415392 0.8360026 0.8325552 0.8337363 0.8339533 0.8912849 0.8867860
+#> layer.2 0.3242198 0.3359588 0.3303278 0.3143945 0.2708325 0.2575975 0.2809245
+#> layer.3 0.8136049 0.7866027 0.7045769 0.6519655 0.5398928 0.8305082 0.8359634
+#> layer.4 0.4008068 0.4572360 0.5471036 0.5718452 0.5700792 0.2632826 0.3020677
+#> layer.5 0.5108757 0.5127704 0.5521633 0.5850800 0.6559584 0.6024207 0.5734186
+#>                                                                              
+#> layer.1 0.8807106 0.8738915 0.8672825 0.8616340 0.8571536 0.8533099 0.8488533
+#> layer.2 0.3037493 0.3216412 0.3308881 0.3295497 0.3179543 0.2985197 0.2749763
+#> layer.3 0.8312740 0.8171942 0.7939453 0.7616869 0.7210738 0.6737960 0.6228802
+#> layer.4 0.3465595 0.3945501 0.4425012 0.4859430 0.5203217 0.5418532 0.5479865
+#> layer.5 0.5520171 0.5408934 0.5413574 0.5531961 0.5746993 0.6028225 0.6335755
+#>                                                                              
+#> layer.1 0.8419808 0.9117805 0.9090526 0.9042812 0.8979800 0.8833313 0.8758136
+#> layer.2 0.2512416 0.2570026 0.2809260 0.3035274 0.3201754 0.3229680 0.3083414
+#> layer.3 0.5724977 0.8175488 0.8267526 0.8253873 0.8145533 0.7665224 0.7305762
+#> layer.4 0.5375278 0.2860727 0.3163391 0.3506471 0.3876575 0.4590604 0.4860971
+#> layer.5 0.6626552 0.6287730 0.6001593 0.5792111 0.5681102 0.5773113 0.5951498
+#>                                                                              
+#> layer.1 0.8679237 0.8586633 0.8463772 0.9251764 0.9199524 0.9141710 0.9067838
+#> layer.2 0.2863445 0.2611997 0.2370352 0.2589605 0.3047683 0.3200938 0.3251705
+#> layer.3 0.6886562 0.6435894 0.5991429 0.7972733 0.8129275 0.8053968 0.7890073
+#> layer.4 0.5023710 0.5050812 0.4927354 0.3133764 0.3566663 0.3816158 0.4070643
+#> layer.5 0.6183284 0.6433893 0.6667633 0.6461805 0.5990580 0.5886663 0.5878728
+#>                                                                              
+#> layer.1 0.8981802 0.8643680 0.8473654 0.9322748 0.9317639 0.9287528 0.9159813
+#> layer.2 0.3186414 0.2521341 0.2280966 0.2641903 0.2872474 0.3081174 0.3253428
+#> layer.3 0.7645150 0.6570162 0.6186335 0.7690767 0.7873422 0.7936492 0.7768533
+#> layer.4 0.4304725 0.4559778 0.4408970 0.3437657 0.3535038 0.3646749 0.3908502
+#> layer.5 0.5957192 0.6486412 0.6667338 0.6528235 0.6269821 0.6089827 0.5991743
+#>                                                                              
+#> layer.1 0.9066665 0.8822224 0.8658993 0.8449602 0.9336696 0.9339562 0.9315392
+#> layer.2 0.3170430 0.2740393 0.2478477 0.2243090 0.2736019 0.2951441 0.3143908
+#> layer.3 0.7561399 0.6972504 0.6635963 0.6310227 0.7330271 0.7567352 0.7677462
+#> layer.4 0.4031866 0.4135759 0.4061247 0.3879679 0.3750617 0.3743479 0.3741982
+#> layer.5 0.6058227 0.6325923 0.6479832 0.6617020 0.6480034 0.6238690 0.6078230
+#>                                                                    
+#> layer.1 0.9265291 0.9190510 0.8968893 0.8817701 0.8629508 0.8388748
+#> layer.2 0.3265712 0.3282949 0.2992975 0.2742826 0.2483226 0.2255383
+#> layer.3 0.7679649 0.7589920 0.7195554 0.6927858 0.6644491 0.6371886
+#> layer.4 0.3753241 0.3774461 0.3785580 0.3729116 0.3601426 0.3391285
+#> layer.5 0.6002171 0.6002851 0.6166497 0.6288149 0.6410043 0.6515710
+
+# create rij matrix using raster stack planning units
+rij_zones_raster <- rij_matrix(sim_pu_zones_stack, sim_features)
+print(rij_zones_raster)
+#> 5 x 90 sparse Matrix of class "dgCMatrix"
+#>                                                                              
+#> layer.1 0.7150548 0.6990429 0.6859317 0.6783193 0.6782107 0.6863252 0.7219284
+#> layer.2 0.2900901 0.3052216 0.3266036 0.3510977 0.3750470 0.3950113 0.4142271
+#> layer.3 0.8178213 0.8064534 0.7852441 0.7541320 0.7131559 0.6628435 0.5411391
+#> layer.4 0.2199663 0.2713800 0.3296247 0.3900085 0.4468281 0.4946333 0.5479991
+#> layer.5 0.4533809 0.4413639 0.4343547 0.4355628 0.4474871 0.4714105 0.5510725
+#>                                                                              
+#> layer.1 0.7435505 0.7631509 0.7505900 0.7357791 0.7233151 0.7156627 0.7147517
+#> layer.2 0.4123446 0.4038949 0.2800841 0.2967547 0.3181723 0.3409791 0.3615030
+#> layer.3 0.4763017 0.4147364 0.8275983 0.8194545 0.8013062 0.7730503 0.7345400
+#> layer.4 0.5498153 0.5348758 0.2208512 0.2738525 0.3350935 0.3998241 0.4618047
+#> layer.5 0.5991256 0.6448475 0.4741697 0.4569167 0.4453572 0.4428185 0.4517499
+#>                                                                              
+#> layer.1 0.7212831 0.7343615 0.7699543 0.7861227 0.7897989 0.7772875 0.7561971
+#> layer.2 0.3765606 0.3841340 0.3759393 0.3627013 0.2716298 0.2901825 0.3508138
+#> layer.3 0.6860553 0.6288231 0.5000330 0.4375452 0.8346555 0.8298830 0.7553823
+#> layer.4 0.5148344 0.5541170 0.5815260 0.5684388 0.2249796 0.2776009 0.4684589
+#> layer.5 0.4732935 0.5068285 0.5965013 0.6415349 0.5022737 0.4802429 0.4649525
+#>                                                                              
+#> layer.1 0.7599327 0.7690602 0.7816119 0.7948577 0.8059966 0.8286461 0.8189872
+#> layer.2 0.3612252 0.3631965 0.3568911 0.3438730 0.3265679 0.2650109 0.2854743
+#> layer.3 0.7102172 0.6558247 0.5945687 0.5304188 0.4684656 0.8381119 0.8367193
+#> layer.4 0.5238040 0.5655910 0.5906737 0.5976491 0.5863706 0.2330116 0.2831343
+#> layer.5 0.4840959 0.5153215 0.5556964 0.6003282 0.6432595 0.5353515 0.5095593
+#>                                                                              
+#> layer.1 0.8095434 0.8020377 0.7980313 0.7983424 0.8026563 0.8095316 0.8167839
+#> layer.2 0.3077757 0.3280176 0.3424767 0.3485511 0.3453627 0.3338433 0.3163452
+#> layer.3 0.8254115 0.8043530 0.7733527 0.7323690 0.6821137 0.6246373 0.5636095
+#> layer.4 0.3416658 0.4047077 0.4665769 0.5210694 0.5629582 0.5888172 0.5969403
+#> layer.5 0.4907792 0.4822721 0.4860960 0.5028092 0.5312405 0.5683321 0.6093528
+#>                                                                              
+#> layer.1 0.8220091 0.8633036 0.8564520 0.8487799 0.8360026 0.8330038 0.8337363
+#> layer.2 0.2959188 0.2603208 0.2824472 0.3051395 0.3359588 0.3380832 0.3143945
+#> layer.3 0.5039577 0.8370439 0.8390267 0.8310691 0.7866027 0.7500573 0.6519655
+#> layer.4 0.5869119 0.2456164 0.2910969 0.3438600 0.4572360 0.5076754 0.5718452
+#> layer.5 0.6487382 0.5700379 0.5418938 0.5211593 0.5127704 0.5270232 0.5850800
+#>                                                                              
+#> layer.1 0.8348882 0.8339533 0.8912849 0.8867860 0.8807106 0.8738915 0.8672825
+#> layer.2 0.2933767 0.2708325 0.2575975 0.2809245 0.3037493 0.3216412 0.3308881
+#> layer.3 0.5955431 0.5398928 0.8305082 0.8359634 0.8312740 0.8171942 0.7939453
+#> layer.4 0.5797670 0.5700792 0.2632826 0.3020677 0.3465595 0.3945501 0.4425012
+#> layer.5 0.6213430 0.6559584 0.6024207 0.5734186 0.5520171 0.5408934 0.5413574
+#>                                                                              
+#> layer.1 0.8616340 0.8571536 0.8488533 0.9117805 0.9090526 0.9042812 0.8979800
+#> layer.2 0.3295497 0.3179543 0.2749763 0.2570026 0.2809260 0.3035274 0.3201754
+#> layer.3 0.7616869 0.7210738 0.6228802 0.8175488 0.8267526 0.8253873 0.8145533
+#> layer.4 0.4859430 0.5203217 0.5479865 0.2860727 0.3163391 0.3506471 0.3876575
+#> layer.5 0.5531961 0.5746993 0.6335755 0.6287730 0.6001593 0.5792111 0.5681102
+#>                                                                              
+#> layer.1 0.8908018 0.8833313 0.8758136 0.8679237 0.8586633 0.8463772 0.9251764
+#> layer.2 0.3271982 0.3229680 0.3083414 0.2863445 0.2611997 0.2370352 0.2589605
+#> layer.3 0.7947903 0.7665224 0.7305762 0.6886562 0.6435894 0.5991429 0.7972733
+#> layer.4 0.4249398 0.4590604 0.4860971 0.5023710 0.5050812 0.4927354 0.3133764
+#> layer.5 0.5676758 0.5773113 0.5951498 0.6183284 0.6433893 0.6667633 0.6461805
+#>                                                                              
+#> layer.1 0.9237208 0.9199524 0.9141710 0.9067838 0.8981802 0.8885294 0.8775561
+#> layer.2 0.2828033 0.3047683 0.3200938 0.3251705 0.3186414 0.3017897 0.2781030
+#> layer.3 0.8107003 0.8129275 0.8053968 0.7890073 0.7645150 0.7330004 0.6962687
+#> layer.4 0.3337335 0.3566663 0.3816158 0.4070643 0.4304725 0.4485815 0.4580145
+#> layer.5 0.6187615 0.5990580 0.5886663 0.5878728 0.5957192 0.6102524 0.6288607
+#>                                                                              
+#> layer.1 0.8643680 0.8473654 0.9322748 0.9317639 0.9287528 0.9234146 0.9159813
+#> layer.2 0.2521341 0.2280966 0.2641903 0.2872474 0.3081174 0.3219892 0.3253428
+#> layer.3 0.6570162 0.6186335 0.7690767 0.7873422 0.7936492 0.7897301 0.7768533
+#> layer.4 0.4559778 0.4408970 0.3437657 0.3535038 0.3646749 0.3773969 0.3908502
+#> layer.5 0.6486412 0.6667338 0.6528235 0.6269821 0.6089827 0.5997976 0.5991743
+#>                                                                              
+#> layer.1 0.9066665 0.8955188 0.8822224 0.8658993 0.8449602 0.9336696 0.9339562
+#> layer.2 0.3170430 0.2986799 0.2740393 0.2478477 0.2243090 0.2736019 0.2951441
+#> layer.3 0.7561399 0.7289606 0.6972504 0.6635963 0.6310227 0.7330271 0.7567352
+#> layer.4 0.4031866 0.4117466 0.4135759 0.4061247 0.3879679 0.3750617 0.3743479
+#> layer.5 0.6058227 0.6177441 0.6325923 0.6479832 0.6617020 0.6480034 0.6238690
+#>                                                                    
+#> layer.1 0.9315392 0.9190510 0.9091912 0.8968893 0.8629508 0.8388748
+#> layer.2 0.3143908 0.3282949 0.3186099 0.2992975 0.2483226 0.2255383
+#> layer.3 0.7677462 0.7589920 0.7423054 0.7195554 0.6644491 0.6371886
+#> layer.4 0.3741982 0.3774461 0.3792402 0.3785580 0.3601426 0.3391285
+#> layer.5 0.6078230 0.6002851 0.6064383 0.6166497 0.6410043 0.6515710
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/run_calculations.html b/docs/reference/run_calculations.html index abe2b3d73..b7506cf06 100644 --- a/docs/reference/run_calculations.html +++ b/docs/reference/run_calculations.html @@ -1,105 +1,22 @@ - - - - - - - -Run calculations — run_calculations • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Run calculations — run_calculations • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Run calculations

      - Source: R/run_calculations.R + Source: R/run_calculations.R
      @@ -188,115 +105,110 @@

      Run calculations

      Execute preliminary calculations in a conservation problem and store the results for later use. This function is useful when creating slightly different versions of the same conservation planning problem that involve -the same pre-processing steps (e.g. calculating boundary data), because +the same pre-processing steps (e.g., calculating boundary data), because means that the same calculations will not be run multiple times.

      - 
      run_calculations(x)
      - -

      Arguments

      - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      - -

      Value

      +
      Usage,
      run_calculations(x)
      +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      +
      +

      Value

      Invisible TRUE indicating success.

      -

      Details

      - +
      +
      +

      Details

      This function is used for the effect of modifying the input -ConservationProblem object. As such, it does not return -anything. To use this function with pipe() operators, use the +ConservationProblem object. As such, it does not return +anything. To use this function with pipe() operators, use the %T>% operator and not the %>% operator.

      +
      -

      Examples

      - 
      # \dontrun{
-# Let us imagine a scenario where we wanted to understand the effect of
-# setting different targets on our solution.
-
-# create a conservation problem with no targets
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_boundary_penalties(10, 0.5) %>%
-     add_binary_decisions() %>%
-     add_default_solver(verbose = FALSE)
-
-# create a copies of p and add targets
-p1 <- p %>% add_relative_targets(0.1)
-p2 <- p %>% add_relative_targets(0.2)
-p3 <- p %>% add_relative_targets(0.3)
-
-# now solve each of the different problems and record the time spent
-# solving them
-s1 <- system.time({solve(p1); solve(p2); solve(p3)})
-
-# This approach is inefficient. Since these problems all share the same
-# planning units it is actually performing the same calculations three times.
-# To avoid this, we can use the "run_calculations" function before creating
-# the copies. Normally, R runs the calculations just before solving the
-# problem
-
-# recreate a conservation problem with no targets and tell R run the
-# preliminary calculations. Note how we use the %T>% operator here.
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_boundary_penalties(10, 0.5) %>%
-     add_binary_decisions() %>%
-     add_default_solver(verbose = FALSE) %T>%
-     run_calculations()
-
-# create a copies of p and add targets just like before
-p1 <- p %>% add_relative_targets(0.1)
-p2 <- p %>% add_relative_targets(0.2)
-p3 <- p %>% add_relative_targets(0.3)
-
-# solve each of the different problems and record the time spent
-# solving them
-s2 <- system.time({solve(p1); solve(p2); solve(p3)})
-
-# now lets compare the times
-print(s1) # time spent without running preliminary calculations
-#>    user  system elapsed 
-#>   1.216   0.016   1.295 
-print(s2) # time spent after running preliminary calculations
-#>    user  system elapsed 
-#>   1.134   0.024   1.200 
-
-# As we can see, we can save time by running the preliminary
-# calculations before making copies of the problem with slightly
-# different constraints. Although the time saved in this example
-# is rather small, this is because the example data are very small.
-# We would expect larger time savings for larger datasets.
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# Let us imagine a scenario where we wanted to understand the effect of
+# setting different targets on our solution.
+
+# create a conservation problem with no targets
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_boundary_penalties(10, 0.5) %>%
+     add_binary_decisions() %>%
+     add_default_solver(verbose = FALSE)
+
+# create a copies of p and add targets
+p1 <- p %>% add_relative_targets(0.1)
+p2 <- p %>% add_relative_targets(0.2)
+p3 <- p %>% add_relative_targets(0.3)
+
+# now solve each of the different problems and record the time spent
+# solving them
+s1 <- system.time({solve(p1); solve(p2); solve(p3)})
+
+# This approach is inefficient. Since these problems all share the same
+# planning units it is actually performing the same calculations three times.
+# To avoid this, we can use the "run_calculations" function before creating
+# the copies. Normally, R runs the calculations just before solving the
+# problem
+
+# recreate a conservation problem with no targets and tell R run the
+# preliminary calculations. Note how we use the %T>% operator here.
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_boundary_penalties(10, 0.5) %>%
+     add_binary_decisions() %>%
+     add_default_solver(verbose = FALSE) %T>%
+     run_calculations()
+
+# create a copies of p and add targets just like before
+p1 <- p %>% add_relative_targets(0.1)
+p2 <- p %>% add_relative_targets(0.2)
+p3 <- p %>% add_relative_targets(0.3)
+
+# solve each of the different problems and record the time spent
+# solving them
+s2 <- system.time({solve(p1); solve(p2); solve(p3)})
+
+# now lets compare the times
+print(s1) # time spent without running preliminary calculations
+#>    user  system elapsed 
+#>   1.260   0.026   1.369 
+print(s2) # time spent after running preliminary calculations
+#>    user  system elapsed 
+#>   1.147   0.026   1.216 
+
+# As we can see, we can save time by running the preliminary
+# calculations before making copies of the problem with slightly
+# different constraints. Although the time saved in this example
+# is rather small, this is because the example data are very small.
+# We would expect larger time savings for larger datasets.
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/scalar_parameters.html b/docs/reference/scalar_parameters.html index b0028aeca..9e16e2aff 100644 --- a/docs/reference/scalar_parameters.html +++ b/docs/reference/scalar_parameters.html @@ -1,104 +1,21 @@ - - - - - - - -Scalar parameters — scalar_parameters • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Scalar parameters — scalar_parameters • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Scalar parameters

      - Source: R/parameters.R + Source: R/parameters.R
      @@ -190,169 +107,162 @@

      Scalar parameters

      that are unacceptable then an error is thrown.

      - 
      proportion_parameter(name, value)
-
-binary_parameter(name, value)
-
-integer_parameter(
-  name,
-  value,
-  lower_limit = as.integer(-.Machine$integer.max),
-  upper_limit = as.integer(.Machine$integer.max)
-)
-
-numeric_parameter(
-  name,
-  value,
-  lower_limit = .Machine$double.xmin,
-  upper_limit = .Machine$double.xmax
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - -
      name

      character name of parameter.

      value

      integer or double value depending on the -parameter.

      lower_limit

      integer or double value representing +

      Usage,
      proportion_parameter(name, value)
+
+binary_parameter(name, value)
+
+integer_parameter(
+  name,
+  value,
+  lower_limit = as.integer(-.Machine$integer.max),
+  upper_limit = as.integer(.Machine$integer.max)
+)
+
+numeric_parameter(
+  name,
+  value,
+  lower_limit = .Machine$double.xmin,
+  upper_limit = .Machine$double.xmax
+)
      + +
      +

      Arguments

      +
      name
      +

      character name of parameter.

      +
      value
      +

      integer or double value depending on the +parameter.

      +
      lower_limit
      +

      integer or double value representing the smallest acceptable value for value. Defaults to -the smallest possible number on the system.

      upper_limit

      integer or double value representing +the smallest possible number on the system.

      +
      upper_limit
      +

      integer or double value representing the largest acceptable value for value. Defaults to -the largest possible number on the system.

      - -

      Value

      - -

      ScalarParameter object.

      -

      Details

      - +the largest possible number on the system.

      +
      +
      +

      Value

      +

      ScalarParameter object.

      +
      +
      +

      Details

      Below is a list of parameter generating functions and a brief description of each.

      -
      - -
      proportion_parameter

      A parameter that is a double and bounded +

      proportion_parameter
      +

      A parameter that is a double and bounded between zero and one.

      -
      integer_parameter

      A parameter that is a integer.

      -
      numeric_parameter

      A parameter that is a double.

      +
      integer_parameter
      +

      A parameter that is a integer.

      -
      binary_parameter

      A parameter that is restricted to integer -values of zero or one.

      +
      numeric_parameter
      +

      A parameter that is a double.

      -
      + +
      binary_parameter
      +

      A parameter that is restricted to integer +values of zero or one.

      -

      Examples

      - 
      # proportion parameter
-p1 <- proportion_parameter('prop', 0.5) # create new object
-print(p1) # print it
-#> prop (0.5)
-p1$get() # get value
-#> [1] 0.5
-p1$id # get id
-#> id: 69135dfd-ab6e-44ba-a1b8-c6131db3faec
-p1$validate(5) # check if 5 is a validate input
-p1$validate(0.1) # check if 0.1 is a validate input
-p1$set(0.1) # change value to 0.1
-print(p1)
-#> prop (0.1)
-
-# binary parameter
-p2 <- binary_parameter('bin', 0) # create new object
-print(p2) # print it
-#> bin (0)
-p2$get() # get value
-#> [1] 0
-p2$id # get id
-#> id: 6bf50b76-c926-4683-8f3c-bbc9f19cb949
-p2$validate(5) # check if 5 is a validate input
-p2$validate(1L) # check if 1L is a validate input
-p2$set(1L) # change value to 1L
-print(p1) # print it again
-#> prop (0.1)
-
-# integer parameter
-p3 <- integer_parameter('int', 5L) # create new object
-print(p3) # print it
-#> int (5)
-p3$get() # get value
-#> [1] 5
-p3$id # get id
-#> id: 19ad0815-7343-4a4c-8e03-238890668805
-p3$validate(5.6) # check if 5.6 is a validate input
-p3$validate(2L) # check if 2L is a validate input
-p3$set(2L) # change value to 2L
-print(p3) # print it again
-#> int (2)
-
-# numeric parameter
-p4 <- numeric_parameter('dbl', -7.6) # create new object
-print(p4) # print it
-#> dbl (-7.6)
-p4$get() # get value
-#> [1] -7.6
-p4$id # get id
-#> id: 1337d728-1756-4f22-8a4d-90e2e19b4bbc
-p4$validate(NA) # check if NA is a validate input
-p4$validate(8.9) # check if 8.9 is a validate input
-p4$set(8.9) # change value to 8.9
-print(p4) # print it again
-#> dbl (8.9)
-
-# numeric parameter with lower bounds
-p5 <- numeric_parameter('bdbl', 6, lower_limit=0) # create new object
-print(p5) # print it
-#> bdbl (6)
-p5$get() # get value
-#> [1] 6
-p5$id # get id
-#> id: 29bdc6c4-bc59-4fdb-b457-703823d4340b
-p5$validate(-10) # check if -10 is a validate input
-p5$validate(90) # check if 90 is a validate input
-p5$set(90) # change value to 8.9
-print(p5) # print it again
-#> bdbl (90)
-
+
+
      + +
      +

      Examples

      + 
      # proportion parameter
+p1 <- proportion_parameter('prop', 0.5) # create new object
+print(p1) # print it
+#> prop (0.5)
+p1$get() # get value
+#> [1] 0.5
+p1$id # get id
+#> id: 068b405e-07c9-4fb7-a30c-fcf2313b2dca
+p1$validate(5) # check if 5 is a validate input
+p1$validate(0.1) # check if 0.1 is a validate input
+p1$set(0.1) # change value to 0.1
+print(p1)
+#> prop (0.1)
+
+# binary parameter
+p2 <- binary_parameter('bin', 0) # create new object
+print(p2) # print it
+#> bin (0)
+p2$get() # get value
+#> [1] 0
+p2$id # get id
+#> id: a7775ce5-14f3-43df-8a3c-4aec6734f7e9
+p2$validate(5) # check if 5 is a validate input
+p2$validate(1L) # check if 1L is a validate input
+p2$set(1L) # change value to 1L
+print(p1) # print it again
+#> prop (0.1)
+
+# integer parameter
+p3 <- integer_parameter('int', 5L) # create new object
+print(p3) # print it
+#> int (5)
+p3$get() # get value
+#> [1] 5
+p3$id # get id
+#> id: d632827c-e7fb-458a-9124-aa0926a7f3b1
+p3$validate(5.6) # check if 5.6 is a validate input
+p3$validate(2L) # check if 2L is a validate input
+p3$set(2L) # change value to 2L
+print(p3) # print it again
+#> int (2)
+
+# numeric parameter
+p4 <- numeric_parameter('dbl', -7.6) # create new object
+print(p4) # print it
+#> dbl (-7.6)
+p4$get() # get value
+#> [1] -7.6
+p4$id # get id
+#> id: 97e2b191-90d2-4477-a7a7-2216c5c5a477
+p4$validate(NA) # check if NA is a validate input
+p4$validate(8.9) # check if 8.9 is a validate input
+p4$set(8.9) # change value to 8.9
+print(p4) # print it again
+#> dbl (8.9)
+
+# numeric parameter with lower bounds
+p5 <- numeric_parameter('bdbl', 6, lower_limit=0) # create new object
+print(p5) # print it
+#> bdbl (6)
+p5$get() # get value
+#> [1] 6
+p5$id # get id
+#> id: 7d17fad3-226b-4ed9-9c83-227b586d3804
+p5$validate(-10) # check if -10 is a validate input
+p5$validate(90) # check if 90 is a validate input
+p5$set(90) # change value to 8.9
+print(p5) # print it again
+#> bdbl (90)
+
      +
      + - - - - - - - - - - - + diff --git a/docs/reference/show.html b/docs/reference/show.html index fc5d9a085..7c84bae3f 100644 --- a/docs/reference/show.html +++ b/docs/reference/show.html @@ -1,101 +1,18 @@ - - - - - - - -Show — show • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Show — show • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Show

      - Source: R/show.R + Source: R/show.R
      @@ -184,64 +101,57 @@

      Show

      Display information about an object.

      - 
      # S4 method for ConservationModifier
-show(x)
-
-# S4 method for ConservationProblem
-show(x)
+    
      Usage,
      # S4 method for ConservationModifier
+show(x)
 
-# S4 method for Id
-show(x)
+# S4 method for ConservationProblem
+show(x)
 
-# S4 method for OptimizationProblem
-show(x)
+# S4 method for Id
+show(x)
 
-# S4 method for Parameter
-show(x)
+# S4 method for OptimizationProblem
+show(x)
 
-# S4 method for Solver
-show(x)
      
+# S4 method for Parameter
+show(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      Any object.
      
-
-    
      Value
      
+# S4 method for Solver
+show(x)
      +
      +

      Arguments

      +
      x
      +

      Any object.

      +
      +
      +

      Value

      None.

      -

      See also

      - -

      methods::show().

      +
      +
      +

      See also

      +

      methods::show().

      +
      + - - - - - - - - - - - + diff --git a/docs/reference/sim_data.html b/docs/reference/sim_data.html index 53b78c2c3..bdbff2808 100644 --- a/docs/reference/sim_data.html +++ b/docs/reference/sim_data.html @@ -1,101 +1,18 @@ - - - - - - - -Simulated conservation planning data — sim_data • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Simulated conservation planning data — sim_data • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Simulated conservation planning data

      - Source: R/data.R + Source: R/data.R
      @@ -184,116 +101,153 @@

      Simulated conservation planning data

      Simulated data for making spatial prioritizations.

      - 
      data(sim_pu_polygons)
+    
      Usage,
      data(sim_pu_polygons)
+
+data(sim_pu_zones_polygons)
 
-data(sim_pu_zones_polygons)
+data(sim_pu_points)
 
-data(sim_pu_points)
+data(sim_pu_lines)
 
-data(sim_pu_lines)
+data(sim_pu_sf)
 
-data(sim_pu_sf)
+data(sim_pu_zones_sf)
 
-data(sim_pu_zones_sf)
+data(sim_pu_raster)
 
-data(sim_pu_raster)
+data(sim_locked_in_raster)
 
-data(sim_locked_in_raster)
+data(sim_locked_out_raster)
 
-data(sim_locked_out_raster)
+data(sim_pu_zones_stack)
 
-data(sim_pu_zones_stack)
+data(sim_features)
 
-data(sim_features)
+data(sim_features_zones)
 
-data(sim_features_zones)
+data(sim_phylogeny)
      
 
-data(sim_phylogeny)
      +
      +

      Format

      + +
      sim_pu_polygons
      +

      SpatialPolygonsDataFrame +object.

      -

      Format

      +
      sim_pu_zones_polygons
      +

      SpatialPolygonsDataFrame object.

      - -
      -
      sim_pu_polygons

      SpatialPolygonsDataFrame -object.

      +
      sim_pu_sf
      +

      sf::sf() object.

      + -
      sim_pu_zones_polygons

      SpatialPolygonsDataFrame object.

      +
      sim_pu_zones_sf
      +

      sf::sf() object.

      -
      sim_pu_sf

      sf::sf() object.

      -
      sim_pu_zones_sf

      sf::sf() object.

      +
      sim_pu_lines
      +

      SpatialLinesDataFrame object.

      -
      sim_pu_lines

      SpatialLinesDataFrame object.

      -
      sim_pu_points

      SpatialPointsDataFrame +

      sim_pu_points
      +

      SpatialPointsDataFrame object.

      -
      sim_pu_raster

      RasterLayer object.

      -
      sim_pu_zones_stack

      RasterStack object.

      +
      sim_pu_raster
      +

      RasterLayer object.

      -
      sim_locked_in_raster

      RasterLayer + +

      sim_pu_zones_stack
      +

      RasterStack object.

      + + +
      sim_locked_in_raster
      +

      RasterLayer object.

      -
      sim_locked_out_raster

      RasterLayer + +

      sim_locked_out_raster
      +

      RasterLayer object.

      -
      sim_features

      RasterStack object.

      -
      sim_features_zones

      ZonesRaster() object.

      +
      sim_features
      +

      RasterStack object.

      -
      sim_phylogeny

      ape::phylo() object.

      +
      sim_features_zones
      +

      ZonesRaster() object.

      -
      -

      Details

      +
      sim_phylogeny
      +

      ape::phylo() object.

      - -
      -
      sim_pu_raster

      Planning units are represented as raster data. + +

      +
      +

      Details

      + +
      sim_pu_raster
      +

      Planning units are represented as raster data. Pixel values indicate planning unit cost and NA values indicate that a pixel is not a planning unit.

      -
      sim_pu_zones_stack

      Planning units are represented as raster + +

      sim_pu_zones_stack
      +

      Planning units are represented as raster stack data. Each layer indicates the cost for a different management zone. Pixels with NA values in a given zone indicate that a planning unit cannot be allocated to that zone in a solution. Additionally, pixels with NA values in all layers are not a planning unit.

      -
      sim_locked_in_raster

      Planning units are represented as raster + +

      sim_locked_in_raster
      +

      Planning units are represented as raster data. Pixel values are binary and indicate if planning units should be locked in to the solution.

      -
      sim_locked_out_raster

      Planning units are represented as + +

      sim_locked_out_raster
      +

      Planning units are represented as raster data. Pixel values are binary and indicate if planning units should be locked out from the solution.

      -
      sim_pu_polygons

      Planning units represented as polygon data. + +

      sim_pu_polygons
      +

      Planning units represented as polygon data. The attribute table contains fields (columns) indicating the expenditure required for prioritizing each planning unit ("cost" field), if the planning units should be selected in the solution ("locked_in" field), and if the planning units should never be selected in the solution ("locked_out" field).

      -
      sim_pu_points

      Planning units represented as point data. + +

      sim_pu_points
      +

      Planning units represented as point data. The attribute table follows the same conventions as for sim_pu_polygons.

      -
      sim_pu_lines

      Planning units represented as line data. + +

      sim_pu_lines
      +

      Planning units represented as line data. The attribute table follows the same conventions as for sim_pu_polygons.

      -
      sim_pu_sf

      Planning units represented as polygon data -using the sf::sf() package. + +

      sim_pu_sf
      +

      Planning units represented as polygon data +using the sf::sf() package. The attribute table follows the same conventions as for sim_pu_polygons.

      -
      sim_pu_zones_polygons

      Planning units represented as polygon + +

      sim_pu_zones_polygons
      +

      Planning units represented as polygon data. The attribute table contains fields (columns) indicating the expenditure required for prioritizing each planning unit under different management zones ("cost_1", "cost_2", and "cost_3" fields), and a series @@ -302,94 +256,99 @@

      Details In these locked fields, planning units that should not be locked to a specific value are assigned a NA value.

      -
      sim_pu_zones_sf

      Planning units represented as polygon data -using the sf::sf() package. The attribute tables follows + +

      sim_pu_zones_sf
      +

      Planning units represented as polygon data +using the sf::sf() package. The attribute tables follows the same conventions as for sim_pu_zone_polygons.

      -
      sim_features

      The simulated distribution of ten species. + +

      sim_features
      +

      The simulated distribution of ten species. Pixel values indicate habitat suitability.

      -
      sim_features_zones

      The simulated distribution for five + +

      sim_features_zones
      +

      The simulated distribution for five species under three different management zones.

      -
      sim_phylogeny

      The phylogenetic tree for the ten species.

      - - -
      - - -

      Examples

      - 
      # load data
-data(sim_pu_polygons, sim_pu_lines, sim_pu_points, sim_pu_raster,
-     sim_locked_in_raster, sim_locked_out_raster, sim_phylogeny,
-     sim_features, sim_pu_sf)
-
-# plot example Spatial-class planning unit data
-# \dontrun{
-par(mfrow = c(2, 3))
-plot(sim_pu_raster, main = "planning units (raster)")
-plot(sim_locked_in_raster, main = "locked in units (raster)")
-plot(sim_locked_out_raster, main = "locked out units (raster)")
-plot(sim_pu_polygons, main = "planning units (polygons)")
-plot(sim_pu_lines, main = "planning units (lines)")
-plot(sim_pu_points, main = "planning units (points)")
-
-
-# plot example sf-class planning unit data
-plot(sim_pu_sf)
-
-
-# plot example phylogeny data
-par(mfrow = c(1, 1))
-ape::plot.phylo(sim_phylogeny, main = "simulated phylogeny")
-
-
-# plot example feature data
-par(mfrow = c(1, 1))
-plot(sim_features)
-
-
-# plot example management zone cost data
-par(mfrow = c(1, 1))
-plot(sim_pu_zones_stack)
-
-
-# plot example feature data for each management zone
-plot(do.call(stack, sim_features_zones),
-     main = paste0("Species ",
-                   rep(seq_len(number_of_zones(sim_features_zones)),
-                       number_of_features(sim_features_zones)),
-                   " (zone ",
-                   rep(seq_len(number_of_features(sim_features_zones)),
-                       each = number_of_zones(sim_features_zones)),
-                   ")"))
-
-# }
+
+
      sim_phylogeny
      
+
      The phylogenetic tree for the ten species.
      
+
+
+
+
      + +
      +

      Examples

      + 
      # load data
+data(sim_pu_polygons, sim_pu_lines, sim_pu_points, sim_pu_raster,
+     sim_locked_in_raster, sim_locked_out_raster, sim_phylogeny,
+     sim_features, sim_pu_sf)
+
+# plot example Spatial-class planning unit data
+# \dontrun{
+par(mfrow = c(2, 3))
+plot(sim_pu_raster, main = "planning units (raster)")
+plot(sim_locked_in_raster, main = "locked in units (raster)")
+plot(sim_locked_out_raster, main = "locked out units (raster)")
+plot(sim_pu_polygons, main = "planning units (polygons)")
+plot(sim_pu_lines, main = "planning units (lines)")
+plot(sim_pu_points, main = "planning units (points)")
+
+
+# plot example sf-class planning unit data
+plot(sim_pu_sf)
+
+
+# plot example phylogeny data
+par(mfrow = c(1, 1))
+ape::plot.phylo(sim_phylogeny, main = "simulated phylogeny")
+
+
+# plot example feature data
+par(mfrow = c(1, 1))
+plot(sim_features)
+
+
+# plot example management zone cost data
+par(mfrow = c(1, 1))
+plot(sim_pu_zones_stack)
+
+
+# plot example feature data for each management zone
+plot(do.call(stack, sim_features_zones),
+     main = paste0("Species ",
+                   rep(seq_len(number_of_zones(sim_features_zones)),
+                       number_of_features(sim_features_zones)),
+                   " (zone ",
+                   rep(seq_len(number_of_features(sim_features_zones)),
+                       each = number_of_zones(sim_features_zones)),
+                   ")"))
+
+# }
      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/simulate_cost.html b/docs/reference/simulate_cost.html index 2a9bd4f51..293a3b5d0 100644 --- a/docs/reference/simulate_cost.html +++ b/docs/reference/simulate_cost.html @@ -1,102 +1,19 @@ - - - - - - - -Simulate cost data — simulate_cost • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Simulate cost data — simulate_cost • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Simulate cost data

      - Source: R/simulate.R + Source: R/simulate.R
      @@ -186,91 +103,78 @@

      Simulate cost data

      it returns spatially auto-correlated integer values.

      - 
      simulate_cost(
-  x,
-  n = 1,
-  model = RandomFields::RPpoisson(RandomFields::RMtruncsupport(radius = raster::xres(x)
-    * 10, RandomFields::RMgauss())),
-  transform = identity,
-  ...
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - -
      x

      RasterLayer object to use as -a template.

      n

      integer number of species to simulate.

      model

      RandomFields::RP() model object -to use for simulating data.

      transform

      function to transform values output -from the random fields simulation.

      ...

      additional arguments passed to -RandomFields::RFsimulate().

      - -

      Value

      - -

      RasterStack object.

      -

      See also

      - -

      simulate_data().

      +
      Usage,
      simulate_cost(
+  x,
+  n = 1,
+  model = RandomFields::RPpoisson(RandomFields::RMtruncsupport(radius = raster::xres(x)
+    * 10, RandomFields::RMgauss())),
+  transform = identity,
+  ...
+)
      + +
      +

      Arguments

      +
      x
      +

      RasterLayer object to use as +a template.

      +
      n
      +

      integer number of species to simulate.

      +
      model
      +

      RandomFields::RP() model object +to use for simulating data.

      +
      transform
      +

      function to transform values output +from the random fields simulation.

      +
      ...
      +

      additional arguments passed to +RandomFields::RFsimulate().

      +
      +
      +

      Value

      +

      RasterStack object.

      +
      +
      +

      See also

      +

      simulate_data().

      +
      -

      Examples

      - 
      # \dontrun{
-# create raster
-r <- raster(ncol=10, nrow=10, xmn=0, xmx=1, ymn=0, ymx=1)
-values(r) <- 1
-
-# simulate data
-# (note this requires the RandomFields package to be installed)
-cost <- simulate_cost(r)
-
-# plot simulated species
-plot(cost, main = "simulated cost data")
-
-# }
-
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# create raster
+r <- raster(ncol=10, nrow=10, xmn=0, xmx=1, ymn=0, ymx=1)
+values(r) <- 1
+
+# simulate data
+# (note this requires the RandomFields package to be installed)
+cost <- simulate_cost(r)
+
+# plot simulated species
+plot(cost, main = "simulated cost data")
+
+# }
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/simulate_data.html b/docs/reference/simulate_data.html index 3dbfab1c3..c8a8fe155 100644 --- a/docs/reference/simulate_data.html +++ b/docs/reference/simulate_data.html @@ -1,101 +1,18 @@ - - - - - - - -Simulate data — simulate_data • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Simulate data — simulate_data • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Simulate data

      - Source: R/simulate.R + Source: R/simulate.R
      @@ -184,85 +101,72 @@

      Simulate data

      Simulate spatially auto-correlated data.

      - 
      simulate_data(x, n, model, transform = identity, ...)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - -
      x

      RasterLayer object to use as -a template.

      n

      integer number of species to simulate.

      model

      RandomFields::RP() model object -to use for simulating data.

      transform

      function to transform values output -from the random fields simulation.

      ...

      additional arguments passed to -RandomFields::RFsimulate().

      - -

      Value

      - -

      RasterStack object with a +

      Usage,
      simulate_data(x, n, model, transform = identity, ...)
      + +
      +

      Arguments

      +
      x
      +

      RasterLayer object to use as +a template.

      +
      n
      +

      integer number of species to simulate.

      +
      model
      +

      RandomFields::RP() model object +to use for simulating data.

      +
      transform
      +

      function to transform values output +from the random fields simulation.

      +
      ...
      +

      additional arguments passed to +RandomFields::RFsimulate().

      +
      +
      +

      Value

      +

      RasterStack object with a layer for each species.

      -

      See also

      - -

      RandomFields::RFsimulate(), -simulate_cost(), simulate_species().

      +
      + -

      Examples

      - 
      # \dontrun{
-# create raster
-r <- raster(ncol=10, nrow=10, xmn=0, xmx=1, ymn=0, ymx=1)
-values(r) <- 1
-
-# simulate data using a Gaussian field
-# (note this requires the RandomFields package to be installed)
-d <- simulate_data(r, n = 1, model = RandomFields::RMgauss())
-
-# plot simulated data
-plot(d, main = "random Gaussian field")
-
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# create raster
+r <- raster(ncol=10, nrow=10, xmn=0, xmx=1, ymn=0, ymx=1)
+values(r) <- 1
+
+# simulate data using a Gaussian field
+# (note this requires the RandomFields package to be installed)
+d <- simulate_data(r, n = 1, model = RandomFields::RMgauss())
+
+# plot simulated data
+plot(d, main = "random Gaussian field")
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/simulate_species.html b/docs/reference/simulate_species.html index 8713f4f90..815e268f0 100644 --- a/docs/reference/simulate_species.html +++ b/docs/reference/simulate_species.html @@ -1,102 +1,19 @@ - - - - - - - -Simulate species habitat suitability data — simulate_species • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Simulate species habitat suitability data — simulate_species • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Simulate species habitat suitability data

      - Source: R/simulate.R + Source: R/simulate.R
      @@ -186,91 +103,78 @@

      Simulate species habitat suitability data

      the output will contain values between zero and one.

      - 
      simulate_species(
-  x,
-  n = 1,
-  model = RandomFields::RMgauss(),
-  transform = stats::plogis,
-  ...
-)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - -
      x

      RasterLayer object to use as -a template.

      n

      integer number of species to simulate.

      model

      RandomFields::RP() model object -to use for simulating data.

      transform

      function to transform values output -from the random fields simulation.

      ...

      additional arguments passed to -RandomFields::RFsimulate().

      - -

      Value

      - -

      RasterStack object.

      -

      See also

      - -

      simulate_data().

      +
      Usage,
      simulate_species(
+  x,
+  n = 1,
+  model = RandomFields::RMgauss(),
+  transform = stats::plogis,
+  ...
+)
      + +
      +

      Arguments

      +
      x
      +

      RasterLayer object to use as +a template.

      +
      n
      +

      integer number of species to simulate.

      +
      model
      +

      RandomFields::RP() model object +to use for simulating data.

      +
      transform
      +

      function to transform values output +from the random fields simulation.

      +
      ...
      +

      additional arguments passed to +RandomFields::RFsimulate().

      +
      +
      +

      Value

      +

      RasterStack object.

      +
      +
      +

      See also

      +

      simulate_data().

      +
      -

      Examples

      - 
      # \dontrun{
-# create raster
-r <- raster(ncol=10, nrow=10, xmn=0, xmx=1, ymn=0, ymx=1)
-values(r) <- 1
-
-# simulate data for 4 species
-# (note this requires the RandomFields package to be installed)
-spp <- simulate_species(r, 4)
-#> ....
-
-# plot simulated species
-plot(spp, main = "simulated species distributions")
-
-# }
-
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# create raster
+r <- raster(ncol=10, nrow=10, xmn=0, xmx=1, ymn=0, ymx=1)
+values(r) <- 1
+
+# simulate data for 4 species
+# (note this requires the RandomFields package to be installed)
+spp <- simulate_species(r, 4)
+#> ....
+
+# plot simulated species
+plot(spp, main = "simulated species distributions")
+
+# }
+
 
      
+
      +
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      -
      -

      Solve

      - Source: R/solve.R + Source: R/solve.R
      -

      Solve a conservation planning problem().

      +

      Solve a conservation planning problem().

      - 
      # S4 method for OptimizationProblem,Solver
-solve(a, b, ...)
-
-# S4 method for ConservationProblem,missing
-solve(a, b, ..., run_checks = TRUE, force = FALSE)
      - -

      Arguments

      - - - - - - - - - - - - - - - - - - - - - - -
      a

      problem() (i.e. ConservationProblem) or -OptimizationProblem object.

      b

      Solver object. Not used if a is an -ConservationProblem object.

      ...

      arguments passed to compile().

      run_checks

      logical flag indicating whether presolve checks +

      Usage,
      # S4 method for OptimizationProblem,Solver
+solve(a, b, ...)
+
+# S4 method for ConservationProblem,missing
+solve(a, b, ..., run_checks = TRUE, force = FALSE)
      + +
      +

      Arguments

      +
      a
      +

      problem() (i.e., ConservationProblem) or +OptimizationProblem object.

      +
      b
      +

      Solver object. Not used if a is an +ConservationProblem object.

      +
      ...
      +

      arguments passed to compile().

      +
      run_checks
      +

      logical flag indicating whether presolve checks should be run prior solving the problem. These checks are performed using -the presolve_check() function. Defaults to TRUE. -Skipping these checks may reduce run time for large problems.

      force

      logical flag indicating if an attempt to should be +the presolve_check() function. Defaults to TRUE. +Skipping these checks may reduce run time for large problems.

      +
      force
      +

      logical flag indicating if an attempt to should be made to solve the problem even if potential issues were detected during -the presolve checks. Defaults to FALSE.

      - -

      Value

      - +the presolve checks. Defaults to FALSE.

      +
      +
      +

      Value

      A numeric, matrix, -RasterLayer, Spatial, -or sf::sf() object containing the solution to the problem. +RasterLayer, Spatial, +or sf::sf() object containing the solution to the problem. Additionally, the returned object will have the following additional attributes: "objective" containing the solution's objective, "runtime" denoting the number of seconds that elapsed while solving the problem, and "status" describing the status of the solution -(e.g. "OPTIMAL" indicates that the optimal solution was found). -In most cases, the first solution (e.g. "solution_1") +(e.g., "OPTIMAL" indicates that the optimal solution was found). +In most cases, the first solution (e.g., "solution_1") will contain the best solution found by the solver (note that this may not be an optimal solution depending on the gap used to solve the problem and noting that the default gap is 0.1).

      -

      Details

      - -

      After formulating a conservation planning problem(), -it can be solved using an exact algorithm solver (see solvers +

      +
      +

      Details

      +

      After formulating a conservation planning problem(), +it can be solved using an exact algorithm solver (see solvers for available solvers). If no solver has been explicitly specified, then the best available exact algorithm solver will be used by default -(see add_default_solver(). Although these exact algorithm +(see add_default_solver(). Although these exact algorithm solvers will often display a lot of information that isn't really that -helpful (e.g. nodes, cutting planes), they do display information -about the progress they are making on solving the problem (e.g. the +helpful (e.g., nodes, cutting planes), they do display information +about the progress they are making on solving the problem (e.g., the performance of the best solution found at a given point in time). If potential issues were detected during the -presolve checks (see presolve_check()) -and the problem is being forcibly solved (i.e. with force = TRUE), +presolve checks (see presolve_check()) +and the problem is being forcibly solved (i.e., with force = TRUE), then it is also worth checking for any warnings displayed by the solver to see if these potential issues are actually causing issues -(e.g. Gurobi can display warnings that include +(e.g., Gurobi can display warnings that include "Warning: Model contains large matrix coefficient range" and "Warning: Model contains large rhs").

      The object returned from this function depends on the argument to a. If the argument to a is an -OptimizationProblem object, then the +OptimizationProblem object, then the solution is returned as a logical vector showing the status of each planning unit in each zone. However, in most cases, the argument -to a will be a ConservationProblem object, and so +to a will be a ConservationProblem object, and so the type of object returned depends on the number of solutions generated and the data format used to specify the planning units:

      -
      - -
      a has numeric planning units

      The solution will be +

      a has numeric planning units
      +

      The solution will be returned as a numeric vector. Here, each element in the vector corresponds to a different planning unit. Note that if a portfolio is used to generate multiple solutions, then a list of such numeric vectors will be returned.

      -
      a has matrix planning units

      The solution will be + +

      a has matrix planning units
      +

      The solution will be returned as a matrix object. Here, rows correspond to different planning units, and fields (columns) correspond to different management zones. Note that if a portfolio is used to generate multiple solutions, then a list of such matrix objects will be returned.

      -
      a has Raster planning units

      The solution -will be returned as a Raster object. + +

      a has Raster planning units
      +

      The solution +will be returned as a Raster object. If the argument to x contains a single -management zone, then a RasterLayer object will be returned. +management zone, then a RasterLayer object will be returned. Otherwise, if the argument to x contains multiple zones, then a -RasterStack object +RasterStack object will be returned containing a different layer for each management zone. Note that if a portfolio is used to generate multiple solutions, -then a list of such Raster objects will be returned.

      +then a list of such Raster objects will be returned.

      -
      a has Spatial, sf::sf(), or data.frame -planning units

      The solution will be returned in the same data format as the planning + +

      a has Spatial, sf::sf(), or data.frame +planning units
      +

      The solution will be returned in the same data format as the planning units. Here, each row corresponds to a different planning unit, and fields contain solutions. @@ -297,310 +208,308 @@

      Details will contain fields (columns) that solution the values. Specifically, the field name(s) containing the solution values be will named as "solution_XXX" where "XXX" corresponds to a solution -identifier (e.g. "solution_1"). +identifier (e.g., "solution_1"). If the argument to a contains multiple zones, then the fields containing solutions will be named as "solution_XXX_YYY" where "XXX" corresponds to the solution identifier and "YYY" is the name -of the management zone (e.g. "solution_1_zone1").

      - +of the management zone (e.g., "solution_1_zone1").

      -
      -

      See also

      -

      See problem() to create conservation planning problems, and -presolve_check() to check problems for potential issues. -Also, see the category_layer() and category_vector() function to +

      +
      +

      See also

      +

      See problem() to create conservation planning problems, and +presolve_check() to check problems for potential issues. +Also, see the category_layer() and category_vector() function to reformat solutions that contain multiple zones.

      +
      -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_pu_polygons, sim_pu_sf, sim_features,
-     sim_pu_zones_stack, sim_pu_zones_sf, sim_features_zones)
-
-# build minimal conservation problem with raster data
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s1 <- solve(p1)
-
-# print solution
-print(s1)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# print attributes describing the optimization process and the solution
-print(attr(s1, "objective"))
-#> solution_1 
-#>   1987.399 
-print(attr(s1, "runtime"))
-#> solution_1 
-#>      0.004 
-print(attr(s1, "status"))
-#> solution_1 
-#>  "OPTIMAL" 
-
-# calculate feature representation in the solution
-r1 <- eval_feature_representation_summary(p1, s1)
-print(r1)
-#> # A tibble: 5 × 5
-#>   summary feature total_amount absolute_held relative_held
-#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-#> 1 overall layer.1         83.3          8.91         0.107
-#> 2 overall layer.2         31.2          3.13         0.100
-#> 3 overall layer.3         72.0          7.34         0.102
-#> 4 overall layer.4         42.7          4.35         0.102
-#> 5 overall layer.5         56.7          6.01         0.106
-
-# plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# build minimal conservation problem with polygon (Spatial) data
-p2 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s2 <- solve(p2)
-
-# print first six rows of the attribute table
-print(head(s2))
-#>       cost locked_in locked_out solution_1
-#> 1 215.8638     FALSE      FALSE          0
-#> 2 212.7823     FALSE      FALSE          0
-#> 3 207.4962     FALSE      FALSE          0
-#> 4 208.9322     FALSE       TRUE          0
-#> 5 214.0419     FALSE      FALSE          0
-#> 6 213.7636     FALSE      FALSE          0
-
-# calculate feature representation in the solution
-r2 <- eval_feature_representation_summary(p2, s2[, "solution_1"])
-print(r2)
-#> # A tibble: 5 × 5
-#>   summary feature total_amount absolute_held relative_held
-#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-#> 1 overall layer.1         74.5          8.05         0.108
-#> 2 overall layer.2         28.1          2.83         0.101
-#> 3 overall layer.3         64.9          6.65         0.103
-#> 4 overall layer.4         38.2          3.87         0.101
-#> 5 overall layer.5         50.7          5.41         0.107
-
-# plot solution
-spplot(s2, zcol = "solution_1", main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# build minimal conservation problem with polygon (sf) data
-p3 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s3 <- solve(p3)
-
-# print first six rows of the attribute table
-print(head(s3))
-#> Simple feature collection with 6 features and 4 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>       cost locked_in locked_out solution_1                       geometry
-#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# calculate feature representation in the solution
-r3 <- eval_feature_representation_summary(p3, s3[, "solution_1"])
-print(r3)
-#> # A tibble: 5 × 5
-#>   summary feature total_amount absolute_held relative_held
-#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-#> 1 overall layer.1         74.5          8.05         0.108
-#> 2 overall layer.2         28.1          2.83         0.101
-#> 3 overall layer.3         64.9          6.65         0.103
-#> 4 overall layer.4         38.2          3.87         0.101
-#> 5 overall layer.5         50.7          5.41         0.107
-
-# plot solution
-plot(s3[, "solution_1"])
-
-# }
-
-# build multi-zone conservation problem with raster data
-p4 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s4 <- solve(p4)
-
-# print solution
-print(s4)
-#> class      : RasterStack 
-#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> names      : zone_1, zone_2, zone_3 
-#> min values :      0,      0,      0 
-#> max values :      1,      1,      1 
-#> 
-
-# calculate feature representation in the solution
-r4 <- eval_feature_representation_summary(p4, s4)
-print(r4)
-#> # A tibble: 20 × 5
-#>    summary feature   total_amount absolute_held relative_held
-#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
-#>  1 overall feature_1        250.          47.1          0.188
-#>  2 overall feature_2         93.6         17.9          0.191
-#>  3 overall feature_3        216.          41.6          0.193
-#>  4 overall feature_4        128.          23.7          0.185
-#>  5 overall feature_5        170.          31.6          0.186
-#>  6 zone_1  feature_1         83.3         16.5          0.198
-#>  7 zone_1  feature_2         31.2          5.65         0.181
-#>  8 zone_1  feature_3         72.0         14.2          0.198
-#>  9 zone_1  feature_4         42.7          7.56         0.177
-#> 10 zone_1  feature_5         56.7         11.1          0.197
-#> 11 zone_2  feature_1         83.3         15.7          0.189
-#> 12 zone_2  feature_2         31.2          6.03         0.193
-#> 13 zone_2  feature_3         72.0         14.5          0.201
-#> 14 zone_2  feature_4         42.7          7.82         0.183
-#> 15 zone_2  feature_5         56.7         10.3          0.181
-#> 16 zone_3  feature_1         83.3         14.8          0.178
-#> 17 zone_3  feature_2         31.2          6.22         0.199
-#> 18 zone_3  feature_3         72.0         13.0          0.180
-#> 19 zone_3  feature_4         42.7          8.27         0.194
-#> 20 zone_3  feature_5         56.7         10.2          0.180
-
-# plot solution
-plot(category_layer(s4), main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# build multi-zone conservation problem with polygon (sf) data
-p5 <- problem(sim_pu_zones_sf, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s5 <- solve(p5)
-
-# print first six rows of the attribute table
-print(head(s5))
-#> Simple feature collection with 6 features and 9 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
-#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
-#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
-#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
-#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
-#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
-#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
-#>   solution_1_zone_2 solution_1_zone_3                       geometry
-#> 1                 1                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2                 1                 0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4                 1                 0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5                 1                 0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6                 1                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# calculate feature representation in the solution
-r5 <- eval_feature_representation_summary(
-  p5, s5[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-print(r5)
-#> # A tibble: 20 × 5
-#>    summary feature   total_amount absolute_held relative_held
-#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
-#>  1 overall feature_1        225.          37.5          0.166
-#>  2 overall feature_2         83.9         14.6          0.174
-#>  3 overall feature_3        195.          34.0          0.174
-#>  4 overall feature_4        114.          18.4          0.161
-#>  5 overall feature_5        154.          25.1          0.163
-#>  6 zone_1  feature_1         75.1         12.8          0.170
-#>  7 zone_1  feature_2         28.0          4.63         0.165
-#>  8 zone_1  feature_3         65.0         10.6          0.163
-#>  9 zone_1  feature_4         38.0          6.29         0.165
-#> 10 zone_1  feature_5         51.2          8.88         0.174
-#> 11 zone_2  feature_1         75.1         11.0          0.146
-#> 12 zone_2  feature_2         28.0          5.26         0.188
-#> 13 zone_2  feature_3         65.0         10.7          0.165
-#> 14 zone_2  feature_4         38.0          6.49         0.171
-#> 15 zone_2  feature_5         51.2          7.27         0.142
-#> 16 zone_3  feature_1         75.1         13.7          0.182
-#> 17 zone_3  feature_2         28.0          4.75         0.170
-#> 18 zone_3  feature_3         65.0         12.7          0.195
-#> 19 zone_3  feature_4         38.0          5.62         0.148
-#> 20 zone_3  feature_5         51.2          8.93         0.175
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s5$solution <- category_vector(s5[, c("solution_1_zone_1",
-                                      "solution_1_zone_2",
-                                      "solution_1_zone_3")])
-s5$solution <- factor(s5$solution)
-
-# plot solution
-plot(s5[, "solution"])
-
-# }
+    
      
+    
      Examples
      
+    
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_pu_polygons, sim_pu_sf, sim_features,
+     sim_pu_zones_stack, sim_pu_zones_sf, sim_features_zones)
+
+# build minimal conservation problem with raster data
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s1 <- solve(p1)
+
+# print solution
+print(s1)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# print attributes describing the optimization process and the solution
+print(attr(s1, "objective"))
+#> solution_1 
+#>   1987.399 
+print(attr(s1, "runtime"))
+#> solution_1 
+#>      0.005 
+print(attr(s1, "status"))
+#> solution_1 
+#>  "OPTIMAL" 
+
+# calculate feature representation in the solution
+r1 <- eval_feature_representation_summary(p1, s1)
+print(r1)
+#> # A tibble: 5 × 5
+#>   summary feature total_amount absolute_held relative_held
+#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+#> 1 overall layer.1         83.3          8.91         0.107
+#> 2 overall layer.2         31.2          3.13         0.100
+#> 3 overall layer.3         72.0          7.34         0.102
+#> 4 overall layer.4         42.7          4.35         0.102
+#> 5 overall layer.5         56.7          6.01         0.106
+
+# plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# build minimal conservation problem with polygon (Spatial) data
+p2 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s2 <- solve(p2)
+
+# print first six rows of the attribute table
+print(head(s2))
+#>       cost locked_in locked_out solution_1
+#> 1 215.8638     FALSE      FALSE          0
+#> 2 212.7823     FALSE      FALSE          0
+#> 3 207.4962     FALSE      FALSE          0
+#> 4 208.9322     FALSE       TRUE          0
+#> 5 214.0419     FALSE      FALSE          0
+#> 6 213.7636     FALSE      FALSE          0
+
+# calculate feature representation in the solution
+r2 <- eval_feature_representation_summary(p2, s2[, "solution_1"])
+print(r2)
+#> # A tibble: 5 × 5
+#>   summary feature total_amount absolute_held relative_held
+#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+#> 1 overall layer.1         74.5          8.05         0.108
+#> 2 overall layer.2         28.1          2.83         0.101
+#> 3 overall layer.3         64.9          6.65         0.103
+#> 4 overall layer.4         38.2          3.87         0.101
+#> 5 overall layer.5         50.7          5.41         0.107
+
+# plot solution
+spplot(s2, zcol = "solution_1", main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# build minimal conservation problem with polygon (sf) data
+p3 <- problem(sim_pu_sf, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s3 <- solve(p3)
+
+# print first six rows of the attribute table
+print(head(s3))
+#> Simple feature collection with 6 features and 4 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>       cost locked_in locked_out solution_1                       geometry
+#> 1 215.8638     FALSE      FALSE          0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2 212.7823     FALSE      FALSE          0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3 207.4962     FALSE      FALSE          0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4 208.9322     FALSE       TRUE          0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5 214.0419     FALSE      FALSE          0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6 213.7636     FALSE      FALSE          0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# calculate feature representation in the solution
+r3 <- eval_feature_representation_summary(p3, s3[, "solution_1"])
+print(r3)
+#> # A tibble: 5 × 5
+#>   summary feature total_amount absolute_held relative_held
+#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+#> 1 overall layer.1         74.5          8.05         0.108
+#> 2 overall layer.2         28.1          2.83         0.101
+#> 3 overall layer.3         64.9          6.65         0.103
+#> 4 overall layer.4         38.2          3.87         0.101
+#> 5 overall layer.5         50.7          5.41         0.107
+
+# plot solution
+plot(s3[, "solution_1"])
+
+# }
+
+# build multi-zone conservation problem with raster data
+p4 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s4 <- solve(p4)
+
+# print solution
+print(s4)
+#> class      : RasterStack 
+#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> names      : zone_1, zone_2, zone_3 
+#> min values :      0,      0,      0 
+#> max values :      1,      1,      1 
+#> 
+
+# calculate feature representation in the solution
+r4 <- eval_feature_representation_summary(p4, s4)
+print(r4)
+#> # A tibble: 20 × 5
+#>    summary feature   total_amount absolute_held relative_held
+#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
+#>  1 overall feature_1        250.          47.1          0.188
+#>  2 overall feature_2         93.6         17.9          0.191
+#>  3 overall feature_3        216.          41.6          0.193
+#>  4 overall feature_4        128.          23.7          0.185
+#>  5 overall feature_5        170.          31.6          0.186
+#>  6 zone_1  feature_1         83.3         16.5          0.198
+#>  7 zone_1  feature_2         31.2          5.65         0.181
+#>  8 zone_1  feature_3         72.0         14.2          0.198
+#>  9 zone_1  feature_4         42.7          7.56         0.177
+#> 10 zone_1  feature_5         56.7         11.1          0.197
+#> 11 zone_2  feature_1         83.3         15.7          0.189
+#> 12 zone_2  feature_2         31.2          6.03         0.193
+#> 13 zone_2  feature_3         72.0         14.5          0.201
+#> 14 zone_2  feature_4         42.7          7.82         0.183
+#> 15 zone_2  feature_5         56.7         10.3          0.181
+#> 16 zone_3  feature_1         83.3         14.8          0.178
+#> 17 zone_3  feature_2         31.2          6.22         0.199
+#> 18 zone_3  feature_3         72.0         13.0          0.180
+#> 19 zone_3  feature_4         42.7          8.27         0.194
+#> 20 zone_3  feature_5         56.7         10.2          0.180
+
+# plot solution
+plot(category_layer(s4), main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# build multi-zone conservation problem with polygon (sf) data
+p5 <- problem(sim_pu_zones_sf, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s5 <- solve(p5)
+
+# print first six rows of the attribute table
+print(head(s5))
+#> Simple feature collection with 6 features and 9 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
+#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
+#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
+#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
+#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
+#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
+#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
+#>   solution_1_zone_2 solution_1_zone_3                       geometry
+#> 1                 1                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2                 1                 0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4                 1                 0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5                 1                 0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6                 1                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# calculate feature representation in the solution
+r5 <- eval_feature_representation_summary(
+  p5, s5[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+print(r5)
+#> # A tibble: 20 × 5
+#>    summary feature   total_amount absolute_held relative_held
+#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
+#>  1 overall feature_1        225.          37.5          0.166
+#>  2 overall feature_2         83.9         14.6          0.174
+#>  3 overall feature_3        195.          34.0          0.174
+#>  4 overall feature_4        114.          18.4          0.161
+#>  5 overall feature_5        154.          25.1          0.163
+#>  6 zone_1  feature_1         75.1         12.8          0.170
+#>  7 zone_1  feature_2         28.0          4.63         0.165
+#>  8 zone_1  feature_3         65.0         10.6          0.163
+#>  9 zone_1  feature_4         38.0          6.29         0.165
+#> 10 zone_1  feature_5         51.2          8.88         0.174
+#> 11 zone_2  feature_1         75.1         11.0          0.146
+#> 12 zone_2  feature_2         28.0          5.26         0.188
+#> 13 zone_2  feature_3         65.0         10.7          0.165
+#> 14 zone_2  feature_4         38.0          6.49         0.171
+#> 15 zone_2  feature_5         51.2          7.27         0.142
+#> 16 zone_3  feature_1         75.1         13.7          0.182
+#> 17 zone_3  feature_2         28.0          4.75         0.170
+#> 18 zone_3  feature_3         65.0         12.7          0.195
+#> 19 zone_3  feature_4         38.0          5.62         0.148
+#> 20 zone_3  feature_5         51.2          8.93         0.175
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s5$solution <- category_vector(s5[, c("solution_1_zone_1",
+                                      "solution_1_zone_2",
+                                      "solution_1_zone_3")])
+s5$solution <- factor(s5$solution)
+
+# plot solution
+plot(s5[, "solution"])
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/solvers.html b/docs/reference/solvers.html index c5280a80e..e88ddc483 100644 --- a/docs/reference/solvers.html +++ b/docs/reference/solvers.html @@ -1,107 +1,24 @@ - - - - - - - -Problem solvers — solvers • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Problem solvers — solvers • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Problem solvers

      - Source: R/solvers.R + Source: R/solvers.R

      Specify the software and configuration used to solve a conservation planning -problem(). By default, the best available +problem(). By default, the best available software currently installed on the system will be used. For information on the performance of different solvers, please see Schuster et al. (2020) for benchmarks comparing the @@ -196,18 +113,19 @@

      Problem solvers

      different sized datasets.

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      The following solvers can be used to find solutions for a -conservation planning problem():

      -
      - -
      add_default_solver()

      This solver uses the best software +conservation planning problem():

      +
      add_default_solver()
      +

      This solver uses the best software currently installed on the system.

      -
      add_gurobi_solver()

      Gurobi + +

      add_gurobi_solver()
      +

      Gurobi is a state-of-the-art commercial optimization software with an R package interface. We recommend using this solver if at all possible. It is by far the fastest of the solvers available for @@ -216,16 +134,20 @@

      Details gurobi package is distributed with the Gurobi software suite. This solver uses the gurobi package to solve problems.

      -
      add_cplex_solver()

      IBM CPLEX + +

      add_cplex_solver()
      +

      IBM CPLEX is a commercial optimization software. It is faster than the open source solvers available for generating prioritizations, however, it is not freely available. -Similar to the Gurobi +Similar to the Gurobi software, licenses are available to academics at no cost. This solver uses the cplexAPI package to solve problems using IBM CPLEX.

      -
      add_cbc_solver()

      CBC is an + +

      add_cbc_solver()
      +

      CBC is an open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. Preliminary benchmarks indicate that it is the fastest open source @@ -233,134 +155,137 @@

      Details We recommend using this solver if both Gurobi and IBM CPLEX are unavailable. It requires the rcbc package, which is currently only available on -GitHub.

      +GitHub.

      + -
      add_lpsymphony_solver()

      SYMPHONY is an +

      add_lpsymphony_solver()
      +

      SYMPHONY is an open-source mixed integer programming solver that is also part of the COIN-OR project. Although both SYMPHONY and CBC are part of the COIN-OR project, they are different software. The lpsymphony package provides an interface to the SYMPHONY software, and is distributed through -Bioconductor. +Bioconductor. We recommend using this solver if the CBC solver cannot be installed. This solver can use parallel processing to solve problems, so it is faster than Rsymphony package interface (see below).

      -
      add_rsymphony_solver()

      This solver provides an alternative interface to the -SYMPHONY solver using + +

      add_rsymphony_solver()
      +

      This solver provides an alternative interface to the +SYMPHONY solver using the Rsymphony package. Unlike other solvers, the Rsymphony package can be installed directly from the Comprehensive R Archive Network (CRAN). It is also the slowest of the available solvers.

      -
      - -

      References

      +
      +
      +

      References

      Schuster R, Hanson JO, Strimas-Mackey M, and Bennett JR (2020). Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems. PeerJ, 8: e9258.

      -

      See also

      - -

      Other overviews: -constraints, -decisions, -importance, -objectives, -penalties, -portfolios, -summaries, -targets

      +
      +
      +

      See also

      +

      Other overviews: +constraints, +decisions, +importance, +objectives, +penalties, +portfolios, +summaries, +targets

      +
      -

      Examples

      - 
      # \dontrun{
-# load data
-data(sim_pu_raster, sim_features)
-
-# create basic problem
-p <- problem(sim_pu_raster, sim_features) %>%
-  add_min_set_objective() %>%
-  add_relative_targets(0.1) %>%
-  add_proportion_decisions()
-
-# create vector to store plot titles
-titles <- c()
-
-# create empty stack to store solutions
-s <- stack()
-
-# if gurobi is installed: create problem with added gurobi solver
-if (require("gurobi")) {
-  titles <- c(titles, "gurobi")
-  p3 <- p %>% add_gurobi_solver(verbose = FALSE)
-  s <- addLayer(s, solve(p3))
-}
-#> Loading required package: gurobi
-#> Loading required package: slam
-
-# if cplexAPI is installed: create problem with added CPLEX solver
-if (require("cplexAPI")) {
-  titles <- c(titles, "CPLEX")
-  p4 <- p %>% add_cplex_solver(verbose = FALSE)
-  s <- addLayer(s, solve(p4))
-}
-#> Loading required package: cplexAPI
-
-# if rcbc is installed: create problem with added cbc solver
-if (require("rcbc")) {
-  titles <- c(titles, "CBC")
-  p6 <- p %>% add_cbc_solver(verbose = FALSE)
-  s <- addLayer(s, solve(p6))
-}
-#> Loading required package: rcbc
-
-# create problem with added rsymphony solver
-if (require("Rsymphony")) {
-  titles <- c(titles, "Rsymphony")
-  p2 <- p %>% add_rsymphony_solver(verbose = FALSE)
-  s <- addLayer(s, solve(p2))
-}
-#> Loading required package: Rsymphony
-
-# if lpsymphony is installed: create problem with added lpsymphony solver
-if (require("lpsymphony")) {
-  titles <- c(titles, "lpsymphony")
-  p5 <- p %>% add_lpsymphony_solver(verbose = FALSE)
-  s <- addLayer(s, solve(p5))
-}
-#> Loading required package: lpsymphony
-
-# plot solutions
-plot(s, main = titles, axes = FALSE, box = FALSE)
-
-# }
-
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# load data
+data(sim_pu_raster, sim_features)
+
+# create basic problem
+p <- problem(sim_pu_raster, sim_features) %>%
+  add_min_set_objective() %>%
+  add_relative_targets(0.1) %>%
+  add_proportion_decisions()
+
+# create vector to store plot titles
+titles <- c()
+
+# create empty stack to store solutions
+s <- stack()
+
+# if gurobi is installed: create problem with added gurobi solver
+if (require("gurobi")) {
+  titles <- c(titles, "gurobi")
+  p3 <- p %>% add_gurobi_solver(verbose = FALSE)
+  s <- addLayer(s, solve(p3))
+}
+#> Loading required package: gurobi
+#> Loading required package: slam
+
+# if cplexAPI is installed: create problem with added CPLEX solver
+if (require("cplexAPI")) {
+  titles <- c(titles, "CPLEX")
+  p4 <- p %>% add_cplex_solver(verbose = FALSE)
+  s <- addLayer(s, solve(p4))
+}
+#> Loading required package: cplexAPI
+
+# if rcbc is installed: create problem with added cbc solver
+if (require("rcbc")) {
+  titles <- c(titles, "CBC")
+  p6 <- p %>% add_cbc_solver(verbose = FALSE)
+  s <- addLayer(s, solve(p6))
+}
+#> Loading required package: rcbc
+
+# create problem with added rsymphony solver
+if (require("Rsymphony")) {
+  titles <- c(titles, "Rsymphony")
+  p2 <- p %>% add_rsymphony_solver(verbose = FALSE)
+  s <- addLayer(s, solve(p2))
+}
+#> Loading required package: Rsymphony
+
+# if lpsymphony is installed: create problem with added lpsymphony solver
+if (require("lpsymphony")) {
+  titles <- c(titles, "lpsymphony")
+  p5 <- p %>% add_lpsymphony_solver(verbose = FALSE)
+  s <- addLayer(s, solve(p5))
+}
+#> Loading required package: lpsymphony
+
+# plot solutions
+plot(s, main = titles, axes = FALSE, box = FALSE)
+
+# }
+
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/summaries.html b/docs/reference/summaries.html index 8475c25cd..c8cb53041 100644 --- a/docs/reference/summaries.html +++ b/docs/reference/summaries.html @@ -1,104 +1,21 @@ - - - - - - - -Evaluate solutions using summary statistics — summaries • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Evaluate solutions using summary statistics — summaries • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Evaluate solutions using summary statistics

      - Source: R/summaries.R + Source: R/summaries.R
      -

      After generating a solution to a conservation planning problem(), +

      After generating a solution to a conservation planning problem(), it can be useful to evaluate how well it performs. These functions can be used to evaluate a solution according to various different summary statistics.

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      The following functions can be used to summarize the performance -of a solution to a conservation planning problem():

      -
      - -
      eval_n_summary()

      Calculate the number of planning units selected +of a solution to a conservation planning problem():

      +
      eval_n_summary()
      +

      Calculate the number of planning units selected within a solution.

      -
      eval_cost_summary()

      Calculate the total cost of a solution.

      -
      eval_feature_representation_summary()

      Calculate how well features +

      eval_cost_summary()
      +

      Calculate the total cost of a solution.

      + + +
      eval_feature_representation_summary()
      +

      Calculate how well features are represented by a solution. This function can be used for all problems.

      -
      eval_target_coverage_summary()

      Calculate how well feature -representation targets are met by a solution. This function can only be -used with problems contain targets.

      -
      eval_boundary_summary()

      Calculate the exposed boundary length +

      eval_target_coverage_summary()
      +

      Calculate how well feature +representation targets are met by a solution. This function can only be +used with problems contain targets.

      + + +
      eval_boundary_summary()
      +

      Calculate the exposed boundary length (perimeter) associated with a solution.

      -
      eval_connectivity_summary()

      Calculate the connectivity held within -a solution.

      +
      eval_connectivity_summary()
      +

      Calculate the connectivity held within +a solution.

      -
      -

      See also

      -

      Other overviews: -constraints, -decisions, -importance, -objectives, -penalties, -portfolios, -solvers, -targets

      +
      +
      +

      See also

      +

      Other overviews: +constraints, +decisions, +importance, +objectives, +penalties, +portfolios, +solvers, +targets

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create a minimal problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.1) %>%
-     add_binary_decisions() %>%
-     add_default_solver(verbose = FALSE)
-
-# \dontrun{
-# solve problem
-s <- solve(p)
-
-# evaluate number of selected planning units in solution
-eval_n_summary(p, s)
-#> # A tibble: 1 × 2
-#>   summary  cost
-#>   <chr>   <dbl>
-#> 1 overall    10
-
-# evaluate solution cost
-eval_cost_summary(p, s)
-#> # A tibble: 1 × 2
-#>   summary  cost
-#>   <chr>   <dbl>
-#> 1 overall 1987.
-
-# evaluate feature representation by solution
-eval_feature_representation_summary(p, s)
-#> # A tibble: 5 × 5
-#>   summary feature total_amount absolute_held relative_held
-#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-#> 1 overall layer.1         83.3          8.91         0.107
-#> 2 overall layer.2         31.2          3.13         0.100
-#> 3 overall layer.3         72.0          7.34         0.102
-#> 4 overall layer.4         42.7          4.35         0.102
-#> 5 overall layer.5         56.7          6.01         0.106
-
-# evaluate target coverage by solution
-eval_target_coverage_summary(p, s)
-#> # A tibble: 5 × 9
-#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
-#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
-#> 1 layer.1 TRUE          83.3            8.33          8.91                  0
-#> 2 layer.2 TRUE          31.2            3.12          3.13                  0
-#> 3 layer.3 TRUE          72.0            7.20          7.34                  0
-#> 4 layer.4 TRUE          42.7            4.27          4.35                  0
-#> 5 layer.5 TRUE          56.7            5.67          6.01                  0
-#> # … with 3 more variables: relative_target <dbl>, relative_held <dbl>,
-#> #   relative_shortfall <dbl>
-
-
-# evaluate exposed boundary (perimeter) length by solution
-eval_boundary_summary(p, s)
-#> # A tibble: 1 × 2
-#>   summary boundary
-#>   <chr>      <dbl>
-#> 1 overall     2.25
-
-# create a connectivity matrix to describe pair-wise connectivity
-# values between combinations of planning units,
-# see ?connectivity_matrix for more information
-
-# for brevity, we will do this using the cost data
-# cost valuers have high connectivity between them
-cm <- connectivity_matrix(sim_pu_raster, sim_pu_raster)
-
-# evaluate connectivity of solution
-eval_connectivity_summary(p, s, data = cm)
-#> # A tibble: 1 × 2
-#>   summary connectivity
-#>   <chr>          <dbl>
-#> 1 overall         198.
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create a minimal problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.1) %>%
+     add_binary_decisions() %>%
+     add_default_solver(verbose = FALSE)
+
+# \dontrun{
+# solve problem
+s <- solve(p)
+
+# evaluate number of selected planning units in solution
+eval_n_summary(p, s)
+#> # A tibble: 1 × 2
+#>   summary  cost
+#>   <chr>   <dbl>
+#> 1 overall    10
+
+# evaluate solution cost
+eval_cost_summary(p, s)
+#> # A tibble: 1 × 2
+#>   summary  cost
+#>   <chr>   <dbl>
+#> 1 overall 1987.
+
+# evaluate feature representation by solution
+eval_feature_representation_summary(p, s)
+#> # A tibble: 5 × 5
+#>   summary feature total_amount absolute_held relative_held
+#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+#> 1 overall layer.1         83.3          8.91         0.107
+#> 2 overall layer.2         31.2          3.13         0.100
+#> 3 overall layer.3         72.0          7.34         0.102
+#> 4 overall layer.4         42.7          4.35         0.102
+#> 5 overall layer.5         56.7          6.01         0.106
+
+# evaluate target coverage by solution
+eval_target_coverage_summary(p, s)
+#> # A tibble: 5 × 9
+#>   feature met   total_amount absolute_target absolute_held absolute_shortfall
+#>   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
+#> 1 layer.1 TRUE          83.3            8.33          8.91                  0
+#> 2 layer.2 TRUE          31.2            3.12          3.13                  0
+#> 3 layer.3 TRUE          72.0            7.20          7.34                  0
+#> 4 layer.4 TRUE          42.7            4.27          4.35                  0
+#> 5 layer.5 TRUE          56.7            5.67          6.01                  0
+#> # … with 3 more variables: relative_target <dbl>, relative_held <dbl>,
+#> #   relative_shortfall <dbl>
+
+
+# evaluate exposed boundary (perimeter) length by solution
+eval_boundary_summary(p, s)
+#> # A tibble: 1 × 2
+#>   summary boundary
+#>   <chr>      <dbl>
+#> 1 overall     2.25
+
+# create a connectivity matrix to describe pair-wise connectivity
+# values between combinations of planning units,
+# see ?connectivity_matrix for more information
+
+# for brevity, we will do this using the cost data
+# cost valuers have high connectivity between them
+cm <- connectivity_matrix(sim_pu_raster, sim_pu_raster)
+
+# evaluate connectivity of solution
+eval_connectivity_summary(p, s, data = cm)
+#> # A tibble: 1 × 2
+#>   summary connectivity
+#>   <chr>          <dbl>
+#> 1 overall         198.
+
+# }
 
      
+
      +
      -
      - - - - - - - - - - + diff --git a/docs/reference/targets.html b/docs/reference/targets.html index 6786b3d7a..759ea7d3d 100644 --- a/docs/reference/targets.html +++ b/docs/reference/targets.html @@ -1,102 +1,19 @@ - - - - - - - -Add representation targets — targets • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Add representation targets — targets • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Add representation targets

      - Source: R/targets.R + Source: R/targets.R
      @@ -186,101 +103,104 @@

      Add representation targets

      distribution that should (ideally) be covered (represented) by a solution.

      +
      Usage,NULL
      - -

      Details

      - +
      +

      Details

      Please note that most objectives require targets, and attempting to solve a problem that requires targets will throw an error.

      The following functions can be used to specify targets for a -conservation planning problem():

      -
      - -
      add_relative_targets()

      Set targets as a proportion +conservation planning problem():

      +
      add_relative_targets()
      +

      Set targets as a proportion (between 0 and 1) of the total amount of each feature in the the study area.

      -
      add_absolute_targets()

      Set targets that denote the + +

      add_absolute_targets()
      +

      Set targets that denote the minimum amount of each feature required in the prioritization.

      -
      add_loglinear_targets()

      Set targets as a proportion + +

      add_loglinear_targets()
      +

      Set targets as a proportion (between 0 and 1) that are calculated using log-linear interpolation.

      -
      add_manual_targets()

      Set targets manually.

      +
      add_manual_targets()
      +

      Set targets manually.

      -
      -

      See also

      -

      Other overviews: -constraints, -decisions, -importance, -objectives, -penalties, -portfolios, -solvers, -summaries

      +
      +
      +

      See also

      +

      Other overviews: +constraints, +decisions, +importance, +objectives, +penalties, +portfolios, +solvers, +summaries

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_raster, sim_features)
-
-# create base problem
-p <- problem(sim_pu_raster, sim_features) %>%
-     add_min_set_objective() %>%
-     add_binary_decisions() %>%
-     add_default_solver(verbose = FALSE)
-
-# create problem with added relative targets
-p1 <- p %>% add_relative_targets(0.1)
-
-# create problem with added absolute targets
-p2 <- p %>% add_absolute_targets(3)
-
-# create problem with added loglinear targets
-p3 <- p %>% add_loglinear_targets(10, 0.9, 100, 0.2)
-
-# create problem with manual targets that equate to 10% relative targets
-p4 <- p %>% add_manual_targets(data.frame(feature = names(sim_features),
-                                          target = 0.1,
-                                          type = "relative"))
-# \dontrun{
-# solve problem
-s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
-
-# plot solution
-plot(s, axes = FALSE, box = FALSE,
-     main = c("relative targets", "absolute targets", "loglinear targets",
-              "manual targets"))
-
-# }
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_raster, sim_features)
+
+# create base problem
+p <- problem(sim_pu_raster, sim_features) %>%
+     add_min_set_objective() %>%
+     add_binary_decisions() %>%
+     add_default_solver(verbose = FALSE)
+
+# create problem with added relative targets
+p1 <- p %>% add_relative_targets(0.1)
+
+# create problem with added absolute targets
+p2 <- p %>% add_absolute_targets(3)
+
+# create problem with added loglinear targets
+p3 <- p %>% add_loglinear_targets(10, 0.9, 100, 0.2)
+
+# create problem with manual targets that equate to 10% relative targets
+p4 <- p %>% add_manual_targets(data.frame(feature = names(sim_features),
+                                          target = 0.1,
+                                          type = "relative"))
+# \dontrun{
+# solve problem
+s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
+
+# plot solution
+plot(s, axes = FALSE, box = FALSE,
+     main = c("relative targets", "absolute targets", "loglinear targets",
+              "manual targets"))
+
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/tee.html b/docs/reference/tee.html index e3da7d8fa..1d8635e59 100644 --- a/docs/reference/tee.html +++ b/docs/reference/tee.html @@ -1,101 +1,18 @@ - - - - - - - -Tee operator — %T>% • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Tee operator — %T>% • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Tee operator

      - Source: R/magrittr-operators.R + Source: R/magrittr-operators.R
      @@ -184,71 +101,67 @@

      Tee operator

      This package uses the "tee" operator (\%T>\%) to modify objects.

      +
      Usage,NULL
      -

      Arguments

      - - - - - - -
      lhs, rhs

      An object and a function.

      - -

      Value

      - +
      +

      Arguments

      +
      lhs, rhs
      +

      An object and a function.

      +
      +
      +

      Value

      An object.

      -

      See also

      - -

      magrittr::%T>%(), pipe().

      +
      +
      +

      See also

      +

      magrittr::%T>%(), pipe().

      +
      -

      Examples

      - 
      # the tee operator returns the left-hand side of the result and can be
-# useful when dealing with mutable objects. In this example we want
-# to use the function "f" to modify the object "e" and capture the
-# result
-
-# create an empty environment
-e <- new.env()
-
-# create a function to modify an environment and return NULL
-f <- function(x) {x$a <- 5; return(NULL)}
-
-# if we use the pipe operator we won't capture the result since "f"()
-# returns a NULL
-e2 <- e %>% f()
-print(e2)
-#> NULL
-
-# but if we use the tee operator then the result contains a copy of "e"
-e3 <- e %T>% f()
-print(e3)
-#> <environment: 0x56421c3d1b00>
-
+    
      
+    
      Examples
      
+    
      # the tee operator returns the left-hand side of the result and can be
+# useful when dealing with mutable objects. In this example we want
+# to use the function "f" to modify the object "e" and capture the
+# result
+
+# create an empty environment
+e <- new.env()
+
+# create a function to modify an environment and return NULL
+f <- function(x) {x$a <- 5; return(NULL)}
+
+# if we use the pipe operator we won't capture the result since "f"()
+# returns a NULL
+e2 <- e %>% f()
+print(e2)
+#> NULL
+
+# but if we use the tee operator then the result contains a copy of "e"
+e3 <- e %T>% f()
+print(e3)
+#> <environment: 0x55f2759882e0>
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/tibble-methods.html b/docs/reference/tibble-methods.html index f341c1572..1cbaaa700 100644 --- a/docs/reference/tibble-methods.html +++ b/docs/reference/tibble-methods.html @@ -1,101 +1,18 @@ - - - - - - - -Manipulate tibbles — tibble-methods • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Manipulate tibbles — tibble-methods • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Manipulate tibbles

      - Source: R/tbl_df.R + Source: R/tbl_df.R
      -

      Assorted functions for manipulating tibble::tibble() objects.

      +

      Assorted functions for manipulating tibble::tibble() objects.

      - 
      # S4 method for tbl_df
-nrow(x)
+    
      Usage,
      # S4 method for tbl_df
+nrow(x)
 
-# S4 method for tbl_df
-ncol(x)
+# S4 method for tbl_df
+ncol(x)
 
-# S4 method for tbl_df
-as.list(x)
      
+# S4 method for tbl_df
+as.list(x)
      -

      Arguments

      - - - - - - -
      x

      tibble::tibble() object.

      +
      +

      Arguments

      +
      x
      +

      tibble::tibble() object.

      +
      +
      +

      Details

      +

      The following methods are provided from manipulating +tibble::tibble() objects.

      +
      nrow
      +

      extract integer number of rows.

      -

      Details

      -

      The following methods are provided from manipulating -tibble::tibble() objects.

      -
      -
      nrow

      extract integer number of rows.

      +
      ncol
      +

      extract integer number of columns.

      -
      ncol

      extract integer number of columns.

      -
      as.list

      convert to a list.

      +
      as.list
      +

      convert to a list.

      -
      print

      print the object.

      +
      print
      +

      print the object.

      -
      -

      Examples

      - 
      # load tibble package
-require(tibble)
-#> Loading required package: tibble
-
-# make tibble
-a <- tibble(value = seq_len(5))
-
-# number of rows
-nrow(a)
-#> [1] 5
-
-# number of columns
-ncol(a)
-#> [1] 1
-
-# convert to list
-as.list(a)
-#> $value
-#> [1] 1 2 3 4 5
-#> 
+
      + +
      +

      Examples

      + 
      # load tibble package
+require(tibble)
+#> Loading required package: tibble
+
+# make tibble
+a <- tibble(value = seq_len(5))
+
+# number of rows
+nrow(a)
+#> [1] 5
+
+# number of columns
+ncol(a)
+#> [1] 1
+
+# convert to list
+as.list(a)
+#> $value
+#> [1] 1 2 3 4 5
+#>
      +
      +
      - - - - - - - - - - - + diff --git a/docs/reference/write_problem.html b/docs/reference/write_problem.html index 5f88cb9a3..ff341500d 100644 --- a/docs/reference/write_problem.html +++ b/docs/reference/write_problem.html @@ -1,103 +1,20 @@ - - - - - - - -Write problem — write_problem • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Write problem — write_problem • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Write problem

      - Source: R/write_problem.R + Source: R/write_problem.R
      -

      Save the mathematical formulation for a conservation planning problem() +

      Save the mathematical formulation for a conservation planning problem() to a file for mixed integer programming solvers. Note that this function requires the Rsymphony package to be installed.

      - 
      write_problem(x, path)
      +
      Usage,
      write_problem(x, path)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      path

      character file path to save the problem formulation. +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      path
      +

      character file path to save the problem formulation. The argument should contain a ".lp" or .mps" file extension to specify whether the problem formulation will be saved in the -LP or -MPS -format (respectively).

      - -

      Value

      - +LP or +MPS +format (respectively).

      +
      +
      +

      Value

      Invisible TRUE indicating success.

      +
      -

      Examples

      - 
      # \dontrun{
-# set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_features)
-
-# create minimal problem
-p <- problem(sim_pu_sf[1:4, , drop = FALSE], sim_features,
-             cost_column = "cost") %>%
-     add_min_set_objective() %>%
-     add_relative_targets(0.1) %>%
-     add_binary_decisions()
-
-# specify file path to save problem formulation
-path <- file.path(tempdir(), "model.lp")
-
-# save problem to file (using the Rsymphony package)
-write_problem(p, path)
-
-# print model file
-cat(readLines(path), sep = "\n")
-#> \Problem name: 
-#> 
-#> Minimize
-#> obj: 215.863839903 x0 + 212.782348080 x1 + 207.496243710 x2 + 208.932169949 x3
-#> Subject To
-#> cons0:  -0.277834868 x0 -0.277834868 x1 -0.277834868 x2 -0.277834868 x3 <= -0.277834868
-#> cons1:  -0.127301291 x0 -0.127301291 x1 -0.127301291 x2 -0.127301291 x3 <= -0.127301291
-#> cons2:  -0.316365083 x0 -0.316365083 x1 -0.316365083 x2 -0.316365083 x3 <= -0.316365083
-#> cons3:  -0.121097958 x0 -0.121097958 x1 -0.121097958 x2 -0.121097958 x3 <= -0.121097958
-#> cons4:  -0.176466230 x0 -0.176466230 x1 -0.176466230 x2 -0.176466230 x3 <= -0.176466230
-#> Bounds
-#>  0 <= x0 <= 1
-#>  0 <= x1 <= 1
-#>  0 <= x2 <= 1
-#>  0 <= x3 <= 1
-#> Integers
-#> x0 x1 x2 x3 
-#> End
-# }
-
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_features)
+
+# create minimal problem
+p <- problem(sim_pu_sf[1:4, , drop = FALSE], sim_features,
+             cost_column = "cost") %>%
+     add_min_set_objective() %>%
+     add_relative_targets(0.1) %>%
+     add_binary_decisions()
+
+# specify file path to save problem formulation
+path <- file.path(tempdir(), "model.lp")
+
+# save problem to file (using the Rsymphony package)
+write_problem(p, path)
+
+# print model file
+cat(readLines(path), sep = "\n")
+#> \Problem name: 
+#> 
+#> Minimize
+#> obj: 215.863839903 x0 + 212.782348080 x1 + 207.496243710 x2 + 208.932169949 x3
+#> Subject To
+#> cons0:  -0.277834868 x0 -0.277834868 x1 -0.277834868 x2 -0.277834868 x3 <= -0.277834868
+#> cons1:  -0.127301291 x0 -0.127301291 x1 -0.127301291 x2 -0.127301291 x3 <= -0.127301291
+#> cons2:  -0.316365083 x0 -0.316365083 x1 -0.316365083 x2 -0.316365083 x3 <= -0.316365083
+#> cons3:  -0.121097958 x0 -0.121097958 x1 -0.121097958 x2 -0.121097958 x3 <= -0.121097958
+#> cons4:  -0.176466230 x0 -0.176466230 x1 -0.176466230 x2 -0.176466230 x3 <= -0.176466230
+#> Bounds
+#>  0 <= x0 <= 1
+#>  0 <= x1 <= 1
+#>  0 <= x2 <= 1
+#>  0 <= x3 <= 1
+#> Integers
+#> x0 x1 x2 x3 
+#> End
+# }
+
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/zone_names.html b/docs/reference/zone_names.html index 0ec85aab2..e7fcaa9db 100644 --- a/docs/reference/zone_names.html +++ b/docs/reference/zone_names.html @@ -1,101 +1,18 @@ - - - - - - - -Zone names — zone_names • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Zone names — zone_names • prioritizr - - - - - - - - - - - - - - +
      -
      -

      Zone names

      - Source: R/zone_names.R + Source: R/zone_names.R
      @@ -184,71 +101,65 @@

      Zone names

      Extract the names of zones in an object.

      - 
      zone_names(x)
-
-# S4 method for ConservationProblem
-zone_names(x)
-
-# S4 method for ZonesRaster
-zone_names(x)
+    
      Usage,
      zone_names(x)
 
-# S4 method for ZonesCharacter
-zone_names(x)
      
+# S4 method for ConservationProblem
+zone_names(x)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
      x
      problem() (i.e. ConservationProblem) or Zones()
      
+# S4 method for ZonesRaster
+zone_names(x)
 
-    
      Value
      
+# S4 method for ZonesCharacter
+zone_names(x)
      +
      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) or Zones()

      +
      +
      +

      Value

      character zone names.

      +
      -

      Examples

      - 
      # load data
-data(sim_pu_zones_stack, sim_features_zones)
-
-# print names of zones in a Zones object
-print(zone_names(sim_features_zones))
-#> [1] "zone_1" "zone_2" "zone_3"
-# create problem with multiple zones
-p <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-     add_min_set_objective() %>%
-     add_relative_targets(matrix(0.2, ncol = 3, nrow = 5)) %>%
-     add_binary_decisions()
-
-# print zone names in problem
-print(zone_names(p))
-#> [1] "zone_1" "zone_2" "zone_3"
+    
      
+    
      Examples
      
+    
      # load data
+data(sim_pu_zones_stack, sim_features_zones)
+
+# print names of zones in a Zones object
+print(zone_names(sim_features_zones))
+#> [1] "zone_1" "zone_2" "zone_3"
+# create problem with multiple zones
+p <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+     add_min_set_objective() %>%
+     add_relative_targets(matrix(0.2, ncol = 3, nrow = 5)) %>%
+     add_binary_decisions()
+
+# print zone names in problem
+print(zone_names(p))
+#> [1] "zone_1" "zone_2" "zone_3"
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/reference/zones.html b/docs/reference/zones.html index a0b077b2f..850acf7dc 100644 --- a/docs/reference/zones.html +++ b/docs/reference/zones.html @@ -1,107 +1,24 @@ - - - - - - - -Management zones — zones • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Management zones — zones • prioritizr - - - - - - - - - - - - - - - - - - - - - - - - - - +
      -
      -

      Management zones

      - Source: R/zones.R + Source: R/zones.R
      @@ -191,152 +108,152 @@

      Management zones

      Specifically, the data should describe the expected amount of each feature within each planning unit given each management zone. For example, the data could describe the occupancy -(e.g. presence/absence), probability of occurrence, or +(e.g., presence/absence), probability of occurrence, or abundance expected for each feature when each planning unit is allocated to a different zone.

      - 
      zones(..., zone_names = NULL, feature_names = NULL)
      - -

      Arguments

      - - - - - - - - - - - - - - -
      ...

      raster::raster() or character objects that -pertain to the biodiversity data. See Details for more information.

      zone_names

      character names of the management zones. Defaults -to NULL which results in sequential integers.

      feature_names

      character names of the features zones. Defaults -to NULL which results in sequential integers.

      - -

      Value

      - +
      Usage,
      zones(..., zone_names = NULL, feature_names = NULL)
      + +
      +

      Arguments

      +
      ...
      +

      raster::raster() or character objects that +pertain to the biodiversity data. See Details for more information.

      +
      zone_names
      +

      character names of the management zones. Defaults +to NULL which results in sequential integers.

      +
      feature_names
      +

      character names of the features zones. Defaults +to NULL which results in sequential integers.

      +
      +
      +

      Value

      Zones object.

      -

      Details

      - +
      +
      +

      Details

      This function is used to store and organize data for use in a -conservation planning problem() that has multiple management +conservation planning problem() that has multiple management zones. In all cases, the data for each zone is input as a separate argument. The correct arguments depends on the type of planning unit data -used when building the conservation planning problem().

      -
      -
      planning unit data are a Raster or Spatial object

      Raster object can be supplied to specify the expected amount of +used when building the conservation planning problem().

      +
      planning unit data are a Raster or Spatial object
      +

      Raster object can be supplied to specify the expected amount of each feature within each planning unit under each management zone. Data for each zone should be specified as separate arguments, and the data for each feature in a given zone are specified -in separate layers in a raster::stack() object. +in separate layers in a raster::stack() object. Note that all layers for a given zone must have NA values in exactly the same cells.

      -
      planning unit data are a Spatial or data.frame -object

      character vector containing column names can + +

      planning unit data are a Spatial or data.frame +object
      +

      character vector containing column names can be supplied to specify the expected amount of each feature under each zone. Note that these columns must not contain any NA values.

      -
      planning unit data are a Spatial, data.frame, or -matrix object

      data.frame object can be supplied to specify the + +

      planning unit data are a Spatial, data.frame, or +matrix object
      +

      data.frame object can be supplied to specify the expected amount of each feature under each zone. Following conventions used in Marxan, the -data.frame object should contain the following columns. -

      -
      pu

      integer planning unit identifier.

      -
      species

      integer feature identifier.

      -
      amount

      numeric amount of the feature in the -planning unit for a given zone.

      -Note that data for each zone are specified in a separate argument, and +data.frame object should contain the following columns.

      pu
      +

      integer planning unit identifier.

      + +
      species
      +

      integer feature identifier.

      + +
      amount
      +

      numeric amount of the feature in the +planning unit for a given zone.

      + + +

      Note that data for each zone are specified in a separate argument, and the data contained in a single data.frame object should correspond to a single zone. Also, note that data are not required for all combinations of planning units, features, and zones. The expected amount of features in planning units under management zones that are missing from the table are assumed to be zero.

      -
      - -

      See also

      -

      problem().

      +
      +
      +

      See also

      +

      problem().

      +
      -

      Examples

      - 
      # \dontrun{
-# load planning unit data
-data(sim_pu_raster)
-
-# (note this requires the RandomFields package to be installed)
-zone_1 <- simulate_species(sim_pu_raster, 3)
-#> ...
-zone_2 <- simulate_species(sim_pu_raster, 3)
-#> ...
-
-# create zones using two raster stack objects
-# each object corresponds to a different zone and each layer corresponds to
-# a different species
-z <- zones(zone_1, zone_2, zone_names = c("zone_1", "zone_2"),
-           feature_names = c("feature_1", "feature_2", "feature_3"))
-print(z)
-#> Zones
-#>   zones: zone_1, zone_2 (2 zones)
-#>   features: feature_1, feature_2, feature_3 (3 features)
-#>   data type: RasterStack
-
-# note that the do.call function can also be used to create a Zones object
-# this method for creating a Zones object can be helpful when there are many
-# management zones
-l <- list(zone_1, zone_2, zone_names = c("zone_1", "zone_2"),
-          feature_names = c("feature_1", "feature_2", "feature_3"))
-z <- do.call(zones, l)
-print(z)
-#> Zones
-#>   zones: zone_1, zone_2 (2 zones)
-#>   features: feature_1, feature_2, feature_3 (3 features)
-#>   data type: RasterStack
-
-# create zones using character vectors that represent the names of
-# fields (columns) in a data.frame or Spatial object that contain the amount
-# of each species expected different management zones
-z <- zones(c("spp1_zone1", "spp2_zone1"),
-           c("spp1_zone2", "spp2_zone2"),
-           c("spp1_zone3", "spp2_zone3"),
-           zone_names = c("zone1", "zone2", "zone3"),
-           feature_names = c("spp1", "spp2"))
-print(z)
-#> Zones
-#>   zones: zone1, zone2, zone3 (3 zones)
-#>   features: spp1, spp2 (2 features)
-#>   data type: character
-# }
+    
      
+    
      Examples
      
+    
      # \dontrun{
+# load planning unit data
+data(sim_pu_raster)
+
+# (note this requires the RandomFields package to be installed)
+zone_1 <- simulate_species(sim_pu_raster, 3)
+#> ...
+zone_2 <- simulate_species(sim_pu_raster, 3)
+#> ...
+
+# create zones using two raster stack objects
+# each object corresponds to a different zone and each layer corresponds to
+# a different species
+z <- zones(zone_1, zone_2, zone_names = c("zone_1", "zone_2"),
+           feature_names = c("feature_1", "feature_2", "feature_3"))
+print(z)
+#> Zones
+#>   zones: zone_1, zone_2 (2 zones)
+#>   features: feature_1, feature_2, feature_3 (3 features)
+#>   data type: RasterStack
+
+# note that the do.call function can also be used to create a Zones object
+# this method for creating a Zones object can be helpful when there are many
+# management zones
+l <- list(zone_1, zone_2, zone_names = c("zone_1", "zone_2"),
+          feature_names = c("feature_1", "feature_2", "feature_3"))
+z <- do.call(zones, l)
+print(z)
+#> Zones
+#>   zones: zone_1, zone_2 (2 zones)
+#>   features: feature_1, feature_2, feature_3 (3 features)
+#>   data type: RasterStack
+
+# create zones using character vectors that represent the names of
+# fields (columns) in a data.frame or Spatial object that contain the amount
+# of each species expected different management zones
+z <- zones(c("spp1_zone1", "spp2_zone1"),
+           c("spp1_zone2", "spp2_zone2"),
+           c("spp1_zone3", "spp2_zone3"),
+           zone_names = c("zone1", "zone2", "zone3"),
+           feature_names = c("spp1", "spp2"))
+print(z)
+#> Zones
+#>   zones: zone1, zone2, zone3 (3 zones)
+#>   features: spp1, spp2 (2 features)
+#>   data type: character
+# }
 
      
+
      +
      - - - - - - - - - - - + diff --git a/docs/sitemap.xml b/docs/sitemap.xml index 585a5522f..5f1eaf72d 100644 --- a/docs/sitemap.xml +++ b/docs/sitemap.xml @@ -7,28 +7,31 @@ https://prioritizr.net/CONTRIBUTING.html - https://prioritizr.net/articles/gurobi_installation.html + https://prioritizr.net/articles/calibrating_trade-offs_tutorial.html - https://prioritizr.net/articles/index.html + https://prioritizr.net/articles/connectivity_tutorial.html - https://prioritizr.net/articles/prioritizr.html + https://prioritizr.net/articles/gurobi_installation_guide.html - https://prioritizr.net/articles/publication_record.html + https://prioritizr.net/articles/index.html - https://prioritizr.net/articles/saltspring.html + https://prioritizr.net/articles/management_zones_tutorial.html - https://prioritizr.net/articles/solver_benchmark.html + https://prioritizr.net/articles/package_overview.html - https://prioritizr.net/articles/tasmania.html + https://prioritizr.net/articles/prioritizr.html + + + https://prioritizr.net/articles/publication_record.html - https://prioritizr.net/articles/zones.html + https://prioritizr.net/articles/solver_benchmarks.html https://prioritizr.net/authors.html diff --git a/inst/doc/calibrating_trade-offs_tutorial.Rmd b/inst/doc/calibrating_trade-offs_tutorial.Rmd new file mode 100644 index 000000000..22089a2c7 --- /dev/null +++ b/inst/doc/calibrating_trade-offs_tutorial.Rmd @@ -0,0 +1,678 @@ +--- +title: "Calibrating trade-offs tutorial" +output: + rmarkdown::html_vignette: + toc: true + fig_caption: true + self_contained: yes +fontsize: 11pt +documentclass: article +bibliography: references.bib +csl: reference-style.csl +vignette: > + %\VignetteIndexEntry{Calibrating trade-offs tutorial} + %\VignetteEngine{knitr::rmarkdown_notangle} +--- + +```{r, include = FALSE} +# define dummy variables so that vignette passes package checks +prelim_penalty <- rep(NA_real_, 100) +threshold <- rep(NA_real_, 100) +topsis_results <- data.frame( + alt.row = seq_len(3), score = runif(3), rank = seq_len(3) +) +``` + +```{r, include = FALSE} +# define variables for vignette figures and code execution +h <- 3.5 +w <- 3.5 +is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_", + "_R_CHECK_LICENSE_") %in% names(Sys.getenv())) +knitr::opts_chunk$set(fig.align = "center", eval = !is_check) +``` + +## Introduction + +Systematic conservation planning requires making trade-offs [@r4; @r36]. Since different criteria may conflict with one another -- or not align perfectly -- prioritizations need to make trade-offs between different criteria [@r37]. Although some criteria can easily be accounted for by using locked constraints or representation targets [e.g., @r40; @r39], this is not always the case [e.g., @r38]. For example, prioritizations often need to balance overall cost with the overall level spatial fragmentation among reserves [@r41; @r42]. Additionally, prioritizations often need to balance the overall level of connectivity among reserves against other criteria [@r43]. Since the best trade-off depends on a range of factors -- such as available budgets, species' connectivity requirements, and management capacity -- finding the best balance can be challenging. + +The _prioritizr R_ package provides multi-objective optimization methods to help identify the best trade-offs between different criteria. To achieve this, a conservation planning problem can be formulated with a primary objective (e.g., `add_min_set_objective()`) and penalties (e.g., `add_boundary_penalties()`) that relate to such criteria. When building the problem, the nature of the trade-offs can be specified using certain parameters (e.g., the `penalty` parameter of the `add_boundary_penalties()` function). To identify a prioritization that finds the best balance between different criteria, the trade-off parameters can be tuned using a calibration analysis. These analyses -- in the context of systematic conservation planning -- typically involve generating a set of candidate prioritizations based on different parameters, measuring their performance according to each of the criteria, and then selecting a prioritization (or set of prioritizations) based on how well they achieve the criteria [@r41; @r42; @r43]. For example, the _Marxan_ decision support tool has a range of parameters (e.g., species penalty factors, boundary length modifier) that are calibrated to balance cost, species' representation, and spatial fragmentation [@r45]. + +The aim of this tutorial is to provide guidance on calibrating trade-offs when using the _prioritizr R_ package. Here we will explore a couple of different approaches for generating candidate prioritizations, and methods for finding the best balance between different criteria. Specifically, we will try to generate prioritizations that strike the best balance between total cost and spatial fragmentation (measured as total boundary length). As such, the code used in this vignette will be directly applicable when performing a boundary length calibration analysis. + +## Data + +Let's load the packages and dataset used in this tutorial. Since this tutorial uses the _prioritizrdata R_ package along with several other _R_ packages (see below), please ensure that they are all installed. This particular dataset comprises two object: `tas_pu` and `tas_features`. Although we will briefly discuss this dataset below, please refer to the _Tasmania Tutorial_ vignette for further details. + +```{r, message = FALSE} +# load packages +library(prioritizrdata) +library(prioritizr) +library(dplyr) +library(tibble) +library(scales) +library(ggplot2) +library(topsis) +library(withr) + +# load planning unit data +data(tas_pu) + +# convert planning units to sf format +tas_pu <- st_as_sf(tas_pu) + +# load feature data +data(tas_features) + +# print planning unit data +print(tas_pu) + +# print feature data +print(tas_features) +``` + +The `tas_pu` object contains planning units represented as spatial polygons (i.e., converted to a `sf::st_sf()` object). This object has three columns that denote the following information for each planning unit: a unique identifier (`id`), unimproved land value (`cost`), and current conservation status (`locked_in`). Specifically, the conservation status column indicates if at least half the area planning unit is covered by existing protected areas (denoted by a value of 1) or not (denoted by a value of zero). + +```{r, fig.width = w, fig.height = h} +# plot map of planning unit costs +plot(tas_pu[, "cost"], main = "Planning unit costs") + +# plot map of planning unit statuses +plot(tas_pu[, "locked_in"], main = "Planning unit status") +``` + +The `tas_features` object describes the spatial distribution of different vegetation communities (using presence/absence data). We will use the vegetation communities as the biodiversity features for the prioritization. + +```{r, fig.width = 4.5, fig.height = 4.5} +# plot map of the first four vegetation classes +plot(tas_features[[1:4]], main = paste("Feature", 1:4)) +``` + +We can use this dataset to generate a prioritization. Specifically, we will use the minimum set objective so that the optimization process minimizes total cost. We will add representation targets to ensure that prioritizations cover 17% of each vegetation community. Additionally, we will add constraints to ensure that planning units covered by existing protected areas are selected (i.e., locked in). Finally, we will specify that the conservation planning exercise involves binary decisions (i.e., selecting or not selecting planning units for protected area establishment). + +```{r, fig.width = w, fig.height = h, results = "hide"} +# define a problem +p0 <- problem(tas_pu, tas_features, cost_column = "cost") %>% + add_min_set_objective() %>% + add_relative_targets(0.17) %>% + add_locked_in_constraints("locked_in") %>% + add_binary_decisions() + +# print problem +print(p0) + +# solve problem +s0 <- solve(p0) + +# print result +print(s0) + +# create column for making a map of the prioritization +s0$map_1 <- case_when( + s0$locked_in > 0.5 ~ "locked in", + s0$solution_1 > 0.5 ~ "priority", + TRUE ~ "other" +) + +# plot map of prioritization +plot( + s0[, "map_1"], pal = c("purple", "grey90", "darkgreen"), + main = NULL, key.pos = 1 +) +``` + +We can see that the priority areas identified by the prioritization are scattered across the study area (shown in green). Indeed, none of the priority areas are connect to existing protected areas (shown in purple), and very of them are connect with other priority areas. As such, the prioritization has a high level of spatial fragmentation. If it is important avoid such levels of spatial fragmentation, then we will need to explicitly account spatial fragmentation in the optimization process. + +## Preliminary processing + +We need to conduct some preliminary processing procedures to prepare the data for subsequent analysis. This is important to help make it easier to find suitable trade-off parameters, and avoid numerical scaling issues that can result in overly long run times (see `presolve_check()` for further information). These processing steps are akin to data scaling (or normalization) procedures that are applied in statistical analysis to improve model convergence. + +The first processing procedure involves setting the cost values for all locked in planning units to zero. This is so that the total cost estimates of the prioritization reflects the total cost of establishing new protected areas -- not just total land value. In other words, we want the total cost estimate for a prioritization to reflect the cost of implementing conservation actions. **This procedure is especially important when using the hierarchical approach described below, so that cost thresholds are based on percentage increases in the cost of establishing new protected areas.** + +```{r, fig.width = w, fig.height = h} + +# set costs for planning units covered by existing protected areas to zero +tas_pu$cost[tas_pu$locked_in > 0.5] <- 0 + +# plot map of planning unit costs +plot(tas_pu[, "cost"], main = "Planning unit cost") +``` + +The second procedure involves pre-computing the boundary length data and manually re-scaling the boundary length values. This procedure is important because boundary length values are often very large that, in turn, can cause numerical issues that result in excessive run times (see `presolve_check()` for further details). + +```{r} +# generate boundary length data for the planning units +tas_bd <- boundary_matrix(tas_pu) + +# manually re-scale the boundary length values +tas_bd@x <- rescale(tas_bd@x, to = c(0.01, 100)) +``` + +After applying these procedures, our data is ready for subsequent analysis. + +## Generating candidate prioritizations + +Here we will start the calibration analysis by generating a set of candidate prioritizations. Specifically, these prioritizations will be generated using different parameters to specify different trade-offs between the different criteria. Since this tutorial involves navigating trade-offs between the overall cost of a prioritization and the level of spatial fragmentation associated with a prioritization (as measured by total boundary length), we will generate prioritizations using different parameters related to these criteria. We will examine two approaches for generating candidate prioritizations based on multi-objective optimization procedures. +**Although we'll be examining both approaches in this tutorial, you would normally only use one of these approaches when conducting your own analysis** + +### Blended approach + +The blended approach for multi-objective optimization involves combining separate criteria (e.g., total cost and total boundary length) into a single joint criterion. To achieve this, a trade-off (or scaling) parameter is used to specify the relative importance of each criterion. This approach is the default approach provided by the _prioritizr R_ package. Specifically, each of the functions for adding a penalty to a problem formulation (e.g., `add_boundary_penalties()`) contains a parameter to control the relative importance of the penalties (i.e., the `penalty` parameter). For example, when using the `add_boundary_penalties()` function, setting a high `penalty` value will indicate that it is important to reduce the overall exposed boundary (perimeter) of the prioritization. + +The main challenge with the blended approach is identifying a range of suitable `penalty` values to generate candidate prioritizations. If we set a `penalty` value that is too low, then the penalties will have no effect (e.g., boundary length penalties would have no effect on the prioritization). If we set a `penalty` value too high, then the prioritization will effectively ignore the primary objective. In such cases, the prioritization will be overly spatially clustered -- because the planning unit cost values have no effect --- and contain a single reserve. Thus we need to find a suitable range of `penalty` values before we can generate a set of candidate prioritizations. + +We can find a suitable range of `penalty` values by generating a set of preliminary prioritizations. These preliminary prioritizations will be based on different `penalty` values -- similar to the process for generating the candidate prioritizations -- but solved using customized settings that sacrifice optimality for fast run times (see below for details). This is especially important because specifying a `penalty` value that is too high will cause the optimization process to take a very long time to generate a solutions (due to the numerical scaling issues mentioned previously). To find a suitable range of `penalty` values, we need to identify an upper limit for the `penalty` value (i.e., the highest `penalty` value that result in a prioritization containing a single reserve). Let's create some preliminary `penalty` to identify this upper limit. **Please note that you might need to adjust the `prelim_upper` value to find the upper limit when analyzing different datasets.** + +```{r} +# define a range of different penalty values +## note that we use a power scale to avoid focusing on very high penalty values +prelim_lower <- -5 # change this for your own data +prelim_upper <- 2.8 # change this for your own data +prelim_penalty <- round(10^seq(prelim_lower, prelim_upper, length.out = 9), 5) + +# print penalty values +print(prelim_penalty) +``` + +Next, let's use the preliminary `penalty` values to generate preliminary prioritizations. As mentioned earlier, we will generate these preliminary prioritizations using customized settings to reduce runtime. Specifically, we will set a time limit of 10 minutes per run, and relax the optimality gap to 20%. Although we would not normally use such settings -- because the resulting prioritizations are not guaranteed to be near-optimal (the default gap is 10%) -- this is fine because our goal here is to tune the preliminary `penalty` values. Indeed, none of these preliminary prioritizations will be considered as candidate prioritizations. **Please note that you might need to set a higher time limit, or relax the optimality gap even further (e.g., 40%) when analyzing larger datasets.** + +```{r, results = "hide"} +# define a problem without boundary penalties +p0 <- problem(tas_pu, tas_features, cost_column = "cost") %>% + add_min_set_objective() %>% + add_relative_targets(0.17) %>% + add_locked_in_constraints("locked_in") %>% + add_binary_decisions() + +# generate preliminary prioritizations based on each penalty +## note that we specify a relaxed gap and time limit for the solver +prelim_blended_results <- lapply(prelim_penalty, function(x) { + s <- + p0 %>% + add_boundary_penalties(penalty = x, data = tas_bd) %>% + add_default_solver(gap = 0.2, time_limit = 10 * 60) %>% + solve() + s <- data.frame(s = s$solution_1) + names(s) <- with_options(list(scipen = 30), paste0("penalty_", x)) + s +}) + +# format results as a single spatial object +prelim_blended_results <- cbind( + tas_pu, do.call(bind_cols, prelim_blended_results) +) + +# preview results +print(prelim_blended_results) +``` + +After generating the preliminary prioritizations, let's create some maps to visualize them. In particular, we want to understand how different penalty values influence the spatial fragmentation of the prioritizations. + +```{r, fig.width = 7, fig.height = 5.0} +# plot maps of prioritizations +plot( + x = + prelim_blended_results %>% + dplyr::select(starts_with("penalty_")) %>% + mutate_if(is.numeric, function(x) { + case_when( + prelim_blended_results$locked_in > 0.5 ~ "locked in", + x > 0.5 ~ "priority", + TRUE ~ "other" + ) + }), + pal = c("purple", "grey90", "darkgreen") +) +``` + +We can see that as the `penalty` value used to generate the prioritizations increases, the spatial fragmentation of the prioritizations decreases. In particular, we can see that a `penalty` value of `r prelim_penalty[8]` results in a single reserve -- meaning this is our best guess of the upper limit. Using this `penalty` value as an upper limit, we will now generate a second series of prioritizations that will be the candidate prioritizations. Critically, these candidate prioritizations will not be generated using with time limit and be generated using a more suitable gap (i.e., default gap of 10%). + +```{r, fig.width = 7, fig.height = 5.0, results = "hide"} +# define a new set of penalty values +## note that we use a linear scale to explore both low and high penalty values +penalty <- round(seq(1e-5, prelim_penalty[8], length.out = 9), 5) + +# generate prioritizations based on each penalty +blended_results <- lapply(penalty, function(x) { + ## generate solution + s <- + p0 %>% + add_boundary_penalties(penalty = x, data = tas_bd) %>% + solve() + ## return data frame with solution + s <- data.frame(s = s$solution_1) + names(s) <- with_options(list(scipen = 30), paste0("penalty_", x)) + s +}) + +# format results as a single spatial object +blended_results <- cbind(tas_pu, do.call(bind_cols, blended_results)) + +# plot maps of prioritizations +plot( + x = + blended_results %>% + dplyr::select(starts_with("penalty_")) %>% + mutate_if(is.numeric, function(x) { + case_when( + blended_results$locked_in > 0.5 ~ "locked in", + x > 0.5 ~ "priority", + TRUE ~ "other" + ) + }), + pal = c("purple", "grey90", "darkgreen") +) +``` + +We now have a set of candidate prioritizations generated using the blended approach. The main advantages of this approach is that it is similar calibration analyses used by other decision support tools for conservation (i.e., _Marxan_) and it is relatively straightforward to implement. However, this approach also has a key disadvantage. Because the `penalty` parameter is a unitless trade-off parameter -- meaning that we can't leverage existing knowledge to specify a suitable range of `penalty` values -- we first have to conduct a preliminary analysis to identify an upper limit. Although finding an upper limit was fairly simple for the example datset, it can be difficult to find for more realistic data. In the next section, we will show how to generate a set of candidate prioritzations using the hierachical approach -- which does not have this disadvantage. + +### Hierarchical approach + +The hierarchical approach for multi-objective optimization involves generating a series of incremental prioritizations -- using a different objective at each increment to refine the previous solution -- until the final solution achieves all of the objectives. The advantage with this approach is that we can specify trade-off parameters for each objective based on a percentage from optimality. This means that we can leverage our own knowledge -- or that of decision maker -- when to generate a range of suitable trade-off parameters. As such, this approach does not require us to generate a series of preliminary prioritizations. + +This approach is slightly more complicated to implement within the _prioritizr R_ package then the blended approach. To start off, we generate an initial prioritization based on a problem formulation that does not consider any penalties. Critically, we will generate this prioritization by solving the problem to optimality (using the `gap` parameter of the `add_default_solver()` function). + +```{r, fig.width = w, fig.height = h, results = "hide"} +# define a problem without boundary penalties +p1 <- problem(tas_pu, tas_features, cost_column = "cost") %>% + add_min_set_objective() %>% + add_relative_targets(0.17) %>% + add_locked_in_constraints("locked_in") %>% + add_binary_decisions() %>% + add_default_solver(gap = 0) + +# solve problem +s1 <- solve(p1) + +# add column for making a map of the prioritization +s1$map_1 <- case_when( + s1$locked_in > 0.5 ~ "locked in", + s1$solution_1 > 0.5 ~ "priority", + TRUE ~ "other" +) + +# plot map of prioritization +plot( + s0[, "map_1"], pal = c("purple", "grey90", "darkgreen"), + main = NULL, key.pos = 1 +) +``` + +Next, we will calculate the total cost of the initial prioritization. + +```{r, fig.width = w, fig.height = h} +# calculate cost +s1_cost <- eval_cost_summary(p1, s1[, "solution_1"])$cost + +# print cost +print(s1_cost) +``` + +Now we will calculate a series of cost thresholds. These cost thresholds will be calculated by inflating the cost of the initial prioritization by a range of percentage values. Since these values are percentages -- and not unitless values unlike those used in the blended approach -- we can use domain knowledge to specify a suitable range of cost thresholds. For this tutorial, let's assume that it would be impractical -- per our domain knowledge -- to expend more than four times the total cost of the initial prioritization to reduce spatial fragmentation. + +```{r} +# calculate cost threshold values +threshold <- s1_cost + (s1_cost * seq(1e-5, 4, length.out = 9)) +threshold <- ceiling(threshold) + +# print cost thresholds +print(threshold) +``` + +After generating the cost thresholds, we can use them to generate prioritizations. Specifically, we will generate prioritizations that aim to minimize total boundary length as much as possible -- ignoring the total cost of the prioritizations -- whilst ensuring that the total cost of the prioritization does not exceed a given cost threshold and the other considerations (e.g., locked in constraints). To achieve this, we create a new column in the `tas_pu` object that contains only zero values (called `zeros`) and use this new column to specify the cost data for the prioritizations. +**Although we normally recommend against cost data that contain zero values -- because planning units with zero costs are often selected in prioritizations even if they are not needed -- here we use zero cost values so that the prioritization will focus exclusively on spatial fragmentation.** Additionally, when it comes to generating the prioritization, we will add linear constraints to ensure that the total cost of the prioritization does not exceed a given cost threshold (using the `add_linear_constraints()` function). + +```{r, fig.width = 7, fig.height = 5.0, results = "hide"} +# add a column with zeros +tas_pu$zeros <- 0 + +# define a problem with zero cost values and boundary penalties +## note that because all the costs are all zero, it doesn't actually +## matter what penalty value is used (as long as the value is > 0) +## and so we just use a value of 1 +p2 <- problem(tas_pu, tas_features, cost_column = "zeros") %>% + add_min_set_objective() %>% + add_boundary_penalties(penalty = 1, data = tas_bd) %>% + add_relative_targets(0.17) %>% + add_locked_in_constraints("locked_in") %>% + add_binary_decisions() + +# generate prioritizations based on each cost threshold +## note that the prioritizations are solved to within 10% of optimality +## (the default gap) because the gap is not specified +hierarchical_results <- lapply(threshold, function(x) { + ## generate solution by adding a constraint based on the threshold and + ## using the "real" cost values (i.e., not zeros) + s <- + p2 %>% + add_linear_constraints(threshold = x, sense = "<=", data = "cost") %>% + solve() + ## return data frame with solution + s <- data.frame(s = s$solution_1) + names(s) <- paste0("threshold_", x) + s +}) + +# format results as a single spatial object +hierarchical_results <- cbind(tas_pu, do.call(bind_cols, hierarchical_results)) + +# plot maps of prioritizations +plot( + x = + hierarchical_results %>% + dplyr::select(starts_with("threshold_")) %>% + mutate_if(is.numeric, function(x) { + case_when( + hierarchical_results$locked_in > 0.5 ~ "locked in", + x > 0.5 ~ "priority", + TRUE ~ "other" + ) + }), + pal = c("purple", "grey90", "darkgreen") +) +``` + +We now have a set of candidate prioritizations generated using the hierarchical approach. This approach can be much faster than the blended approach because it does not require generating a set of prioritizations to identify an upper limit for the `penalty` trade-off parameter. After generating a set of candidate prioritizations, we can then calculate performance metrics to compare the prioritizations. + +## Calculating performance metrics + +Here we will calculate performance metrics to compare the prioritizations. Since we aim to navigate trade-offs between the total cost of a prioritization and the overall level of spatial fragmentation associated with a prioritization (as measured by total boundary length), we will calculate metrics to assess these criteria. Although we generated two sets of candidate prioritizations in the previous section; for brevity, here we will consider the candidate prioritizations generated using the hierarchical approach. **Please note that you could also apply the following procedures to candidate prioritizations generated using the blended approach.** + +```{r} +# calculate metrics for prioritizations +## note that we use p0 and not p1 so that cost calculations are based +## on the cost values and not zeros +hierarchical_metrics <- lapply( + grep("threshold_", names(hierarchical_results)), function(x) { + x <- hierarchical_results[, x] + data.frame( + total_cost = eval_cost_summary(p0, x)$cost, + total_boundary_length = eval_boundary_summary(p0, x)$boundary + ) + } +) +hierarchical_metrics <- do.call(bind_rows, hierarchical_metrics) +hierarchical_metrics$threshold <- threshold +hierarchical_metrics <- as_tibble(hierarchical_metrics) + +# preview metrics +print(hierarchical_metrics) +``` + +After calculating the metrics, let's we can use them to help select a prioritization. + +## Selecting a prioritization + +Now we need to decide on which candidate prioritization achieves the best trade-off. There are a range of qualitative and quantitative methods that are available to select a candidate prioritization [@r45]. Here we will consider three different methods. Since some of these methods a set of candidate prioritizations, we will use the candidate prioritizations using the hierarchical approach for these methods. To keep track of the prioritizations selected by different methods, let's create a `results_data` table. + +```{r} +# create data for plotting +result_data <- + hierarchical_metrics %>% + ## rename threshold column to value column + rename(value = "threshold") %>% + ## add column with column names that contain candidate prioritizations + mutate(name = grep( + "threshold_", names(hierarchical_results), value = TRUE, fixed = TRUE + )) %>% + ## add column with labels for plotting + mutate(label = paste("Threshold =", value)) %>% + ## add column to keep track prioritizations selected by different methods + mutate(method = "none") + +# print table +print(result_data) +``` + +Next, let's examine some different methods for selecting prioritizations. + +### Visual method + +One qualitative method involves plotting the relationship between the different criteria, and using the plot to visually select a candidate prioritization. This visual method is often used to help calibrate trade-offs among prioritizations generated using the _Marxan_ decision support tool [e.g., @r41; @r42]. So, let's create a plot to select a prioritization. + +```{r, fig.width = 7, fig.height = 5.0} +# create plot to visualize trade-offs and show selected candidate prioritization +result_plot <- + ggplot( + data = result_data, + aes(x = total_boundary_length, y = total_cost, label = label) + ) + + geom_line() + + geom_point(size = 3) + + geom_text(hjust = -0.15) + + scale_color_manual( + values = c("visual" = "blue", "not selected" ="black") + ) + + xlab("Total boundary length of prioritization") + + ylab("Total cost of prioritization") + + scale_x_continuous(expand = expansion(mult = c(0.05, 0.4))) + + theme(legend.title = element_blank()) + +# render plot +print(result_plot) +``` + +We can see that there is a clear relationship between total cost and total boundary length. It would seem that in order to achieve a lower total boundary length -- and thus lower spatial fragmentation -- the prioritization must have a greater cost. Although we might expect the results to show a smoother curve -- in other words, only Pareto dominant solutions -- this result is expected because we generated candidate prioritizations using the default optimality gap of 10%. Typically, the visual method involves selecting a prioritization near the elbow of the plot. So, let's select the prioritization generated using a `threshold` value of `r threshold[3]`. To keep of the prioritizations selected based on different methods, let's create a `method` column in the `result_data` table. + +```{r} +# specify prioritization selected by visual method +result_data$method[3] <- "visual" +``` + +Next, let's consider a quantitative approach. + +### TOPSIS method + +Multiple-criteria decision analysis is a disciple that uses analytical methods to evaluate trade-offs between multiple criteria [MCDA; reviewed in @r44]. Although this discipline contains many different methods, here we will use the the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method [@r46]. This method requires (i) data describing the performance of each prioritization according the different criteria, (ii) weights to encode the relative importance of each criteria, and (iii) details on whether each criteria should ideally be minimized or maximized. Let's run the analysis, assuming that we equal weighting for total cost and total boundary length. + +```{r} +# calculate TOPSIS scores +topsis_results <- topsis( + decision = + hierarchical_metrics %>% + dplyr::select(total_cost, total_boundary_length) %>% + as.matrix(), + weights = c(1, 1), + impacts = c("-", "-") +) + +# print results +print(topsis_results) +``` + +The candidate prioritization with the greatest TOPSIS score is considered to represent the best trade-off between total cost and total boundary length. So, based on this method, we would select the prioritization generated using a `threshold` value of `r threshold[which.max(topsis_results$score)]`. Let's update the `result_data` with this information. + +```{r} +# add column indicating prioritization selected by TOPSIS method +result_data$method[which.max(topsis_results$score)] <- "TOPSIS" +``` + +Next, let's consider another quantitative method. + +### Cohon *et al.* (1979) method + +This method is based on an algorithm that was originally developed by Cohon *et al.* [@r49], and was later adapted for use in systematic conservation planning [@r50]. Specifically, it involves generating two ideal prioritizations -- with each prioritization representing the ideal prioritization for each criteria -- and then using the performance metrics calculated for these prioritizations to automatically derive a trade-off `penalty` value [@r45; @r49]. Thus, unlike the two other methods, this method does not require a set of candidate prioritizations. **As such, this method can be used to find a prioritization that meets multiple criteria in a much shorter period of time than the other methods.** To implement this method, we first need to generate the ideal prioritizations (note that we specify an gap of 0% to ensure optimality). + +```{r, results = "hide"} +# generate ideal prioritization based on cost criteria +## note that this is simply the same as the s1 prioritization we generated +## for the hierarchical approach +p3 <- problem(tas_pu, tas_features, cost_column = "cost") %>% + add_min_set_objective() %>% + add_relative_targets(0.17) %>% + add_locked_in_constraints("locked_in") %>% + add_binary_decisions() %>% + add_default_solver(gap = 0) + +# solve problem +s3 <- solve(p3) + +# generate ideal prioritization based on spatial fragmentation criteria +## note that any non-zero penalty value would here, +## so we just use a penalty of 1 +p4 <- problem(tas_pu, tas_features, cost_column = "zeros") %>% + add_min_set_objective() %>% + add_boundary_penalties(penalty = 1, data = tas_bd) %>% + add_relative_targets(0.17) %>% + add_locked_in_constraints("locked_in") %>% + add_binary_decisions() %>% + add_default_solver(gap = 0) + +# solve problem +s4 <- solve(p4) +``` + +Next, let's calculate the performance metrics for these prioritizations. + +```{r} +# generate problem formulation with costs and boundary penalties for +# calculating performance metrics +p5 <- problem(tas_pu, tas_features, cost_column = "cost") %>% + add_min_set_objective() %>% + add_boundary_penalties(penalty = 1, data = tas_bd) %>% + add_relative_targets(0.17) %>% + add_locked_in_constraints("locked_in") %>% + add_binary_decisions() + +# calculate performance metrics for ideal cost prioritization +s3_metrics <- tibble( + total_cost = eval_cost_summary(p5, s3[, "solution_1"])$cost, + total_boundary_length = + eval_boundary_summary(p5, s3[, "solution_1"])$boundary +) + +# calculate performance metrics for ideal boundary length prioritization +s4_metrics <- tibble( + total_cost = eval_cost_summary(p5, s4[, "solution_1"])$cost, + total_boundary_length = + eval_boundary_summary(p5, s4[, "solution_1"])$boundary +) +``` + +After calculating these performance metrics, we can use them to automatically calculate a `penalty` value. + +```{r} +# calculate penalty value based on Cohon et al. 1979 +cohon_penalty <- abs( + (s3_metrics$total_cost - s4_metrics$total_cost) / + (s3_metrics$total_boundary_length - s4_metrics$total_boundary_length) +) + +# round to 5 decimal places to avoid numerical issues during optimization +cohon_penalty <- round(cohon_penalty, 5) + +# print penalty value +print(cohon_penalty) +``` + +Now that we have calculated a `penalty` value using this method, we can use it to generate a prioritization. + +```{r, results = "hide"} +# generate prioritization using penalty value calculated using Cohon et al. 1979 +p6 <- problem(tas_pu, tas_features, cost_column = "cost") %>% + add_min_set_objective() %>% + add_boundary_penalties(penalty = cohon_penalty, data = tas_bd) %>% + add_relative_targets(0.17) %>% + add_locked_in_constraints("locked_in") %>% + add_binary_decisions() + +# solve problem +s6 <- solve(p6) +``` + +Let's update the `results_data` table with results about the prioritization. + +```{r} +# add new row with data for prioritization generated following Cohon et al. 1979 +result_data <- bind_rows( + result_data, + tibble( + total_cost = eval_cost_summary(p6, s6[, "solution_1"])$cost, + total_boundary_length = + eval_boundary_summary(p6, s6[, "solution_1"])$boundary, + value = cohon_penalty, + name = paste0("penalty_", cohon_penalty), + label = paste0("Penalty = ", cohon_penalty), + method = "Cohon" + ) +) +``` + +Next, let's compare the prioritizations selected by different methods. + +### Method comparison + +Let's create a plot to visualize the results from the different methods. + +```{r, fig.width = 7, fig.height = 5.0} +# create plot to visualize trade-offs and show selected candidate prioritization +result_plot <- + ggplot( + data = + result_data %>% + mutate(vjust = if_else(method == "Cohon", -1, 0.5)), + aes(x = total_boundary_length, y = total_cost, label = label) + ) + + geom_line() + + geom_point(aes(color = method), size = 3) + + geom_text(aes(vjust = vjust, color = method), hjust = -0.1) + + scale_color_manual( + name = "Method", + values = c( + "visual" = "#984ea3", + "none" = "#000000", + "TOPSIS" = "#e41a1c", + "Cohon" = "#377eb8" + ) + ) + + xlab("Total boundary length of prioritization") + + ylab("Total cost of prioritization") + + scale_x_continuous(expand = expansion(mult = c(0.05, 0.4))) + +# render plot +print(result_plot) +``` + +We can see that the different method selected different prioritizations. To further compare the results from the different methods, let's create some maps showing the selected prioritizations. + +```{r, fig.width = 7.0, fig.height = h} +# extract column names for creating the prioritizations +visual_name <- result_data$name[[which(result_data$method == "visual")]] +topsis_name <- result_data$name[[which(result_data$method == "TOPSIS")]] + +# create object with selected prioritizations +solutions <- bind_cols( + tas_pu, + hierarchical_results %>% + st_drop_geometry() %>% + dplyr::select(all_of(c(visual_name, topsis_name))) %>% + setNames(c("Visual", "TOPSIS")), + s6 %>% + st_drop_geometry() %>% + dplyr::select(solution_1) %>% + rename(Cohon = "solution_1") +) + +# plot maps of selected prioritizations +plot( + x = + solutions %>% + dplyr::select(Visual, TOPSIS, Cohon) %>% + mutate_if(is.numeric, function(x) { + case_when( + hierarchical_results$locked_in > 0.5 ~ "locked in", + x > 0.5 ~ "priority", + TRUE ~ "other" + ) + }), + pal = c("purple", "grey90", "darkgreen") +) +``` + +How do we determine which one is best? This is difficult to say. Ideally, additional information could be used to help select a prioritization, such as knowledge on available resources, species' connectivity requirements, and impacts of neighboring land use. However, from a practical perspective, prioritizations generated for academic contexts might find the quantitative approaches more useful because they have greater transparency and reproducibility. Ultimately, all of these methods are designed to support decision making. This means that they are intended to assist the decision making process, not serve as a replacement. + +## Conclusion + +Hopefully, this vignette has provided a useful introduction for resolving trade-offs in prioritizations. Although we only explored trade-offs between total cost and spatial fragmentation in this tutorial, this analysis could be adapted to explore trade-offs between a wide range of different criteria. For instance, instead of considering total cost as the primary objective, future analyses could explore trade-offs with feature representation (using the `add_min_shortfall_objective()` function). Additionally, instead of spatial fragmentation, future analyses could explore trade-offs that directly relate to connectivity (using the `add_connectivity_penalties()` function) or specific variables of interest -- such as ecosystem intactness or inverse human footprint index [@r47; @r48] -- to inform decision making (using the `add_linear_penalties()` function). Furthermore, after identifying the best `penalty` or `threshold` values to strike a balance between multiple criteria, you could generate a portfolio of prioritizations (e.g., using the `add_gap_portfolio_function()`) to find multiple options for achieving a similar balance. This might be helpful when you need to generate a set of prioritizations that have comparable performance -- in terms of how well they achieve different criteria -- but select different planning units. + +## References diff --git a/inst/doc/calibrating_trade-offs_tutorial.html b/inst/doc/calibrating_trade-offs_tutorial.html new file mode 100644 index 000000000..873c2fc03 --- /dev/null +++ b/inst/doc/calibrating_trade-offs_tutorial.html @@ -0,0 +1,868 @@ + + + + + + + + + + + + + + +Calibrating trade-offs tutorial + + + + + + + + + + + + + + + + + + + + + + + + + + +

      Calibrating trade-offs tutorial

      + + + + +
      +

      Introduction

      +

      Systematic conservation planning requires making trade-offs (Margules & Pressey 2000; Vane-Wright et al. 1991). Since different criteria may conflict with one another – or not align perfectly – prioritizations need to make trade-offs between different criteria (Klein et al. 2013). Although some criteria can easily be accounted for by using locked constraints or representation targets (e.g., Dorji et al. 2020; Hermoso et al. 2018), this is not always the case (e.g., Beger et al. 2010). For example, prioritizations often need to balance overall cost with the overall level spatial fragmentation among reserves (Hermoso et al. 2011; Stewart & Possingham 2005). Additionally, prioritizations often need to balance the overall level of connectivity among reserves against other criteria (Hermoso et al. 2012). Since the best trade-off depends on a range of factors – such as available budgets, species’ connectivity requirements, and management capacity – finding the best balance can be challenging.

      +

      The prioritizr R package provides multi-objective optimization methods to help identify the best trade-offs between different criteria. To achieve this, a conservation planning problem can be formulated with a primary objective (e.g., add_min_set_objective()) and penalties (e.g., add_boundary_penalties()) that relate to such criteria. When building the problem, the nature of the trade-offs can be specified using certain parameters (e.g., the penalty parameter of the add_boundary_penalties() function). To identify a prioritization that finds the best balance between different criteria, the trade-off parameters can be tuned using a calibration analysis. These analyses – in the context of systematic conservation planning – typically involve generating a set of candidate prioritizations based on different parameters, measuring their performance according to each of the criteria, and then selecting a prioritization (or set of prioritizations) based on how well they achieve the criteria (Hermoso et al. 2011; Stewart & Possingham 2005; Hermoso et al. 2012). For example, the Marxan decision support tool has a range of parameters (e.g., species penalty factors, boundary length modifier) that are calibrated to balance cost, species’ representation, and spatial fragmentation (Ardron et al. 2010).

      +

      The aim of this tutorial is to provide guidance on calibrating trade-offs when using the prioritizr R package. Here we will explore a couple of different approaches for generating candidate prioritizations, and methods for finding the best balance between different criteria. Specifically, we will try to generate prioritizations that strike the best balance between total cost and spatial fragmentation (measured as total boundary length). As such, the code used in this vignette will be directly applicable when performing a boundary length calibration analysis.

      +
      +
      +

      Data

      +

      Let’s load the packages and dataset used in this tutorial. Since this tutorial uses the prioritizrdata R package along with several other R packages (see below), please ensure that they are all installed. This particular dataset comprises two object: tas_pu and tas_features. Although we will briefly discuss this dataset below, please refer to the Tasmania Tutorial vignette for further details.

      +
      # load packages
+library(prioritizrdata)
+library(prioritizr)
+library(dplyr)
+library(tibble)
+library(scales)
+library(ggplot2)
+library(topsis)
+library(withr)
+
+# load planning unit data
+data(tas_pu)
+
+# convert planning units to sf format
+tas_pu <- st_as_sf(tas_pu)
+
+# load feature data
+data(tas_features)
+
+# print planning unit data
+print(tas_pu)
      +
      ## Simple feature collection with 1130 features and 5 fields
+## Geometry type: MULTIPOLYGON
+## Dimension:     XY
+## Bounding box:  xmin: 298809.6 ymin: 5167775 xmax: 613818.8 ymax: 5502544
+## Projected CRS: WGS 84 / UTM zone 55S
+## First 10 features:
+##   id      cost status locked_in locked_out                       geometry
+## 0  1 60.246377      0     FALSE      FALSE MULTIPOLYGON (((328497 5497...
+## 1  2 19.863008      0     FALSE      FALSE MULTIPOLYGON (((307121.6 54...
+## 2  3 59.680513      0     FALSE      FALSE MULTIPOLYGON (((321726.1 54...
+## 3  4 32.416138      0     FALSE      FALSE MULTIPOLYGON (((304314.5 54...
+## 4  5 26.177062      0     FALSE      FALSE MULTIPOLYGON (((314958.5 54...
+## 5  6 51.262177      0     FALSE      FALSE MULTIPOLYGON (((327904.3 54...
+## 6  7 32.299112      0     FALSE      FALSE MULTIPOLYGON (((308194.1 54...
+## 7  8 38.404063      0     FALSE      FALSE MULTIPOLYGON (((322792.7 54...
+## 8  9  3.554745      0     FALSE      FALSE MULTIPOLYGON (((334896.6 54...
+## 9 10  1.834921      0     FALSE      FALSE MULTIPOLYGON (((356377.1 54...
      +
      # print feature data
+print(tas_features)
      +
      ## class      : RasterStack 
+## dimensions : 398, 359, 142882, 62  (nrow, ncol, ncell, nlayers)
+## resolution : 1000, 1000  (x, y)
+## extent     : 288801.7, 647801.7, 5142976, 5540976  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## names      : tas_features.1, tas_features.2, tas_features.3, tas_features.4, tas_features.5, tas_features.6, tas_features.7, tas_features.8, tas_features.9, tas_features.10, tas_features.11, tas_features.12, tas_features.13, tas_features.14, tas_features.15, ... 
+## min values :              0,              0,              0,              0,              0,              0,              0,              0,              0,               0,               0,               0,               0,               0,               0, ... 
+## max values :              1,              1,              1,              1,              1,              1,              1,              1,              1,               1,               1,               1,               1,               1,               1, ...
      +

      The tas_pu object contains planning units represented as spatial polygons (i.e., converted to a sf::st_sf() object). This object has three columns that denote the following information for each planning unit: a unique identifier (id), unimproved land value (cost), and current conservation status (locked_in). Specifically, the conservation status column indicates if at least half the area planning unit is covered by existing protected areas (denoted by a value of 1) or not (denoted by a value of zero).

      +
      # plot map of planning unit costs
+plot(tas_pu[, "cost"], main = "Planning unit costs")
      +

      +
      # plot map of planning unit statuses
+plot(tas_pu[, "locked_in"], main = "Planning unit status")
      +

      +

      The tas_features object describes the spatial distribution of different vegetation communities (using presence/absence data). We will use the vegetation communities as the biodiversity features for the prioritization.

      +
      # plot map of the first four vegetation classes
+plot(tas_features[[1:4]], main = paste("Feature", 1:4))
      +

      +

      We can use this dataset to generate a prioritization. Specifically, we will use the minimum set objective so that the optimization process minimizes total cost. We will add representation targets to ensure that prioritizations cover 17% of each vegetation community. Additionally, we will add constraints to ensure that planning units covered by existing protected areas are selected (i.e., locked in). Finally, we will specify that the conservation planning exercise involves binary decisions (i.e., selecting or not selecting planning units for protected area establishment).

      +
      # define a problem
+p0 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# print problem
+print(p0)
      +
      ## Conservation Problem
+##   planning units: sf (1130 units)
+##   cost:           min: 0.19249, max: 61.92727
+##   features:       tas_features.1, tas_features.2, tas_features.3, ... (62 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
+##   decisions:      Binary decision 
+##   constraints:    <Locked in planning units [257 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
      # solve problem
+s0 <- solve(p0)
+
+# print result
+print(s0)
+
+# create column for making a map of the prioritization
+s0$map_1 <- case_when(
+  s0$locked_in > 0.5 ~ "locked in",
+  s0$solution_1 > 0.5 ~ "priority",
+  TRUE ~ "other"
+)
+
+# plot map of prioritization
+plot(
+  s0[, "map_1"], pal = c("purple", "grey90", "darkgreen"),
+  main = NULL, key.pos = 1
+)
      +

      +

      We can see that the priority areas identified by the prioritization are scattered across the study area (shown in green). Indeed, none of the priority areas are connect to existing protected areas (shown in purple), and very of them are connect with other priority areas. As such, the prioritization has a high level of spatial fragmentation. If it is important avoid such levels of spatial fragmentation, then we will need to explicitly account spatial fragmentation in the optimization process.

      +
      +
      +

      Preliminary processing

      +

      We need to conduct some preliminary processing procedures to prepare the data for subsequent analysis. This is important to help make it easier to find suitable trade-off parameters, and avoid numerical scaling issues that can result in overly long run times (see presolve_check() for further information). These processing steps are akin to data scaling (or normalization) procedures that are applied in statistical analysis to improve model convergence.

      +

      The first processing procedure involves setting the cost values for all locked in planning units to zero. This is so that the total cost estimates of the prioritization reflects the total cost of establishing new protected areas – not just total land value. In other words, we want the total cost estimate for a prioritization to reflect the cost of implementing conservation actions. This procedure is especially important when using the hierarchical approach described below, so that cost thresholds are based on percentage increases in the cost of establishing new protected areas.

      +
      # set costs for planning units covered by existing protected areas to zero
+tas_pu$cost[tas_pu$locked_in > 0.5] <- 0
+
+# plot map of planning unit costs
+plot(tas_pu[, "cost"], main = "Planning unit cost")
      +

      +

      The second procedure involves pre-computing the boundary length data and manually re-scaling the boundary length values. This procedure is important because boundary length values are often very large that, in turn, can cause numerical issues that result in excessive run times (see presolve_check() for further details).

      +
      # generate boundary length data for the planning units
+tas_bd <- boundary_matrix(tas_pu)
+
+# manually re-scale the boundary length values
+tas_bd@x <- rescale(tas_bd@x, to = c(0.01, 100))
      +

      After applying these procedures, our data is ready for subsequent analysis.

      +
      +
      +

      Generating candidate prioritizations

      +

      Here we will start the calibration analysis by generating a set of candidate prioritizations. Specifically, these prioritizations will be generated using different parameters to specify different trade-offs between the different criteria. Since this tutorial involves navigating trade-offs between the overall cost of a prioritization and the level of spatial fragmentation associated with a prioritization (as measured by total boundary length), we will generate prioritizations using different parameters related to these criteria. We will examine two approaches for generating candidate prioritizations based on multi-objective optimization procedures. Although we’ll be examining both approaches in this tutorial, you would normally only use one of these approaches when conducting your own analysis

      +
      +

      Blended approach

      +

      The blended approach for multi-objective optimization involves combining separate criteria (e.g., total cost and total boundary length) into a single joint criterion. To achieve this, a trade-off (or scaling) parameter is used to specify the relative importance of each criterion. This approach is the default approach provided by the prioritizr R package. Specifically, each of the functions for adding a penalty to a problem formulation (e.g., add_boundary_penalties()) contains a parameter to control the relative importance of the penalties (i.e., the penalty parameter). For example, when using the add_boundary_penalties() function, setting a high penalty value will indicate that it is important to reduce the overall exposed boundary (perimeter) of the prioritization.

      +

      The main challenge with the blended approach is identifying a range of suitable penalty values to generate candidate prioritizations. If we set a penalty value that is too low, then the penalties will have no effect (e.g., boundary length penalties would have no effect on the prioritization). If we set a penalty value too high, then the prioritization will effectively ignore the primary objective. In such cases, the prioritization will be overly spatially clustered – because the planning unit cost values have no effect — and contain a single reserve. Thus we need to find a suitable range of penalty values before we can generate a set of candidate prioritizations.

      +

      We can find a suitable range of penalty values by generating a set of preliminary prioritizations. These preliminary prioritizations will be based on different penalty values – similar to the process for generating the candidate prioritizations – but solved using customized settings that sacrifice optimality for fast run times (see below for details). This is especially important because specifying a penalty value that is too high will cause the optimization process to take a very long time to generate a solutions (due to the numerical scaling issues mentioned previously). To find a suitable range of penalty values, we need to identify an upper limit for the penalty value (i.e., the highest penalty value that result in a prioritization containing a single reserve). Let’s create some preliminary penalty to identify this upper limit. Please note that you might need to adjust the prelim_upper value to find the upper limit when analyzing different datasets.

      +
      # define a range of different penalty values
+## note that we use a power scale to avoid focusing on very high penalty values
+prelim_lower <- -5   # change this for your own data
+prelim_upper <- 2.8  # change this for your own data
+prelim_penalty <- round(10^seq(prelim_lower, prelim_upper, length.out = 9), 5)
+
+# print penalty values
+print(prelim_penalty)
      +
      ## [1]   0.00001   0.00009   0.00089   0.00841   0.07943   0.74989   7.07946
+## [8]  66.83439 630.95734
      +

      Next, let’s use the preliminary penalty values to generate preliminary prioritizations. As mentioned earlier, we will generate these preliminary prioritizations using customized settings to reduce runtime. Specifically, we will set a time limit of 10 minutes per run, and relax the optimality gap to 20%. Although we would not normally use such settings – because the resulting prioritizations are not guaranteed to be near-optimal (the default gap is 10%) – this is fine because our goal here is to tune the preliminary penalty values. Indeed, none of these preliminary prioritizations will be considered as candidate prioritizations. Please note that you might need to set a higher time limit, or relax the optimality gap even further (e.g., 40%) when analyzing larger datasets.

      +
      # define a problem without boundary penalties
+p0 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# generate preliminary prioritizations based on each penalty
+## note that we specify a relaxed gap and time limit for the solver
+prelim_blended_results <- lapply(prelim_penalty, function(x) {
+  s <-
+    p0 %>%
+    add_boundary_penalties(penalty = x, data = tas_bd) %>%
+    add_default_solver(gap = 0.2, time_limit = 10 * 60) %>%
+    solve()
+  s <- data.frame(s = s$solution_1)
+  names(s) <- with_options(list(scipen = 30), paste0("penalty_", x))
+  s
+})
+
+# format results as a single spatial object
+prelim_blended_results <- cbind(
+  tas_pu, do.call(bind_cols, prelim_blended_results)
+)
+
+# preview results
+print(prelim_blended_results)
      +

      After generating the preliminary prioritizations, let’s create some maps to visualize them. In particular, we want to understand how different penalty values influence the spatial fragmentation of the prioritizations.

      +
      # plot maps of prioritizations
+plot(
+  x =
+    prelim_blended_results %>%
+    dplyr::select(starts_with("penalty_")) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        prelim_blended_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
      +

      +

      We can see that as the penalty value used to generate the prioritizations increases, the spatial fragmentation of the prioritizations decreases. In particular, we can see that a penalty value of 66.83439 results in a single reserve – meaning this is our best guess of the upper limit. Using this penalty value as an upper limit, we will now generate a second series of prioritizations that will be the candidate prioritizations. Critically, these candidate prioritizations will not be generated using with time limit and be generated using a more suitable gap (i.e., default gap of 10%).

      +
      # define a new set of penalty values
+## note that we use a linear scale to explore both low and high penalty values
+penalty <- round(seq(1e-5, prelim_penalty[8], length.out = 9), 5)
+
+# generate prioritizations based on each penalty
+blended_results <- lapply(penalty, function(x) {
+  ## generate solution
+  s <-
+    p0 %>%
+    add_boundary_penalties(penalty = x, data = tas_bd) %>%
+    solve()
+  ## return data frame with solution
+  s <- data.frame(s = s$solution_1)
+  names(s) <- with_options(list(scipen = 30), paste0("penalty_", x))
+  s
+})
+
+# format results as a single spatial object
+blended_results <- cbind(tas_pu, do.call(bind_cols, blended_results))
+
+# plot maps of prioritizations
+plot(
+  x =
+    blended_results %>%
+    dplyr::select(starts_with("penalty_")) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        blended_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
      +

      +

      We now have a set of candidate prioritizations generated using the blended approach. The main advantages of this approach is that it is similar calibration analyses used by other decision support tools for conservation (i.e., Marxan) and it is relatively straightforward to implement. However, this approach also has a key disadvantage. Because the penalty parameter is a unitless trade-off parameter – meaning that we can’t leverage existing knowledge to specify a suitable range of penalty values – we first have to conduct a preliminary analysis to identify an upper limit. Although finding an upper limit was fairly simple for the example datset, it can be difficult to find for more realistic data. In the next section, we will show how to generate a set of candidate prioritzations using the hierachical approach – which does not have this disadvantage.

      +
      +
      +

      Hierarchical approach

      +

      The hierarchical approach for multi-objective optimization involves generating a series of incremental prioritizations – using a different objective at each increment to refine the previous solution – until the final solution achieves all of the objectives. The advantage with this approach is that we can specify trade-off parameters for each objective based on a percentage from optimality. This means that we can leverage our own knowledge – or that of decision maker – when to generate a range of suitable trade-off parameters. As such, this approach does not require us to generate a series of preliminary prioritizations.

      +

      This approach is slightly more complicated to implement within the prioritizr R package then the blended approach. To start off, we generate an initial prioritization based on a problem formulation that does not consider any penalties. Critically, we will generate this prioritization by solving the problem to optimality (using the gap parameter of the add_default_solver() function).

      +
      # define a problem without boundary penalties
+p1 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0)
+
+# solve problem
+s1 <- solve(p1)
+
+# add column for making a map of the prioritization
+s1$map_1 <- case_when(
+  s1$locked_in > 0.5 ~ "locked in",
+  s1$solution_1 > 0.5 ~ "priority",
+  TRUE ~ "other"
+)
+
+# plot map of prioritization
+plot(
+  s0[, "map_1"], pal = c("purple", "grey90", "darkgreen"),
+  main = NULL, key.pos = 1
+)
      +

      +

      Next, we will calculate the total cost of the initial prioritization.

      +
      # calculate cost
+s1_cost <- eval_cost_summary(p1, s1[, "solution_1"])$cost
+
+# print cost
+print(s1_cost)
      +
      ## [1] 904.5156
      +

      Now we will calculate a series of cost thresholds. These cost thresholds will be calculated by inflating the cost of the initial prioritization by a range of percentage values. Since these values are percentages – and not unitless values unlike those used in the blended approach – we can use domain knowledge to specify a suitable range of cost thresholds. For this tutorial, let’s assume that it would be impractical – per our domain knowledge – to expend more than four times the total cost of the initial prioritization to reduce spatial fragmentation.

      +
      # calculate cost threshold values
+threshold <- s1_cost + (s1_cost * seq(1e-5, 4, length.out = 9))
+threshold <- ceiling(threshold)
+
+# print cost thresholds
+print(threshold)
      +
      ## [1]  905 1357 1810 2262 2714 3166 3619 4071 4523
      +

      After generating the cost thresholds, we can use them to generate prioritizations. Specifically, we will generate prioritizations that aim to minimize total boundary length as much as possible – ignoring the total cost of the prioritizations – whilst ensuring that the total cost of the prioritization does not exceed a given cost threshold and the other considerations (e.g., locked in constraints). To achieve this, we create a new column in the tas_pu object that contains only zero values (called zeros) and use this new column to specify the cost data for the prioritizations. Although we normally recommend against cost data that contain zero values – because planning units with zero costs are often selected in prioritizations even if they are not needed – here we use zero cost values so that the prioritization will focus exclusively on spatial fragmentation. Additionally, when it comes to generating the prioritization, we will add linear constraints to ensure that the total cost of the prioritization does not exceed a given cost threshold (using the add_linear_constraints() function).

      +
      # add a column with zeros
+tas_pu$zeros <- 0
+
+# define a problem with zero cost values and boundary penalties
+## note that because all the costs are all zero, it doesn't actually
+## matter what penalty value is used (as long as the value is > 0)
+## and so we just use a value of 1
+p2 <- problem(tas_pu, tas_features, cost_column = "zeros") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 1, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# generate prioritizations based on each cost threshold
+## note that the prioritizations are solved to within 10% of optimality
+## (the default gap) because the gap is not specified
+hierarchical_results <- lapply(threshold, function(x) {
+  ## generate solution by adding a constraint based on the threshold and
+  ## using the "real" cost values (i.e., not zeros)
+  s <-
+    p2 %>%
+    add_linear_constraints(threshold = x, sense = "<=", data = "cost") %>%
+    solve()
+  ## return data frame with solution
+  s <- data.frame(s = s$solution_1)
+  names(s) <- paste0("threshold_", x)
+  s
+})
+
+# format results as a single spatial object
+hierarchical_results <- cbind(tas_pu, do.call(bind_cols, hierarchical_results))
+
+# plot maps of prioritizations
+plot(
+  x =
+    hierarchical_results %>%
+    dplyr::select(starts_with("threshold_")) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        hierarchical_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
      +

      +

      We now have a set of candidate prioritizations generated using the hierarchical approach. This approach can be much faster than the blended approach because it does not require generating a set of prioritizations to identify an upper limit for the penalty trade-off parameter. After generating a set of candidate prioritizations, we can then calculate performance metrics to compare the prioritizations.

      +
      +
      +
      +

      Calculating performance metrics

      +

      Here we will calculate performance metrics to compare the prioritizations. Since we aim to navigate trade-offs between the total cost of a prioritization and the overall level of spatial fragmentation associated with a prioritization (as measured by total boundary length), we will calculate metrics to assess these criteria. Although we generated two sets of candidate prioritizations in the previous section; for brevity, here we will consider the candidate prioritizations generated using the hierarchical approach. Please note that you could also apply the following procedures to candidate prioritizations generated using the blended approach.

      +
      # calculate metrics for prioritizations
+## note that we use p0 and not p1 so that cost calculations are based
+## on the cost values and not zeros
+hierarchical_metrics <- lapply(
+  grep("threshold_", names(hierarchical_results)), function(x) {
+    x <- hierarchical_results[, x]
+    data.frame(
+      total_cost = eval_cost_summary(p0, x)$cost,
+      total_boundary_length = eval_boundary_summary(p0, x)$boundary
+    )
+  }
+)
+hierarchical_metrics <- do.call(bind_rows, hierarchical_metrics)
+hierarchical_metrics$threshold <- threshold
+hierarchical_metrics <- as_tibble(hierarchical_metrics)
+
+# preview metrics
+print(hierarchical_metrics)
      +
      ## # A tibble: 9 × 3
+##   total_cost total_boundary_length threshold
+##        <dbl>                 <dbl>     <dbl>
+## 1       905.              2919388.       905
+## 2      1357.              2407733.      1357
+## 3      1807.              2205799.      1810
+## 4      2256.              2049117.      2262
+## 5      2712.              1945849.      2714
+## 6      3164.              1862288.      3166
+## 7      3608.              1809343.      3619
+## 8      4071.              1755416.      4071
+## 9      4521.              1737961.      4523
      +

      After calculating the metrics, let’s we can use them to help select a prioritization.

      +
      +
      +

      Selecting a prioritization

      +

      Now we need to decide on which candidate prioritization achieves the best trade-off. There are a range of qualitative and quantitative methods that are available to select a candidate prioritization (Ardron et al. 2010). Here we will consider three different methods. Since some of these methods a set of candidate prioritizations, we will use the candidate prioritizations using the hierarchical approach for these methods. To keep track of the prioritizations selected by different methods, let’s create a results_data table.

      +
      # create data for plotting
+result_data <-
+  hierarchical_metrics %>%
+  ## rename threshold column to value column
+  rename(value = "threshold") %>%
+  ## add column with column names that contain candidate prioritizations
+  mutate(name = grep(
+    "threshold_", names(hierarchical_results), value = TRUE, fixed = TRUE
+  )) %>%
+  ## add column with labels for plotting
+  mutate(label = paste("Threshold =", value)) %>%
+  ## add column to keep track prioritizations selected by different methods
+  mutate(method = "none")
+
+# print table
+print(result_data)
      +
      ## # A tibble: 9 × 6
+##   total_cost total_boundary_length value name           label            method
+##        <dbl>                 <dbl> <dbl> <chr>          <chr>            <chr> 
+## 1       905.              2919388.   905 threshold_905  Threshold = 905  none  
+## 2      1357.              2407733.  1357 threshold_1357 Threshold = 1357 none  
+## 3      1807.              2205799.  1810 threshold_1810 Threshold = 1810 none  
+## 4      2256.              2049117.  2262 threshold_2262 Threshold = 2262 none  
+## 5      2712.              1945849.  2714 threshold_2714 Threshold = 2714 none  
+## 6      3164.              1862288.  3166 threshold_3166 Threshold = 3166 none  
+## 7      3608.              1809343.  3619 threshold_3619 Threshold = 3619 none  
+## 8      4071.              1755416.  4071 threshold_4071 Threshold = 4071 none  
+## 9      4521.              1737961.  4523 threshold_4523 Threshold = 4523 none
      +

      Next, let’s examine some different methods for selecting prioritizations.

      +
      +

      Visual method

      +

      One qualitative method involves plotting the relationship between the different criteria, and using the plot to visually select a candidate prioritization. This visual method is often used to help calibrate trade-offs among prioritizations generated using the Marxan decision support tool (e.g., Hermoso et al. 2011; Stewart & Possingham 2005). So, let’s create a plot to select a prioritization.

      +
      # create plot to visualize trade-offs and show selected candidate prioritization
+result_plot <-
+  ggplot(
+    data = result_data,
+    aes(x = total_boundary_length, y = total_cost, label = label)
+  ) +
+  geom_line() +
+  geom_point(size = 3) +
+  geom_text(hjust = -0.15) +
+  scale_color_manual(
+    values = c("visual" = "blue", "not selected" ="black")
+  ) +
+  xlab("Total boundary length of prioritization") +
+  ylab("Total cost of prioritization") +
+  scale_x_continuous(expand = expansion(mult = c(0.05, 0.4))) +
+  theme(legend.title = element_blank())
+
+# render plot
+print(result_plot)
      +

      +

      We can see that there is a clear relationship between total cost and total boundary length. It would seem that in order to achieve a lower total boundary length – and thus lower spatial fragmentation – the prioritization must have a greater cost. Although we might expect the results to show a smoother curve – in other words, only Pareto dominant solutions – this result is expected because we generated candidate prioritizations using the default optimality gap of 10%. Typically, the visual method involves selecting a prioritization near the elbow of the plot. So, let’s select the prioritization generated using a threshold value of 1810. To keep of the prioritizations selected based on different methods, let’s create a method column in the result_data table.

      +
      # specify prioritization selected by visual method
+result_data$method[3] <- "visual"
      +

      Next, let’s consider a quantitative approach.

      +
      +
      +

      TOPSIS method

      +

      Multiple-criteria decision analysis is a disciple that uses analytical methods to evaluate trade-offs between multiple criteria (MCDA; reviewed in Greene et al. 2011). Although this discipline contains many different methods, here we will use the the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method (Hwang & Yoon 1981). This method requires (i) data describing the performance of each prioritization according the different criteria, (ii) weights to encode the relative importance of each criteria, and (iii) details on whether each criteria should ideally be minimized or maximized. Let’s run the analysis, assuming that we equal weighting for total cost and total boundary length.

      +
      # calculate TOPSIS scores
+topsis_results <- topsis(
+  decision =
+    hierarchical_metrics %>%
+    dplyr::select(total_cost, total_boundary_length) %>%
+    as.matrix(),
+  weights = c(1, 1),
+  impacts = c("-", "-")
+)
+
+# print results
+print(topsis_results)
      +
      ##   alt.row     score rank
+## 1       1 0.6861663    3
+## 2       2 0.7570982    1
+## 3       3 0.7218541    2
+## 4       4 0.6442282    4
+## 5       5 0.5530166    5
+## 6       6 0.4697259    6
+## 7       7 0.3999050    7
+## 8       8 0.3480699    8
+## 9       9 0.3138337    9
      +

      The candidate prioritization with the greatest TOPSIS score is considered to represent the best trade-off between total cost and total boundary length. So, based on this method, we would select the prioritization generated using a threshold value of 1357. Let’s update the result_data with this information.

      +
      # add column indicating prioritization selected by TOPSIS method
+result_data$method[which.max(topsis_results$score)] <- "TOPSIS"
      +

      Next, let’s consider another quantitative method.

      +
      +
      +

      Cohon et al. (1979) method

      +

      This method is based on an algorithm that was originally developed by Cohon et al. (Cohon et al. 1979), and was later adapted for use in systematic conservation planning (Fischer & Church 2005). Specifically, it involves generating two ideal prioritizations – with each prioritization representing the ideal prioritization for each criteria – and then using the performance metrics calculated for these prioritizations to automatically derive a trade-off penalty value (Ardron et al. 2010; Cohon et al. 1979). Thus, unlike the two other methods, this method does not require a set of candidate prioritizations. As such, this method can be used to find a prioritization that meets multiple criteria in a much shorter period of time than the other methods. To implement this method, we first need to generate the ideal prioritizations (note that we specify an gap of 0% to ensure optimality).

      +
      # generate ideal prioritization based on cost criteria
+## note that this is simply the same as the s1 prioritization we generated
+## for the hierarchical approach
+p3 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0)
+
+# solve problem
+s3 <- solve(p3)
+
+# generate ideal prioritization based on spatial fragmentation criteria
+## note that any non-zero penalty value would here,
+## so we just use a penalty  of 1
+p4 <- problem(tas_pu, tas_features, cost_column = "zeros") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 1, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0)
+
+# solve problem
+s4 <- solve(p4)
      +

      Next, let’s calculate the performance metrics for these prioritizations.

      +
      # generate problem formulation with costs and boundary penalties for
+# calculating performance metrics
+p5 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 1, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# calculate performance metrics for ideal cost prioritization
+s3_metrics <- tibble(
+  total_cost = eval_cost_summary(p5, s3[, "solution_1"])$cost,
+  total_boundary_length =
+    eval_boundary_summary(p5, s3[, "solution_1"])$boundary
+)
+
+# calculate performance metrics for ideal boundary length prioritization
+s4_metrics <- tibble(
+  total_cost = eval_cost_summary(p5, s4[, "solution_1"])$cost,
+  total_boundary_length =
+    eval_boundary_summary(p5, s4[, "solution_1"])$boundary
+)
      +

      After calculating these performance metrics, we can use them to automatically calculate a penalty value.

      +
      # calculate penalty value based on Cohon et al. 1979
+cohon_penalty <- abs(
+  (s3_metrics$total_cost - s4_metrics$total_cost) /
+  (s3_metrics$total_boundary_length - s4_metrics$total_boundary_length)
+)
+
+# round to 5 decimal places to avoid numerical issues during optimization
+cohon_penalty <- round(cohon_penalty, 5)
+
+# print penalty value
+print(cohon_penalty)
      +
      ## [1] 0.00945
      +

      Now that we have calculated a penalty value using this method, we can use it to generate a prioritization.

      +
      # generate prioritization using penalty value calculated using Cohon et al. 1979
+p6 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = cohon_penalty, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# solve problem
+s6 <- solve(p6)
      +

      Let’s update the results_data table with results about the prioritization.

      +
      # add new row with data for prioritization generated following Cohon et al. 1979
+result_data <- bind_rows(
+  result_data,
+  tibble(
+    total_cost = eval_cost_summary(p6, s6[, "solution_1"])$cost,
+    total_boundary_length =
+      eval_boundary_summary(p6, s6[, "solution_1"])$boundary,
+    value = cohon_penalty,
+    name = paste0("penalty_", cohon_penalty),
+    label = paste0("Penalty = ",  cohon_penalty),
+    method = "Cohon"
+  )
+)
      +

      Next, let’s compare the prioritizations selected by different methods.

      +
      +
      +

      Method comparison

      +

      Let’s create a plot to visualize the results from the different methods.

      +
      # create plot to visualize trade-offs and show selected candidate prioritization
+result_plot <-
+  ggplot(
+    data =
+      result_data %>%
+      mutate(vjust = if_else(method == "Cohon", -1, 0.5)),
+    aes(x = total_boundary_length, y = total_cost, label = label)
+  ) +
+  geom_line() +
+  geom_point(aes(color = method), size = 3) +
+  geom_text(aes(vjust = vjust, color = method), hjust = -0.1) +
+  scale_color_manual(
+    name = "Method",
+    values = c(
+      "visual" = "#984ea3",
+      "none" = "#000000",
+      "TOPSIS" = "#e41a1c",
+      "Cohon" = "#377eb8"
+    )
+  ) +
+  xlab("Total boundary length of prioritization") +
+  ylab("Total cost of prioritization") +
+  scale_x_continuous(expand = expansion(mult = c(0.05, 0.4)))
+
+# render plot
+print(result_plot)
      +

      +

      We can see that the different method selected different prioritizations. To further compare the results from the different methods, let’s create some maps showing the selected prioritizations.

      +
      # extract column names for creating the prioritizations
+visual_name <- result_data$name[[which(result_data$method == "visual")]]
+topsis_name <- result_data$name[[which(result_data$method == "TOPSIS")]]
+
+# create object with selected prioritizations
+solutions  <- bind_cols(
+  tas_pu,
+  hierarchical_results %>%
+    st_drop_geometry() %>%
+    dplyr::select(all_of(c(visual_name, topsis_name))) %>%
+    setNames(c("Visual", "TOPSIS")),
+  s6 %>%
+    st_drop_geometry() %>%
+    dplyr::select(solution_1) %>%
+    rename(Cohon = "solution_1")
+)
+
+# plot maps of selected prioritizations
+plot(
+  x =
+    solutions %>%
+    dplyr::select(Visual, TOPSIS, Cohon) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        hierarchical_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
      +

      +

      How do we determine which one is best? This is difficult to say. Ideally, additional information could be used to help select a prioritization, such as knowledge on available resources, species’ connectivity requirements, and impacts of neighboring land use. However, from a practical perspective, prioritizations generated for academic contexts might find the quantitative approaches more useful because they have greater transparency and reproducibility. Ultimately, all of these methods are designed to support decision making. This means that they are intended to assist the decision making process, not serve as a replacement.

      +
      +
      +
      +

      Conclusion

      +

      Hopefully, this vignette has provided a useful introduction for resolving trade-offs in prioritizations. Although we only explored trade-offs between total cost and spatial fragmentation in this tutorial, this analysis could be adapted to explore trade-offs between a wide range of different criteria. For instance, instead of considering total cost as the primary objective, future analyses could explore trade-offs with feature representation (using the add_min_shortfall_objective() function). Additionally, instead of spatial fragmentation, future analyses could explore trade-offs that directly relate to connectivity (using the add_connectivity_penalties() function) or specific variables of interest – such as ecosystem intactness or inverse human footprint index (Williams et al. 2020; Beyer et al. 2019) – to inform decision making (using the add_linear_penalties() function). Furthermore, after identifying the best penalty or threshold values to strike a balance between multiple criteria, you could generate a portfolio of prioritizations (e.g., using the add_gap_portfolio_function()) to find multiple options for achieving a similar balance. This might be helpful when you need to generate a set of prioritizations that have comparable performance – in terms of how well they achieve different criteria – but select different planning units.

      +
      +
      +

      References

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      +
      +
      + + + + + + + + + + + diff --git a/inst/doc/connectivity_tutorial.Rmd b/inst/doc/connectivity_tutorial.Rmd new file mode 100644 index 000000000..4deb120fc --- /dev/null +++ b/inst/doc/connectivity_tutorial.Rmd @@ -0,0 +1,487 @@ +--- +title: "Connectivity tutorial" +output: + rmarkdown::html_vignette: + toc: true + fig_caption: true + self_contained: yes +fontsize: 11pt +documentclass: article +bibliography: references.bib +csl: reference-style.csl +vignette: > + %\VignetteIndexEntry{Connectivity tutorial} + %\VignetteEngine{knitr::rmarkdown_notangle} +--- + +```{r, include = FALSE} +h <- 4.5 +w <- 4.5 +is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_", + "_R_CHECK_LICENSE_") %in% names(Sys.getenv())) +knitr::opts_knit$set(global.par = TRUE) +knitr::opts_chunk$set( + fig.align = "center", eval = !is_check, + fig.width = 4.0, fig.height = 3.5 +) +``` + +## Introduction + +Connectivity is a key consideration in systematic conservation planning [@r4; @r55]. This is because isolated and fragmented populations are often more vulnerable to extinction [@r60; @r61; @r62]. To promote connectivity in prioritizations, a range of different approaches are available [reviewed in @r56]. These approaches can solely on the spatial configuration of a prioritization to enhance structural connectivity [e.g, reducing the spatial fragmentation of a prioritization\; @r2]. They can also leverage data -- such as environmental, river flow, and telemetry data -- to generate prioritizations that promote functional connectivity [e.g., @r43; @r58; @r59]. + +The aim of this tutorial is to show how connectivity can be incorporated into prioritizations using the _prioritizr R_ package. Here we will explore various approaches for incorporating connectivity, and see how they alter the spatial configuration of prioritizations. As you will discover, many of these approaches involve setting threshold or penalty values to specify the relative importance of connectivity compared to other criteria (e.g., overall cost). For more information on calibrating these values, please see the [_Calibrating trade-offs tutorial_](calibrating_trade-offs-tutorial.html). + +## Data + +The dataset used in this tutorial was created for the Coastal Douglas-fir Conservation Partnership [CDFCP\; @r29]. Although the original dataset covers a much larger area; for brevity, here we focus only on Salt Spring Island, British Columbia. Briefly, Salt Spring Island supports a diverse and globally unique mix of dry forest and savanna habitats. Today, these habitats are critically threatened due to land conversion, invasive species, and altered disturbance regimes. For more information on the data, please refer to the [Marxan tool portal](https://arcese.forestry.ubc.ca/marxan-tool/) and the [tool tutorial](https://peter-arcese-lab.sites.olt.ubc.ca/files/2016/09/CDFCP_tutorial_2017_05.pdf). + +
      + +![Extent of Coastal Douglas-fir Conservation Partnership Tool area and location of Salt Spring Island](figures/map.jpg) + +
      + +Let's begin by loading the packages and data for this tutorial. Since this tutorial requires the _prioritizrdata R_ package, please ensure that it is installed. Specifically, two objects underpin the data for this tutorial. The `salt_pu` object specifies the planning unit data as a raster layer (i.e., `RasterLayer` object), and the `salt_features` object contains biodiversity data represented as a multi-band raster stack (i.e., a `RasterStack` object). + +```{r, message = FALSE} +# load packages +library(prioritizr) +library(prioritizrdata) +library(scales) + +# load planning unit data +data(salt_pu) + +# load ecological data +data(salt_features) +``` + +Now we will conduct some preliminary processing. Specifically, we will aggregate from the 100 m resolution to the 300 m resolution. This is to reduce the time needed to generate prioritizations in this tutorial. In practice, we generally recommend consider other criteria too -- such as the spatial scale that is relevant for decision making and the resolution of available datasets -- when deciding on an appropriate scale for planning units. + +```{r} +# aggregate data to coarser resolution +salt_pu <- aggregate(salt_pu, fact = 3) +salt_features <- aggregate(salt_features, fact = 3) +``` + +Next, let's have a look at the `salt_pu` object. Here each grid cell represents a planning unit, and the grid cell values denote acquisition costs [@r28]. To aid with visualization, we will log-transform the values when plotting them on a map. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r} +# print planning unit data +print(salt_pu) + +# plot map showing the planning units costs on a log-scale +plot(log(salt_pu), main = "Planning unit costs (log)", axes = FALSE) +``` + +Let's also look at the `salt_features` object. This object is a stack of raster layers, with each layer corresponding to a different variable that describes a particular aspect of biodiversity. The first four layers correspond to different ecological communities (i.e., _Old Forest_, _Savannah_, _Wetland_, and _Shrub_ communities), and their cell values indicate the probability of encountering a bird species associated a given community. The fifth layer describes the inverse probability of occurrence of human commensal species. In this tutorial, we will use the first four layers as biodiversity features, and the fifth layer to help parameterize connectivity (wherein higher values denote greater connectivity). So, let's extract the data and visualize them. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r} +# print original data +print(salt_features) + +# extract connectivity data +salt_con <- salt_features[[nlayers(salt_features)]] + +# print connectivity data +print(salt_con) + +# plot map showing the connectivity data +plot(salt_con, main = "Connectivity data", axes = FALSE) +``` + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1), oma = c(0, 0, 0, 0.5)) +``` + +```{r, fig.width = 7.0, fig.height = 7.0} +# extract ecological communities and use these as features +salt_features <- salt_features[[seq_len(4)]] + +# assign names to features +names(salt_features) <- c("Old_Forest", "Savannah", "Wetland", "Shrub") + +# print features +print(salt_features) + +# plot map showing the distribution of the features +plot(salt_features, main = names(salt_features), axes = FALSE) +``` + +## Baseline problem + +In this tutorial, we will explore a few different ways of incorporating connectivity into prioritizations. To enable comparisons among prioritizations based on different approaches, we will first create a baseline problem formulation that we will subsequently customize to incorporate connectivity. Specifically, we will formulate the baseline problem using the minimum set objective. We will use representation targets of 17% -- based on [Aichi Biodiversity Target 11](https://www.cbd.int/sp/targets/) -- to provide adequate coverage of each ecological community. Additionally, because land properties on Salt Spring Island can either be acquired in their entirety or not at all, we will use binary decision types. This means that planning units are either selected in the solution or not selected in the solution---planning units cannot be partially acquired. Given all these details, let's formulate the baseline problem. + +```{r} +# create problem +p0 <- problem(salt_pu, salt_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.17) %>% + add_binary_decisions() %>% + add_default_solver() + +# print problem +print(p0) +``` + +After formulating the baseline problem, we can solve it to generate a prioritization. + +```{r, results = "hide"} +# solve problem +s0 <- solve(p0) +``` + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r} +# print solution +print(s0) + +# plot solution +plot( + s0, main = "Baseline prioritization", axes = FALSE, + breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +Next, let's explore some options for incorporating connectivity. + +## Adding constraints + +Let's explore approaches for promoting connectivity in prioritizations by adding constraints to the baseline problem formulation. These approaches ensure that prioritizations exhibit certain characteristics [e.g., ensure prioritizations form a contiguous reserve\; @r57]. This means that, regardless of the optimality gap used to generate a prioritization, the prioritization will always exhibit these characteristics. + +### Neighbor constraints + +Neighbor constraints can be added to ensure that each selected planning unit has a certain number of neighbors surrounding it (using the `add_neighbor_constraints()` function) [based on @r16]. The `k` parameter can be used to specify the required number of neighbors for each selected planning unit. Let's generate a prioritization by specifying that each planning unit requires at least two neighbors. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with added neighbor constraints and solve it +s1 <- p0 %>% + add_neighbor_constraints(k = 2) %>% + solve() + +# plot solutions +plot( + stack(s0, s1), main = c("baseline", "neighbors constraints"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +### Contiguity constraints + +Contiguity constraints can be added to ensure that all planning units form a single contiguous reserve (using the `add_contiguity_constraints()` function) [similar to @r57]. These constraints are extremely complex. As such, they can only be applied to small conservation planning problems and the _Gurobi_ solver is required to solve them in a feasible period of time. Since it would take a long time to generate a near-optimal prioritization for this dataset with contiguity constraints, we will also tell the solver to simply return the first solution that it finds which meets the representation targets and the contiguity constraints. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with added contiguity constraints and solve it +s2 <- p0 %>% + add_contiguity_constraints() %>% + add_gurobi_solver(first_feasible = TRUE) %>% + solve() + +# plot solutions +plot( + stack(s0, s2), main = c("baseline", "contiguity constraints"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +There is also an even more complex version of the contiguity constraints that is available. These constraints -- termed feature contiguity constraints [similar to @r64] -- can be added to ensure that all of the selected planning units used to the reach representation targets within a prioritization form a contiguous network for each feature (using the `add_feature_contiguity_constraints()` function). In other words, they ensure that each feature can disperse through the prioritization to access a target threshold amount of habitat. However, these constraints are extraordinarily complex, only feasible for small problems, and require preprocessing routines to identify initial solutions. As such, we will not consider them in this tutorial. + +### Linear constraints + +Linear constraints can be used to specify that the prioritizations must meet an arbitrary set of criteria. As such, they can be used to ensure that prioritizations provide adequate coverage of planning units that have facilitate a high level of connectivity. Recall that the `salt_con` data are used to describe connectivity across the study area. Since higher values denote planning units with greater connectivity, we could use linear constraints to ensure that the total sum of connectivity values -- based on this dataset -- meets a particular threshold (e.g. cover at least 30% of the total amount). This would effectively be treating connectivity as an additional feature [similar to @r52]. + +```{r} +# compute threshold for constraints +## here we use a threshold of 30% of the total connectivity values +threshold <- cellStats(salt_con, "sum") * 0.3 + +# print threshold +print(threshold) +``` + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with added linear constraints and solve it +s3 <- p0 %>% + add_linear_constraints( + data = salt_con, threshold = threshold, sense = ">=" + ) %>% + solve() + +# plot solutions +plot( + stack(s0, s3), main = c("baseline", "linear constraints"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +Although using continuous values has the advantage that the prioritization process can explicitly account for differences in the relative amount of connectivity facilitated by different planning units, the disadvantage is that the prioritization could potentially focus on selecting lots of planning units with low connectivity values. To avoid this result, one strategy is to convert the continuous values into binary values using a threshold limit [similar to @r53]. By applying such a threshold limit, linear constraints can then be used to ensure that the prioritization selects a minimum amount of planning units with high connectivity values (i.e., those with connectivity values that are equal to or greater than the threshold limit). + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r} +# calculate threshold limit +## here we set a threshold limit based on the median +threshold_limit <- quantile(salt_con, probs = 0.5) + +# convert continuous values to binary values +salt_con_binary <- round(salt_con <= threshold_limit) + +# plot binary values +plot(salt_con_binary, main = "salt_con_binary", axes = FALSE) +``` + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with added linear constraints and solve it +## note that we use the original threshold computed before, +## to ensure the prioritization covers at least 30% of the total amount +## connectivity values +s4 <- p0 %>% + add_linear_constraints( + data = salt_con_binary, threshold = threshold, sense = ">=" + ) %>% + solve() + +# plot solutions +plot( + stack(s0, s4), main = c("baseline", "linear constraints (binary)"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +Another strategy is to clamp the continuous values below a threshold limit are assigned a value of zero [similar to @r54]. This strategy has the advantage that (i) the prioritization won't focus on selecting lots of planning units with low connectivity values to meet the constraint threshold, and (ii) the optimization process can use semi-continuous values to distinguish between places that can facilitate a moderate amount and a high amount of connectivity. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, results = "hide"} +# clamp continuous values using the threshold limit we computed before +salt_con_clamp <- salt_con +salt_con_clamp[Which(salt_con <= threshold_limit)] <- 0 + +# plot clamped values +plot(salt_con_clamp, main = "salt_con_clamp", axes = FALSE) +``` + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with added linear constraints and solve it +## note that we use the original threshold computed before, +## to ensure the prioritization covers at least 30% of the total amount +## connectivity values +s5 <- p0 %>% + add_linear_constraints( + data = salt_con_clamp, threshold = threshold, sense = ">=" + ) %>% + solve() + +# plot solutions +plot( + stack(s0, s5), main = c("baseline", "linear constraints (clamped)"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +If we were concerned that the prioritization did not facilitate a high enough level of connectivity, we could increase the `threshold` value or the `threshold_limit` value. For example, let's increase the `threshold_limit` value used to clamp the continuous connectivity values. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, results = "hide"} +# compute threshold limit +threshold_limit2 <- quantile(salt_con, probs = 0.7) + +# clamp continuous values using the threshold limit we computed before +salt_con_clamp2 <- salt_con +salt_con_clamp2[Which(salt_con <= threshold_limit2)] <- 0 + +# plot clamped values +plot(salt_con_clamp2, main = "salt_con_clamp", axes = FALSE) +``` + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with added linear constraints and solve it +## note that we use the original threshold computed before, +## to ensure the prioritization covers at least 30% of the total amount +## connectivity values +s6 <- p0 %>% + add_linear_constraints( + data = salt_con_clamp2, threshold = threshold, sense = ">=" + ) %>% + solve() + +# plot solutions +plot( + stack(s0, s6), main = c("baseline", "linear constraints (clamped 2)"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +Despite the advantages of clamping the connectivity values, we can see that the prioritization has a relatively high level of spatial fragmentation. In fact, all prioritizations generated using the linear constraints can potentially have this issue. This is because linear constraints do not explicitly account for the spatial arrangement of the planning units. As such, we recommend combining the linear constraints approach with another approach [e.g., the boundary penalties approach discussed below; @r53]. + +## Adding penalties + +Now let's explore approaches for promoting connectivity in prioritizations by adding penalties to the baseline problem formulation. These approaches involve penalizing solutions according to exhibit certain [e.g., penalize spatial fragmentation of prioritizations\; @r2]. Unlike constraint-based methods for incorporating connectivity -- if the optimality gap used to generate a prioritization is too high -- they may not necessarily produce prioritizations that exhibit desirable characteristics. + +### Boundary penalties + +Boundary penalties can be added to used to reduce the spatial fragmentation of prioritizations (using the `add_boundary_penalties()` function). Specifically, these penalties update the problem formulation to penalize solutions that have a high total amount of exposed boundary length [@r3]. Since boundary data often have large values which can degrade solver performance and result in excessive run times (see the [_Calibrating trade-offs tutorial_](calibrating_trade-offs-tutorial.html) for details), we will first precompute rescale the boundry data. + +```{r} +# precompute the boundary data +salt_boundary_data <- boundary_matrix(salt_pu) + +# rescale boundary data +salt_boundary_data@x <- rescale(salt_boundary_data@x, to = c(0.01, 100)) +``` + +Next, let's generate a prioritization using boundary penalties. To specify the relative importance reducing spatial fragmentation -- compared with the primary objective of a problem (e.g. minimizing cost) -- we need to a value for the `penalty` parameter is used. Setting a higher value for `penalty` indicates that it is more important to avoid highly fragmented solutions. Let's generate a prioritization with a `penalty` value of 0.001. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with added boundary penalties +s7 <- p0 %>% + add_boundary_penalties(penalty = 0.001, data = salt_boundary_data) %>% + solve() + +# plot solutions +plot( + stack(s0, s7), main = c("baseline", "boundary penalties (0.001)"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +We can see that the resulting prioritization is still relatively fragmented, so let's try generating another prioritization with a higher `penalty` value. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with increased boundary penalties +s8 <- p0 %>% + add_boundary_penalties(penalty = 10, data = salt_boundary_data) %>% + solve() + +# plot solutions +plot( + stack(s0, s8), main = c("baseline", "boundary penalties (10)"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +Although the prioritization is now less fragmented, it has also selected a greater number of planning units. Let's calculate the cost of the prioritizations to see how they vary in overall cost. + +```{r} +# calculate cost of baseline prioritization +eval_cost_summary(p0, s0) + +# calculate cost of prioritization with low boundary penalties (i.e., 0.001) +eval_cost_summary(p0, s7) + +# calculate cost of prioritization high low boundary penalties (i.e., 0.1) +eval_cost_summary(p0, s8) +``` + +We can see that the cost of the prioritizations increase with when we use higher `penalty` values. This is because there is a trade-off between the cost of a prioritization and the level of spatial fragmentation. Although it can be challenging to find the best balance, there are qualitative and quantitative methods available to help navigate such trade-offs. Please see the [_Calibrating trade-offs tutorial_](calibrating_trade-offs-tutorial.html) for a details on these methods. + +### Connectivity penalties + +Connectivity penalties can be used to promote connectivity in prioritizations (using the `add_connectivity_penalties()` function). These penalties use connectivity scores to parametrize the strength of connectivity between pairs of planning units [@r38]. Thus higher scores denote a greater level of connectivity between different planning units. For example, previous studies have parametrized connectivity scores using habitat quality, environmental, and river flow data [e.g. @r59; @r63; @r43]. Although there are many approaches to calculate connectivity scores, one approach involves using conductance data -- data that describe how much each planning unit facilitates movement (opposite of landscape resistance data) -- and calculating scores for each pair of planning units by averaging their conductance values (implemented using the `connectivity_matrix()` function). + +Let's compute connectivity scores by treating the `salt_con` object as conductance data. This means that we assume that neighboring planning units with higher values in the `salt_con` object are capable of facilitating a greater amount of connectivity. **Note that the data used to compute connectivity scores must conform to the same spatial properties as the planning unit data (e.g., resolution, spatial extent, coordinate reference system).** Also, although we are using raster data here, these scores can also be computed for vector data too (e.g., `sf::st_sf()` objects). Similar to the boundary data, we will also rescale the connectivity scores to avoid numerical issues during optimization. + +```{r} +# compute connectivity scores +salt_con_scores <- connectivity_matrix(salt_pu, salt_con) + +# rescale scores +salt_con_scores@x <- rescale(salt_con_scores@x, to = c(0.01, 100)) +``` + +After computing the connectivity scores, we can use them to generate prioritizations using connectivity penalties. Similar to the boundary penalties, we use the `penalty` parameter to specify the relative importance of promoting connectivity relative to the primary objective of a problem (i.e., minimizing overall cost). Let's generate a prioritization with a `penalty` value of 0.001. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with added connectivity penalties +s9 <- p0 %>% + add_connectivity_penalties(penalty = 0.001, data = salt_con_scores) %>% + solve() + +# plot solutions +plot( + stack(s0, s9), main = c("baseline", "connectivity penalties (0.001)"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +Now let's try generating another prioritization with a higher `penalty` value. + +```{r, include = FALSE} +par(mar = c(1.1, 4.1, 4.1, 2.1)) +``` + +```{r, fig.width = 7.0, results = "hide"} +# create problem with increased connectivity penalties +s10 <- p0 %>% + add_connectivity_penalties(penalty = 0.002, data = salt_con_scores) %>% + solve() + +# plot solutions +plot( + stack(s0, s10), main = c("baseline", "connectivity penalties (0.002)"), + axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen") +) +``` + +We can see that increasing the `penalty` parameter causes the prioritizations to select planning units in regions with greater connectivity values (i.e., per the `salt_con` object). As discussed with the boundary penalties, increasing the `penalty` value tells the optimization process to focus more on promoting connectivity---meaning that it won't focus as much on the primary objective (i.e., because the primary objective is to minimize overall costs). For details on calibrating these trade-offs please see the [_Calibrating trade-offs tutorial_](calibrating_trade-offs-tutorial.html). **Note that you will need to the use `eval_connectivity_summary()` function -- instead of the `eval_boundary_summary()` function -- when adapting the tutorial code for connectivity penalties.** + +## Conclusion + +Hopefully, this tutorial has provided a helpful introduction for incorporating connectivity into prioritizations. Broadly speaking, we recommend using the boundary penalties or the connectivity penalties to ensure that prioritizations explicitly account for the spatial configuration of selected planning units. Additionally, though not fully explored here, the connectivity penalties are a very flexible approach for promoting connectivity. For instance, in addition to parameterizing pair-wise connectivity scores for neighboring planning units, they can also be used to parametrize pair-wise connectivity scores between more distant planning units. Thus connectivity penalties could be used to parametrize connectivity across both small scales and large spatial scales (e.g., using a scaling procedure wherein connectivity scores between pairs of planning units decline with the distance between them). + +## References diff --git a/inst/doc/connectivity_tutorial.html b/inst/doc/connectivity_tutorial.html new file mode 100644 index 000000000..411b7e4ab --- /dev/null +++ b/inst/doc/connectivity_tutorial.html @@ -0,0 +1,642 @@ + + + + + + + + + + + + + + +Connectivity tutorial + + + + + + + + + + + + + + + + + + + + + + + + + + +

      Connectivity tutorial

      + + + + +
      +

      Introduction

      +

      Connectivity is a key consideration in systematic conservation planning (Margules & Pressey 2000; Briers 2002). This is because isolated and fragmented populations are often more vulnerable to extinction (Dixo et al. 2009; Olds et al. 2012; Hodgson et al. 2009). To promote connectivity in prioritizations, a range of different approaches are available (reviewed in Balbar & Metaxas 2019). These approaches can solely on the spatial configuration of a prioritization to enhance structural connectivity (e.g, reducing the spatial fragmentation of a prioritization; Watts et al. 2009). They can also leverage data – such as environmental, river flow, and telemetry data – to generate prioritizations that promote functional connectivity (e.g., Hermoso et al. 2012; Dwyer et al. 2019; Leonard et al. 2017).

      +

      The aim of this tutorial is to show how connectivity can be incorporated into prioritizations using the prioritizr R package. Here we will explore various approaches for incorporating connectivity, and see how they alter the spatial configuration of prioritizations. As you will discover, many of these approaches involve setting threshold or penalty values to specify the relative importance of connectivity compared to other criteria (e.g., overall cost). For more information on calibrating these values, please see the Calibrating trade-offs tutorial.

      +
      +
      +

      Data

      +

      The dataset used in this tutorial was created for the Coastal Douglas-fir Conservation Partnership (CDFCP; Morrell et al. 2017). Although the original dataset covers a much larger area; for brevity, here we focus only on Salt Spring Island, British Columbia. Briefly, Salt Spring Island supports a diverse and globally unique mix of dry forest and savanna habitats. Today, these habitats are critically threatened due to land conversion, invasive species, and altered disturbance regimes. For more information on the data, please refer to the Marxan tool portal and the tool tutorial.

      +
      +
      + +

      Extent of Coastal Douglas-fir Conservation Partnership Tool area and location of Salt Spring Island

      +
      +
      +

      Let’s begin by loading the packages and data for this tutorial. Since this tutorial requires the prioritizrdata R package, please ensure that it is installed. Specifically, two objects underpin the data for this tutorial. The salt_pu object specifies the planning unit data as a raster layer (i.e., RasterLayer object), and the salt_features object contains biodiversity data represented as a multi-band raster stack (i.e., a RasterStack object).

      +
      # load packages
+library(prioritizr)
+library(prioritizrdata)
+library(scales)
+
+# load planning unit data
+data(salt_pu)
+
+# load ecological data
+data(salt_features)
      +

      Now we will conduct some preliminary processing. Specifically, we will aggregate from the 100 m resolution to the 300 m resolution. This is to reduce the time needed to generate prioritizations in this tutorial. In practice, we generally recommend consider other criteria too – such as the spatial scale that is relevant for decision making and the resolution of available datasets – when deciding on an appropriate scale for planning units.

      +
      # aggregate data to coarser resolution
+salt_pu <- aggregate(salt_pu, fact = 3)
+salt_features <- aggregate(salt_features, fact = 3)
      +

      Next, let’s have a look at the salt_pu object. Here each grid cell represents a planning unit, and the grid cell values denote acquisition costs (BC Assessment 2015). To aid with visualization, we will log-transform the values when plotting them on a map.

      +
      # print planning unit data
+print(salt_pu)
      +
      ## class      : RasterLayer 
+## dimensions : 94, 67, 6298  (nrow, ncol, ncell)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : salt_pu 
+## values     : 0.02552, 8290.383  (min, max)
      +
      # plot map showing the planning units costs on a log-scale
+plot(log(salt_pu), main = "Planning unit costs (log)", axes = FALSE)
      +

      +

      Let’s also look at the salt_features object. This object is a stack of raster layers, with each layer corresponding to a different variable that describes a particular aspect of biodiversity. The first four layers correspond to different ecological communities (i.e., Old Forest, Savannah, Wetland, and Shrub communities), and their cell values indicate the probability of encountering a bird species associated a given community. The fifth layer describes the inverse probability of occurrence of human commensal species. In this tutorial, we will use the first four layers as biodiversity features, and the fifth layer to help parameterize connectivity (wherein higher values denote greater connectivity). So, let’s extract the data and visualize them.

      +
      # print original data
+print(salt_features)
      +
      ## class      : RasterBrick 
+## dimensions : 94, 67, 6298, 5  (nrow, ncol, ncell, nlayers)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : salt_features.1, salt_features.2, salt_features.3, salt_features.4, salt_features.5 
+## min values :       0.3596232,       0.3340984,       0.1420134,       0.4415211,       0.4060181 
+## max values :       0.8951858,       0.6440319,       0.5926431,       0.8065580,       0.8969550
      +
      # extract connectivity data
+salt_con <- salt_features[[nlayers(salt_features)]]
+
+# print connectivity data
+print(salt_con)
      +
      ## class      : RasterLayer 
+## dimensions : 94, 67, 6298  (nrow, ncol, ncell)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : salt_features.5 
+## values     : 0.4060181, 0.896955  (min, max)
      +
      # plot map showing the connectivity data
+plot(salt_con, main = "Connectivity data", axes = FALSE)
      +

      +
      # extract ecological communities and use these as features
+salt_features <- salt_features[[seq_len(4)]]
+
+# assign names to features
+names(salt_features) <- c("Old_Forest", "Savannah", "Wetland", "Shrub")
+
+# print features
+print(salt_features)
      +
      ## class      : RasterBrick 
+## dimensions : 94, 67, 6298, 4  (nrow, ncol, ncell, nlayers)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : Old_Forest,  Savannah,   Wetland,     Shrub 
+## min values :  0.3596232, 0.3340984, 0.1420134, 0.4415211 
+## max values :  0.8951858, 0.6440319, 0.5926431, 0.8065580
      +
      # plot map showing the distribution of the features
+plot(salt_features, main = names(salt_features), axes = FALSE)
      +

      +
      +
      +

      Baseline problem

      +

      In this tutorial, we will explore a few different ways of incorporating connectivity into prioritizations. To enable comparisons among prioritizations based on different approaches, we will first create a baseline problem formulation that we will subsequently customize to incorporate connectivity. Specifically, we will formulate the baseline problem using the minimum set objective. We will use representation targets of 17% – based on Aichi Biodiversity Target 11 – to provide adequate coverage of each ecological community. Additionally, because land properties on Salt Spring Island can either be acquired in their entirety or not at all, we will use binary decision types. This means that planning units are either selected in the solution or not selected in the solution—planning units cannot be partially acquired. Given all these details, let’s formulate the baseline problem.

      +
      # create problem
+p0 <- problem(salt_pu, salt_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_binary_decisions() %>%
+      add_default_solver()
+
+# print problem
+print(p0)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (2389 units)
+##   cost:           min: 0.02552, max: 8290.38315
+##   features:       Old_Forest, Savannah, Wetland, Shrub (4 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (1)]
      +

      After formulating the baseline problem, we can solve it to generate a prioritization.

      +
      # solve problem
+s0 <- solve(p0)
      +
      # print solution
+print(s0)
      +
      ## class      : RasterLayer 
+## dimensions : 94, 67, 6298  (nrow, ncol, ncell)
+## resolution : 300, 300  (x, y)
+## extent     : 454589.9, 474689.9, 5394414, 5422614  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## source     : memory
+## names      : salt_pu 
+## values     : 0, 1  (min, max)
      +
      # plot solution
+plot(
+  s0, main = "Baseline prioritization", axes = FALSE,
+  breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      Next, let’s explore some options for incorporating connectivity.

      +
      +
      +

      Adding constraints

      +

      Let’s explore approaches for promoting connectivity in prioritizations by adding constraints to the baseline problem formulation. These approaches ensure that prioritizations exhibit certain characteristics (e.g., ensure prioritizations form a contiguous reserve; Önal & Briers 2006). This means that, regardless of the optimality gap used to generate a prioritization, the prioritization will always exhibit these characteristics.

      +
      +

      Neighbor constraints

      +

      Neighbor constraints can be added to ensure that each selected planning unit has a certain number of neighbors surrounding it (using the add_neighbor_constraints() function) (based on Billionnet 2013). The k parameter can be used to specify the required number of neighbors for each selected planning unit. Let’s generate a prioritization by specifying that each planning unit requires at least two neighbors.

      +
      # create problem with added neighbor constraints and solve it
+s1 <- p0 %>%
+      add_neighbor_constraints(k = 2) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s1), main = c("baseline", "neighbors constraints"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +
      +
      +

      Contiguity constraints

      +

      Contiguity constraints can be added to ensure that all planning units form a single contiguous reserve (using the add_contiguity_constraints() function) (similar to Önal & Briers 2006). These constraints are extremely complex. As such, they can only be applied to small conservation planning problems and the Gurobi solver is required to solve them in a feasible period of time. Since it would take a long time to generate a near-optimal prioritization for this dataset with contiguity constraints, we will also tell the solver to simply return the first solution that it finds which meets the representation targets and the contiguity constraints.

      +
      # create problem with added contiguity constraints and solve it
+s2 <- p0 %>%
+      add_contiguity_constraints() %>%
+      add_gurobi_solver(first_feasible = TRUE) %>%
+      solve()
      +
      ## Warning in res(x, ...): overwriting previously defined solver
      +
      # plot solutions
+plot(
+  stack(s0, s2), main = c("baseline", "contiguity constraints"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      There is also an even more complex version of the contiguity constraints that is available. These constraints – termed feature contiguity constraints (similar to Cerdeira et al. 2010) – can be added to ensure that all of the selected planning units used to the reach representation targets within a prioritization form a contiguous network for each feature (using the add_feature_contiguity_constraints() function). In other words, they ensure that each feature can disperse through the prioritization to access a target threshold amount of habitat. However, these constraints are extraordinarily complex, only feasible for small problems, and require preprocessing routines to identify initial solutions. As such, we will not consider them in this tutorial.

      +
      +
      +

      Linear constraints

      +

      Linear constraints can be used to specify that the prioritizations must meet an arbitrary set of criteria. As such, they can be used to ensure that prioritizations provide adequate coverage of planning units that have facilitate a high level of connectivity. Recall that the salt_con data are used to describe connectivity across the study area. Since higher values denote planning units with greater connectivity, we could use linear constraints to ensure that the total sum of connectivity values – based on this dataset – meets a particular threshold (e.g. cover at least 30% of the total amount). This would effectively be treating connectivity as an additional feature (similar to Daigle et al. 2020).

      +
      # compute threshold for constraints
+## here we use a threshold of 30% of the total connectivity values
+threshold <- cellStats(salt_con, "sum") * 0.3
+
+# print threshold
+print(threshold)
      +
      ## [1] 520.7628
      +
      # create problem with added linear constraints and solve it
+s3 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s3), main = c("baseline", "linear constraints"),
+   axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      Although using continuous values has the advantage that the prioritization process can explicitly account for differences in the relative amount of connectivity facilitated by different planning units, the disadvantage is that the prioritization could potentially focus on selecting lots of planning units with low connectivity values. To avoid this result, one strategy is to convert the continuous values into binary values using a threshold limit (similar to Carroll 2021). By applying such a threshold limit, linear constraints can then be used to ensure that the prioritization selects a minimum amount of planning units with high connectivity values (i.e., those with connectivity values that are equal to or greater than the threshold limit).

      +
      # calculate threshold limit
+## here we set a threshold limit based on the median
+threshold_limit <- quantile(salt_con, probs = 0.5)
+
+# convert continuous values to binary values
+salt_con_binary <- round(salt_con <= threshold_limit)
+
+# plot binary values
+plot(salt_con_binary, main = "salt_con_binary", axes = FALSE)
      +

      +
      # create problem with added linear constraints and solve it
+## note that we use the original threshold computed before,
+## to ensure the prioritization covers at least 30% of the total amount
+## connectivity values
+s4 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con_binary, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s4), main = c("baseline", "linear constraints (binary)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      Another strategy is to clamp the continuous values below a threshold limit are assigned a value of zero (similar to Hanson et al. 2020). This strategy has the advantage that (i) the prioritization won’t focus on selecting lots of planning units with low connectivity values to meet the constraint threshold, and (ii) the optimization process can use semi-continuous values to distinguish between places that can facilitate a moderate amount and a high amount of connectivity.

      +
      # clamp continuous values using the threshold limit we computed before
+salt_con_clamp <- salt_con
+salt_con_clamp[Which(salt_con <= threshold_limit)] <- 0
+
+# plot clamped values
+plot(salt_con_clamp, main = "salt_con_clamp", axes = FALSE)
      +

      +
      # create problem with added linear constraints and solve it
+## note that we use the original threshold computed before,
+## to ensure the prioritization covers at least 30% of the total amount
+## connectivity values
+s5 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con_clamp, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s5), main = c("baseline", "linear constraints (clamped)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      If we were concerned that the prioritization did not facilitate a high enough level of connectivity, we could increase the threshold value or the threshold_limit value. For example, let’s increase the threshold_limit value used to clamp the continuous connectivity values.

      +
      # compute threshold limit
+threshold_limit2 <- quantile(salt_con, probs = 0.7)
+
+# clamp continuous values using the threshold limit we computed before
+salt_con_clamp2 <- salt_con
+salt_con_clamp2[Which(salt_con <= threshold_limit2)] <- 0
+
+# plot clamped values
+plot(salt_con_clamp2, main = "salt_con_clamp", axes = FALSE)
      +

      +
      # create problem with added linear constraints and solve it
+## note that we use the original threshold computed before,
+## to ensure the prioritization covers at least 30% of the total amount
+## connectivity values
+s6 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con_clamp2, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s6), main = c("baseline", "linear constraints (clamped 2)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      Despite the advantages of clamping the connectivity values, we can see that the prioritization has a relatively high level of spatial fragmentation. In fact, all prioritizations generated using the linear constraints can potentially have this issue. This is because linear constraints do not explicitly account for the spatial arrangement of the planning units. As such, we recommend combining the linear constraints approach with another approach [e.g., the boundary penalties approach discussed below; Carroll (2021)].

      +
      +
      +
      +

      Adding penalties

      +

      Now let’s explore approaches for promoting connectivity in prioritizations by adding penalties to the baseline problem formulation. These approaches involve penalizing solutions according to exhibit certain (e.g., penalize spatial fragmentation of prioritizations; Watts et al. 2009). Unlike constraint-based methods for incorporating connectivity – if the optimality gap used to generate a prioritization is too high – they may not necessarily produce prioritizations that exhibit desirable characteristics.

      +
      +

      Boundary penalties

      +

      Boundary penalties can be added to used to reduce the spatial fragmentation of prioritizations (using the add_boundary_penalties() function). Specifically, these penalties update the problem formulation to penalize solutions that have a high total amount of exposed boundary length (Ball et al. 2009). Since boundary data often have large values which can degrade solver performance and result in excessive run times (see the Calibrating trade-offs tutorial for details), we will first precompute rescale the boundry data.

      +
      # precompute the boundary data
+salt_boundary_data <- boundary_matrix(salt_pu)
+
+# rescale boundary data
+salt_boundary_data@x <- rescale(salt_boundary_data@x, to = c(0.01, 100))
      +

      Next, let’s generate a prioritization using boundary penalties. To specify the relative importance reducing spatial fragmentation – compared with the primary objective of a problem (e.g. minimizing cost) – we need to a value for the penalty parameter is used. Setting a higher value for penalty indicates that it is more important to avoid highly fragmented solutions. Let’s generate a prioritization with a penalty value of 0.001.

      +
      # create problem with added boundary penalties
+s7 <- p0 %>%
+      add_boundary_penalties(penalty = 0.001, data = salt_boundary_data) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s7), main = c("baseline", "boundary penalties (0.001)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      We can see that the resulting prioritization is still relatively fragmented, so let’s try generating another prioritization with a higher penalty value.

      +
      # create problem with increased boundary penalties
+s8 <- p0 %>%
+      add_boundary_penalties(penalty = 10, data = salt_boundary_data) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s8), main = c("baseline", "boundary penalties (10)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      Although the prioritization is now less fragmented, it has also selected a greater number of planning units. Let’s calculate the cost of the prioritizations to see how they vary in overall cost.

      +
      # calculate cost of baseline prioritization
+eval_cost_summary(p0, s0)
      +
      ## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall  46.0
      +
      # calculate cost of prioritization with low boundary penalties (i.e., 0.001)
+eval_cost_summary(p0, s7)
      +
      ## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall  46.0
      +
      # calculate cost of prioritization high low boundary penalties (i.e., 0.1)
+eval_cost_summary(p0, s8)
      +
      ## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall  52.3
      +

      We can see that the cost of the prioritizations increase with when we use higher penalty values. This is because there is a trade-off between the cost of a prioritization and the level of spatial fragmentation. Although it can be challenging to find the best balance, there are qualitative and quantitative methods available to help navigate such trade-offs. Please see the Calibrating trade-offs tutorial for a details on these methods.

      +
      +
      +

      Connectivity penalties

      +

      Connectivity penalties can be used to promote connectivity in prioritizations (using the add_connectivity_penalties() function). These penalties use connectivity scores to parametrize the strength of connectivity between pairs of planning units (Beger et al. 2010). Thus higher scores denote a greater level of connectivity between different planning units. For example, previous studies have parametrized connectivity scores using habitat quality, environmental, and river flow data (e.g. Leonard et al. 2017; Alagador et al. 2012; Hermoso et al. 2012). Although there are many approaches to calculate connectivity scores, one approach involves using conductance data – data that describe how much each planning unit facilitates movement (opposite of landscape resistance data) – and calculating scores for each pair of planning units by averaging their conductance values (implemented using the connectivity_matrix() function).

      +

      Let’s compute connectivity scores by treating the salt_con object as conductance data. This means that we assume that neighboring planning units with higher values in the salt_con object are capable of facilitating a greater amount of connectivity. Note that the data used to compute connectivity scores must conform to the same spatial properties as the planning unit data (e.g., resolution, spatial extent, coordinate reference system). Also, although we are using raster data here, these scores can also be computed for vector data too (e.g., sf::st_sf() objects). Similar to the boundary data, we will also rescale the connectivity scores to avoid numerical issues during optimization.

      +
      # compute connectivity scores
+salt_con_scores <- connectivity_matrix(salt_pu, salt_con)
+
+# rescale scores
+salt_con_scores@x <- rescale(salt_con_scores@x, to = c(0.01, 100))
      +

      After computing the connectivity scores, we can use them to generate prioritizations using connectivity penalties. Similar to the boundary penalties, we use the penalty parameter to specify the relative importance of promoting connectivity relative to the primary objective of a problem (i.e., minimizing overall cost). Let’s generate a prioritization with a penalty value of 0.001.

      +
      # create problem with added connectivity penalties
+s9 <- p0 %>%
+      add_connectivity_penalties(penalty = 0.001, data = salt_con_scores) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s9), main = c("baseline", "connectivity penalties (0.001)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      Now let’s try generating another prioritization with a higher penalty value.

      +
      # create problem with increased connectivity penalties
+s10 <- p0 %>%
+      add_connectivity_penalties(penalty = 0.002, data = salt_con_scores) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s10), main = c("baseline", "connectivity penalties (0.002)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
      +

      +

      We can see that increasing the penalty parameter causes the prioritizations to select planning units in regions with greater connectivity values (i.e., per the salt_con object). As discussed with the boundary penalties, increasing the penalty value tells the optimization process to focus more on promoting connectivity—meaning that it won’t focus as much on the primary objective (i.e., because the primary objective is to minimize overall costs). For details on calibrating these trade-offs please see the Calibrating trade-offs tutorial. Note that you will need to the use eval_connectivity_summary() function – instead of the eval_boundary_summary() function – when adapting the tutorial code for connectivity penalties.

      +
      +
      +
      +

      Conclusion

      +

      Hopefully, this tutorial has provided a helpful introduction for incorporating connectivity into prioritizations. Broadly speaking, we recommend using the boundary penalties or the connectivity penalties to ensure that prioritizations explicitly account for the spatial configuration of selected planning units. Additionally, though not fully explored here, the connectivity penalties are a very flexible approach for promoting connectivity. For instance, in addition to parameterizing pair-wise connectivity scores for neighboring planning units, they can also be used to parametrize pair-wise connectivity scores between more distant planning units. Thus connectivity penalties could be used to parametrize connectivity across both small scales and large spatial scales (e.g., using a scaling procedure wherein connectivity scores between pairs of planning units decline with the distance between them).

      +
      +
      +

      References

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      +
      +
      + + + + + + + + + + + diff --git a/vignettes/gurobi_installation.Rmd b/inst/doc/gurobi_installation_guide.Rmd similarity index 88% rename from vignettes/gurobi_installation.Rmd rename to inst/doc/gurobi_installation_guide.Rmd index 016dd7dfd..e36fe4832 100644 --- a/vignettes/gurobi_installation.Rmd +++ b/inst/doc/gurobi_installation_guide.Rmd @@ -1,5 +1,5 @@ --- -title: "Gurobi Installation Guide" +title: "Gurobi installation guide" author: "Richard Schuster" date: "`r Sys.Date()`" output: @@ -10,7 +10,7 @@ output: fontsize: 11pt documentclass: article vignette: > - %\VignetteIndexEntry{Gurobi Installation Guide} + %\VignetteIndexEntry{Gurobi installation guide} %\VignetteEngine{knitr::rmarkdown_notangle} --- @@ -28,7 +28,7 @@ devtools::load_all() ## Introduction -_Gurobi_ is the most powerful and fastest solver that the _prioritizr R_ package can use to solve conservation planning problems. This vignette will walk you through the process of setting up _Gurobi_ on your computer so that you can use it to solve conservation planning problems. If you encounter any problems while following the instructions below, check out the [official _Gurobi_ documentation](https://www.gurobi.com/documentation/). +_Gurobi_ is the most powerful and fastest solver that the _prioritizr R_ package can use to solve conservation planning problems (see the [_Solver benchmarks_](solver_benchmarks.html) vignette for further details). This guide will walk you through the process of setting up _Gurobi_ on your computer so that it can be used to solve conservation planning problems. If you encounter any problems while following the instructions below, please refer to the [official _Gurobi_ documentation](https://www.gurobi.com/documentation/). ## Obtaining a license @@ -48,7 +48,7 @@ After obtaining a license, you will need to download the _Gurobi_ installer to y ## Software installation -The process for installing the _Gurobi_ software depends on the operating system on your computer. Fortunately, _Gurobi_ provide platform-specific ["Quick Start Guides"](https://www.gurobi.com/documentation/) for [Windows](https://www.gurobi.com/documentation/9.0/quickstart_windows/software_installation_guid.html#section:Installation), [MacOS](https://www.gurobi.com/documentation/9.0/quickstart_mac/software_installation_guid.html), and [Linux](https://www.gurobi.com/documentation/9.0/quickstart_linux/software_installation_guid.html) systems that should help with this. Briefly, on Windows systems, you just need to double-click on the _Gurobi_ installer, follow the prompts, and the installer will automatically handle everything for you. On Linux and MacOS systems, you will need to manually extract the downloaded file's contents to a folder, move the extracted contents to a suitable location (typically _/opt/gurobi_), and update your system's variables so that it knows where to find _Gurobi_ (i.e. the `PATH` variable). +The process for installing the _Gurobi_ software depends on the operating system on your computer. Fortunately, _Gurobi_ provide platform-specific ["Quick Start Guides"](https://www.gurobi.com/documentation/) for [Windows](https://www.gurobi.com/documentation/9.0/quickstart_windows/software_installation_guid.html#section:Installation), [MacOS](https://www.gurobi.com/documentation/9.0/quickstart_mac/software_installation_guid.html), and [Linux](https://www.gurobi.com/documentation/9.0/quickstart_linux/software_installation_guid.html) systems that should help with this. Briefly, on Windows systems, you just need to double-click on the _Gurobi_ installer, follow the prompts, and the installer will automatically handle everything for you. On Linux and MacOS systems, you will need to manually extract the downloaded file's contents to a folder, move the extracted contents to a suitable location (typically _/opt/gurobi_), and update your system's variables so that it knows where to find _Gurobi_ (i.e., the `PATH` variable). Additionally, if you are using [_RStudio_](https://www.rstudio.com/products/rstudio/) on a Linux system, you might need to add the following text to a Rstudio configuration file (located at `/etc/rstudio/rserver.conf`). @@ -64,7 +64,7 @@ Now we will activate the _Gurobi_ software using the license you obtained earlie
      ![](figures/cmd-windows-success.png){ width=75% }

      -Next, we will now check that the license has been successfully activated. To achieve this, we will try running _Gurobi_ directly from the command line. Note that the following commands assume you are using version 8.0.0 of _Gurobi_, and so you will need to modify the command if you are using a more recent version (e.g. if using version 9.1.2, then use `gurobi912` instead of `gurobi800` below). +Next, we will now check that the license has been successfully activated. To achieve this, we will try running _Gurobi_ directly from the command line. Note that the following commands assume you are using version 8.0.0 of _Gurobi_, and so you will need to modify the command if you are using a more recent version (e.g., if using version 9.1.2, then use `gurobi912` instead of `gurobi800` below). On Windows systems, users can type in the following system command to check their license activation. @@ -86,7 +86,7 @@ After activating the license, you now need to install the _gurobi R_ package. Th ## _R_ package installation -Now we will install the _gurobi R_ package. This package is not available on the Comprehensive R Archive Network and is instead distributed with the _Gurobi_ software suite. Specifically, the _gurobi_ _R_ package should be located within the folder where you installed the _Gurobi_ software suite. We will install the _gurobi_ _R_ package by running the following _R_ code within your _R_ session. Note that the following code assumes that you are using version 8.0.0 of _Gurobi_, and so you will need to modify the code if you are using a more recent version (e.g. if using version 9.1.2, then use `gurobi912` instead of `gurobi800` below). +Now we will install the _gurobi R_ package. This package is not available on the Comprehensive R Archive Network and is instead distributed with the _Gurobi_ software suite. Specifically, the _gurobi_ _R_ package should be located within the folder where you installed the _Gurobi_ software suite. We will install the _gurobi_ _R_ package by running the following _R_ code within your _R_ session. Note that the following code assumes that you are using version 8.0.0 of _Gurobi_, and so you will need to modify the code if you are using a more recent version (e.g., if using version 9.1.2, then use `gurobi912` instead of `gurobi800` below). Assuming you installed _Gurobi_ in the default location, Windows users can install _gurobi_ _R_ package using the following code. @@ -102,7 +102,7 @@ install.packages(file.path(Sys.getenv("GUROBI_HOME"), repos = NULL) ``` -Next, you will need to install the _slam R_ package because the _gurobi_ _R_ package needs this package to work. Users of all platforms (i.e. Windows, Linux, and MacOS) can install the package using the following _R_ code. +Next, you will need to install the _slam R_ package because the _gurobi_ _R_ package needs this package to work. Users of all platforms (i.e., Windows, Linux, and MacOS) can install the package using the following _R_ code. ```{r, eval = FALSE} install.packages("slam", repos = "https://cloud.r-project.org") @@ -136,7 +136,7 @@ If you see the outputs for `result$objval` and `result$x` and you don't see any ## Solving a _prioritzr_ problem with _Gurobi_ -If you successfully installed the _Gurobi_ software suite and the _gurobi_ _R_ package, you can now try solving conservation planning problems using the _prioritzr_ _R_ package. Although the _prioritizr_ _R_ package should automatically detect that _Gurobi_ has been installed, you can use the function `add_gurobi_solver` to manually specify that _Gurobi_ should be used to solve problems. This function is also useful because you can use it to customize the optimization process (e.g. specify the desired optimality gap or set a limit on how much time should be spent searching for a solution). +If you successfully installed the _Gurobi_ software suite and the _gurobi_ _R_ package, you can now try solving conservation planning problems using the _prioritzr_ _R_ package. Although the _prioritizr_ _R_ package should automatically detect that _Gurobi_ has been installed, you can use the function `add_gurobi_solver()` to manually specify that _Gurobi_ should be used to solve problems. This function is also useful because you can use it to customize the optimization process (e.g., specify the desired optimality gap or set a limit on how much time should be spent searching for a solution). Finally, to check that everything has been installed correctly, we will use the _Gurobi_ software suite to solve a reserve selection problem created using the _prioritzr_ _R_ package. diff --git a/inst/doc/gurobi_installation.html b/inst/doc/gurobi_installation_guide.html similarity index 99% rename from inst/doc/gurobi_installation.html rename to inst/doc/gurobi_installation_guide.html index 9c6613b8b..263f45ca2 100644 --- a/inst/doc/gurobi_installation.html +++ b/inst/doc/gurobi_installation_guide.html @@ -12,9 +12,9 @@ - + -Gurobi Installation Guide +Gurobi installation guide @@ -139,9 +139,9 @@ -

      Gurobi Installation Guide

      +

      Gurobi installation guide

      Richard Schuster

      -

      2021-11-16

      +

      2021-12-02

      @@ -158,7 +158,7 @@

      2021-11-16

      Introduction

      -

      Gurobi is the most powerful and fastest solver that the prioritizr R package can use to solve conservation planning problems. This vignette will walk you through the process of setting up Gurobi on your computer so that you can use it to solve conservation planning problems. If you encounter any problems while following the instructions below, check out the official Gurobi documentation.

      +

      Gurobi is the most powerful and fastest solver that the prioritizr R package can use to solve conservation planning problems (see the Solver benchmarks vignette for further details). This guide will walk you through the process of setting up Gurobi on your computer so that it can be used to solve conservation planning problems. If you encounter any problems while following the instructions below, please refer to the official Gurobi documentation.

      Obtaining a license

      @@ -182,7 +182,7 @@

      Downloading the software

      Software installation

      -

      The process for installing the Gurobi software depends on the operating system on your computer. Fortunately, Gurobi provide platform-specific “Quick Start Guides” for Windows, MacOS, and Linux systems that should help with this. Briefly, on Windows systems, you just need to double-click on the Gurobi installer, follow the prompts, and the installer will automatically handle everything for you. On Linux and MacOS systems, you will need to manually extract the downloaded file’s contents to a folder, move the extracted contents to a suitable location (typically /opt/gurobi), and update your system’s variables so that it knows where to find Gurobi (i.e. the PATH variable).

      +

      The process for installing the Gurobi software depends on the operating system on your computer. Fortunately, Gurobi provide platform-specific “Quick Start Guides” for Windows, MacOS, and Linux systems that should help with this. Briefly, on Windows systems, you just need to double-click on the Gurobi installer, follow the prompts, and the installer will automatically handle everything for you. On Linux and MacOS systems, you will need to manually extract the downloaded file’s contents to a folder, move the extracted contents to a suitable location (typically /opt/gurobi), and update your system’s variables so that it knows where to find Gurobi (i.e., the PATH variable).

      Additionally, if you are using RStudio on a Linux system, you might need to add the following text to a Rstudio configuration file (located at /etc/rstudio/rserver.conf).

      rsession-ld-library-path=/opt/gurobi650/linux64/lib

      After installing the Gurobi software suite on your computer, you will need to activate your license.

      @@ -195,7 +195,7 @@

      License activation


      -

      Next, we will now check that the license has been successfully activated. To achieve this, we will try running Gurobi directly from the command line. Note that the following commands assume you are using version 8.0.0 of Gurobi, and so you will need to modify the command if you are using a more recent version (e.g. if using version 9.1.2, then use gurobi912 instead of gurobi800 below).

      +

      Next, we will now check that the license has been successfully activated. To achieve this, we will try running Gurobi directly from the command line. Note that the following commands assume you are using version 8.0.0 of Gurobi, and so you will need to modify the command if you are using a more recent version (e.g., if using version 9.1.2, then use gurobi912 instead of gurobi800 below).

      On Windows systems, users can type in the following system command to check their license activation.

      gurobi_cl c:\gurobi800\win64\examples\data\coins.lp

      On Linux and MacOS systems, users can type in the following system command.

      @@ -210,14 +210,14 @@

      License activation

      R package installation

      -

      Now we will install the gurobi R package. This package is not available on the Comprehensive R Archive Network and is instead distributed with the Gurobi software suite. Specifically, the gurobi R package should be located within the folder where you installed the Gurobi software suite. We will install the gurobi R package by running the following R code within your R session. Note that the following code assumes that you are using version 8.0.0 of Gurobi, and so you will need to modify the code if you are using a more recent version (e.g. if using version 9.1.2, then use gurobi912 instead of gurobi800 below).

      +

      Now we will install the gurobi R package. This package is not available on the Comprehensive R Archive Network and is instead distributed with the Gurobi software suite. Specifically, the gurobi R package should be located within the folder where you installed the Gurobi software suite. We will install the gurobi R package by running the following R code within your R session. Note that the following code assumes that you are using version 8.0.0 of Gurobi, and so you will need to modify the code if you are using a more recent version (e.g., if using version 9.1.2, then use gurobi912 instead of gurobi800 below).

      Assuming you installed Gurobi in the default location, Windows users can install gurobi R package using the following code.

      install.packages("c:/gurobi800/win64/R/gurobi_8.0-0.zip", repos = NULL)

      Similarly, Linux and MacOS users can install the gurobi R package using the following code.

      install.packages(file.path(Sys.getenv("GUROBI_HOME"),
                            "R/gurobi_8.0-0_R_x86_64-pc-linux-gnu.tar.gz"),
                  repos = NULL)
      -

      Next, you will need to install the slam R package because the gurobi R package needs this package to work. Users of all platforms (i.e. Windows, Linux, and MacOS) can install the package using the following R code.

      +

      Next, you will need to install the slam R package because the gurobi R package needs this package to work. Users of all platforms (i.e., Windows, Linux, and MacOS) can install the package using the following R code.

      install.packages("slam", repos = "https://cloud.r-project.org")

      Let’s check that the gurobi R package has been successfully installed. To do this, we can try using the gurobi R package to solve an optimization problem. Copy and paste the R code below into R.

      # load gurobi package
@@ -266,7 +266,7 @@ 
      R package installation

      Solving a prioritzr problem with Gurobi

      -

      If you successfully installed the Gurobi software suite and the gurobi R package, you can now try solving conservation planning problems using the prioritzr R package. Although the prioritizr R package should automatically detect that Gurobi has been installed, you can use the function add_gurobi_solver to manually specify that Gurobi should be used to solve problems. This function is also useful because you can use it to customize the optimization process (e.g. specify the desired optimality gap or set a limit on how much time should be spent searching for a solution).

      +

      If you successfully installed the Gurobi software suite and the gurobi R package, you can now try solving conservation planning problems using the prioritzr R package. Although the prioritizr R package should automatically detect that Gurobi has been installed, you can use the function add_gurobi_solver() to manually specify that Gurobi should be used to solve problems. This function is also useful because you can use it to customize the optimization process (e.g., specify the desired optimality gap or set a limit on how much time should be spent searching for a solution).

      Finally, to check that everything has been installed correctly, we will use the Gurobi software suite to solve a reserve selection problem created using the prioritzr R package.

      library(prioritizr)
 
diff --git a/vignettes/zones.Rmd b/inst/doc/management_zones_tutorial.Rmd
similarity index 70%
rename from vignettes/zones.Rmd
rename to inst/doc/management_zones_tutorial.Rmd
index b28c8541d..48efd1835 100644
--- a/vignettes/zones.Rmd
+++ b/inst/doc/management_zones_tutorial.Rmd
@@ -1,5 +1,5 @@
 ---
-title: "Management Zones"
+title: "Management zones tutorial"
 output:
   rmarkdown::html_vignette:
     toc: true
@@ -10,7 +10,7 @@ documentclass: article
 bibliography: references.bib
 csl: reference-style.csl
 vignette: >
-  %\VignetteIndexEntry{Management Zones}
+  %\VignetteIndexEntry{Management zones tutorial}
   %\VignetteEngine{knitr::rmarkdown_notangle}
 ---
 
@@ -23,21 +23,22 @@ knitr::opts_chunk$set(fig.align = "center", eval = !is_check,
 
 ## Introduction
 
-One of the main aims in conservation planning is to identify the most cost-effective set of areas to manage biodiversity [@r4]. To achieve this, prioritizations are generally created to identify areas for expanding protected area systems. However, many real-world conservation problems do not simply involve deciding if an area should be protected or not [e.g. @r5; @r18]. Instead, many real-world problems involve a range of different management categories and the goal is to determine which areas should be allocated to which management category. For example, a manager might have a range of different methods (e.g. baiting or trapping at various intensities) for controlling invasive pests in a set of different areas [e.g. @r25]. They would need a prioritization that shows which control methods should be implemented in which areas. In this particular case, a binary prioritization showing which areas contain the most biodiversity is simply not helpful. Furthermore, many real-world problems require decisions that meet multiple, and sometimes conflicting, objectives from different stakeholders. For example, a manager might need to implement a set of no-take and partial-take areas to prevent overfishing, but also ensure that there still remain plenty of areas for fishing activities [e.g. @r26; @r27]. Popularized by _Marxan with Zones_ [@r2], this concept has become known as "zones" and is becoming increasingly important in conservation planning.
+One of the main aims in conservation planning is to identify the most cost-effective set of areas to manage biodiversity [@r4]. To achieve this, prioritizations are generally created to identify areas for expanding protected area systems. However, many real-world conservation problems do not simply involve deciding if an area should be protected or not [e.g., @r5; @r18]. Instead, many problems involve a range of different management categories and the goal is to determine which areas should be allocated to which management category. For example, a manager might have a range of different methods (e.g., baiting or trapping at various intensities) for controlling invasive pests in a set of different areas [e.g., @r25]. They would need a prioritization that shows which control methods should be implemented in which areas. In this particular case, a binary prioritization showing which areas contain the most biodiversity is simply not helpful. Furthermore, many real-world problems require decisions that meet multiple, and sometimes conflicting, objectives from different stakeholders. For example, a manager might need to implement a set of no-take and partial-take areas to prevent overfishing, but also ensure that there still remain plenty of areas for fishing activities [e.g., @r26; @r27]. Popularized by the _Marxan with Zones_ decision support tool [@r2], this concept has become known as "zones" and is becoming increasingly important in conservation planning.
 
-The aim of this vignette is to showcase the zones functionality of the _prioritizr R_ package. It will assume a certain level of familiarity with conservation planning terminology and the _prioritizr R_ package. We recommend reading the [_prioritizr_ vignette](prioritizr.html) first if you don't have much experience in either of these topics.
+The aim of this tutorial is to showcase the zones functionality of the _prioritizr R_ package. It will assume a certain level of familiarity with conservation planning terminology and the package. If you don't have much experience in either of these topics, we recommend first reading the [_Package overview_](package_overview.html) vignette.
 
 ## Usage
 
-
 ### Simple minimum set problem
 
-In the _prioritizr R_ package, all conservation planning problems---including those which contain multiple management zones or actions---are initialized using the `problem` function. To refresh our memory on how we can construct problems using the _prioritizr R_ package, let us quickly construct a simple conservation planning problem. This problem will use the simulated built-in planning unit and feature data distributed with the package. It will have a minimum set objective, targets which require that solution secure to 10 % of the habitat in the study area for each feature, and binary decision variables indicating that planning units are selected or not selected for protection.
+In the _prioritizr R_ package, all conservation planning problems -- including those which contain multiple management zones or actions -- are initialized using the `problem` function. To refresh our memory on how we can construct problems, let us quickly construct a simple conservation planning problem. This problem will use the simulated built-in planning unit and feature data distributed with the package. It will have a minimum set objective, targets which require that solution secure to 10 % of the habitat in the study area for each feature, and binary decision variables indicating that planning units are selected or not selected for protection.
 
-```{r}
+```{r, results = "hide"}
 # load prioritizr package
 library(prioritizr)
+```
 
+```{r}
 # load data
 data(sim_pu_raster, sim_features)
 
@@ -66,7 +67,7 @@ plot(s1, main = "solution", axes = FALSE, box = FALSE)
 
 ### Adding management zones
 
-Now let us imagine that instead of having a single management zone (e.g. protected area), we have two management zones. Similar to the example above, we require a solution that secures 10 % of the habitat in the study area for each feature in the first management zone. But we also require a solution that secures 5 % of the habitat in the study area for each feature in the second management zone. Each planning unit must be allocated to either zone or not selected for management at all. In this example, each planning unit costs the same when it is allocated to either of the two zones. We can formulate and solve this problem using the following code.
+Now let us imagine that instead of having a single management zone (e.g., protected area), we have two management zones. Similar to the example above, we require a solution that secures 10 % of the habitat in the study area for each feature in the first management zone. But we also require a solution that secures 5 % of the habitat in the study area for each feature in the second management zone. Each planning unit must be allocated to either zone or not selected for management at all. In this example, each planning unit costs the same when it is allocated to either of the two zones. We can formulate and solve this problem using the following code.
 
 ```{r}
 # create a matrix with the targets
@@ -125,7 +126,7 @@ plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
 
 ### Multiple zones with varying costs
 
-Real-world problems often have different costs for managing planning units under different zones. These problems also tend to have different expected amounts of each feature when planning units are managed differently. So let us consider a slightly more complex example. Similar to before we will have two management zones. But this time, the cost of managing each planning unit is different depending on which management zone it is assigned to in the solution. Furthermore, when we assign a planning unit to the second zone, we only expect to end up with half of the habitat we would get if we managed the unit in the first zone (e.g. because the second zone is a partial-take zone and the first zone is a no-take zone). We will use the same target data as in the previous example.
+Real-world problems often have different costs for managing planning units under different zones. These problems also tend to have different expected amounts of each feature when planning units are managed differently. So let us consider a slightly more complex example. Similar to before we will have two management zones. But this time, the cost of managing each planning unit is different depending on which management zone it is assigned to in the solution. Furthermore, when we assign a planning unit to the second zone, we only expect to end up with half of the habitat we would get if we managed the unit in the first zone (e.g., because the second zone is a partial-take zone and the first zone is a no-take zone). We will use the same target data as in the previous example.
 
 ```{r, fig.width = 4.0}
 # create new planning unit and cost data
@@ -159,7 +160,7 @@ plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
 
 ### Multiple zones with complex targets
 
-So far, we have dealt with problems where each feature has a target that pertains to a single zone. But sometimes we have targets that pertain to multiple zones. For example, what if we were in charge of managing pest control in a set of areas and we had three different pest control methods we could implement in any given planning unit. We could (1) set up a few traps in a given planning unit and make 10 % of the habitat in the unit pest-free, (2) set up a lot of traps and make 50 % of the habitat in the unit pest-free, or (3) drop baits over a given planning unit and make 80 % of the planning unit pest-free. Each of these different actions has a different cost, with a few low intensity trapping costing $100 per planning unit, a high intensity trapping costing $300, and baiting costing $200 (please note these costs aren't meant to be realistic). After defining our management actions and costs, we require a solution that will yield 8 units of pest free habitat per feature. It's important to note that unlike the previous examples, here we don't have targets for each feature in each zone, but rather our targets are for each feature and across multiple zones. In other words, we don't really care which management actions we implement, we just want the set of actions that will meet our targets for minimum expenditure. We can formulate and solve this problem using the following code.
+So far, we have dealt with problems where each feature has a target that pertains to a single zone. But sometimes we have targets that pertain to multiple zones. For example, what if we were in charge of managing pest control in a set of areas and we had three different pest control methods we could implement in any given planning unit. We could (i) set up a few traps in a given planning unit and make 10 % of the habitat in the unit pest-free, (ii) set up a lot of traps and make 50 % of the habitat in the unit pest-free, or (iii) drop baits over a given planning unit and make 80 % of the planning unit pest-free. Each of these different actions has a different cost, with a few low intensity trapping costing $100 per planning unit, a high intensity trapping costing $300, and baiting costing $200 (please note these costs aren't meant to be realistic). After defining our management actions and costs, we require a solution that will yield 8 units of pest free habitat per feature. It's important to note that unlike the previous examples, here we don't have targets for each feature in each zone, but rather our targets are for each feature and across multiple zones. In other words, we don't really care which management actions we implement, we just want the set of actions that will meet our targets for minimum expenditure. We can formulate and solve this problem using the following code.
 
 ```{r, fig.width = 4.5, fig.height = 3}
 # create planning unit data with costs
@@ -318,6 +319,6 @@ plot(category_layer(s7), main = "solution", axes = FALSE, box = FALSE)
 
 ## Conclusion
 
-Hopefully, this vignette has provided an informative introduction to building and solving problems with multiple zones using the _prioritizr R_ package. Although we have examined only a few different functions here, almost every single function for modifying conservation planning problems is compatible with problems that contain zones. It's worth noting that working with multiple zones is a lot trickier than working with a single zone, so we would recommend playing around with the code in the Examples sections of the help pages to get a feel for what different functions do when they are applied to problems with multiple zones.
+Hopefully, this vignette has provided an informative introduction to building and solving problems with multiple zones. Although we have examined only a few different functions here, almost every single function for modifying conservation planning problems is compatible with problems that contain zones. It's worth noting that working with multiple zones is a lot trickier than working with a single zone, so we would recommend playing around with the code in the _Examples_ sections of the package documentation to help understand how functions work when applied to multiple zones.
 
 ## References
diff --git a/inst/doc/zones.html b/inst/doc/management_zones_tutorial.html
similarity index 88%
rename from inst/doc/zones.html
rename to inst/doc/management_zones_tutorial.html
index ee267c7be..2e9134293 100644
--- a/inst/doc/zones.html
+++ b/inst/doc/management_zones_tutorial.html
@@ -12,7 +12,7 @@
 
 
 
-Management Zones
+Management zones tutorial
 
 
 
@@ -159,7 +159,7 @@
 
 
 
-
      Management Zones
      
+
      Management zones tutorial
      
 
 
 
      
@@ -182,31 +182,30 @@ 
      Management Zones
      
 
 
      
 
      Introduction
      
-
      One of the main aims in conservation planning is to identify the most cost-effective set of areas to manage biodiversity (Margules & Pressey 2000). To achieve this, prioritizations are generally created to identify areas for expanding protected area systems. However, many real-world conservation problems do not simply involve deciding if an area should be protected or not (e.g. Klein et al. 2009; Stigner et al. 2016). Instead, many real-world problems involve a range of different management categories and the goal is to determine which areas should be allocated to which management category. For example, a manager might have a range of different methods (e.g. baiting or trapping at various intensities) for controlling invasive pests in a set of different areas (e.g. Cattarino et al. 2018). They would need a prioritization that shows which control methods should be implemented in which areas. In this particular case, a binary prioritization showing which areas contain the most biodiversity is simply not helpful. Furthermore, many real-world problems require decisions that meet multiple, and sometimes conflicting, objectives from different stakeholders. For example, a manager might need to implement a set of no-take and partial-take areas to prevent overfishing, but also ensure that there still remain plenty of areas for fishing activities (e.g. Wilson et al. 2010; Klein et al. 2013). Popularized by Marxan with Zones (Watts et al. 2009), this concept has become known as “zones” and is becoming increasingly important in conservation planning.
      
-
      The aim of this vignette is to showcase the zones functionality of the prioritizr R package. It will assume a certain level of familiarity with conservation planning terminology and the prioritizr R package. We recommend reading the prioritizr vignette first if you don’t have much experience in either of these topics.
      
+
      One of the main aims in conservation planning is to identify the most cost-effective set of areas to manage biodiversity (Margules & Pressey 2000). To achieve this, prioritizations are generally created to identify areas for expanding protected area systems. However, many real-world conservation problems do not simply involve deciding if an area should be protected or not (e.g., Klein et al. 2009; Stigner et al. 2016). Instead, many problems involve a range of different management categories and the goal is to determine which areas should be allocated to which management category. For example, a manager might have a range of different methods (e.g., baiting or trapping at various intensities) for controlling invasive pests in a set of different areas (e.g., Cattarino et al. 2018). They would need a prioritization that shows which control methods should be implemented in which areas. In this particular case, a binary prioritization showing which areas contain the most biodiversity is simply not helpful. Furthermore, many real-world problems require decisions that meet multiple, and sometimes conflicting, objectives from different stakeholders. For example, a manager might need to implement a set of no-take and partial-take areas to prevent overfishing, but also ensure that there still remain plenty of areas for fishing activities (e.g., Wilson et al. 2010; Klein et al. 2013). Popularized by the Marxan with Zones decision support tool (Watts et al. 2009), this concept has become known as “zones” and is becoming increasingly important in conservation planning.
      
+
      The aim of this tutorial is to showcase the zones functionality of the prioritizr R package. It will assume a certain level of familiarity with conservation planning terminology and the package. If you don’t have much experience in either of these topics, we recommend first reading the Package overview vignette.
      
 
      
 
      
 
      Usage
      
 
      
 
      Simple minimum set problem
      
-
      In the prioritizr R package, all conservation planning problems—including those which contain multiple management zones or actions—are initialized using the problem function. To refresh our memory on how we can construct problems using the prioritizr R package, let us quickly construct a simple conservation planning problem. This problem will use the simulated built-in planning unit and feature data distributed with the package. It will have a minimum set objective, targets which require that solution secure to 10 % of the habitat in the study area for each feature, and binary decision variables indicating that planning units are selected or not selected for protection.
      
+
      In the prioritizr R package, all conservation planning problems – including those which contain multiple management zones or actions – are initialized using the problem function. To refresh our memory on how we can construct problems, let us quickly construct a simple conservation planning problem. This problem will use the simulated built-in planning unit and feature data distributed with the package. It will have a minimum set objective, targets which require that solution secure to 10 % of the habitat in the study area for each feature, and binary decision variables indicating that planning units are selected or not selected for protection.
      
 
      # load prioritizr package
-library(prioritizr)
-
-# load data
-data(sim_pu_raster, sim_features)
-
-# create targets for each of the five features
-t1 <- rep(0.1, 5)
-
-# build single-zone problem
-p1 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(t1) %>%
-      add_binary_decisions()
-
-# print problem
-print(p1)
      
+library(prioritizr)
      +
      # load data
+data(sim_pu_raster, sim_features)
+
+# create targets for each of the five features
+t1 <- rep(0.1, 5)
+
+# build single-zone problem
+p1 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(t1) %>%
+      add_binary_decisions()
+
+# print problem
+print(p1)
      ## Conservation Problem
 ##   planning units: RasterLayer (90 units)
 ##   cost:           min: 190.13276, max: 215.86384
@@ -218,8 +217,8 @@ 
      Simple minimum set problem
      
 ##   penalties:      <none>
 ##   portfolio:      default
 ##   solver:         default
      -
      # solve problem
-s1 <- solve(p1)
      +
      # solve problem
+s1 <- solve(p1)
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
 ## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
 ## Optimize a model with 5 rows, 90 columns and 450 nonzeros
@@ -253,9 +252,9 @@ 
      Simple minimum set problem
      
 ## 
 ## Optimal solution found (tolerance 1.00e-01)
 ## Best objective 1.987398526526e+03, best bound 1.931581908865e+03, gap 2.8085%
      -
      # calculate feature representation
-r1 <- eval_feature_representation_summary(p1, s1)
-print(r1)
      +
      # calculate feature representation
+r1 <- eval_feature_representation_summary(p1, s1)
+print(r1)
      ## # A tibble: 5 × 5
 ##   summary feature total_amount absolute_held relative_held
 ##   <chr>   <chr>          <dbl>         <dbl>         <dbl>
@@ -264,48 +263,48 @@ 
      Simple minimum set problem
      
 ## 3 overall layer.3         72.0          7.34         0.102
 ## 4 overall layer.4         42.7          4.35         0.102
 ## 5 overall layer.5         56.7          6.01         0.106
      -
      # plot solution
-plot(s1, main = "solution", axes = FALSE, box = FALSE)
      +
      # plot solution
+plot(s1, main = "solution", axes = FALSE, box = FALSE)

      Adding management zones

      -

      Now let us imagine that instead of having a single management zone (e.g. protected area), we have two management zones. Similar to the example above, we require a solution that secures 10 % of the habitat in the study area for each feature in the first management zone. But we also require a solution that secures 5 % of the habitat in the study area for each feature in the second management zone. Each planning unit must be allocated to either zone or not selected for management at all. In this example, each planning unit costs the same when it is allocated to either of the two zones. We can formulate and solve this problem using the following code.

      -
      # create a matrix with the targets
-# here each column corresponds to a different zone,
-# each row corresponds to a different feature, and
-# each cell value corresponds to the target
-t2 <- matrix(NA, ncol = 2, nrow = 5)
-t2[, 1] <- 0.1
-t2[, 2] <- 0.05
-
-# print targets
-print(t2)
      +

      Now let us imagine that instead of having a single management zone (e.g., protected area), we have two management zones. Similar to the example above, we require a solution that secures 10 % of the habitat in the study area for each feature in the first management zone. But we also require a solution that secures 5 % of the habitat in the study area for each feature in the second management zone. Each planning unit must be allocated to either zone or not selected for management at all. In this example, each planning unit costs the same when it is allocated to either of the two zones. We can formulate and solve this problem using the following code.

      +
      # create a matrix with the targets
+# here each column corresponds to a different zone,
+# each row corresponds to a different feature, and
+# each cell value corresponds to the target
+t2 <- matrix(NA, ncol = 2, nrow = 5)
+t2[, 1] <- 0.1
+t2[, 2] <- 0.05
+
+# print targets
+print(t2)
      ##      [,1] [,2]
 ## [1,]  0.1 0.05
 ## [2,]  0.1 0.05
 ## [3,]  0.1 0.05
 ## [4,]  0.1 0.05
 ## [5,]  0.1 0.05
      -
      # create a zones object that contains the amount of each feature
-# in each planning unit when it is allocated to each zone
-# since our zones pertain to the same habitat data, we will
-# to specify the same habitat data for each zone
-z2 <- zones("zone 1" = sim_features, "zone 2" = sim_features)
-
-# print zones
-print(z2)
      +
      # create a zones object that contains the amount of each feature
+# in each planning unit when it is allocated to each zone
+# since our zones pertain to the same habitat data, we will
+# to specify the same habitat data for each zone
+z2 <- zones("zone 1" = sim_features, "zone 2" = sim_features)
+
+# print zones
+print(z2)
      ## Zones
 ##   zones: zone 1, zone 2 (2 zones)
 ##   features: 1, 2, 3, ... (5 features)
 ##   data type: RasterStack
      -
      # create a raster stack with the planning unit data
-# since our planning unit costs are the same for each zone,
-# we will create a stack with two replicates of the cost data
-pu2 <- stack(sim_pu_raster, sim_pu_raster)
-
-# print stack
-print(pu2)
      +
      # create a raster stack with the planning unit data
+# since our planning unit costs are the same for each zone,
+# we will create a stack with two replicates of the cost data
+pu2 <- stack(sim_pu_raster, sim_pu_raster)
+
+# print stack
+print(pu2)
      ## class      : RasterStack 
 ## dimensions : 10, 10, 100, 2  (nrow, ncol, ncell, nlayers)
 ## resolution : 0.1, 0.1  (x, y)
@@ -314,14 +313,14 @@ 
      Adding management zones
      
 ## names      :  layer.1,  layer.2 
 ## min values : 190.1328, 190.1328 
 ## max values : 215.8638, 215.8638
      -
      # build two-zone problem
-p2 <- problem(pu2, z2) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(t2) %>%
-      add_binary_decisions()
-
-# print problem
-print(p2)
      +
      # build two-zone problem
+p2 <- problem(pu2, z2) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(t2) %>%
+      add_binary_decisions()
+
+# print problem
+print(p2)
      ## Conservation Problem
 ##   zones:          zone 1, zone 2 (2 zones)
 ##   planning units: RasterStack (90 units)
@@ -334,8 +333,8 @@ 
      Adding management zones
      
 ##   penalties:      <none>
 ##   portfolio:      default
 ##   solver:         default
      -
      # solve problem
-s2 <- solve(p2)
      +
      # solve problem
+s2 <- solve(p2)
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
 ## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
 ## Optimize a model with 100 rows, 180 columns and 1080 nonzeros
@@ -369,9 +368,9 @@ 
      Adding management zones
      
 ## 
 ## Optimal solution found (tolerance 1.00e-01)
 ## Best objective 3.003874397435e+03, best bound 2.911333350606e+03, gap 3.0807%
      -
      # calculate feature representation
-r2 <- eval_feature_representation_summary(p2, s2)
-print(r2)
      +
      # calculate feature representation
+r2 <- eval_feature_representation_summary(p2, s2)
+print(r2)
      ## # A tibble: 15 × 5
 ##    summary feature total_amount absolute_held relative_held
 ##    <chr>   <chr>          <dbl>         <dbl>         <dbl>
@@ -390,34 +389,34 @@ 
      Adding management zones
      
 ## 13 zone 2  3               72.0          3.72        0.0517
 ## 14 zone 2  4               42.7          2.17        0.0508
 ## 15 zone 2  5               56.7          2.96        0.0521
      -
      # plot solution
-# here we use the category layer function to generate raster showing the zone
-# that each planning unit was allocated. Specifically, pixels with the
-# value 1 are allocated to "zone 1" and pixels with the value 2 are allocated
-# to "zone 2". Thus units depicted in gray are not allocated
-# to any zone, units depicted in yellow are allocated to zone 1, and units
-# depicted in green are allocated to zone 2
-plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
      +
      # plot solution
+# here we use the category layer function to generate raster showing the zone
+# that each planning unit was allocated. Specifically, pixels with the
+# value 1 are allocated to "zone 1" and pixels with the value 2 are allocated
+# to "zone 2". Thus units depicted in gray are not allocated
+# to any zone, units depicted in yellow are allocated to zone 1, and units
+# depicted in green are allocated to zone 2
+plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)

      Multiple zones with varying costs

      -

      Real-world problems often have different costs for managing planning units under different zones. These problems also tend to have different expected amounts of each feature when planning units are managed differently. So let us consider a slightly more complex example. Similar to before we will have two management zones. But this time, the cost of managing each planning unit is different depending on which management zone it is assigned to in the solution. Furthermore, when we assign a planning unit to the second zone, we only expect to end up with half of the habitat we would get if we managed the unit in the first zone (e.g. because the second zone is a partial-take zone and the first zone is a no-take zone). We will use the same target data as in the previous example.

      -
      # create new planning unit and cost data
-data(sim_pu_zones_stack)
-pu3 <- sim_pu_zones_stack[[1:2]]
-
-# plot cost data
-plot(pu3, main = c("zone 1", "zone 2"), axes = FALSE, box = FALSE)
      +

      Real-world problems often have different costs for managing planning units under different zones. These problems also tend to have different expected amounts of each feature when planning units are managed differently. So let us consider a slightly more complex example. Similar to before we will have two management zones. But this time, the cost of managing each planning unit is different depending on which management zone it is assigned to in the solution. Furthermore, when we assign a planning unit to the second zone, we only expect to end up with half of the habitat we would get if we managed the unit in the first zone (e.g., because the second zone is a partial-take zone and the first zone is a no-take zone). We will use the same target data as in the previous example.

      +
      # create new planning unit and cost data
+data(sim_pu_zones_stack)
+pu3 <- sim_pu_zones_stack[[1:2]]
+
+# plot cost data
+plot(pu3, main = c("zone 1", "zone 2"), axes = FALSE, box = FALSE)

      -
      # create problem
-p3 <- problem(pu3, zones(sim_features, sim_features * 0.5)) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(t2) %>%
-      add_binary_decisions()
-
-# print problem
-print(p3)
      +
      # create problem
+p3 <- problem(pu3, zones(sim_features, sim_features * 0.5)) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(t2) %>%
+      add_binary_decisions()
+
+# print problem
+print(p3)
      ## Conservation Problem
 ##   zones:          1, 2 (2 zones)
 ##   planning units: RasterStack (90 units)
@@ -430,8 +429,8 @@ 
      Multiple zones with varying costs
      
 ##   penalties:      <none>
 ##   portfolio:      default
 ##   solver:         default
      -
      # solve problem
-s3 <- solve(p3)
      +
      # solve problem
+s3 <- solve(p3)
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
 ## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
 ## Optimize a model with 100 rows, 180 columns and 1080 nonzeros
@@ -458,16 +457,16 @@ 
      Multiple zones with varying costs
      
 ##      0     0 2884.87200    0    8 3388.02489 2884.87200  14.9%     -    0s
 ## H    0     0                    2958.1201508 2884.87200  2.48%     -    0s
 ## 
-## Explored 1 nodes (38 simplex iterations) in 0.00 seconds (0.00 work units)
+## Explored 1 nodes (38 simplex iterations) in 0.01 seconds (0.00 work units)
 ## Thread count was 1 (of 8 available processors)
 ## 
 ## Solution count 3: 2958.12 3388.02 3667.77 
 ## 
 ## Optimal solution found (tolerance 1.00e-01)
 ## Best objective 2.958120150795e+03, best bound 2.884871999973e+03, gap 2.4762%
      -
      # calculate feature representation
-r3 <- eval_feature_representation_summary(p3, s3)
-print(r3)
      +
      # calculate feature representation
+r3 <- eval_feature_representation_summary(p3, s3)
+print(r3)
      ## # A tibble: 15 × 5
 ##    summary feature total_amount absolute_held relative_held
 ##    <chr>   <chr>          <dbl>         <dbl>         <dbl>
@@ -486,30 +485,30 @@ 
      Multiple zones with varying costs
      
 ## 13 2       3               36.0         1.87         0.0519
 ## 14 2       4               21.3         1.08         0.0505
 ## 15 2       5               28.4         1.44         0.0509
      -
      # plot solution
-plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
      +
      # plot solution
+plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)

      Multiple zones with complex targets

      -

      So far, we have dealt with problems where each feature has a target that pertains to a single zone. But sometimes we have targets that pertain to multiple zones. For example, what if we were in charge of managing pest control in a set of areas and we had three different pest control methods we could implement in any given planning unit. We could (1) set up a few traps in a given planning unit and make 10 % of the habitat in the unit pest-free, (2) set up a lot of traps and make 50 % of the habitat in the unit pest-free, or (3) drop baits over a given planning unit and make 80 % of the planning unit pest-free. Each of these different actions has a different cost, with a few low intensity trapping costing $100 per planning unit, a high intensity trapping costing $300, and baiting costing $200 (please note these costs aren’t meant to be realistic). After defining our management actions and costs, we require a solution that will yield 8 units of pest free habitat per feature. It’s important to note that unlike the previous examples, here we don’t have targets for each feature in each zone, but rather our targets are for each feature and across multiple zones. In other words, we don’t really care which management actions we implement, we just want the set of actions that will meet our targets for minimum expenditure. We can formulate and solve this problem using the following code.

      -
      # create planning unit data with costs
-pu4 <- stack(Which(!is.na(sim_pu_raster)) * 100,
-             Which(!is.na(sim_pu_raster)) * 300,
-             Which(!is.na(sim_pu_raster)) * 200)
-names(pu4) <- c("few.traps", "many.traps", "baiting")
-
-# plot planning unit data
-plot(pu4, nr = 1, axes = FALSE, box = FALSE)
      -

      -
      # create targets
-t4 <- tibble::tibble(feature = names(sim_features),
-                     zone = list(names(pu4))[rep(1, 5)],
-                     target = rep(8, 5),
-                     type = rep("absolute", 5))
+
      So far, we have dealt with problems where each feature has a target that pertains to a single zone. But sometimes we have targets that pertain to multiple zones. For example, what if we were in charge of managing pest control in a set of areas and we had three different pest control methods we could implement in any given planning unit. We could (i) set up a few traps in a given planning unit and make 10 % of the habitat in the unit pest-free, (ii) set up a lot of traps and make 50 % of the habitat in the unit pest-free, or (iii) drop baits over a given planning unit and make 80 % of the planning unit pest-free. Each of these different actions has a different cost, with a few low intensity trapping costing $100 per planning unit, a high intensity trapping costing $300, and baiting costing $200 (please note these costs aren’t meant to be realistic). After defining our management actions and costs, we require a solution that will yield 8 units of pest free habitat per feature. It’s important to note that unlike the previous examples, here we don’t have targets for each feature in each zone, but rather our targets are for each feature and across multiple zones. In other words, we don’t really care which management actions we implement, we just want the set of actions that will meet our targets for minimum expenditure. We can formulate and solve this problem using the following code.
      
+
      # create planning unit data with costs
+pu4 <- stack(Which(!is.na(sim_pu_raster)) * 100,
+             Which(!is.na(sim_pu_raster)) * 300,
+             Which(!is.na(sim_pu_raster)) * 200)
+names(pu4) <- c("few.traps", "many.traps", "baiting")
 
-# print targets
-print(t4)
      
+# plot planning unit data
+plot(pu4, nr = 1, axes = FALSE, box = FALSE)
      +

      +
      # create targets
+t4 <- tibble::tibble(feature = names(sim_features),
+                     zone = list(names(pu4))[rep(1, 5)],
+                     target = rep(8, 5),
+                     type = rep("absolute", 5))
+
+# print targets
+print(t4)
      ## # A tibble: 5 × 4
 ##   feature zone      target type    
 ##   <chr>   <list>     <dbl> <chr>   
@@ -518,17 +517,17 @@ 
      Multiple zones with complex targets
      
 ## 3 layer.3 <chr [3]>      8 absolute
 ## 4 layer.4 <chr [3]>      8 absolute
 ## 5 layer.5 <chr [3]>      8 absolute
      -
      # create problem
-p4 <- problem(pu4, zones(few.traps = sim_features * 0.1,
-                         many.traps = sim_features * 0.5,
-                         baiting = sim_features * 0.8,
-                         feature_names = names(sim_features))) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(t4) %>%
-      add_binary_decisions()
-
-# print problem
-print(p4)
      +
      # create problem
+p4 <- problem(pu4, zones(few.traps = sim_features * 0.1,
+                         many.traps = sim_features * 0.5,
+                         baiting = sim_features * 0.8,
+                         feature_names = names(sim_features))) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(t4) %>%
+      add_binary_decisions()
+
+# print problem
+print(p4)
      ## Conservation Problem
 ##   zones:          few.traps, many.traps, baiting (3 zones)
 ##   planning units: RasterStack (100 units)
@@ -541,8 +540,8 @@ 
      Multiple zones with complex targets
      
 ##   penalties:      <none>
 ##   portfolio:      default
 ##   solver:         default
      -
      # solve problem
-s4 <- solve(p4)
      +
      # solve problem
+s4 <- solve(p4)
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
 ## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
 ## Optimize a model with 105 rows, 300 columns and 1800 nonzeros
@@ -577,9 +576,9 @@ 
      Multiple zones with complex targets
      
 ## 
 ## Optimal solution found (tolerance 1.00e-01)
 ## Best objective 3.800000000000e+03, best bound 3.700000000000e+03, gap 2.6316%
      -
      # calculate feature representation
-r4 <- eval_feature_representation_summary(p4, s4)
-print(r4)
      +
      # calculate feature representation
+r4 <- eval_feature_representation_summary(p4, s4)
+print(r4)
      ## # A tibble: 20 × 5
 ##    summary    feature total_amount absolute_held relative_held
 ##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
@@ -603,20 +602,20 @@ 
      Multiple zones with complex targets
      
 ## 18 baiting    layer.3        57.6          15.2          0.264
 ## 19 baiting    layer.4        34.1          11.6          0.340
 ## 20 baiting    layer.5        45.4          12.7          0.281
      -
      # plot solution
-plot(category_layer(s4), main = "solution", axes = FALSE, box = FALSE)
      +
      # plot solution
+plot(category_layer(s4), main = "solution", axes = FALSE, box = FALSE)

      Multiple zones with extra constraints

      So it looks like baiting is the way to go! Except that we might recall that we can’t use baits in most of the planning units because they contain native species that are susceptible to baits. So now we need to specify that which of our planning units cannot be assigned to the third zone (baiting) to obtain a more useful solution.

      -
      # create data.frame to specify that we cannot bait in the first 40 units
-l5 <- data.frame(pu = seq(1, 80),
-                 zone = "baiting",
-                 status = 0)
-
-# preview locked data
-head(l5)
      +
      # create data.frame to specify that we cannot bait in the first 40 units
+l5 <- data.frame(pu = seq(1, 80),
+                 zone = "baiting",
+                 status = 0)
+
+# preview locked data
+head(l5)
      ##   pu    zone status
 ## 1  1 baiting      0
 ## 2  2 baiting      0
@@ -624,18 +623,18 @@ 
      Multiple zones with extra constraints
      
 ## 4  4 baiting      0
 ## 5  5 baiting      0
 ## 6  6 baiting      0
      -
      # create problem
-p5 <- problem(pu4, zones(few.traps = sim_features * 0.1,
-                         many.traps = sim_features * 0.5,
-                         baiting = sim_features * 0.8,
-                         feature_names = names(sim_features))) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(t4) %>%
-      add_manual_locked_constraints(l5) %>%
-      add_binary_decisions()
-
-# print problem
-print(p5)
      +
      # create problem
+p5 <- problem(pu4, zones(few.traps = sim_features * 0.1,
+                         many.traps = sim_features * 0.5,
+                         baiting = sim_features * 0.8,
+                         feature_names = names(sim_features))) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(t4) %>%
+      add_manual_locked_constraints(l5) %>%
+      add_binary_decisions()
+
+# print problem
+print(p5)
      ## Conservation Problem
 ##   zones:          few.traps, many.traps, baiting (3 zones)
 ##   planning units: RasterStack (100 units)
@@ -648,8 +647,8 @@ 
      Multiple zones with extra constraints
      
 ##   penalties:      <none>
 ##   portfolio:      default
 ##   solver:         default
      -
      # solve problem
-s5 <- solve(p5)
      +
      # solve problem
+s5 <- solve(p5)
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
 ## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
 ## Optimize a model with 105 rows, 300 columns and 1800 nonzeros
@@ -685,9 +684,9 @@ 
      Multiple zones with extra constraints
      
 ## 
 ## Optimal solution found (tolerance 1.00e-01)
 ## Best objective 7.000000000000e+03, best bound 7.000000000000e+03, gap 0.0000%
      -
      # calculate feature representation
-r5 <- eval_feature_representation_summary(p5, s5)
-print(r5)
      +
      # calculate feature representation
+r5 <- eval_feature_representation_summary(p5, s5)
+print(r5)
      ## # A tibble: 20 × 5
 ##    summary    feature total_amount absolute_held relative_held
 ##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
@@ -711,40 +710,40 @@ 
      Multiple zones with extra constraints
      
 ## 18 baiting    layer.3        57.6          11.7          0.203
 ## 19 baiting    layer.4        34.1           6.05         0.177
 ## 20 baiting    layer.5        45.4           9.98         0.220
      -
      # plot solution
-plot(category_layer(s5), main = "solution", axes = FALSE, box = FALSE)
      +
      # plot solution
+plot(category_layer(s5), main = "solution", axes = FALSE, box = FALSE)

      Multiple zones with fragmentation penalties

      So now the best strategy seems to be a combination of high intensity trapping and baiting. But we can also see that this solution is fairly fragmented, so we can add penalties to cluster managed planning units together. Here we will add penalties that will cluster the planning units allocated to the two trapping zones together, and penalties that will cluster the planning units allocated to the baiting zone together. We will also set an overall penalty factor to 640 to strongly penalize fragmented solutions.

      -
      # create matrix that describe boundary penalties between planning units
-# allocated to different zones
-z6 <- diag(3)
-z6[1, 2] <- 1
-z6[2, 1] <- 1
-colnames(z6) <- c("few.traps", "many.traps", "baiting")
-rownames(z6) <- colnames(z6)
-
-# print matrix
-print(z6)
      +
      # create matrix that describe boundary penalties between planning units
+# allocated to different zones
+z6 <- diag(3)
+z6[1, 2] <- 1
+z6[2, 1] <- 1
+colnames(z6) <- c("few.traps", "many.traps", "baiting")
+rownames(z6) <- colnames(z6)
+
+# print matrix
+print(z6)
      ##            few.traps many.traps baiting
 ## few.traps          1          1       0
 ## many.traps         1          1       0
 ## baiting            0          0       1
      -
      # create problem
-p6 <- problem(pu4, zones("few.traps" = sim_features * 0.1,
-                         "many.traps" = sim_features * 0.5,
-                         "baiting" = sim_features * 0.8,
-                         feature_names = names(sim_features))) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(t4) %>%
-      add_manual_locked_constraints(l5) %>%
-      add_boundary_penalties(penalty = 640, zones = z6) %>%
-      add_binary_decisions()
-
-# print problem
-print(p6)
      +
      # create problem
+p6 <- problem(pu4, zones("few.traps" = sim_features * 0.1,
+                         "many.traps" = sim_features * 0.5,
+                         "baiting" = sim_features * 0.8,
+                         feature_names = names(sim_features))) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(t4) %>%
+      add_manual_locked_constraints(l5) %>%
+      add_boundary_penalties(penalty = 640, zones = z6) %>%
+      add_binary_decisions()
+
+# print problem
+print(p6)
      ## Conservation Problem
 ##   zones:          few.traps, many.traps, baiting (3 zones)
 ##   planning units: RasterStack (100 units)
@@ -757,8 +756,8 @@ 
      Multiple zones with fragmentation penalties
      
 ##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (640), zones]>
 ##   portfolio:      default
 ##   solver:         default
      -
      # solve problem
-s6 <- solve(p6)
      +
      # solve problem
+s6 <- solve(p6)
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
 ## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
 ## Optimize a model with 1905 rows, 1200 columns and 5400 nonzeros
@@ -771,7 +770,7 @@ 
      Multiple zones with fragmentation penalties
      
 ##   RHS range        [1e+00, 8e+00]
 ## Found heuristic solution: objective 20096.000000
 ## Presolve removed 1028 rows and 232 columns
-## Presolve time: 0.01s
+## Presolve time: 0.02s
 ## Presolved: 877 rows, 968 columns, 2712 nonzeros
 ## Variable types: 0 continuous, 968 integer (968 binary)
 ## Found heuristic solution: objective 19632.000000
@@ -794,9 +793,9 @@ 
      Multiple zones with fragmentation penalties
      
 ## 
 ## Optimal solution found (tolerance 1.00e-01)
 ## Best objective 1.058800000000e+04, best bound 1.005600000000e+04, gap 5.0246%
      -
      # calculate feature representation
-r6 <- eval_feature_representation_summary(p6, s6)
-print(r6)
      +
      # calculate feature representation
+r6 <- eval_feature_representation_summary(p6, s6)
+print(r6)
      ## # A tibble: 20 × 5
 ##    summary    feature total_amount absolute_held relative_held
 ##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
@@ -820,29 +819,29 @@ 
      Multiple zones with fragmentation penalties
      
 ## 18 baiting    layer.3        57.6          11.7          0.203
 ## 19 baiting    layer.4        34.1           6.05         0.177
 ## 20 baiting    layer.5        45.4           9.98         0.220
      -
      # plot solution
-plot(category_layer(s6), main = "solution", axes = FALSE, box = FALSE)
      +
      # plot solution
+plot(category_layer(s6), main = "solution", axes = FALSE, box = FALSE)

      Finally, it appears we might have a viable solution for this made-up conservation problem.

      Multiple zones with fragmentation penalties and mandatory allocations

      Finally, we might be interested in conservation planning scenarios where every single planning unit must be allocated to a management zone. This is often the case when developing land-use plans where every single planning unit needs to be allocated to a specific management zone. Though it makes less sense here, let’s see what happens to the solution if we needed to do at least one form of control in every single planning unit.

      -
      # create matrix that describe boundary penalties between planning units
-# allocated to different zones
-p7 <- problem(pu4, zones("few.traps" = sim_features * 0.1,
-                         "many.traps" = sim_features * 0.5,
-                         "baiting" = sim_features * 0.8,
-                         feature_names = names(sim_features))) %>%
-      add_min_set_objective() %>%
-      add_manual_targets(t4) %>%
-      add_mandatory_allocation_constraints() %>%
-      add_manual_locked_constraints(l5) %>%
-      add_boundary_penalties(penalty = 640, zones = z6) %>%
-      add_binary_decisions()
-
-# print problem
-print(p7)
      +
      # create matrix that describe boundary penalties between planning units
+# allocated to different zones
+p7 <- problem(pu4, zones("few.traps" = sim_features * 0.1,
+                         "many.traps" = sim_features * 0.5,
+                         "baiting" = sim_features * 0.8,
+                         feature_names = names(sim_features))) %>%
+      add_min_set_objective() %>%
+      add_manual_targets(t4) %>%
+      add_mandatory_allocation_constraints() %>%
+      add_manual_locked_constraints(l5) %>%
+      add_boundary_penalties(penalty = 640, zones = z6) %>%
+      add_binary_decisions()
+
+# print problem
+print(p7)
      ## Conservation Problem
 ##   zones:          few.traps, many.traps, baiting (3 zones)
 ##   planning units: RasterStack (100 units)
@@ -856,8 +855,8 @@ 
      Multiple zones with fragmentation penalties and mandatory allocations
      
 ##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (640), zones]>
 ##   portfolio:      default
 ##   solver:         default
      -
      # solve problem
-s7 <- solve(p7)
      +
      # solve problem
+s7 <- solve(p7)
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
 ## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
 ## Optimize a model with 1905 rows, 1200 columns and 5400 nonzeros
@@ -892,9 +891,9 @@ 
      Multiple zones with fragmentation penalties and mandatory allocations
      
 ## 
 ## Optimal solution found (tolerance 1.00e-01)
 ## Best objective 1.326000000000e+04, best bound 1.323200000000e+04, gap 0.2112%
      -
      # calculate feature representation
-r7 <- eval_feature_representation_summary(p7, s7)
-print(r7)
      +
      # calculate feature representation
+r7 <- eval_feature_representation_summary(p7, s7)
+print(r7)
      ## # A tibble: 20 × 5
 ##    summary    feature total_amount absolute_held relative_held
 ##    <chr>      <chr>          <dbl>         <dbl>         <dbl>
@@ -918,14 +917,14 @@ 
      Multiple zones with fragmentation penalties and mandatory allocations
      
 ## 18 baiting    layer.3        57.6          11.7         0.203 
 ## 19 baiting    layer.4        34.1           6.05        0.177 
 ## 20 baiting    layer.5        45.4           9.98        0.220
      -
      # plot solution
-plot(category_layer(s7), main = "solution", axes = FALSE, box = FALSE)
      +
      # plot solution
+plot(category_layer(s7), main = "solution", axes = FALSE, box = FALSE)

      Conclusion

      -

      Hopefully, this vignette has provided an informative introduction to building and solving problems with multiple zones using the prioritizr R package. Although we have examined only a few different functions here, almost every single function for modifying conservation planning problems is compatible with problems that contain zones. It’s worth noting that working with multiple zones is a lot trickier than working with a single zone, so we would recommend playing around with the code in the Examples sections of the help pages to get a feel for what different functions do when they are applied to problems with multiple zones.

      +

      Hopefully, this vignette has provided an informative introduction to building and solving problems with multiple zones. Although we have examined only a few different functions here, almost every single function for modifying conservation planning problems is compatible with problems that contain zones. It’s worth noting that working with multiple zones is a lot trickier than working with a single zone, so we would recommend playing around with the code in the Examples sections of the package documentation to help understand how functions work when applied to multiple zones.

      References

      diff --git a/inst/doc/package_overview.Rmd b/inst/doc/package_overview.Rmd new file mode 100644 index 000000000..eb1d5ddf3 --- /dev/null +++ b/inst/doc/package_overview.Rmd @@ -0,0 +1,905 @@ +--- +title: "Package overview" +output: + rmarkdown::html_vignette: + toc: true + fig_caption: true + self_contained: yes +fontsize: 11pt +documentclass: article +bibliography: references.bib +csl: reference-style.csl +vignette: > + %\VignetteIndexEntry{Package overview} + %\VignetteEngine{knitr::rmarkdown_notangle} +--- + +```{r, include = FALSE} +h = 3.5 +w = 3.5 +is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_", + "_R_CHECK_LICENSE_") %in% names(Sys.getenv())) +knitr::opts_chunk$set(fig.align = "center", eval = !is_check, + root.dir = normalizePath("../..")) +``` + +## Summary + +The _prioritizr R_ package uses integer linear programming (ILP) techniques to provide a flexible interface for building and solving conservation planning problems [@r11; @r16]. It supports a broad range of objectives, constraints, and penalties that can be used to custom-tailor conservation planning problems to the specific needs of a conservation planning exercise. Once built, conservation planning problems can be solved using a variety of commercial and open-source exact algorithm solvers. In contrast to the algorithms conventionally used to solve conservation problems, such as heuristics or simulated annealing [@r3], the exact algorithms used here are guaranteed to find optimal solutions. Furthermore, conservation problems can be constructed to optimize the spatial allocation of different management zone (or actions), meaning that conservation practitioners can identify solutions that benefit multiple stakeholders. Finally, this package has the functionality to read input data formatted for the _Marxan_ conservation planning program [@r3], and find much cheaper solutions in a much shorter period of time than _Marxan_ [@r1]. + +## Introduction + +Systematic conservation planning is a rigorous, repeatable, and structured approach to designing new protected areas that efficiently meet conservation objectives [@r4]. Historically, conservation decision-making has often evaluated parcels opportunistically as they became available for purchase, donation, or under threat. Although purchasing such areas may improve the _status quo_, such decisions may not substantially enhance the long-term persistence of target species or communities. Faced with this realization, conservation planners began using decision support tools to help simulate alternative reserve designs over a range of different biodiversity and management goals and, ultimately, guide protected area acquisitions and management actions. Due to the systematic, evidence-based nature of these tools, conservation prioritization can help contribute to a transparent, inclusive, and more defensible decision making process. + +A conservation planning exercise typically starts by defining a study area. This study area should encompass all the areas relevant to the decision maker or the hypothesis being tested. The extent of a study area could encompass a few important localities [e.g., @r18], a single state [e.g., @r17], an entire country [@r19], or the entire planet [@r20]. Next, the study area is divided into a set of discrete areas termed _planning units_. Each planning unit represents a discrete locality in the study area that can be managed independently of other areas. The general idea is that some combination of the planning units can be selected for conservation actions (e.g., protected area establishment, habitat restoration). Planning units are often created as square or hexagon cells that are sized according to the scale of the conservation actions, and the resolution of the data that underpin the planning exercise [but see @r5]. + +Cost data (or a surrogate thereof) are needed to inform the prioritization process. Specifically, these cost data describe the relative expenditure associated with managing each planning unit for conservation. For example, if the goal of the conservation planning exercise is to identify priority areas for expanding a local protected area system, then the cost data could represent the physical cost of purchasing the land. Alternatively, if such data are not available, then surrogate data could are often used instead (e.g., human population density, opportunity cost of foregone commercial activities, or planning unit size). + +Conservation planning exercises also require data on the biodiversity elements that are of conservation interest (termed _conservation features_). These features could be species (e.g., _Neofelis nebulosa_, the Clouded Leopard), populations, or habitats (e.g., mangroves or cloud forest). After identifying the set of relevant conservation features for a conservation planning exercise, spatially explicit data need to be obtained for each and every feature to describe their spatial distribution (e.g., habitat suitability data, probability of occurrence data, presence/absence data). This is important to ensure that conservation features are adequately covered (represented) by prioritizations. After assembling all the data, the next step is to define the conservation planning problem. + +The _prioritizr R_ package is designed to help you build and solve conservation planning problems. Specifically, prioritizations are generated by using formulating a mathematical optimization problem and then solving it to generate a solution. These mathematical optimization problems are formulated using the planning unit data, cost data, and feature data, and with information related to the overarching aim of the prioritization process. In general, the goal of an optimization problem is to minimize (or maximize) an _objective function_ that is calculated using a set of _decision variables_, subject to a series of constraints to ensure that solution exhibits specific properties. The objective function describes the quantity which we are trying to minimize (e.g., cost of the solution) or maximize (e.g., number of features conserved). The decision variables describe the entities that we can control, and indicate which planning units are selected for conservation management and which of those are not. The constraints can be thought of as rules that the need decision variables need to follow. For example, a commonly used constraint is specifying that the solution must not exceed a certain budget. + +A wide variety of approaches have been developed for solving optimization problems. Reserve design problems are frequently solved using simulated annealing [@r6] or heuristics [@r8; @r7]. These methods are conceptually simple and can be applied to a wide variety of optimization problems. However, they do not scale well for large or complex problems [@r1]. Additionally, these methods cannot tell you how close any given solution is to the optimal solution. The package uses exact algorithms to efficiently solve conservation planning problems to within a pre-specified a optimality gap. In other words, you can specify that you need the optimal solution (i.e., a gap of 0%) and the algorithms will, given enough time, find a solution that meets this criteria. In the past, exact algorithms have been too slow for conservation planning exercises [@r9]. However, improvements over the last decade mean that they are now much faster [@r23; @r1]. + +In this package, optimization problems are expressed using _integer linear programming_ (ILP) so that they can be solved using (linear) exact algorithm solvers. The general form of an integer programming problem can be expressed in matrix notation using the following equation. + +$$\text{Minimize} \space \boldsymbol{c}^\text{T} \boldsymbol{x} \space +\space \text{subject to} \space A\boldsymbol{x} +\space \Box \space \boldsymbol{b}$$ + +Here, where $x$ is a vector of decision variables, $c$ and $b$ are vectors of known coefficients, and $A$ is the constraint matrix. The final term specifies a series of structural constants and the $\Box$ symbol is used to indicate that the relational operators for the constraints can be either $\geq$, $=$, or $\leq$. In the context of a conservation planning problem, $c$ could be used to represent the planning unit costs, $A$ could be used to store the data showing the presence / absence (or amount) of each feature in each planning unit, $b$ could be used to represent minimum amount of habitat required for each species in the solution, the $\Box$ could be set to $\geq$ symbols to indicate that the total amount of each feature in the solution must exceed the quantities in $b$. But there are many other ways of formulating the reserve selection problem [@r11]. + +## A grammar for conservation planning + +The _prioritizr R_ package uses a grammar to describe elements of conservation planning. This means that functions are organized into verbs that relate to specific concepts. For example, all of the functions used to specify the primary objective for optimization end with the `_objective` suffix (e.g., `add_min_set_objective()` and `add_min_shortfall_objective()`). By combining multiple functions together, they can be used to formulate a complete conservation planning problem. Specifically, the verbs for formulating problems are described below. + +* Create a new conservation planning [problem](https://prioritizr.net/reference/problem.html) by specifying the planning units, features, and management zones of conservation interest. +* Add a primary [objective](https://prioritizr.net/reference/objectives.html) to a conservation planning problem (e.g., minimize overall cost). +* Add [penalties](https://prioritizr.net/reference/penalties.html) to a conservation planning problem to penalize solutions according to specific metric (e.g., connectivity). +* Add [targets](https://prioritizr.net/reference/targets.html) to a conservation planning problem to specify how much of each feature should ideally be represented solutions. +* Add [constraints](https://prioritizr.net/reference/constraints.html) to a conservation planning problem to ensure that solutions exhibit specific properties (e.g., select specific planning units for protection). +* Add [decisions](https://prioritizr.net/reference/decisions.html) to a conservation planning problem to specify the nature of the decisions in the problem (e.g., binary decisions indicate the planning units should be selected or not selected for management). +* Add a [portfolio](https://prioritizr.net/reference/portfolios.html) to a conservation planning problem to specify a methodological approach for generating multiple solutions (e.g. generate multiple solutions by finding 100 solutions within 10% of optimality). +* Add a [solver](https://prioritizr.net/reference/solvers.html) to a conservation problem to specify the optimization software (e.g. Gurobi) for generating solutions and customize the optimization settings (e.g. generate an optimal solution). + +After building a conservation planning problem, it can be solved to generate a prioritization (using the `solve()` function). There are also verbs available to help evaluate and interpret solutions. These verbs are described below. + +* Evaluate performance by computing [summary statistics](https://prioritizr.net/reference/summaries.html) (e.g. overall cost, feature representation, or total boundary length). +* Evaluate the relative [importance](https://prioritizr.net/reference/importance.html) of planning units selected by a solution (e.g. based on irreplaceability). + +## Workflow + +The general workflow when using the _prioritizr R_ package starts with creating a new conservation planning `problem()` object using data. Specifically, the `problem()` object should be constructed using data that specify the planning units, biodiversity features, management zones (if applicable), and costs. After creating a new `problem()` object, it can be customized---by adding objectives, penalties, constraints, and other information---to build a precise representation of the conservation planning problem required, and then solved to obtain a solutions. + +All conservation planning problems require an objective. An objective specifies the property which is used to compare different feasible solutions. Simply put, the objective is the property of the solution which should be maximized or minimized during the optimization process. For instance, with the minimum set objective (specified using `add_min_set_objective()`), we are seeking to minimize the cost of the solution (similar to _Marxan_). On the other hand, with the minimum shortfall objective (specified using `add_min_shortfall_objective()`), we are seeking to minimize the average target shortfall for all features represented in the solution, subject to a budget. + +Many objectives require representation targets (e.g., the minimum set objective). These targets are a specialized set of constraints that relate to the total quantity of each feature secured in the solution (e.g., amount of suitable habitat or number of individuals). In the case of the minimum set objective ( `add_min_set_objective()`), they are used to ensure that solutions secure a sufficient quantity of each feature, and in other objectives, such as the maximum features objective ( `add_max_features_objective()`) they are used to assess whether a feature has been adequately conserved by a candidate solution. Targets can be expressed numerically as the total amount required for a given feature (using `add_absolute_targets()`), or as a proportion of the total amount found in the planning units (using `add_relative_targets()`). Note that not all objectives require targets, and a warning will be thrown if an attempt is made to add targets to a problem with an objective that does not use them. + +Constraints and penalties can be added to a conservation planning problem to ensure that solutions exhibit a specific property or penalize solutions which don't exhibit a specific property (respectively). The difference between constraints and penalties, strictly speaking, is constraints are used to rule out potential solutions that don't exhibit a specific property. For instance, constraints can be used to ensure that specific planning units are selected in the solution for prioritization (using `add_locked_in_constraints()`) or not selected in the solution for prioritization (using `add_locked_out_constraints()`). On the other hand, penalties are combined with the objective of a problem, with a penalty factor, and the overall objective of the problem then becomes to minimize (or maximize) the primary objective function and the penalty function. For example, penalties can be added to a problem to penalize solutions that are excessively fragmented (using `add_boundary_penalties()`). These penalties have a `penalty` argument that specifies the relative importance of having spatially clustered solutions. When the argument to `penalty` is high, then solutions which are less fragmented are valued more highly -- even if they cost more -- and when the argument to `penalty` is low, then the solutions which are more fragmented are valued less highly. + +After building a conservation problem, it can then be solved to obtain a solution (or portfolio of solutions if desired). The solution is returned in the same format as the planning unit data used to construct the problem. For instance, this means that if raster data was used to initialize the problem, then the solution will also be output in raster format. This can be very helpful when it comes to interpreting and visualizing solutions because it means that the solution data does not first have to be merged with spatial data before they can be plotted on a map. + +## Usage + +Here we will provide an introduction to using the _prioritizr R_ package to build and solve a conservation planning problem. Please note that we will not discuss conservation planning with multiple zones in this vignette, for more information on working with multiple management zones please see the [zones vignette](zones.html). + +First, we will load the _prioritizr_ package. + +```{r, results = "hide", message = FALSE} +# load package +library(prioritizr) + +# set default options for printing tabular data +options(tibble.width = Inf) +``` + +### Data + +Now we will load some built-in data sets that are distributed with the _prioritizr R_ package. This package contains several different planning unit data sets. To provide a comprehensive overview of the different ways that we can initialize a conservation planning problem, we will load each of them. + +First, we will load the raster planning unit data (`sim_pu_raster`). Here, the planning units are represented as a raster (i.e., a `RasterLayer` object) and each pixel corresponds to the spatial extent of each panning unit. The pixel values correspond to the acquisition costs of each planning unit. + +```{r} +# load raster planning unit data +data(sim_pu_raster) + +# print description of the data +print(sim_pu_raster) + +# plot the data +plot(sim_pu_raster) +``` + +Secondly, we will load one of the spatial vector planning unit data sets (`sim_pu_polygons`). Here, each polygon (i.e., feature using ArcGIS terminology) corresponds to a different planning unit. This data set has an attribute table that contains additional information about each polygon. Namely, the `cost` field (column) in the attribute table contains the acquisition cost for each planning unit. + +```{r} +# load polygon planning unit data +data(sim_pu_polygons) + +# print first six rows of attribute table +head(sim_pu_polygons@data) + +# plot the planning units +spplot(sim_pu_polygons, zcol = "cost") +``` + +Thirdly, we will load some planning unit data stored in tabular format (i.e., `data.frame` format). For those familiar with _Marxan_ or dealing with very large conservation planning problems (> 10 million planning units), it may be useful to work with data in this format because it does not contain any spatial information which will reduce computational burden. When using tabular data to initialize conservation planning problems, the data must follow the conventions used by _Marxan_. Specifically, each row in the planning unit table must correspond to a different planning unit. The table must also have an "id" column to provide a unique integer identifier for each planning unit, and it must also have a column that indicates the cost of each planning unit. For more information, please see the [official _Marxan_ documentation](https://marxansolutions.org/). + +```{r} +# specify file path for planning unit data +pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr") + +# load in the tabular planning unit data +# note that we use the data.table::fread function, as opposed to the read.csv +# function, because it is much faster +pu_dat <- data.table::fread(pu_path, data.table = FALSE) + +# preview first six rows of the tabular planning unit data +# note that it has some extra columns other than id and cost as per the +# Marxan format +head(pu_dat) +``` + +Finally, we will load data showing the spatial distribution of the conservation features. Our conservation features (`sim_features`) are represented as a stack of raster objects (i.e., a `RasterStack` object) where each layer corresponds to a different feature (e.g., a multi-band GeoTIFF where each band corresponds to a different feature). The pixel values in each layer correspond to the amount of suitable habitat available in a given planning unit. Note that our planning unit raster layer and our conservation feature stack have exactly the same spatial properties (i.e., resolution, extent, coordinate reference system) so their pixels line up perfectly. + +```{r, fig.width = 4, fig.height = 3} +# load feature data +data(sim_features) + +# plot the distribution of suitable habitat for each feature +plot(sim_features, main = paste("Feature", seq_len(nlayers(sim_features))), + nr = 2, box = FALSE, axes = FALSE) +``` + +### Initialize a problem + +After having loaded our planning unit and feature data, we will now try initializing the some conservation planning problems. There are a lot of different ways to initialize a conservation planning problem, so here we will just showcase a few of the more commonly used methods. For an exhaustive description of all the ways you can initialize a conservation problem, see the help file for the `problem()` function. First off, we will initialize a conservation planning problem using the raster data. + +```{r} +# create problem +p1 <- problem(sim_pu_raster, sim_features) + +# print problem +print(p1) + +# print number of planning units +number_of_planning_units(p1) + +# print number of features +number_of_features(p1) +``` + +Generally, we recommend initializing problems using raster data where possible. This is because the `problem()` function needs to calculate the amount of each feature in each planning unit, and by providing both the planning unit and feature data in raster format with the same spatial resolution, extents, and coordinate systems, this means that the `problem()` function does not need to do any geoprocessing behind the scenes. But sometimes we can't use raster planning unit data because our planning units aren't equal-sized grid cells. So, below is an example showing how we can initialize a conservation planning problem using planning units that are formatted as spatial vector data. Note that if we had precomputed the amount of each feature in each planning unit and stored the data in the attribute table, we could pass in the names of the columns as an argument to the `problem()` function. + +```{r} +# create problem with spatial vector data +# note that we have to specify which column in the attribute table contains +# the cost data +p2 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") + +# print problem +print(p2) +``` + +We can also initialize a conservation planning problem using tabular planning unit data (i.e., `data.frame` format). Since the tabular planning unit data does not contain any spatial information, we also have to provide the feature data in tabular format (i.e., `data.frame` format) and data showing the amount of each feature in each planning unit in tabular format (i.e., `data.frame` format). The feature data must have an "id" column containing a unique integer identifier for each feature, and the planning unit by feature data must contain the following three columns: `pu` corresponding to the planning unit identifiers, `species` corresponding to the feature identifiers, and `amount` showing the amount of a given feature in a given planning unit. + +```{r} +# set file path for feature data +spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr") + +# load in feature data +spec_dat <- data.table::fread(spec_path, data.table = FALSE) + +# print first six rows of the data +# note that it contains extra columns +head(spec_dat) + +# set file path for planning unit vs. feature data +puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr") + +# load in planning unit vs feature data +puvspr_dat <- data.table::fread(puvspr_path, data.table = FALSE) + +# print first six rows of the data +head(puvspr_dat) + +# create problem +p3 <- problem(pu_dat, spec_dat, cost_column = "cost", rij = puvspr_dat) + +# print problem +print(p3) +``` + +For more information on initializing problems, please see the help page for the `problem()` function (which you can open by entering the code: `?problem`). Now that we have initialized a conservation planning problem, we will show you how you can customize it to suit the exact needs of your conservation planning scenario. Although we initialized the conservation planning problems using several different methods, moving forward, we will only use raster-based planning unit data to keep things simple. + +### Add an objective + +The next step is to add a primary objective to the problem. A problem objective is used to specify the primary goal of the problem (i.e., the quantity that is to be maximized or minimized). All conservation planning problems involve minimizing or maximizing some kind of objective. For instance, we might require a solution that conserves enough habitat for each species while minimizing the overall cost of the reserve network. Alternatively, we might require a solution that maximizes the number of conserved species while ensuring that the cost of the reserve network does not exceed the budget. Please note that objectives are added in the same way regardless of the type of data used to initialize the problem. The following objectives are available. + +* __Minimum set objective__: Minimize the cost of the solution whilst ensuring that all targets are met [@r11]. This objective is similar to that used in _Marxan_ [@r3]. For example, we can add a minimum set objective to a problem using the following code. +```{r} +# create a new problem that has the minimum set objective +p3 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() + +# print the problem +print(p3) +``` +* __Maximum cover objective__: Represent at least one instance of as many features as possible within a given budget [@r12]. +```{r} +# create a new problem that has the maximum coverage objective and a budget +# of 5000 +p4 <- problem(sim_pu_raster, sim_features) %>% + add_max_cover_objective(5000) + +# print the problem +print(p4) +``` +* __Maximum features objective__: Fulfill as many targets as possible while ensuring that the cost of the solution does not exceed a budget [inspired by @r10]. This object is similar to the maximum cover objective except that we have the option of later specifying targets for each feature. In practice, this objective is more useful than the maximum cover objective because features often require a certain amount of area for them to persist and simply capturing a single instance of habitat for each feature is generally unlikely to enhance their long-term persistence. +```{r} +# create a new problem that has the maximum features objective and a budget +# of 5000 +p5 <- problem(sim_pu_raster, sim_features) %>% + add_max_features_objective(budget = 5000) + +# print the problem +print(p5) +``` +* __Minimum shortfall objective__: Minimize the overall (weighted sum) shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when there is a large amount of left-over budget when using the maximum feature representation objective and the remaining funds need to be allocated to places that will enhance the representation of features with unmet targets. +```{r} +# create a new problem that has the minimum shortfall objective and a budget +# of 5000 +p6 <- problem(sim_pu_raster, sim_features) %>% + add_min_shortfall_objective(budget = 5000) + +# print the problem +print(p6) +``` +* __Minimum largest shortfall objective__: Minimize the largest (maximum) shortfall while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when the minimum shortfall objective returns solutions that focus too much on representing a small number of features (e.g., because they occur in much cheaper planning units), and solutions are needed to spread conservation effort out more evenly among all features---even if it means that all features will have (relatively) poor representation. +```{r} +# create a new problem that has the minimum largest shortfall objective and a +# budget of 5000 +p7 <- problem(sim_pu_raster, sim_features) %>% + add_min_largest_shortfall_objective(budget = 5000) + +# print the problem +print(p7) +``` +* __Maximum phylogenetic diversity objective__: Maximize the phylogenetic diversity of the features represented in the solution subject to a budget [inspired by @r13; @r14]. This objective is similar to the maximum features objective except that emphasis is placed on protecting features which are associated with a diverse range of evolutionary histories. The package contains a simulated phylogeny that can be used with the simulated feature data (`sim_phylogny`). +```{r} +# load simulated phylogeny data +data(sim_phylogeny) + +# create a new problem that has the maximum phylogenetic diversity +# objective and a budget of 5000 +p8 <- problem(sim_pu_raster, sim_features) %>% + add_max_phylo_div_objective(budget = 5000, tree = sim_phylogeny) + +# print the problem +print(p8) +``` +* __Maximum phylogenetic endemism objective__: Maximize the phylogenetic endemism of the features represented in the solution subject to a budget [inspired by @r13; @r14; @r32]. This objective is similar to the maximum phylogenetic diversity except that emphasis is placed conserving features that are associated with geographically restricted periods of evolutionary history rather than a diverse range of evolutionary histories. +```{r} +# load simulated phylogeny data +data(sim_phylogeny) + +# create a new problem that has the maximum phylogenetic diversity +# objective and a budget of 5000 +p9 <- problem(sim_pu_raster, sim_features) %>% + add_max_phylo_end_objective(budget = 5000, tree = sim_phylogeny) + +# print the problem +print(p9) +``` +* __Maximum utility objective__: Secure as much of the features as possible without exceeding a budget. This objective is functionally equivalent to selecting the planning units with the greatest amounts of each feature (e.g., species richness). Generally, we don't encourage the use of this objective because it will only rarely identify complementary solutions--solutions which adequately conserve a range of different features---except perhaps to explore trade-offs or provide a baseline solution with which to compare other solutions. +```{r} +# create a new problem that has the maximum utility objective and a budget +# of 5000 +p10 <- problem(sim_pu_raster, sim_features) %>% + add_max_utility_objective(budget = 5000) + +# print the problem +print(p10) +``` + +### Add targets + +Most conservation planning problems require targets. Targets are used to specify the minimum amount or proportion of a feature's distribution that needs to be protected in the solution. For example, we may want to develop a reserve network that will secure 20% of the distribution for each feature for minimal cost. The following methods are available for specifying targets. + +* __Absolute targets__: Targets are expressed as the total amount of each feature in the study area that need to be secured. For example, if we had binary feature data that showed the absence or presence of suitable habitat across the study area, we could set an absolute target as 5 to mean that we require 5 planning units with suitable habitat in the solution. +```{r} +# create a problem with targets which specify that the solution must conserve +# a need a sum total of 3 units of suitable habitat for each feature +p11 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_absolute_targets(3) + +# print problem +print(p11) +``` +* __Relative targets__: Targets are set as a proportion (between 0 and 1) of the total amount of each feature in the study area. For example, if we had binary feature data and the feature occupied a total of 20 planning units in the study area, we could set a relative target of 50 % to specify that the solution must secure 10 planning units for the feature. We could alternatively specify an absolute target of 10 to achieve the same result, but sometimes proportions are easier to work with. +```{r} +# create a problem with the minimum set objective and relative targets of 10 % +# for each feature +p12 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) + +# print problem +print(p12) + +# create a problem with targets which specify that we need 10 % of the habitat +# for the first feature, 15 % for the second feature, 20 % for the third feature +# 25 % for the fourth feature and 30 % of the habitat for the fifth feature +targets <- c(0.1, 0.15, 0.2, 0.25, 0.3) +p13 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(targets) + +# print problem +print(p13) +``` +* __Log-linear targets__: Targets are expressed using scaling factors and log-linear interpolation. This method for specifying targets is commonly used for global prioritization analyses [@r15]. +```{r} +# create problem with added log-linear targets +p14 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_loglinear_targets(10, 0.9, 100, 0.2) + +# print problem +print(p14) +``` +* __Manual targets__: Targets are manually specified. This is only really recommended for advanced users or problems that involve multiple management zones. See the [zones vignette](zones.html) for more information on these targets. + +As with the functions for specifying the objective of a problem, if we try adding multiple targets to a problem, only the most recently added set of targets are used. + +### Add constraints + +A constraint can be added to a conservation planning problem to ensure that all solutions exhibit a specific property. For example, they can be used to make sure that all solutions select a specific planning unit or that all selected planning units in the solution follow a certain configuration. The following constraints are available. + +* __Locked in constraints__: Add constraints to ensure that certain planning units are prioritized in the solution. For example, it may be desirable to lock in planning units that are inside existing protected areas so that the solution fills in the gaps in the existing reserve network. +```{r} +# create problem with constraints which specify that the first planning unit +# must be selected in the solution +p15 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_locked_in_constraints(1) + +# print problem +print(p15) +``` +* __Locked out constraints__: Add constraints to ensure that certain planning units are not prioritized in the solution. For example, it may be useful to lock out planning units that have been degraded and are not suitable for conserving species. +```{r} +# create problem with constraints which specify that the second planning unit +# must not be selected in the solution +p16 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_locked_out_constraints(2) + +# print problem +print(p16) +``` +* __Neighbor constraints__: Add constraints to a conservation problem to ensure that all selected planning units have at least a certain number of neighbors. +```{r} +# create problem with constraints which specify that all selected planning units +# in the solution must have at least 1 neighbor +p17 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_neighbor_constraints(1) + +# print problem +print(p17) +``` +* __Contiguity constraints__: Add constraints to a conservation problem to ensure that all selected planning units are spatially connected to each other and form spatially contiguous unit. +```{r} +# create problem with constraints which specify that all selected planning units +# in the solution must form a single contiguous unit +p18 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_contiguity_constraints() + +# print problem +print(p18) +``` +* __Feature contiguity constraints__: Add constraints to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of those implemented in the `add_contiguity_constraints` function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit. +```{r} +# create problem with constraints which specify that the planning units used +# to conserve each feature must form a contiguous unit +p19 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_feature_contiguity_constraints() + +# print problem +print(p19) +``` + +* __Linear constraints__: Add constraints to ensure that all selected planning units meet certain criteria. For example, they can be used to add multiple budgets, or limit the number of planning units selected in different administrative areas within a study region (e.g., different countries). + +```{r} +# create problem with constraints which specify that the sum of +# values in sim_features[[1]] among selected planning units must not exceed a +#' threshold value of 190. +p20 <- problem(sim_pu_raster, sim_features) %>% + add_min_shortfall_objective(budget = 1800) %>% + add_relative_targets(0.1) %>% + add_linear_constraints(190, "<=", sim_features[[1]]) + +# print problem +print(p20) +``` + +* __Mandatory allocation constraints__: Add constraints to ensure that every planning unit is allocated to a management zone in the solution. Please note that this function can only be used with problems that contain multiple zones. For more information on problems with multiple zones and an example using this function, see the Management Zones vignette. + +In particular, The `add_locked_in_constraints` and `add_locked_out_constraints` functions are incredibly useful for real-world conservation planning exercises, so it's worth pointing out that there are several ways we can specify which planning units should be locked in or out of the solutions. If we use raster planning unit data, we can also use raster data to specify which planning units should be locked in our locked out. + +```{r, fig.width = 6.5, fig.height = 2.5} +# load data to lock in or lock out planning units +data(sim_locked_in_raster) +data(sim_locked_out_raster) + +# plot the locked data +plot(stack(sim_locked_in_raster, sim_locked_out_raster), + main = c("Locked In", "Locked Out")) + +# create a problem using raster planning unit data and use the locked raster +# data to lock in some planning units and lock out some other planning units +p21 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_locked_in_constraints(sim_locked_in_raster) %>% + add_locked_out_constraints(sim_locked_out_raster) + +# print problem +print(p21) +``` + +If our planning unit data are in a spatial vector format (similar to the `sim_pu_polygons` data) or a tabular format (similar to `pu_dat`), we can use the field names in the data to refer to which planning units should be locked in and / or out. For example, the `sim_pu_polygons` object has `TRUE` / `FALSE` values in the "locked_in" field which indicate which planning units should be selected in the solution. We could use the data in this field to specify that those planning units with `TRUE` values should be locked in using the following methods. + +```{r} +# preview first six rows of the attribute table for sim_pu_polygons +head(sim_pu_polygons@data) + +# specify locked in data using the field name +p22 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_locked_in_constraints("locked_in") + +# print problem +print(p22) + +# specify locked in data using the values in the field +p23 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_locked_in_constraints(which(sim_pu_polygons$locked_in)) + +# print problem +print(p23) +``` + +### Add penalties + +We can also add penalties to a problem to favor or penalize solutions according to a secondary objective. Unlike the constraint functions, these functions will add extra information to the objective function of the optimization function to penalize solutions that do not exhibit specific characteristics. For example, penalties can be added to a problem to avoid highly fragmented solutions at the expense of accepting slightly more expensive solutions. All penalty functions have a `penalty` argument that controls the relative importance of the secondary penalty function compared to the primary objective function. It is worth noting that incredibly low or incredibly high `penalty` values -- relative to the main objective function -- can cause problems to take a very long time to solve, so when trying out a range of different penalty values it can be helpful to limit the solver to run for a set period of time. The following penalties are available. + +* __Boundary penalties__: Add penalties to penalize solutions that are excessively fragmented. These penalties are similar to those used in _Marxan_ [@r3; @r1]. +```{r} +# create problem with penalties that penalize fragmented solutions with a +# penalty factor of 0.01 +p24 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_boundary_penalties(penalty = 0.01) + +# print problem +print(p24) +``` +* __Connectivity penalties__: Add penalties to favor solutions that select combinations of planning units with high connectivity between them. These penalties are similar to those used in _Marxan with Zones_ [@r2; @r1]. This function supports both symmetric and asymmetric connectivities among planning units. +```{r} +# create problem with penalties that favor combinations of planning units with +# high connectivity, here we will use only the first four layers in +# sim_features for the features and we will use the fifth layer in sim_features +# to represent the connectivity data, where the connectivity_matrix function +# will create a matrix showing the average strength of connectivity between +# adjacent planning units using the data in the fifth layer of sim_features +p25 <- problem(sim_pu_raster, sim_features[[1:4]]) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_boundary_penalties( + penalty = 5, + data = connectivity_matrix(sim_pu_raster, sim_features[[5]])) + +# print problem +print(p25) +``` +* __Linear penalties__: Add penalties to penalize solutions that select planning units according to a certain variable (e.g., anthropogenic pressure). +```{r} +# create data for penalizing planning units +# (note this requires the RandomFields package to be installed) +pen_raster <- simulate_cost(sim_pu_raster) + +# create problem with penalties that penalize solutions that select +# planning units with high values in the pen_raster object, +# here we will use a penalty value of 5 to indicate the trade-off (scaling) +# between the penalty values (in the sim_pu_raster) and the main objective +# (i.e., the cost of the solution) +p26 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_linear_penalties(penalty = 5, data = pen_raster) + +# print problem +print(p26) +``` + +### Add the decision types + +Conservation planning problems involve making decisions on how planning units will be managed. These decisions are then associated with management actions (e.g., turning a planning unit into a protected area). The type of decision describes how the action is applied to planning units. For instance, the default decision-type is a binary decision type, meaning that we are either selecting or not selecting planning units for management. The following decision types are available. + +* __Binary decisions__: Add a binary decision to a conservation planning problem. This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem object, then this decision class will be used by default. +```{r} +# add binary decisions to a problem +p27 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() + +# print problem +print(p27) +``` +* __Proportion decisions__: Add a proportion decision to a problem. This is a relaxed decision where a part of a planning unit can be prioritized, as opposed to the default of the entire planning unit. Typically, this decision has the assumed action of buying a fraction of a planning unit to include in a protected area network. Generally, problems can be solved much faster with proportion-type decisions than binary-type decisions, so they can be very useful when commercial solvers are not available. +```{r} +# add proportion decisions to a problem +p28 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_proportion_decisions() + +# print problem +print(p28) +``` +* __Semi-continuous decisions__: Add a semi-continuous decision to a problem. This decision is similar to proportion decisions except that it has an upper bound parameter. By default, the decision can range from prioritizing none (0%) to all (100%) of a planning unit. However, a upper bound can be specified to ensure that at most only a fraction (e.g., 80%) of a planning unit can be purchased. This type of decision may be useful when it is not practical to conserve the entire area indicated by a planning unit. +```{r} +# add semi-continuous decisions to a problem, where we can only manage at most +# 50 % of the area encompassed by a planning unit +p29 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_semicontinuous_decisions(0.5) + +# print problem +print(p29) +``` + +### Add a solver + +Next, after specifying the mathematical formulation that underpins your conservation planning problem, you can specify how the problem should be solved. If you do not specify this information, the _prioritizr R_ package will automatically use the best solver currently installed on your system with some reasonable defaults. __We strongly recommend installing the [Gurobi software suite and the _gurobi_ _R_ package](https://www.gurobi.com/) to solve problems, and for more information on this topic please refer to the [Gurobi Installation Guide](gurobi_installation.html)__. The following solvers are available. + +* __*Gurobi* solver__: [_Gurobi_](https://www.gurobi.com/) is a state of the art commercial optimization software. It is by far the fastest of the solvers that can be used to solve conservation problems. However, it is not freely available. That said, special licenses are available to academics at no cost. +```{r} +# create a problem and specify that Gurobi should be used to solve the problem +# and specify an optimality gap of zero to obtain the optimal solution +p30 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_gurobi_solver(gap = 0) + +# print problem +print(p30) +``` +* __*IBM CPLEX* solver__: [_IBM CPLEX_](https://www.ibm.com/analytics/cplex-optimizer) is a commercial optimization software. It is faster than the open source solvers available for generating prioritizations (see below), however, it is not freely available. Similar to the _Gurobi_ software, special licenses are available to academics at no cost. +```{r} +# create a problem and specify that IBM CPLEX should be used to solve the +# problem and specify an optimality gap of zero to obtain the optimal solution +p31 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_cplex_solver(gap = 0) + +# print problem +print(p31) +``` +* __*CBC* solver__: [*CBC*](https://projects.coin-or.org/Cbc) is an +open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. Although formal benchmarks have yet to be completed, preliminary analyses suggest that it is +the fastest open-source solver available for generating prioritizations. It requires the _rcbc R_ package, which is currently only available on [GitHub](https://github.com/dirkschumacher/rcbc). +```{r} +# create a problem and specify that CBC should be used to solve the +# problem and specify an optimality gap of zero to obtain the optimal solution +p32 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_cbc_solver(gap = 0) + +# print problem +print(p32) +``` +* __*lpsymphony* solver__: [_SYMPHONY_](https://projects.coin-or.org/SYMPHONY) is an open-source integer programming solver that is also part of the COIN-OR project. This solver uses the _lpsymphony R_ package (available on [Bioconductor](http://bioconductor.org/packages/release/bioc/html/lpsymphony.html)) to interface with the _SYMPHONY_ software. +```{r} +# create a problem and specify that lpsymphony should be used to solve the +# problem and specify an optimality gap of zero to obtain the optimal solution +p33 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_lpsymphony_solver(gap = 0) + +# print problem +print(p33) +``` +* __*Rsymphony* solver__: This solver provides a different interface to the [_SYMPHONY_](https://projects.coin-or.org/SYMPHONY) software. It uses the _Rsymphony R_ package which is available on The Comprehensive R Archive Network (CRAN). This solver is generally slower than the other solvers, because it cannot use parallel processing. +```{r} +# create a problem and specify that Rsymphony should be used to solve the +# problem and specify an optimality gap of zero to obtain the optimal solution +p34 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_rsymphony_solver(gap = 0) + +# print problem +print(p34) +``` + +### Add a portfolio + +Many conservation planning exercises require a portfolio of solutions. For example, real-world exercises can involve presenting decision makers with a range of near-optimal decisions. Additionally, the number of times that different planning units are selected in different solutions can provide insight into their relative importance. The following portfolio methods are available. + +* __Gap portfolio__: Generate a portfolio of solutions by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is especially useful for generating multiple solutions that can used be to calculate selection frequencies (similar to _Marxan_). Note that this method requires that the _Gurobi_ optimization software is used to generate solutions. +```{r} +# create a problem and specify that a portfolio should be created by +# finding five solutions within 10% of optimality +p35 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_gap_portfolio(number_solutions = 5, pool_gap = 0.2) + +# print problem +print(p35) +``` +* __Top portfolio__: Generate a portfolio of solutions by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions). Note that this method requires that the _Gurobi_ optimization software is used to generate solutions. +```{r} +# create a problem and specify that a portfolio should be created using +# the top five solutions +p36 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_top_portfolio(number_solutions = 5) + +# print problem +print(p36) +``` +* __Extra portfolio__: Generate a portfolio of solutions by storing feasible solutions found during the optimization process. Note that this method requires that the _Gurobi_ optimization software is used to generate solutions. +```{r} +# create a problem and specify that a portfolio should be created using +# extra solutions found while solving the problem +p37 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_extra_portfolio() + +# print problem +print(p37) +``` +* __Cuts portfolio__: Generate a portfolio of distinct solutions within a pre-specified optimality gap. This method is only recommended if the _Gurobi_ optimization solver is not available. +```{r} +# create a problem and specify that a portfolio containing 10 solutions +# should be created using using Bender's cuts +p38 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_cuts_portfolio(number_solutions = 10) + +# print problem +print(p38) +``` +* __Shuffle portfolio__: Generate a portfolio of solutions by randomly reordering the data prior to attempting to solve the problem. If the _Gurobi_ optimization solver is not available, this method is the fastest method for generating a set number of solutions within a specified distance from optimality. +```{r} +# create a problem and specify a portfolio should be created that contains +# 10 solutions and that any duplicate solutions should not be removed +p39 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() %>% + add_shuffle_portfolio(number_solutions = 10, remove_duplicates = FALSE) + +# print problem +print(p39) +``` + +### Solve the problem + +After formulating our conservation planning problem and specifying how the problem should be solved, we can use the `solve` function to obtain a solution. Note that the solver will typically print out some information describing the size of the problem and report its progress when searching for a suitable solution. + +```{r, fig.height = h, fig.width = w} +# formulate the problem +p40 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_boundary_penalties(penalty = 500, edge_factor = 0.5) %>% + add_binary_decisions() + +# solve the problem (using the default solver) +s40 <- solve(p40) + +# plot solution +plot(s40, col = c("grey90", "darkgreen"), main = "Solution", + xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1)) +``` + +We can plot this solution because the planning unit input data are spatially referenced in a raster format. The output format will always match the planning unit data used to initialize the problem. For example, the solution to a problem with planning units in a spatial vector (shapefile) format would also be in a spatial vector format. Similarly, if the planning units were in a tabular format (i.e., `data.frame`), the solution would also be returned in a tabular format. + +We can also extract attributes from the solution that describe the quality of the solution and the optimization process. + +```{r} +# extract the objective (numerical value being minimized or maximized) +print(attr(s40, "objective")) + +# extract time spent solving solution +print(attr(s40, "runtime")) + +# extract state message from the solver that describes why this specific +# solution was returned +print(attr(s40, "status")) +``` + +## Evaluate the solution + +Conservation planning involves making trade-offs between different criteria (e.g. overall cost, feature representation, connectivity). After obtaining a solution to a conservation planning problem, it is important to evaluate it to help understand the trade-offs made by the prioritization. This is also useful to compare different solutions with each other. + +### Evaluating performance + +Summary statistics can be computed to evaluate the overall performance of a solution based on certain criteria. The following summaries can be computed. + +The following functions are available to summarize a solution: + +* __Number summary__: Calculate the number of planning units selected by a solution. +```{r} +# calculate statistic +eval_n_summary(p40, s40) +``` +* __Cost summary__: Calculate the total cost of a solution. +```{r} +# calculate statistic +eval_cost_summary(p40, s40) +``` +* __Feature representation summary__: Calculate how well features are represented by a solution. This function can be used for any type of problem. +```{r} +# calculate statistics +eval_feature_representation_summary(p40, s40) +``` +* __Target coverage summary__: Calculate how well representation targets are met by a solution. This function can only be used with problems contain targets. +```{r} +# calculate statistics +eval_target_coverage_summary(p40, s40) +``` +* __Boundary summary__: Calculate the total exposed boundary length (perimeter) associated with a solution. +```{r} +# calculate statistic +eval_boundary_summary(p40, s40) +``` +* __Connectivity summary__: Calculate the connectivity facilitated within a solution. +```{r} +# calculate statistic +# here we use the raster data for the first feature as an example +# to parametrize pair-wise connectivity between different planning units +eval_connectivity_summary( + p40, s40, data = connectivity_matrix(sim_pu_raster, sim_features[[1]])) +``` + +### Evaluating relative importance + +Conservation plans can take a long time to implement. Since funding availability and habitat quality can decline over time, it is critical that the most important places in a prioritization are scheduled for management as early as possible. For instance, some planning units in a solution might contain many rare species which do not occur in any other planning units. Alternatively, some planning units might offer an especially high return on investment that reduces costs considerably. As a consequence, conservation planners often need information on which planning units selected in a prioritization are most important to the overall success of the prioritization. To achieve this, conservation planners can use importance scores for each planning unit selected by a solution. + +Let's generate a prioritization so that can compare the different importance methods. + +```{r, fig.height = h, fig.width = w} +# formulate the problem +p41 <- problem(sim_pu_raster, sim_features) %>% + add_min_set_objective() %>% + add_relative_targets(0.1) %>% + add_binary_decisions() + +# solve the problem +s41 <- solve(p41) + +# plot solution +plot(s41, col = c("grey90", "darkgreen"), main = "Solution", + xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1)) +``` + + The following methods are available for computing importance scores. + +* __Replacement cost__: Evaluate importance using the replacement cost method [@r31]. This method quantifies the importance of a given planning unit as the decrease in the performance of the solution (based on the objective function) if the planning unit cannot be acquired (e.g., in terms of the additional costs required to meet feature targets). The advantages of this method are that it (i) accounts for the costs of the planning units, (ii) can be applied to multiple management zones, (iii) can be applied to any objective function, and (iv) can identify truly irreplaceable planning units (denoted with infinite values). However, the key disadvantage of this method, is that can take an infeasible amount of time to complete for large and complex problems. +```{r, fig.height = h, fig.width = w} +# calculate replacement cost scores and make the solver quiet +rc41 <- p41 %>% + add_default_solver(gap = 0, verbose = FALSE) %>% + eval_replacement_importance(s41) + +# plot replacement cost scores +plot(rc41, main = "Replacement cost scores") +``` +* __Ferrier method__: Evaluate importance by computing irreplaceability scores following Ferrier *et al.* [@r-34]. The advantages of this method are that it (i) can be computed relatively quickly for moderate and large-sized problems, and (ii) calculates a score for each feature within each planning unit to provide insight into why certain planning units are more important than others. The disadvatange with this method is that it can only be applied to conservation problems with a minimum set objective and a single zone (i.e., similar to _Marxan_-type problems). +```{r, fig.height = h, fig.width = w} +# calculate Ferrier scores and extract total score +fs41 <- eval_ferrier_importance(p40, s40)[["total"]] + +# plot Ferrier scores +plot(fs41, main = "Ferrier scores") +``` +* __Rarity weighted richness__: Evaluate importance by computing rarity weighted richness scores [@r33]. The only advantage with this method is that it can be computed very quickly for very large problems. The key disadvantage with this approach is that it merely describes the spatial patterns of biodiversity, and does not consider any of the goals that underpin conservation planning exercise. For instance, it does not account for planning costs, management zones, objective functions, or feature representation targets. +```{r, fig.height = h, fig.width = w} +# calculate rarity weighted richness scores +rwr41 <- eval_rare_richness_importance(p40, s40) + +# plot rarity weighted richness scores +plot(rwr41, main = "Rarity weighted richness") +``` + +In general, we recommend using replacement cost scores for small and moderate sized problems (e.g., less than 30,000 planning units) when it is feasible to do so. It can take a very long time to compute replacement cost scores, and so it is simply not feasible to compute these scores for particularly large problems. For moderate and large sized problems (e.g., more than 30,000 planning units), we recommend using the Ferrier method. This is because it explicitly accounts for representation targets, unlike the rarity weighted richness scores. We almost never recommend using the rarity weighted richness scores. This is because they do not consider criteria needed to inform conservation decision making [@r51]. + +## _Marxan_ problems + +Although we encourage users to build and tailor conservation planning problems to suit their own needs, sometimes it just simply easier to use something you're already familiar with. The `marxan_problem()` function is provided as a convenient wrapper for building and solving _Marxan_-style conservation problems. If users already have their conservation planning data formatted for use with _Marxan_, this function can also read _Marxan_ data files and solve the _Marxan_-style problems using exact algorithm solvers. __Please note that problems built using the `marxan_problem()` function are still solved the same way as a problem initialized using the `problem()` function, and therefore still require the installation of one of the solver packages.__ + +Here is a short example showing how the `marxan_problem()` function can be used to read _Marxan_ input files and the `solve` function can be used to solve the problem. + +```{r, results = "hide"} +# set file path for Marxan input file +minput <- system.file("extdata/input.dat", package = "prioritizr") + +# read Marxan input file +mp <- marxan_problem(minput) + +# print problem +print(mp) + +# solve the problem +ms <- solve(mp) + +# since the Marxan data was in a tabular format, the solution is also returned +# in a tabular format, so we will print the first six rows of the table +# containing the solution +head(ms) +``` + +Alternatively, rather then using a _Marxan_ input file to construct the problem, we can manually read in the _Marxan_ data files and input these to the `marxan_problem()` function. + +```{r} +# load data +pu <- system.file("extdata/input/pu.dat", package = "prioritizr") %>% + read.table(sep = ",", header = TRUE) +features <- system.file("extdata/input/spec.dat", package = "prioritizr") %>% + read.table(sep = ",", header = TRUE) +bound <- system.file("extdata/input/bound.dat", package = "prioritizr") %>% + read.table(sep = "\t", header = TRUE) +rij <- system.file("extdata/input/puvspr.dat", package = "prioritizr") %>% + read.table(sep = ",", header = TRUE) + +# build Marxan problem using data.frame objects +mp2 <- marxan_problem(x = pu, spec = features, puvspr = rij, bound = bound, + blm = 0) + +# print problem +print(mp2) +``` + +Conservation planning problems that are built using the `marxan_problem()` function can also be customized. For example, we could change the decision type for `mp2` to involve selecting a proportion of each planing unit (using the `add_proportion_decisions()` function). + +## Conclusion + +Hopefully, this vignette has provided an informative overview of the _prioritizr R_ package. For more examples using the package, please see the other vignettes. Perhaps, one of the best ways to learn a new piece of software is to just try it out. Test it, try breaking it, make mistakes, and learn from them. We would recommend trying to build conservation planning problems that resemble those you face in your own work---but using the built-in example data sets. This way you can quickly verify that the problems you build actually mean what you think they mean. For instance, you can try playing around with the targets and see what effect they have on the solutions, or try playing around with penalties and see what effect they have on the solutions. Finally, if you have any questions about using the package or suggestions for it, please [post an issue on the package's online coding repository](https://github.com/prioritizr/prioritizr/issues). + +## References diff --git a/inst/doc/package_overview.html b/inst/doc/package_overview.html new file mode 100644 index 000000000..68e2990e2 --- /dev/null +++ b/inst/doc/package_overview.html @@ -0,0 +1,1704 @@ + + + + + + + + + + + + + + +Package overview + + + + + + + + + + + + + + + + + + + + + + + + + + +

      Package overview

      + + + + +
      +

      Summary

      +

      The prioritizr R package uses integer linear programming (ILP) techniques to provide a flexible interface for building and solving conservation planning problems (Rodrigues et al. 2000; Billionnet 2013). It supports a broad range of objectives, constraints, and penalties that can be used to custom-tailor conservation planning problems to the specific needs of a conservation planning exercise. Once built, conservation planning problems can be solved using a variety of commercial and open-source exact algorithm solvers. In contrast to the algorithms conventionally used to solve conservation problems, such as heuristics or simulated annealing (Ball et al. 2009), the exact algorithms used here are guaranteed to find optimal solutions. Furthermore, conservation problems can be constructed to optimize the spatial allocation of different management zone (or actions), meaning that conservation practitioners can identify solutions that benefit multiple stakeholders. Finally, this package has the functionality to read input data formatted for the Marxan conservation planning program (Ball et al. 2009), and find much cheaper solutions in a much shorter period of time than Marxan (Beyer et al. 2016).

      +
      +
      +

      Introduction

      +

      Systematic conservation planning is a rigorous, repeatable, and structured approach to designing new protected areas that efficiently meet conservation objectives (Margules & Pressey 2000). Historically, conservation decision-making has often evaluated parcels opportunistically as they became available for purchase, donation, or under threat. Although purchasing such areas may improve the status quo, such decisions may not substantially enhance the long-term persistence of target species or communities. Faced with this realization, conservation planners began using decision support tools to help simulate alternative reserve designs over a range of different biodiversity and management goals and, ultimately, guide protected area acquisitions and management actions. Due to the systematic, evidence-based nature of these tools, conservation prioritization can help contribute to a transparent, inclusive, and more defensible decision making process.

      +

      A conservation planning exercise typically starts by defining a study area. This study area should encompass all the areas relevant to the decision maker or the hypothesis being tested. The extent of a study area could encompass a few important localities (e.g., Stigner et al. 2016), a single state (e.g., Kirkpatrick 1983), an entire country (Fuller et al. 2010), or the entire planet (Butchart et al. 2015). Next, the study area is divided into a set of discrete areas termed planning units. Each planning unit represents a discrete locality in the study area that can be managed independently of other areas. The general idea is that some combination of the planning units can be selected for conservation actions (e.g., protected area establishment, habitat restoration). Planning units are often created as square or hexagon cells that are sized according to the scale of the conservation actions, and the resolution of the data that underpin the planning exercise (but see Klein et al. 2009).

      +

      Cost data (or a surrogate thereof) are needed to inform the prioritization process. Specifically, these cost data describe the relative expenditure associated with managing each planning unit for conservation. For example, if the goal of the conservation planning exercise is to identify priority areas for expanding a local protected area system, then the cost data could represent the physical cost of purchasing the land. Alternatively, if such data are not available, then surrogate data could are often used instead (e.g., human population density, opportunity cost of foregone commercial activities, or planning unit size).

      +

      Conservation planning exercises also require data on the biodiversity elements that are of conservation interest (termed conservation features). These features could be species (e.g., Neofelis nebulosa, the Clouded Leopard), populations, or habitats (e.g., mangroves or cloud forest). After identifying the set of relevant conservation features for a conservation planning exercise, spatially explicit data need to be obtained for each and every feature to describe their spatial distribution (e.g., habitat suitability data, probability of occurrence data, presence/absence data). This is important to ensure that conservation features are adequately covered (represented) by prioritizations. After assembling all the data, the next step is to define the conservation planning problem.

      +

      The prioritizr R package is designed to help you build and solve conservation planning problems. Specifically, prioritizations are generated by using formulating a mathematical optimization problem and then solving it to generate a solution. These mathematical optimization problems are formulated using the planning unit data, cost data, and feature data, and with information related to the overarching aim of the prioritization process. In general, the goal of an optimization problem is to minimize (or maximize) an objective function that is calculated using a set of decision variables, subject to a series of constraints to ensure that solution exhibits specific properties. The objective function describes the quantity which we are trying to minimize (e.g., cost of the solution) or maximize (e.g., number of features conserved). The decision variables describe the entities that we can control, and indicate which planning units are selected for conservation management and which of those are not. The constraints can be thought of as rules that the need decision variables need to follow. For example, a commonly used constraint is specifying that the solution must not exceed a certain budget.

      +

      A wide variety of approaches have been developed for solving optimization problems. Reserve design problems are frequently solved using simulated annealing (Kirkpatrick et al. 1983) or heuristics (Nicholls & Margules 1993; Moilanen 2007). These methods are conceptually simple and can be applied to a wide variety of optimization problems. However, they do not scale well for large or complex problems (Beyer et al. 2016). Additionally, these methods cannot tell you how close any given solution is to the optimal solution. The package uses exact algorithms to efficiently solve conservation planning problems to within a pre-specified a optimality gap. In other words, you can specify that you need the optimal solution (i.e., a gap of 0%) and the algorithms will, given enough time, find a solution that meets this criteria. In the past, exact algorithms have been too slow for conservation planning exercises (Pressey et al. 1996). However, improvements over the last decade mean that they are now much faster (Achterberg & Wunderling 2013; Beyer et al. 2016).

      +

      In this package, optimization problems are expressed using integer linear programming (ILP) so that they can be solved using (linear) exact algorithm solvers. The general form of an integer programming problem can be expressed in matrix notation using the following equation.

      +

      \[\text{Minimize} \space \boldsymbol{c}^\text{T} \boldsymbol{x} \space +\space \text{subject to} \space A\boldsymbol{x} +\space \Box \space \boldsymbol{b}\]

      +

      Here, where \(x\) is a vector of decision variables, \(c\) and \(b\) are vectors of known coefficients, and \(A\) is the constraint matrix. The final term specifies a series of structural constants and the \(\Box\) symbol is used to indicate that the relational operators for the constraints can be either \(\geq\), \(=\), or \(\leq\). In the context of a conservation planning problem, \(c\) could be used to represent the planning unit costs, \(A\) could be used to store the data showing the presence / absence (or amount) of each feature in each planning unit, \(b\) could be used to represent minimum amount of habitat required for each species in the solution, the \(\Box\) could be set to \(\geq\) symbols to indicate that the total amount of each feature in the solution must exceed the quantities in \(b\). But there are many other ways of formulating the reserve selection problem (Rodrigues et al. 2000).

      +
      +
      +

      A grammar for conservation planning

      +

      The prioritizr R package uses a grammar to describe elements of conservation planning. This means that functions are organized into verbs that relate to specific concepts. For example, all of the functions used to specify the primary objective for optimization end with the _objective suffix (e.g., add_min_set_objective() and add_min_shortfall_objective()). By combining multiple functions together, they can be used to formulate a complete conservation planning problem. Specifically, the verbs for formulating problems are described below.

      +
        +
      • Create a new conservation planning problem by specifying the planning units, features, and management zones of conservation interest.
        • +
      • Add a primary objective to a conservation planning problem (e.g., minimize overall cost).
        • +
      • Add penalties to a conservation planning problem to penalize solutions according to specific metric (e.g., connectivity).
        • +
      • Add targets to a conservation planning problem to specify how much of each feature should ideally be represented solutions.
        • +
      • Add constraints to a conservation planning problem to ensure that solutions exhibit specific properties (e.g., select specific planning units for protection).
        • +
      • Add decisions to a conservation planning problem to specify the nature of the decisions in the problem (e.g., binary decisions indicate the planning units should be selected or not selected for management).
        • +
      • Add a portfolio to a conservation planning problem to specify a methodological approach for generating multiple solutions (e.g. generate multiple solutions by finding 100 solutions within 10% of optimality).
        • +
      • Add a solver to a conservation problem to specify the optimization software (e.g. Gurobi) for generating solutions and customize the optimization settings (e.g. generate an optimal solution).
        • +
      +

      After building a conservation planning problem, it can be solved to generate a prioritization (using the solve() function). There are also verbs available to help evaluate and interpret solutions. These verbs are described below.

      +
        +
      • Evaluate performance by computing summary statistics (e.g. overall cost, feature representation, or total boundary length).
        • +
      • Evaluate the relative importance of planning units selected by a solution (e.g. based on irreplaceability).
        • +
      +
      +
      +

      Workflow

      +

      The general workflow when using the prioritizr R package starts with creating a new conservation planning problem() object using data. Specifically, the problem() object should be constructed using data that specify the planning units, biodiversity features, management zones (if applicable), and costs. After creating a new problem() object, it can be customized—by adding objectives, penalties, constraints, and other information—to build a precise representation of the conservation planning problem required, and then solved to obtain a solutions.

      +

      All conservation planning problems require an objective. An objective specifies the property which is used to compare different feasible solutions. Simply put, the objective is the property of the solution which should be maximized or minimized during the optimization process. For instance, with the minimum set objective (specified using add_min_set_objective()), we are seeking to minimize the cost of the solution (similar to Marxan). On the other hand, with the minimum shortfall objective (specified using add_min_shortfall_objective()), we are seeking to minimize the average target shortfall for all features represented in the solution, subject to a budget.

      +

      Many objectives require representation targets (e.g., the minimum set objective). These targets are a specialized set of constraints that relate to the total quantity of each feature secured in the solution (e.g., amount of suitable habitat or number of individuals). In the case of the minimum set objective ( add_min_set_objective()), they are used to ensure that solutions secure a sufficient quantity of each feature, and in other objectives, such as the maximum features objective ( add_max_features_objective()) they are used to assess whether a feature has been adequately conserved by a candidate solution. Targets can be expressed numerically as the total amount required for a given feature (using add_absolute_targets()), or as a proportion of the total amount found in the planning units (using add_relative_targets()). Note that not all objectives require targets, and a warning will be thrown if an attempt is made to add targets to a problem with an objective that does not use them.

      +

      Constraints and penalties can be added to a conservation planning problem to ensure that solutions exhibit a specific property or penalize solutions which don’t exhibit a specific property (respectively). The difference between constraints and penalties, strictly speaking, is constraints are used to rule out potential solutions that don’t exhibit a specific property. For instance, constraints can be used to ensure that specific planning units are selected in the solution for prioritization (using add_locked_in_constraints()) or not selected in the solution for prioritization (using add_locked_out_constraints()). On the other hand, penalties are combined with the objective of a problem, with a penalty factor, and the overall objective of the problem then becomes to minimize (or maximize) the primary objective function and the penalty function. For example, penalties can be added to a problem to penalize solutions that are excessively fragmented (using add_boundary_penalties()). These penalties have a penalty argument that specifies the relative importance of having spatially clustered solutions. When the argument to penalty is high, then solutions which are less fragmented are valued more highly – even if they cost more – and when the argument to penalty is low, then the solutions which are more fragmented are valued less highly.

      +

      After building a conservation problem, it can then be solved to obtain a solution (or portfolio of solutions if desired). The solution is returned in the same format as the planning unit data used to construct the problem. For instance, this means that if raster data was used to initialize the problem, then the solution will also be output in raster format. This can be very helpful when it comes to interpreting and visualizing solutions because it means that the solution data does not first have to be merged with spatial data before they can be plotted on a map.

      +
      +
      +

      Usage

      +

      Here we will provide an introduction to using the prioritizr R package to build and solve a conservation planning problem. Please note that we will not discuss conservation planning with multiple zones in this vignette, for more information on working with multiple management zones please see the zones vignette.

      +

      First, we will load the prioritizr package.

      +
      # load package
+library(prioritizr)
+
+# set default options for printing tabular data
+options(tibble.width = Inf)
      +
      +

      Data

      +

      Now we will load some built-in data sets that are distributed with the prioritizr R package. This package contains several different planning unit data sets. To provide a comprehensive overview of the different ways that we can initialize a conservation planning problem, we will load each of them.

      +

      First, we will load the raster planning unit data (sim_pu_raster). Here, the planning units are represented as a raster (i.e., a RasterLayer object) and each pixel corresponds to the spatial extent of each panning unit. The pixel values correspond to the acquisition costs of each planning unit.

      +
      # load raster planning unit data
+data(sim_pu_raster)
+
+# print description of the data
+print(sim_pu_raster)
      +
      ## class      : RasterLayer 
+## dimensions : 10, 10, 100  (nrow, ncol, ncell)
+## resolution : 0.1, 0.1  (x, y)
+## extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+## crs        : NA 
+## source     : memory
+## names      : layer 
+## values     : 190.1328, 215.8638  (min, max)
      +
      # plot the data
+plot(sim_pu_raster)
      +

      +

      Secondly, we will load one of the spatial vector planning unit data sets (sim_pu_polygons). Here, each polygon (i.e., feature using ArcGIS terminology) corresponds to a different planning unit. This data set has an attribute table that contains additional information about each polygon. Namely, the cost field (column) in the attribute table contains the acquisition cost for each planning unit.

      +
      # load polygon planning unit data
+data(sim_pu_polygons)
+
+# print first six rows of attribute table
+head(sim_pu_polygons@data)
      +
      ##       cost locked_in locked_out
+## 1 215.8638     FALSE      FALSE
+## 2 212.7823     FALSE      FALSE
+## 3 207.4962     FALSE      FALSE
+## 4 208.9322     FALSE       TRUE
+## 5 214.0419     FALSE      FALSE
+## 6 213.7636     FALSE      FALSE
      +
      # plot the planning units
+spplot(sim_pu_polygons, zcol = "cost")
      +

      +

      Thirdly, we will load some planning unit data stored in tabular format (i.e., data.frame format). For those familiar with Marxan or dealing with very large conservation planning problems (> 10 million planning units), it may be useful to work with data in this format because it does not contain any spatial information which will reduce computational burden. When using tabular data to initialize conservation planning problems, the data must follow the conventions used by Marxan. Specifically, each row in the planning unit table must correspond to a different planning unit. The table must also have an “id” column to provide a unique integer identifier for each planning unit, and it must also have a column that indicates the cost of each planning unit. For more information, please see the official Marxan documentation.

      +
      # specify file path for planning unit data
+pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr")
+
+# load in the tabular planning unit data
+# note that we use the data.table::fread function, as opposed to the read.csv
+# function, because it is much faster
+pu_dat <- data.table::fread(pu_path, data.table = FALSE)
+
+# preview first six rows of the tabular planning unit data
+# note that it has some extra columns other than id and cost as per the
+# Marxan format
+head(pu_dat)
      +
      ##   id       cost status    xloc     yloc
+## 1  3        0.0      0 1116623 -4493479
+## 2 30   752727.5      3 1110623 -4496943
+## 3 56  3734907.5      0 1092623 -4500408
+## 4 58  1695902.1      0 1116623 -4500408
+## 5 84  3422025.6      0 1098623 -4503872
+## 6 85 17890758.4      0 1110623 -4503872
      +

      Finally, we will load data showing the spatial distribution of the conservation features. Our conservation features (sim_features) are represented as a stack of raster objects (i.e., a RasterStack object) where each layer corresponds to a different feature (e.g., a multi-band GeoTIFF where each band corresponds to a different feature). The pixel values in each layer correspond to the amount of suitable habitat available in a given planning unit. Note that our planning unit raster layer and our conservation feature stack have exactly the same spatial properties (i.e., resolution, extent, coordinate reference system) so their pixels line up perfectly.

      +
      # load feature data
+data(sim_features)
+
+# plot the distribution of suitable habitat for each feature
+plot(sim_features, main = paste("Feature", seq_len(nlayers(sim_features))),
+     nr = 2, box = FALSE, axes = FALSE)
      +

      +
      +
      +

      Initialize a problem

      +

      After having loaded our planning unit and feature data, we will now try initializing the some conservation planning problems. There are a lot of different ways to initialize a conservation planning problem, so here we will just showcase a few of the more commonly used methods. For an exhaustive description of all the ways you can initialize a conservation problem, see the help file for the problem() function. First off, we will initialize a conservation planning problem using the raster data.

      +
      # create problem
+p1 <- problem(sim_pu_raster, sim_features)
+
+# print problem
+print(p1)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      none
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
      # print number of planning units
+number_of_planning_units(p1)
      +
      ## [1] 90
      +
      # print number of features
+number_of_features(p1)
      +
      ## [1] 5
      +

      Generally, we recommend initializing problems using raster data where possible. This is because the problem() function needs to calculate the amount of each feature in each planning unit, and by providing both the planning unit and feature data in raster format with the same spatial resolution, extents, and coordinate systems, this means that the problem() function does not need to do any geoprocessing behind the scenes. But sometimes we can’t use raster planning unit data because our planning units aren’t equal-sized grid cells. So, below is an example showing how we can initialize a conservation planning problem using planning units that are formatted as spatial vector data. Note that if we had precomputed the amount of each feature in each planning unit and stored the data in the attribute table, we could pass in the names of the columns as an argument to the problem() function.

      +
      # create problem with spatial vector data
+# note that we have to specify which column in the attribute table contains
+# the cost data
+p2 <- problem(sim_pu_polygons, sim_features, cost_column = "cost")
+
+# print problem
+print(p2)
      +
      ## Conservation Problem
+##   planning units: SpatialPolygonsDataFrame (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      none
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +

      We can also initialize a conservation planning problem using tabular planning unit data (i.e., data.frame format). Since the tabular planning unit data does not contain any spatial information, we also have to provide the feature data in tabular format (i.e., data.frame format) and data showing the amount of each feature in each planning unit in tabular format (i.e., data.frame format). The feature data must have an “id” column containing a unique integer identifier for each feature, and the planning unit by feature data must contain the following three columns: pu corresponding to the planning unit identifiers, species corresponding to the feature identifiers, and amount showing the amount of a given feature in a given planning unit.

      +
      # set file path for feature data
+spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr")
+
+# load in feature data
+spec_dat <- data.table::fread(spec_path, data.table = FALSE)
+
+# print first six rows of the data
+# note that it contains extra columns
+head(spec_dat)
      +
      ##   id prop spf   name
+## 1 10  0.3   1  bird1
+## 2 11  0.3   1  nvis2
+## 3 12  0.3   1  nvis8
+## 4 13  0.3   1  nvis9
+## 5 14  0.3   1 nvis14
+## 6 15  0.3   1 nvis20
      +
      # set file path for planning unit vs. feature data
+puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr")
+
+# load in planning unit vs feature data
+puvspr_dat <- data.table::fread(puvspr_path, data.table = FALSE)
+
+# print first six rows of the data
+head(puvspr_dat)
      +
      ##   species  pu     amount
+## 1      26  56 1203448.84
+## 2      26  58  451670.10
+## 3      26  84  680473.75
+## 4      26  85   97356.24
+## 5      26  86   78034.76
+## 6      26 111 4783274.17
      +
      # create problem
+p3 <- problem(pu_dat, spec_dat, cost_column = "cost", rij = puvspr_dat)
+
+# print problem
+print(p3)
      +
      ## Conservation Problem
+##   planning units: data.frame (1751 units)
+##   cost:           min: 0, max: 41569219.38232
+##   features:       bird1, nvis2, nvis8, ... (17 features)
+##   objective:      none
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +

      For more information on initializing problems, please see the help page for the problem() function (which you can open by entering the code: ?problem). Now that we have initialized a conservation planning problem, we will show you how you can customize it to suit the exact needs of your conservation planning scenario. Although we initialized the conservation planning problems using several different methods, moving forward, we will only use raster-based planning unit data to keep things simple.

      +
      +
      +

      Add an objective

      +

      The next step is to add a primary objective to the problem. A problem objective is used to specify the primary goal of the problem (i.e., the quantity that is to be maximized or minimized). All conservation planning problems involve minimizing or maximizing some kind of objective. For instance, we might require a solution that conserves enough habitat for each species while minimizing the overall cost of the reserve network. Alternatively, we might require a solution that maximizes the number of conserved species while ensuring that the cost of the reserve network does not exceed the budget. Please note that objectives are added in the same way regardless of the type of data used to initialize the problem. The following objectives are available.

      +
        +
      • Minimum set objective: Minimize the cost of the solution whilst ensuring that all targets are met (Rodrigues et al. 2000). This objective is similar to that used in Marxan (Ball et al. 2009). For example, we can add a minimum set objective to a problem using the following code.
        • +
      +
      # create a new problem that has the minimum set objective
+p3 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective()
+
+# print the problem
+print(p3)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Maximum cover objective: Represent at least one instance of as many features as possible within a given budget (Church et al. 1996).
        • +
      +
      # create a new problem that has the maximum coverage objective and a budget
+# of 5000
+p4 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_cover_objective(5000)
+
+# print the problem
+print(p4)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Maximum coverage objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Maximum features objective: Fulfill as many targets as possible while ensuring that the cost of the solution does not exceed a budget (inspired by Cabeza & Moilanen 2001). This object is similar to the maximum cover objective except that we have the option of later specifying targets for each feature. In practice, this objective is more useful than the maximum cover objective because features often require a certain amount of area for them to persist and simply capturing a single instance of habitat for each feature is generally unlikely to enhance their long-term persistence.
        • +
      +
      # create a new problem that has the maximum features objective and a budget
+# of 5000
+p5 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_features_objective(budget = 5000)
+
+# print the problem
+print(p5)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Maximum representation objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Minimum shortfall objective: Minimize the overall (weighted sum) shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when there is a large amount of left-over budget when using the maximum feature representation objective and the remaining funds need to be allocated to places that will enhance the representation of features with unmet targets.
        • +
      +
      # create a new problem that has the minimum shortfall objective and a budget
+# of 5000
+p6 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_shortfall_objective(budget = 5000)
+
+# print the problem
+print(p6)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum shortfall objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Minimum largest shortfall objective: Minimize the largest (maximum) shortfall while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when the minimum shortfall objective returns solutions that focus too much on representing a small number of features (e.g., because they occur in much cheaper planning units), and solutions are needed to spread conservation effort out more evenly among all features—even if it means that all features will have (relatively) poor representation.
        • +
      +
      # create a new problem that has the minimum largest shortfall objective and a
+# budget of 5000
+p7 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_largest_shortfall_objective(budget = 5000)
+
+# print the problem
+print(p7)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum largest shortfall objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Maximum phylogenetic diversity objective: Maximize the phylogenetic diversity of the features represented in the solution subject to a budget (inspired by Faith 1992; Rodrigues & Gaston 2002). This objective is similar to the maximum features objective except that emphasis is placed on protecting features which are associated with a diverse range of evolutionary histories. The package contains a simulated phylogeny that can be used with the simulated feature data (sim_phylogny).
        • +
      +
      # load simulated phylogeny data
+data(sim_phylogeny)
+
+# create a new problem that has the maximum phylogenetic diversity
+# objective and a budget of 5000
+p8 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_phylo_div_objective(budget = 5000, tree = sim_phylogeny)
+
+# print the problem
+print(p8)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Phylogenetic diversity objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Maximum phylogenetic endemism objective: Maximize the phylogenetic endemism of the features represented in the solution subject to a budget (inspired by Faith 1992; Rodrigues & Gaston 2002; Rosauer et al. 2009). This objective is similar to the maximum phylogenetic diversity except that emphasis is placed conserving features that are associated with geographically restricted periods of evolutionary history rather than a diverse range of evolutionary histories.
        • +
      +
      # load simulated phylogeny data
+data(sim_phylogeny)
+
+# create a new problem that has the maximum phylogenetic diversity
+# objective and a budget of 5000
+p9 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_phylo_end_objective(budget = 5000, tree = sim_phylogeny)
+
+# print the problem
+print(p9)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Phylogenetic endemism objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Maximum utility objective: Secure as much of the features as possible without exceeding a budget. This objective is functionally equivalent to selecting the planning units with the greatest amounts of each feature (e.g., species richness). Generally, we don’t encourage the use of this objective because it will only rarely identify complementary solutions–solutions which adequately conserve a range of different features—except perhaps to explore trade-offs or provide a baseline solution with which to compare other solutions.
        • +
      +
      # create a new problem that has the maximum utility objective and a budget
+# of 5000
+p10 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_utility_objective(budget = 5000)
+
+# print the problem
+print(p10)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Maximum utility objective [budget (5000)]
+##   targets:        none
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
      +
      +

      Add targets

      +

      Most conservation planning problems require targets. Targets are used to specify the minimum amount or proportion of a feature’s distribution that needs to be protected in the solution. For example, we may want to develop a reserve network that will secure 20% of the distribution for each feature for minimal cost. The following methods are available for specifying targets.

      +
        +
      • Absolute targets: Targets are expressed as the total amount of each feature in the study area that need to be secured. For example, if we had binary feature data that showed the absence or presence of suitable habitat across the study area, we could set an absolute target as 5 to mean that we require 5 planning units with suitable habitat in the solution.
        • +
      +
      # create a problem with targets which specify that the solution must conserve
+# a need a sum total of 3 units of suitable habitat for each feature
+p11 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_absolute_targets(3)
+
+# print problem
+print(p11)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Absolute targets [targets (min: 3, max: 3)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Relative targets: Targets are set as a proportion (between 0 and 1) of the total amount of each feature in the study area. For example, if we had binary feature data and the feature occupied a total of 20 planning units in the study area, we could set a relative target of 50 % to specify that the solution must secure 10 planning units for the feature. We could alternatively specify an absolute target of 10 to achieve the same result, but sometimes proportions are easier to work with.
        • +
      +
      # create a problem with the minimum set objective and relative targets of 10 %
+# for each feature
+p12 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1)
+
+# print problem
+print(p12)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
      # create a problem with targets which specify that we need 10 % of the habitat
+# for the first feature, 15 % for the second feature, 20 % for the third feature
+# 25 % for the fourth feature and 30 % of the habitat for the fifth feature
+targets <- c(0.1, 0.15, 0.2, 0.25, 0.3)
+p13 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(targets)
+
+# print problem
+print(p13)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.3)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Log-linear targets: Targets are expressed using scaling factors and log-linear interpolation. This method for specifying targets is commonly used for global prioritization analyses (Rodrigues et al. 2004).
        • +
      +
      # create problem with added log-linear targets
+p14 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_loglinear_targets(10, 0.9, 100, 0.2)
+
+# print problem
+print(p14)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Absolute targets [targets (min: 17.290505409161, max: 21.5906174426385)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Manual targets: Targets are manually specified. This is only really recommended for advanced users or problems that involve multiple management zones. See the zones vignette for more information on these targets.
        • +
      +

      As with the functions for specifying the objective of a problem, if we try adding multiple targets to a problem, only the most recently added set of targets are used.

      +
      +
      +

      Add constraints

      +

      A constraint can be added to a conservation planning problem to ensure that all solutions exhibit a specific property. For example, they can be used to make sure that all solutions select a specific planning unit or that all selected planning units in the solution follow a certain configuration. The following constraints are available.

      +
        +
      • Locked in constraints: Add constraints to ensure that certain planning units are prioritized in the solution. For example, it may be desirable to lock in planning units that are inside existing protected areas so that the solution fills in the gaps in the existing reserve network.
        • +
      +
      # create problem with constraints which specify that the first planning unit
+# must be selected in the solution
+p15 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints(1)
+
+# print problem
+print(p15)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked in planning units [1 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Locked out constraints: Add constraints to ensure that certain planning units are not prioritized in the solution. For example, it may be useful to lock out planning units that have been degraded and are not suitable for conserving species.
        • +
      +
      # create problem with constraints which specify that the second planning unit
+# must not be selected in the solution
+p16 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_out_constraints(2)
+
+# print problem
+print(p16)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked out planning units [1 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Neighbor constraints: Add constraints to a conservation problem to ensure that all selected planning units have at least a certain number of neighbors.
        • +
      +
      # create problem with constraints which specify that all selected planning units
+# in the solution must have at least 1 neighbor
+p17 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_neighbor_constraints(1)
+
+# print problem
+print(p17)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Neighbor constraint [number of neighbors (1), zones]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Contiguity constraints: Add constraints to a conservation problem to ensure that all selected planning units are spatially connected to each other and form spatially contiguous unit.
        • +
      +
      # create problem with constraints which specify that all selected planning units
+# in the solution must form a single contiguous unit
+p18 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_contiguity_constraints()
+
+# print problem
+print(p18)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Contiguity constraints [apply constraints? (1), zones]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Feature contiguity constraints: Add constraints to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of those implemented in the add_contiguity_constraints function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit.
        • +
      +
      # create problem with constraints which specify that the planning units used
+# to conserve each feature must form a contiguous unit
+p19 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_feature_contiguity_constraints()
+
+# print problem
+print(p19)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Feature contiguity constraints [apply constraints? (1), layer.1 zones, layer.2 zones, layer.3 zones, layer.4 zones, layer.5 zones]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Linear constraints: Add constraints to ensure that all selected planning units meet certain criteria. For example, they can be used to add multiple budgets, or limit the number of planning units selected in different administrative areas within a study region (e.g., different countries).
        • +
      +
      # create problem with constraints which specify that the sum of
+# values in sim_features[[1]] among selected planning units must not exceed a
+#' threshold value of 190.
+p20 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_shortfall_objective(budget = 1800) %>%
+       add_relative_targets(0.1) %>%
+       add_linear_constraints(190, "<=", sim_features[[1]])
+
+# print problem
+print(p20)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum shortfall objective [budget (1800)]
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Linear constraints [threshold (190)]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Mandatory allocation constraints: Add constraints to ensure that every planning unit is allocated to a management zone in the solution. Please note that this function can only be used with problems that contain multiple zones. For more information on problems with multiple zones and an example using this function, see the Management Zones vignette.
        • +
      +

      In particular, The add_locked_in_constraints and add_locked_out_constraints functions are incredibly useful for real-world conservation planning exercises, so it’s worth pointing out that there are several ways we can specify which planning units should be locked in or out of the solutions. If we use raster planning unit data, we can also use raster data to specify which planning units should be locked in our locked out.

      +
      # load data to lock in or lock out planning units
+data(sim_locked_in_raster)
+data(sim_locked_out_raster)
+
+# plot the locked data
+plot(stack(sim_locked_in_raster, sim_locked_out_raster),
+     main = c("Locked In", "Locked Out"))
      +

      +
      # create a problem using raster planning unit data and use the locked raster
+# data to lock in some planning units and lock out some other planning units
+p21 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints(sim_locked_in_raster) %>%
+       add_locked_out_constraints(sim_locked_out_raster)
+
+# print problem
+print(p21)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked out planning units [10 locked units]
+##                    Locked in planning units [10 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +

      If our planning unit data are in a spatial vector format (similar to the sim_pu_polygons data) or a tabular format (similar to pu_dat), we can use the field names in the data to refer to which planning units should be locked in and / or out. For example, the sim_pu_polygons object has TRUE / FALSE values in the “locked_in” field which indicate which planning units should be selected in the solution. We could use the data in this field to specify that those planning units with TRUE values should be locked in using the following methods.

      +
      # preview first six rows of the attribute table for sim_pu_polygons
+head(sim_pu_polygons@data)
      +
      ##       cost locked_in locked_out
+## 1 215.8638     FALSE      FALSE
+## 2 212.7823     FALSE      FALSE
+## 3 207.4962     FALSE      FALSE
+## 4 208.9322     FALSE       TRUE
+## 5 214.0419     FALSE      FALSE
+## 6 213.7636     FALSE      FALSE
      +
      # specify locked in data using the field name
+p22 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints("locked_in")
+
+# print problem
+print(p22)
      +
      ## Conservation Problem
+##   planning units: SpatialPolygonsDataFrame (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked in planning units [10 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
      # specify locked in data using the values in the field
+p23 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints(which(sim_pu_polygons$locked_in))
+
+# print problem
+print(p23)
      +
      ## Conservation Problem
+##   planning units: SpatialPolygonsDataFrame (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <Locked in planning units [10 locked units]>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
      +
      +

      Add penalties

      +

      We can also add penalties to a problem to favor or penalize solutions according to a secondary objective. Unlike the constraint functions, these functions will add extra information to the objective function of the optimization function to penalize solutions that do not exhibit specific characteristics. For example, penalties can be added to a problem to avoid highly fragmented solutions at the expense of accepting slightly more expensive solutions. All penalty functions have a penalty argument that controls the relative importance of the secondary penalty function compared to the primary objective function. It is worth noting that incredibly low or incredibly high penalty values – relative to the main objective function – can cause problems to take a very long time to solve, so when trying out a range of different penalty values it can be helpful to limit the solver to run for a set period of time. The following penalties are available.

      +
        +
      • Boundary penalties: Add penalties to penalize solutions that are excessively fragmented. These penalties are similar to those used in Marxan (Ball et al. 2009; Beyer et al. 2016).
        • +
      +
      # create problem with penalties that penalize fragmented solutions with a
+# penalty factor of 0.01
+p24 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_boundary_penalties(penalty = 0.01)
+
+# print problem
+print(p24)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (0.01), zones]>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Connectivity penalties: Add penalties to favor solutions that select combinations of planning units with high connectivity between them. These penalties are similar to those used in Marxan with Zones (Watts et al. 2009; Beyer et al. 2016). This function supports both symmetric and asymmetric connectivities among planning units.
        • +
      +
      # create problem with penalties that favor combinations of planning units with
+# high connectivity, here we will use only the first four layers in
+# sim_features for the features and we will use the fifth layer in sim_features
+# to represent the connectivity data, where the connectivity_matrix function
+# will create a matrix showing the average strength of connectivity between
+# adjacent planning units using the data in the fifth layer of sim_features
+p25 <- problem(sim_pu_raster, sim_features[[1:4]]) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_boundary_penalties(
+         penalty = 5,
+         data = connectivity_matrix(sim_pu_raster, sim_features[[5]]))
+
+# print problem
+print(p25)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, layer.4 (4 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (5), zones]>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Linear penalties: Add penalties to penalize solutions that select planning units according to a certain variable (e.g., anthropogenic pressure).
        • +
      +
      # create data for penalizing planning units
+# (note this requires the RandomFields package to be installed)
+pen_raster <- simulate_cost(sim_pu_raster)
+
+# create problem with penalties that penalize solutions that select
+# planning units with high values in the pen_raster object,
+# here we will use a penalty value of 5 to indicate the trade-off (scaling)
+# between the penalty values (in the sim_pu_raster) and the main objective
+# (i.e., the cost of the solution)
+p26 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_linear_penalties(penalty = 5, data = pen_raster)
+
+# print problem
+print(p26)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      default
+##   constraints:    <none>
+##   penalties:      <Linear penalties [penalty (5)]>
+##   portfolio:      default
+##   solver:         default
      +
      +
      +

      Add the decision types

      +

      Conservation planning problems involve making decisions on how planning units will be managed. These decisions are then associated with management actions (e.g., turning a planning unit into a protected area). The type of decision describes how the action is applied to planning units. For instance, the default decision-type is a binary decision type, meaning that we are either selecting or not selecting planning units for management. The following decision types are available.

      +
        +
      • Binary decisions: Add a binary decision to a conservation planning problem. This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem object, then this decision class will be used by default.
        • +
      +
      # add binary decisions to a problem
+p27 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions()
+
+# print problem
+print(p27)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Proportion decisions: Add a proportion decision to a problem. This is a relaxed decision where a part of a planning unit can be prioritized, as opposed to the default of the entire planning unit. Typically, this decision has the assumed action of buying a fraction of a planning unit to include in a protected area network. Generally, problems can be solved much faster with proportion-type decisions than binary-type decisions, so they can be very useful when commercial solvers are not available.
        • +
      +
      # add proportion decisions to a problem
+p28 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_proportion_decisions()
+
+# print problem
+print(p28)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Proportion decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
        +
      • Semi-continuous decisions: Add a semi-continuous decision to a problem. This decision is similar to proportion decisions except that it has an upper bound parameter. By default, the decision can range from prioritizing none (0%) to all (100%) of a planning unit. However, a upper bound can be specified to ensure that at most only a fraction (e.g., 80%) of a planning unit can be purchased. This type of decision may be useful when it is not practical to conserve the entire area indicated by a planning unit.
        • +
      +
      # add semi-continuous decisions to a problem, where we can only manage at most
+# 50 % of the area encompassed by a planning unit
+p29 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_semicontinuous_decisions(0.5)
+
+# print problem
+print(p29)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Semicontinuous decision [upper limit (0.5)]
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         default
      +
      +
      +

      Add a solver

      +

      Next, after specifying the mathematical formulation that underpins your conservation planning problem, you can specify how the problem should be solved. If you do not specify this information, the prioritizr R package will automatically use the best solver currently installed on your system with some reasonable defaults. We strongly recommend installing the Gurobi software suite and the gurobi R package to solve problems, and for more information on this topic please refer to the Gurobi Installation Guide. The following solvers are available.

      +
        +
      • Gurobi solver: Gurobi is a state of the art commercial optimization software. It is by far the fastest of the solvers that can be used to solve conservation problems. However, it is not freely available. That said, special licenses are available to academics at no cost.
        • +
      +
      # create a problem and specify that Gurobi should be used to solve the problem
+# and specify an optimality gap of zero to obtain the optimal solution
+p30 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_gurobi_solver(gap = 0)
+
+# print problem
+print(p30)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         Gurobi [first_feasible (0), gap (0), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (1)]
      +
        +
      • IBM CPLEX solver: IBM CPLEX is a commercial optimization software. It is faster than the open source solvers available for generating prioritizations (see below), however, it is not freely available. Similar to the Gurobi software, special licenses are available to academics at no cost.
        • +
      +
      # create a problem and specify that IBM CPLEX should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p31 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_cplex_solver(gap = 0)
+
+# print problem
+print(p31)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         CPLEX [gap (0), presolve (1), threads (1), time_limit (2147483647), verbose (1)]
      +
        +
      • CBC solver: CBC is an open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. Although formal benchmarks have yet to be completed, preliminary analyses suggest that it is the fastest open-source solver available for generating prioritizations. It requires the rcbc R package, which is currently only available on GitHub.
        • +
      +
      # create a problem and specify that CBC should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p32 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_cbc_solver(gap = 0)
+
+# print problem
+print(p32)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         CBC [first_feasible (0), gap (0), presolve (1), threads (1), time_limit (2147483647), verbose (1)]
      +
        +
      • lpsymphony solver: SYMPHONY is an open-source integer programming solver that is also part of the COIN-OR project. This solver uses the lpsymphony R package (available on Bioconductor) to interface with the SYMPHONY software.
        • +
      +
      # create a problem and specify that lpsymphony should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p33 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_lpsymphony_solver(gap = 0)
+
+# print problem
+print(p33)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         Lpsymphony [first_feasible (0), gap (0), time_limit (2147483647), verbose (1)]
      +
        +
      • Rsymphony solver: This solver provides a different interface to the SYMPHONY software. It uses the Rsymphony R package which is available on The Comprehensive R Archive Network (CRAN). This solver is generally slower than the other solvers, because it cannot use parallel processing.
        • +
      +
      # create a problem and specify that Rsymphony should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p34 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_rsymphony_solver(gap = 0)
+
+# print problem
+print(p34)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      default
+##   solver:         Rsymphony [first_feasible (0), gap (0), time_limit (2147483647), verbose (1)]
      +
      +
      +

      Add a portfolio

      +

      Many conservation planning exercises require a portfolio of solutions. For example, real-world exercises can involve presenting decision makers with a range of near-optimal decisions. Additionally, the number of times that different planning units are selected in different solutions can provide insight into their relative importance. The following portfolio methods are available.

      +
        +
      • Gap portfolio: Generate a portfolio of solutions by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is especially useful for generating multiple solutions that can used be to calculate selection frequencies (similar to Marxan). Note that this method requires that the Gurobi optimization software is used to generate solutions.
        • +
      +
      # create a problem and specify that a portfolio should be created by
+# finding five solutions within 10% of optimality
+p35 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_gap_portfolio(number_solutions = 5, pool_gap = 0.2)
+
+# print problem
+print(p35)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Gap portfolio [number_solutions (5), pool_gap (0.2)]
+##   solver:         default
      +
        +
      • Top portfolio: Generate a portfolio of solutions by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions). Note that this method requires that the Gurobi optimization software is used to generate solutions.
        • +
      +
      # create a problem and specify that a portfolio should be created using
+# the top five solutions
+p36 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_top_portfolio(number_solutions = 5)
+
+# print problem
+print(p36)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Top portfolio [number_solutions (5)]
+##   solver:         default
      +
        +
      • Extra portfolio: Generate a portfolio of solutions by storing feasible solutions found during the optimization process. Note that this method requires that the Gurobi optimization software is used to generate solutions.
        • +
      +
      # create a problem and specify that a portfolio should be created using
+# extra solutions found while solving the problem
+p37 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_extra_portfolio()
+
+# print problem
+print(p37)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Extra portfolio
+##   solver:         default
      +
        +
      • Cuts portfolio: Generate a portfolio of distinct solutions within a pre-specified optimality gap. This method is only recommended if the Gurobi optimization solver is not available.
        • +
      +
      # create a problem and specify that a portfolio containing 10 solutions
+# should be created using using Bender's cuts
+p38 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_cuts_portfolio(number_solutions = 10)
+
+# print problem
+print(p38)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Cuts portfolio [number_solutions (10)]
+##   solver:         default
      +
        +
      • Shuffle portfolio: Generate a portfolio of solutions by randomly reordering the data prior to attempting to solve the problem. If the Gurobi optimization solver is not available, this method is the fastest method for generating a set number of solutions within a specified distance from optimality.
        • +
      +
      # create a problem and specify a portfolio should be created that contains
+# 10 solutions and that any duplicate solutions should not be removed
+p39 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_shuffle_portfolio(number_solutions = 10, remove_duplicates = FALSE)
+
+# print problem
+print(p39)
      +
      ## Conservation Problem
+##   planning units: RasterLayer (90 units)
+##   cost:           min: 190.13276, max: 215.86384
+##   features:       layer.1, layer.2, layer.3, ... (5 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   decisions:      Binary decision 
+##   constraints:    <none>
+##   penalties:      <none>
+##   portfolio:      Shuffle portfolio [number_solutions (10), remove_duplicates (0), threads (1)]
+##   solver:         default
      +
      +
      +

      Solve the problem

      +

      After formulating our conservation planning problem and specifying how the problem should be solved, we can use the solve function to obtain a solution. Note that the solver will typically print out some information describing the size of the problem and report its progress when searching for a suitable solution.

      +
      # formulate the problem
+p40 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_boundary_penalties(penalty = 500, edge_factor = 0.5) %>%
+       add_binary_decisions()
+
+# solve the problem (using the default solver)
+s40 <- solve(p40)
      +
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 293 rows, 234 columns and 1026 nonzeros
+## Model fingerprint: 0xbd38144b
+## Variable types: 0 continuous, 234 integer (234 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-01, 1e+00]
+##   Objective range  [1e+02, 4e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [3e+00, 8e+00]
+## Found heuristic solution: objective 20287.196992
+## Found heuristic solution: objective 3087.9617505
+## Presolve time: 0.00s
+## Presolved: 293 rows, 234 columns, 1026 nonzeros
+## Variable types: 0 continuous, 234 integer (234 binary)
+## Root relaxation presolved: 293 rows, 234 columns, 1026 nonzeros
+## 
+## 
+## Root relaxation: objective 2.265862e+03, 220 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 2265.86242    0  234 3087.96175 2265.86242  26.6%     -    0s
+##      0     0 2325.53449    0  232 3087.96175 2325.53449  24.7%     -    0s
+##      0     0 2361.03063    0  223 3087.96175 2361.03063  23.5%     -    0s
+##      0     0 2371.27288    0  222 3087.96175 2371.27288  23.2%     -    0s
+##      0     0 2371.27288    0  222 3087.96175 2371.27288  23.2%     -    0s
+## H    0     0                    2790.8740409 2371.27288  15.0%     -    0s
+## H    0     0                    2730.9524342 2371.27288  13.2%     -    0s
+##      0     2 2372.02804    0  222 2730.95243 2372.02804  13.1%     -    0s
+## H    6     6                    2604.7426048 2375.46233  8.80%  21.0    0s
+## 
+## Cutting planes:
+##   Gomory: 3
+## 
+## Explored 7 nodes (489 simplex iterations) in 0.09 seconds (0.10 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 5: 2604.74 2730.95 2790.87 ... 20287.2
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 2.604742604847e+03, best bound 2.375462328932e+03, gap 8.8024%
      +
      # plot solution
+plot(s40, col = c("grey90", "darkgreen"), main = "Solution",
+     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
      +

      +

      We can plot this solution because the planning unit input data are spatially referenced in a raster format. The output format will always match the planning unit data used to initialize the problem. For example, the solution to a problem with planning units in a spatial vector (shapefile) format would also be in a spatial vector format. Similarly, if the planning units were in a tabular format (i.e., data.frame), the solution would also be returned in a tabular format.

      +

      We can also extract attributes from the solution that describe the quality of the solution and the optimization process.

      +
      # extract the objective (numerical value being minimized or maximized)
+print(attr(s40, "objective"))
      +
      ## solution_1 
+##   2604.743
      +
      # extract time spent solving solution
+print(attr(s40, "runtime"))
      +
      ## solution_1 
+##       0.11
      +
      # extract state message from the solver that describes why this specific
+# solution was returned
+print(attr(s40, "status"))
      +
      ## solution_1 
+##  "OPTIMAL"
      +
      +
      +
      +

      Evaluate the solution

      +

      Conservation planning involves making trade-offs between different criteria (e.g. overall cost, feature representation, connectivity). After obtaining a solution to a conservation planning problem, it is important to evaluate it to help understand the trade-offs made by the prioritization. This is also useful to compare different solutions with each other.

      +
      +

      Evaluating performance

      +

      Summary statistics can be computed to evaluate the overall performance of a solution based on certain criteria. The following summaries can be computed.

      +

      The following functions are available to summarize a solution:

      +
        +
      • Number summary: Calculate the number of planning units selected by a solution.
        • +
      +
      # calculate statistic
+eval_n_summary(p40, s40)
      +
      ## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall    10
      +
        +
      • Cost summary: Calculate the total cost of a solution.
        • +
      +
      # calculate statistic
+eval_cost_summary(p40, s40)
      +
      ## # A tibble: 1 × 2
+##   summary  cost
+##   <chr>   <dbl>
+## 1 overall 2005.
      +
        +
      • Feature representation summary: Calculate how well features are represented by a solution. This function can be used for any type of problem.
        • +
      +
      # calculate statistics
+eval_feature_representation_summary(p40, s40)
      +
      ## # A tibble: 5 × 5
+##   summary feature total_amount absolute_held relative_held
+##   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+## 1 overall layer.1         83.3          8.95         0.107
+## 2 overall layer.2         31.2          3.22         0.103
+## 3 overall layer.3         72.0          7.59         0.106
+## 4 overall layer.4         42.7          4.34         0.102
+## 5 overall layer.5         56.7          5.89         0.104
      +
        +
      • Target coverage summary: Calculate how well representation targets are met by a solution. This function can only be used with problems contain targets.
        • +
      +
      # calculate statistics
+eval_target_coverage_summary(p40, s40)
      +
      ## # A tibble: 5 × 9
+##   feature met   total_amount absolute_target absolute_held absolute_shortfall
+##   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
+## 1 layer.1 TRUE          83.3            8.33          8.95                  0
+## 2 layer.2 TRUE          31.2            3.12          3.22                  0
+## 3 layer.3 TRUE          72.0            7.20          7.59                  0
+## 4 layer.4 TRUE          42.7            4.27          4.34                  0
+## 5 layer.5 TRUE          56.7            5.67          5.89                  0
+##   relative_target relative_held relative_shortfall
+##             <dbl>         <dbl>              <dbl>
+## 1             0.1         0.107                  0
+## 2             0.1         0.103                  0
+## 3             0.1         0.106                  0
+## 4             0.1         0.102                  0
+## 5             0.1         0.104                  0
      +
        +
      • Boundary summary: Calculate the total exposed boundary length (perimeter) associated with a solution.
        • +
      +
      # calculate statistic
+eval_boundary_summary(p40, s40)
      +
      ## # A tibble: 1 × 2
+##   summary boundary
+##   <chr>      <dbl>
+## 1 overall      1.2
      +
        +
      • Connectivity summary: Calculate the connectivity facilitated within a solution.
        • +
      +
      # calculate statistic
+# here we use the raster data for the first feature as an example
+# to parametrize pair-wise connectivity between different planning units
+eval_connectivity_summary(
+  p40, s40, data = connectivity_matrix(sim_pu_raster, sim_features[[1]]))
      +
      ## # A tibble: 1 × 2
+##   summary connectivity
+##   <chr>          <dbl>
+## 1 overall         1.97
      +
      +
      +

      Evaluating relative importance

      +

      Conservation plans can take a long time to implement. Since funding availability and habitat quality can decline over time, it is critical that the most important places in a prioritization are scheduled for management as early as possible. For instance, some planning units in a solution might contain many rare species which do not occur in any other planning units. Alternatively, some planning units might offer an especially high return on investment that reduces costs considerably. As a consequence, conservation planners often need information on which planning units selected in a prioritization are most important to the overall success of the prioritization. To achieve this, conservation planners can use importance scores for each planning unit selected by a solution.

      +

      Let’s generate a prioritization so that can compare the different importance methods.

      +
      # formulate the problem
+p41 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions()
+
+# solve the problem
+s41 <- solve(p41)
      +
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 5 rows, 90 columns and 450 nonzeros
+## Model fingerprint: 0x6442bf6e
+## Variable types: 0 continuous, 90 integer (90 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-01, 9e-01]
+##   Objective range  [2e+02, 2e+02]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [3e+00, 8e+00]
+## Found heuristic solution: objective 2337.9617505
+## Presolve time: 0.00s
+## Presolved: 5 rows, 90 columns, 450 nonzeros
+## Variable types: 0 continuous, 90 integer (90 binary)
+## Found heuristic solution: objective 2332.1003790
+## Root relaxation presolved: 5 rows, 90 columns, 450 nonzeros
+## 
+## 
+## Root relaxation: objective 1.931582e+03, 12 iterations, 0.00 seconds (0.00 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 1931.58191    0    4 2332.10038 1931.58191  17.2%     -    0s
+## H    0     0                    1987.3985265 1931.58191  2.81%     -    0s
+## 
+## Explored 1 nodes (12 simplex iterations) in 0.00 seconds (0.00 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 3: 1987.4 2332.1 2337.96 
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 1.987398526526e+03, best bound 1.931581908865e+03, gap 2.8085%
      +
      # plot solution
+plot(s41, col = c("grey90", "darkgreen"), main = "Solution",
+     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
      +

      +

      The following methods are available for computing importance scores.

      +
        +
      • Replacement cost: Evaluate importance using the replacement cost method (Cabeza & Moilanen 2006). This method quantifies the importance of a given planning unit as the decrease in the performance of the solution (based on the objective function) if the planning unit cannot be acquired (e.g., in terms of the additional costs required to meet feature targets). The advantages of this method are that it (i) accounts for the costs of the planning units, (ii) can be applied to multiple management zones, (iii) can be applied to any objective function, and (iv) can identify truly irreplaceable planning units (denoted with infinite values). However, the key disadvantage of this method, is that can take an infeasible amount of time to complete for large and complex problems.
        • +
      +
      # calculate replacement cost scores and make the solver quiet
+rc41 <- p41 %>%
+        add_default_solver(gap = 0, verbose = FALSE) %>%
+        eval_replacement_importance(s41)
+
+# plot replacement cost scores
+plot(rc41, main = "Replacement cost scores")
      +

      * Ferrier method: Evaluate importance by computing irreplaceability scores following Ferrier et al. (r-34?). The advantages of this method are that it (i) can be computed relatively quickly for moderate and large-sized problems, and (ii) calculates a score for each feature within each planning unit to provide insight into why certain planning units are more important than others. The disadvatange with this method is that it can only be applied to conservation problems with a minimum set objective and a single zone (i.e., similar to Marxan-type problems).

      +
      # calculate Ferrier scores and extract total score
+fs41 <- eval_ferrier_importance(p40, s40)[["total"]]
+
+# plot Ferrier scores
+plot(fs41, main = "Ferrier scores")
      +

      * Rarity weighted richness: Evaluate importance by computing rarity weighted richness scores (Williams et al. 1996). The only advantage with this method is that it can be computed very quickly for very large problems. The key disadvantage with this approach is that it merely describes the spatial patterns of biodiversity, and does not consider any of the goals that underpin conservation planning exercise. For instance, it does not account for planning costs, management zones, objective functions, or feature representation targets.

      +
      # calculate rarity weighted richness scores
+rwr41 <- eval_rare_richness_importance(p40, s40)
+
+# plot rarity weighted richness scores
+plot(rwr41, main = "Rarity weighted richness")
      +

      +

      In general, we recommend using replacement cost scores for small and moderate sized problems (e.g., less than 30,000 planning units) when it is feasible to do so. It can take a very long time to compute replacement cost scores, and so it is simply not feasible to compute these scores for particularly large problems. For moderate and large sized problems (e.g., more than 30,000 planning units), we recommend using the Ferrier method. This is because it explicitly accounts for representation targets, unlike the rarity weighted richness scores. We almost never recommend using the rarity weighted richness scores. This is because they do not consider criteria needed to inform conservation decision making (Brown et al. 2015).

      +
      +
      +
      +

      Marxan problems

      +

      Although we encourage users to build and tailor conservation planning problems to suit their own needs, sometimes it just simply easier to use something you’re already familiar with. The marxan_problem() function is provided as a convenient wrapper for building and solving Marxan-style conservation problems. If users already have their conservation planning data formatted for use with Marxan, this function can also read Marxan data files and solve the Marxan-style problems using exact algorithm solvers. Please note that problems built using the marxan_problem() function are still solved the same way as a problem initialized using the problem() function, and therefore still require the installation of one of the solver packages.

      +

      Here is a short example showing how the marxan_problem() function can be used to read Marxan input files and the solve function can be used to solve the problem.

      +
      # set file path for Marxan input file
+minput <- system.file("extdata/input.dat", package = "prioritizr")
+
+# read Marxan input file
+mp <- marxan_problem(minput)
+
+# print problem
+print(mp)
      +
      ## Conservation Problem
+##   planning units: data.frame (1751 units)
+##   cost:           min: 0, max: 41569219.38232
+##   features:       bird1, nvis2, nvis8, ... (17 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.3, max: 0.3)]
+##   decisions:      default
+##   constraints:    <Locked out planning units [1 locked units]
+##                    Locked in planning units [317 locked units]>
+##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (1), zones]>
+##   portfolio:      default
+##   solver:         default
      +
      # solve the problem
+ms <- solve(mp)
+
+# since the Marxan data was in a tabular format, the solution is also returned
+# in a tabular format, so we will print the first six rows of the table
+# containing the solution
+head(ms)
      +

      Alternatively, rather then using a Marxan input file to construct the problem, we can manually read in the Marxan data files and input these to the marxan_problem() function.

      +
      # load data
+pu <- system.file("extdata/input/pu.dat", package = "prioritizr") %>%
+      read.table(sep = ",", header = TRUE)
+features <- system.file("extdata/input/spec.dat", package = "prioritizr") %>%
+            read.table(sep = ",", header = TRUE)
+bound <- system.file("extdata/input/bound.dat", package = "prioritizr") %>%
+         read.table(sep = "\t", header = TRUE)
+rij <- system.file("extdata/input/puvspr.dat", package = "prioritizr") %>%
+       read.table(sep = ",", header = TRUE)
+
+# build Marxan problem using data.frame objects
+mp2 <- marxan_problem(x = pu, spec = features, puvspr = rij, bound = bound,
+                      blm = 0)
+
+# print problem
+print(mp2)
      +
      ## Conservation Problem
+##   planning units: data.frame (1751 units)
+##   cost:           min: 0, max: 41569219.38232
+##   features:       bird1, nvis2, nvis8, ... (17 features)
+##   objective:      Minimum set objective 
+##   targets:        Relative targets [targets (min: 0.3, max: 0.3)]
+##   decisions:      default
+##   constraints:    <Locked out planning units [1 locked units]
+##                    Locked in planning units [317 locked units]>
+##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (0), zones]>
+##   portfolio:      default
+##   solver:         default
      +

      Conservation planning problems that are built using the marxan_problem() function can also be customized. For example, we could change the decision type for mp2 to involve selecting a proportion of each planing unit (using the add_proportion_decisions() function).

      +
      +
      +

      Conclusion

      +

      Hopefully, this vignette has provided an informative overview of the prioritizr R package. For more examples using the package, please see the other vignettes. Perhaps, one of the best ways to learn a new piece of software is to just try it out. Test it, try breaking it, make mistakes, and learn from them. We would recommend trying to build conservation planning problems that resemble those you face in your own work—but using the built-in example data sets. This way you can quickly verify that the problems you build actually mean what you think they mean. For instance, you can try playing around with the targets and see what effect they have on the solutions, or try playing around with penalties and see what effect they have on the solutions. Finally, if you have any questions about using the package or suggestions for it, please post an issue on the package’s online coding repository.

      +
      +
      +

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      +
      +
      + + + + + + + + + + + diff --git a/inst/doc/prioritizr.Rmd b/inst/doc/prioritizr.Rmd index d6f896ebd..dc2883a47 100644 --- a/inst/doc/prioritizr.Rmd +++ b/inst/doc/prioritizr.Rmd @@ -1,5 +1,5 @@ --- -title: "prioritizr: Systematic Conservation Prioritization in R" +title: "Getting started" output: rmarkdown::html_vignette: toc: true @@ -10,900 +10,278 @@ documentclass: article bibliography: references.bib csl: reference-style.csl vignette: > - %\VignetteIndexEntry{prioritizr: Systematic Conservation Prioritization in R} + %\VignetteIndexEntry{Getting started} %\VignetteEngine{knitr::rmarkdown_notangle} --- ```{r, include = FALSE} -h = 3.5 -w = 3.5 +# define dummy variables so that vignette passes package checks +tas_features <- raster::raster(matrix(1)) +``` + +```{r, include = FALSE} +# define variables for vignette figures and code execution +h <- 3.5 +w <- 3.5 is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_", "_R_CHECK_LICENSE_") %in% names(Sys.getenv())) -knitr::opts_chunk$set(fig.align = "center", eval = !is_check, - root.dir = normalizePath("../..")) +knitr::opts_chunk$set(fig.align = "center", eval = !is_check) ``` -## Summary - -The _prioritizr R_ package uses integer linear programming (ILP) techniques to provide a flexible interface for building and solving conservation planning problems [@r11; @r16]. It supports a broad range of objectives, constraints, and penalties that can be used to custom-tailor conservation planning problems to the specific needs of a conservation planning exercise. Once built, conservation planning problems can be solved using a variety of commercial and open-source exact algorithm solvers. In contrast to the algorithms conventionally used to solve conservation problems, such as heuristics or simulated annealing [@r3], the exact algorithms used here are guaranteed to find optimal solutions. Furthermore, conservation problems can be constructed to optimize the spatial allocation of different management zone (or actions), meaning that conservation practitioners can identify solutions that benefit multiple stakeholders. Finally, this package has the functionality to read input data formatted for the _Marxan_ conservation planning program [@r3], and find much cheaper solutions in a much shorter period of time than _Marxan_ [@r1]. - ## Introduction -Systematic conservation planning is a rigorous, repeatable, and structured approach to designing new protected areas that efficiently meet conservation objectives [@r4]. Historically, conservation decision-making has often evaluated parcels opportunistically as they became available for purchase, donation, or under threat. Although purchasing such areas may improve the _status quo_, such decisions may not substantially enhance the long-term persistence of target species or communities. Faced with this realization, conservation planners began using decision support tools to help simulate alternative reserve designs over a range of different biodiversity and management goals and, ultimately, guide protected area acquisitions and management actions. Due to the systematic, evidence-based nature of these tools, conservation prioritization can help contribute to a transparent, inclusive, and more defensible decision making process. - -A conservation planning exercise typically starts by defining a study area. This study area should encompass all the areas relevant to the decision maker or the hypothesis being tested. The extent of a study area could encompass a few important localities [e.g. @r18], a single state [e.g. @r17], an entire country [@r19], or the entire planet [@r20]. Next, the study area is divided into a set of discrete areas termed _planning units_. Each planning unit represents a discrete locality in the study area that can be managed independently of other areas. The general idea is that some combination of the planning units can be selected for conservation actions (e.g. protected area establishment, habitat restoration). Planning units are often created as square or hexagon cells that are sized according to the scale of the conservation actions, and the resolution of the data that underpin the planning exercise [but see @r5]. - -Cost data (or a surrogate thereof) are needed to inform the prioritization process. Specifically, these cost data describe the relative expenditure associated with managing each planning unit for conservation. For example, if the goal of the conservation planning exercise is to identify priority areas for expanding a local protected area system, then the cost data could represent the physical cost of purchasing the land. Alternatively, if such data are not available, then surrogate data could are often used instead (e.g. human population density, opportunity cost of foregone commercial activities, or planning unit size). - -Conservation planning exercises also require data on the biodiversity elements that are of conservation interest (termed _conservation features_). These features could be species (e.g. _Neofelis nebulosa_, the Clouded Leopard), populations, or habitats (e.g. mangroves or cloud forest). After identifying the set of relevant conservation features for a conservation planning exercise, spatially explicit data need to be obtained for each and every feature to describe their spatial distribution (e.g. habitat suitability data, probability of occurrence data, presence/absence data). This is important to ensure that conservation features are adequately covered (represented) by prioritizations. After assembling all the data, the next step is to define the conservation planning problem. - -The _prioritizr R_ package is designed to help you build and solve conservation planning problems. Specifically, prioritizations are generated by using formulating a mathematical optimization problem and then solving it to generate a solution. These mathematical optimization problems are formulated using the planning unit data, cost data, and feature data, and with information related to the overarching aim of the prioritization process. In general, the goal of an optimization problem is to minimize (or maximize) an _objective function_ that is calculated using a set of _decision variables_, subject to a series of constraints to ensure that solution exhibits specific properties. The objective function describes the quantity which we are trying to minimize (e.g. cost of the solution) or maximize (e.g. number of features conserved). The decision variables describe the entities that we can control, and indicate which planning units are selected for conservation management and which of those are not. The constraints can be thought of as rules that the need decision variables need to follow. For example, a commonly used constraint is specifying that the solution must not exceed a certain budget. - -A wide variety of approaches have been developed for solving optimization problems. Reserve design problems are frequently solved using simulated annealing [@r6] or heuristics [@r8; @r7]. These methods are conceptually simple and can be applied to a wide variety of optimization problems. However, they do not scale well for large or complex problems [@r1]. Additionally, these methods cannot tell you how close any given solution is to the optimal solution. The _prioritizr R_ package uses exact algorithms to efficiently solve conservation planning problems to within a pre-specified a optimality gap. In other words, you can specify that you need the optimal solution (i.e. a gap of 0%) and the algorithms will, given enough time, find a solution that meets this criteria. In the past, exact algorithms have been too slow for conservation planning exercises [@r9]. However, improvements over the last decade mean that they are now much faster [@r23; @r1]. - -In this package, optimization problems are expressed using _integer linear programming_ (ILP) so that they can be solved using (linear) exact algorithm solvers. The general form of an integer programming problem can be expressed in matrix notation using the following equation. - -$$\text{Minimize} \space \boldsymbol{c}^\text{T} \boldsymbol{x} \space -\space \text{subject to} \space A\boldsymbol{x} -\space \Box \space \boldsymbol{b}$$ - -Here, where $x$ is a vector of decision variables, $c$ and $b$ are vectors of known coefficients, and $A$ is the constraint matrix. The final term specifies a series of structural constants and the $\Box$ symbol is used to indicate that the relational operators for the constraints can be either $\geq$, $=$, or $\leq$. In the context of a conservation planning problem, $c$ could be used to represent the planning unit costs, $A$ could be used to store the data showing the presence / absence (or amount) of each feature in each planning unit, $b$ could be used to represent minimum amount of habitat required for each species in the solution, the $\Box$ could be set to $\geq$ symbols to indicate that the total amount of each feature in the solution must exceed the quantities in $b$. But there are many other ways of formulating the reserve selection problem [@r11]. - -## Package overview - -The _prioritizr R_ package contains eight main types of functions. These -functions are used to: - -* create a new conservation planning [problem](https://prioritizr.net/reference/problem.html) by specifying the planning units, features, and management zones of conservation interest (e.g. species, ecosystems). -* add an [objective](https://prioritizr.net/reference/objectives.html) to a conservation planning problem. -* add [targets](https://prioritizr.net/reference/targets.html) to a problem to specify how much of each feature is desired or required to be conserved in the solutions. -* add [constraints](https://prioritizr.net/reference/constraints.html) to a conservation planning problem to ensure that solutions exhibit specific properties (e.g. select specific planning units for protection). -* add [penalties](https://prioritizr.net/reference/penalties.html) to a problem to penalize solutions according to specific metric (e.g. connectivity). -* add [decisions](https://prioritizr.net/reference/decisions.html) to a problem to specify the nature of the decisions in the problem. -* add methods to generate a [portfolio](https://prioritizr.net/reference/portfolios.html) of solutions. -* add a [solver](https://prioritizr.net/reference/solvers.html) to a conservation problem to specify which software should be used to generate solutions and customize the optimization process. -* [solve](https://prioritizr.net/reference/solve.html) a conservation problem. -* evaluate a solution by computing [summary](https://prioritizr.net/reference/summaries.html) statistics. -* evaluate the relative [importance](https://prioritizr.net/reference/importance.html) (irreplaceability) of planning units selected in a solution. +The aim of this tutorial is to provide a short introduction to the _prioritizr R_ package. It is also intended for helping conservation planners familiar the _Marxan_ decision support tool [@r3] to start using the package for their work. -## Package workflow +## Data -The general workflow when using the _prioritizr R_ package starts with creating a new conservation planning `problem` object using data. Specifically, the `problem` object should be constructed using data that specify the planning units, biodiversity features, management zones (if applicable), and costs. After creating a new `problem` object, it can be customized---by adding objectives, penalties, constraints, and other information---to build a precise representation of the conservation planning problem required, and then solved to obtain a solutions. +Let's load the packages and data used in this tutorial. Since this tutorial uses data from the _prioritizrdata R_ package, please ensure that it is installed. The data used in this tutorial were obtained from the _Introduction to Marxan_ course. Specifically, the data were originally a subset of a larger spatial prioritization project performed under contract to Australia's Department of Environment and Water Resources [@r30]. -All conservation planning problems require an objective. An objective specifies the property which is used to compare different feasible solutions. Simply put, the objective is the property of the solution which should be maximized or minimized during the optimization process. For instance, with the minimum set objective (specified using `add_min_set_objective`), we are seeking to minimize the cost of the solution (similar to _Marxan_). On the other hand, with the maximum coverage objective (specified using `add_max_cover_objective`), we are seeking to maximize the number of different features represented in the solution. - -Many objectives require `targets` (e.g. the minimum set objective). Targets are a specialized set of constraints that relate to the total quantity of each feature secured in the solution (e.g. amount of suitable habitat or number of individuals). In the case of the minimum set objective ( `add_min_set_objective`), they are used to ensure that solutions secure a sufficient quantity of each feature, and in other objectives, such as the maximum features objective ( `add_max_features_objective`) they are used to assess whether a feature has been adequately conserved by a candidate solution. Targets can be expressed numerically as the total amount required for a given feature (using `add_absolute_targets`), or as a proportion of the total amount found in the planning units (using `add_relative_targets`). Note that not all objectives require targets, and a warning will be thrown if an attempt is made to add targets to a problem with an objective that does not use them. - -Constraints and penalties can be added to a conservation planning problem to ensure that solutions exhibit a specific property or penalize solutions which don't exhibit a specific property (respectively). The difference between constraints and penalties, strictly speaking, is constraints are used to rule out potential solutions that don't exhibit a specific property. For instance, constraints can be used to ensure that specific planning units are selected in the solution for prioritization (using `add_locked_in_constraints`) or not selected in the solution for prioritization (using `add_locked_out_constraints`). On the other hand, penalties are combined with the objective of a problem, with a penalty factor, and the overall objective of the problem then becomes to minimize (or maximize) the primary objective function and the penalty function. For example, penalties can be added to a problem to penalize solutions that are excessively fragmented (using `add_boundary_penalties`). These penalties have a `penalty` argument that specifies the relative importance of having spatially clustered solutions. When the argument to `penalty` is high, then solutions which are less fragmented are valued more highly---even if they cost more---and when the argument to `penalty` is low, then the solutions which are more fragmented are valued less highly. - -After building a conservation problem, it can then be solved to obtain a solution (or portfolio of solutions if desired). The solution is returned in the same format as the planning unit data used to construct the problem. This means that if raster or shapefile / vector data was used when initializing the problem, then the solution will also be in raster or shapefile / vector data. This can be very helpful when it comes to interpreting and visualizing solutions because it means that the solution data does not first have to be merged with spatial data before they can be plotted on a map. - -## Usage - -Here we will provide an introduction to using the _prioritizr R_ package to build and solve a conservation planning problem. Please note that we will not discuss conservation planning with multiple zones in this vignette, for more information on working with multiple management zones please see the [zones vignette](zones.html). - -First, we will load the _prioritizr_ package. - -```{r, results = "hide", message = FALSE} -# load package +```{r, message = FALSE} +# load packages +library(prioritizrdata) library(prioritizr) +library(vegan) +library(cluster) -# set default options for printing tabular data -options(tibble.width = Inf) -``` - -### Data - -Now we will load some built-in data sets that are distributed with the _prioritizr R_ package. This package contains several different planning unit data sets. To provide a comprehensive overview of the different ways that we can initialize a conservation planning problem, we will load each of them. - -First, we will load the raster planning unit data (`sim_pu_raster`). Here, the planning units are represented as a raster (i.e. a `RasterLayer` object) and each pixel corresponds to the spatial extent of each panning unit. The pixel values correspond to the acquisition costs of each planning unit. - -```{r} -# load raster planning unit data -data(sim_pu_raster) - -# print description of the data -print(sim_pu_raster) - -# plot the data -plot(sim_pu_raster) -``` - -Secondly, we will load one of the spatial vector planning unit data sets (`sim_pu_polygons`). Here, each polygon (i.e. feature using ArcGIS terminology) corresponds to a different planning unit. This data set has an attribute table that contains additional information about each polygon. Namely, the `cost` field (column) in the attribute table contains the acquisition cost for each planning unit. - -```{r} -# load polygon planning unit data -data(sim_pu_polygons) - -# print first six rows of attribute table -head(sim_pu_polygons@data) - -# plot the planning units -spplot(sim_pu_polygons, zcol = "cost") -``` - -Thirdly, we will load some planning unit data stored in tabular format (i.e. `data.frame` format). For those familiar with _Marxan_ or dealing with very large conservation planning problems (> 10 million planning units), it may be useful to work with data in this format because it does not contain any spatial information which will reduce computational burden. When using tabular data to initialize conservation planning problems, the data must follow the conventions used by _Marxan_. Specifically, each row in the planning unit table must correspond to a different planning unit. The table must also have an "id" column to provide a unique integer identifier for each planning unit, and it must also have a column that indicates the cost of each planning unit. For more information, please see the [official _Marxan_ documentation](https://marxansolutions.org/). - -```{r} -# specify file path for planning unit data -pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr") - -# load in the tabular planning unit data -# note that we use the data.table::fread function, as opposed to the read.csv -# function, because it is much faster -pu_dat <- data.table::fread(pu_path, data.table = FALSE) - -# preview first six rows of the tabular planning unit data -# note that it has some extra columns other than id and cost as per the -# Marxan format -head(pu_dat) -``` - -Finally, we will load data showing the spatial distribution of the conservation features. Our conservation features (`sim_features`) are represented as a stack of raster objects (i.e. a `RasterStack` object) where each layer corresponds to a different feature (e.g. a multi-band GeoTIFF where each band corresponds to a different feature). The pixel values in each layer correspond to the amount of suitable habitat available in a given planning unit. Note that our planning unit raster layer and our conservation feature stack have exactly the same spatial properties (i.e. resolution, extent, coordinate reference system) so their pixels line up perfectly. +# load planning unit data +data(tas_pu) -```{r, fig.width = 4, fig.height = 3} # load feature data -data(sim_features) - -# plot the distribution of suitable habitat for each feature -plot(sim_features, main = paste("Feature", seq_len(nlayers(sim_features))), - nr = 2, box = FALSE, axes = FALSE) -``` - -### Initialize a problem - -After having loaded our planning unit and feature data, we will now try initializing the some conservation planning problems. There are a lot of different ways to initialize a conservation planning problem, so here we will just showcase a few of the more commonly used methods. For an exhaustive description of all the ways you can initialize a conservation problem, see the help file for the `problem` function (which you can open using the code `?problem`). First off, we will initialize a conservation planning problem using the raster data. - -```{r} -# create problem -p1 <- problem(sim_pu_raster, sim_features) - -# print problem -print(p1) - -# print number of planning units -number_of_planning_units(p1) - -# print number of features -number_of_features(p1) -``` - -Generally, we recommend initializing problems using raster data where possible. This is because the `problem` function needs to calculate the amount of each feature in each planning unit, and by providing both the planning unit and feature data in raster format with the same spatial resolution, extents, and coordinate systems, this means that the `problem` function does not need to do any geo-processing behind the scenes. But sometimes we can't use raster planning unit data because our planning units aren't equal-sized grid cells. So, below is an example showing how we can initialize a conservation planning problem using planning units that are formatted as spatial vector data. Note that if we had pre-computed the amount of each feature in each planning unit and stored the data in the attribute table, we could pass in the names of the columns as an argument to the `problem` function. - -```{r} -# create problem with spatial vector data -# note that we have to specify which column in the attribute table contains -# the cost data -p2 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") - -# print problem -print(p2) -``` - -We can also initialize a conservation planning problem using tabular planning unit data (i.e. a `data.frame`). Since the tabular planning unit data does not contain any spatial information, we also have to provide the feature data in tabular format (i.e. a `data.frame`) and data showing the amount of each feature in each planning unit in tabular format (i.e. a `data.frame`). The feature data must have an "id" column containing a unique integer identifier for each feature, and the planning unit by feature data must contain the following three columns: "pu" corresponding to the planning unit identifiers, "species" corresponding to the feature identifiers, and "amount" showing the amount of a given feature in a given planning unit. - -```{r} -# set file path for feature data -spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr") - -# load in feature data -spec_dat <- data.table::fread(spec_path, data.table = FALSE) - -# print first six rows of the data -# note that it contains extra columns -head(spec_dat) - -# set file path for planning unit vs. feature data -puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr") - -# load in planning unit vs feature data -puvspr_dat <- data.table::fread(puvspr_path, data.table = FALSE) - -# print first six rows of the data -head(puvspr_dat) - -# create problem -p3 <- problem(pu_dat, spec_dat, cost_column = "cost", rij = puvspr_dat) - -# print problem -print(p3) +data(tas_features) ``` -For more information on initializing problems, please see the help page for the `problem` function (which you can open using the code `?problem`). Now that we have initialized a conservation planning problem, we will show you how you can customize it to suit the exact needs of your conservation planning scenario. Although we initialized the conservation planning problems using several different methods, moving forward, we will only use raster-based planning unit data to keep things simple. +The `tas_pu` object contains planning units represented as spatial polygons (i.e., a `SpatialPolygonsDataFrame` object). This object has three columns that denote the following information for each planning unit: a unique identifier (`id`), unimproved land value (`cost`), and current conservation status (`locked_in`). Planning units that have at least half of their area overlapping with existing protected areas are denoted with a locked in value of 1, otherwise they are denoted with a value of 0. If you are familiar with the _Marxan_ decision support tool, then you will notice that some of these columns are formatted similar conventions. -### Add an objective +Now, let's have a look at the planning unit data. We can see that the planning units correspond to hexagonal land parcels. We can also see that is a clear spatial pattern in the cost and conservation status the planning units. -The next step is to add an objective to the problem. A problem objective is used to specify the primary goal of the problem (i.e. the quantity that is to be maximized or minimized). All conservation planning problems involve minimizing or maximizing some kind of objective. For instance, we might require a solution that conserves enough habitat for each species while minimizing the overall cost of the reserve network. Alternatively, we might require a solution that maximizes the number of conserved species while ensuring that the cost of the reserve network does not exceed the budget. Please note that objectives are added in the same way regardless of the type of data used to initialize the problem. +```{r, fig.width = w, fig.height = h} +# print planning unit data +print(tas_pu) -The _prioritizr R_ package supports a variety of different objective functions. +# plot map of planning unit costs +plot(st_as_sf(tas_pu[, "cost"]), main = "Planning unit costs") -* __Minimum set objective__: Minimize the cost of the solution whilst ensuring that all targets are met [@r11]. This objective is similar to that used in _Marxan_ [@r3]. For example, we can add a minimum set objective to a problem using the following code. -```{r} -# create a new problem that has the minimum set objective -p3 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() - -# print the problem -print(p3) +# plot map of planning unit coverage by protected areas +plot(st_as_sf(tas_pu[, "locked_in"]), main = "Protected area coverage") ``` -* __Maximum cover objective__: Represent at least one instance of as many features as possible within a given budget [@r12]. -```{r} -# create a new problem that has the maximum coverage objective and a budget -# of 5000 -p4 <- problem(sim_pu_raster, sim_features) %>% - add_max_cover_objective(5000) -# print the problem -print(p4) -``` -* __Maximum features objective__: Fulfill as many targets as possible while ensuring that the cost of the solution does not exceed a budget [inspired by @r10]. This object is similar to the maximum cover objective except that we have the option of later specifying targets for each feature. In practice, this objective is more useful than the maximum cover objective because features often require a certain amount of area for them to persist and simply capturing a single instance of habitat for each feature is generally unlikely to enhance their long-term persistence. -```{r} -# create a new problem that has the maximum features objective and a budget -# of 5000 -p5 <- problem(sim_pu_raster, sim_features) %>% - add_max_features_objective(budget = 5000) +The `tas_features` object describes the spatial distribution of the features. Specifically, the feature data are expressed as a stack of `r raster::nlayers(tas_features)` rasters (i.e., a `RasterStack` object). Each layer in the stack corresponds to one of `r raster::nlayers(tas_features)` different vegetation communities. To describe the spatial distribution of a given vegetation community, each layer contains a spatially referenced grid of rectangular cells and each of these grid cells is associated with information on the distribution of the a given vegetation community. Specifically, these grid cells are assigned values that indicate if a given vegetation community is present (using value of 1) or absent (using value of 0) within the spatial extent of each grid cell. -# print the problem -print(p5) -``` -* __Minimum shortfall objective__: Minimize the overall (weighted sum) shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when there is a large amount of left-over budget when using the maximum feature representation objective and the remaining funds need to be allocated to places that will enhance the representation of features with unmet targets. -```{r} -# create a new problem that has the minimum shortfall objective and a budget -# of 5000 -p6 <- problem(sim_pu_raster, sim_features) %>% - add_min_shortfall_objective(budget = 5000) +Next, let's examine the feature data. Here we will only plot the first four features as an example. The pixel values denote the presence (denoted by a value of 1) or absence (denoted by a value of zero) of each feature within the extent of the study area. -# print the problem -print(p6) -``` -* __Minimum largest shortfall objective__: Minimize the largest (maximum) shortfall while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when the minimum shortfall objective returns solutions that focus too much on representing a small number of features (e.g. because they occur in much cheaper planning units), and solutions are needed to spread conservation effort out more evenly amongst all features---even if it means that all features will have (relatively) poor representation. -```{r} -# create a new problem that has the minimum largest shortfall objective and a -# budget of 5000 -p7 <- problem(sim_pu_raster, sim_features) %>% - add_min_largest_shortfall_objective(budget = 5000) +```{r, fig.width = 4.5, fig.height = 4.5} +# print planning unit data +print(tas_features) -# print the problem -print(p7) +# plot map of the first four vegetation classes +plot(tas_features[[1:4]], main = paste("Feature", 1:4)) ``` -* __Maximum phylogenetic diversity objective__: Maximize the phylogenetic diversity of the features represented in the solution subject to a budget [inspired by @r13; @r14]. This objective is similar to the maximum features objective except that emphasis is placed on protecting features which are associated with a diverse range of evolutionary histories. The _prioritizr R_ package contains a simulated phylogeny that can be used with the simulated feature data (`sim_phylogny`). -```{r} -# load simulated phylogeny data -data(sim_phylogeny) -# create a new problem that has the maximum phylogenetic diversity -# objective and a budget of 5000 -p8 <- problem(sim_pu_raster, sim_features) %>% - add_max_phylo_div_objective(budget = 5000, tree = sim_phylogeny) +The planning units in this tutorial are stored as spatial polygons. Although spatial polygons provide considerable flexibility in the shape and size of the planning units, such flexibility comes at a cost. This is because the spatial data processing routines needed to combine spatial polygon data and raster data for optimization can be very computationally expensive (e.g., calculating zonal statistics). As a consequence, we generally recommend using raster-based planning unit data where possible to reduce processing time. Another strategy is to complete spatial data processing routines manually using other software (e.g., _ESRI ArcGIS_) and use the pre-processed data directly with the _prioritizr R_ package. -# print the problem -print(p8) -``` -* __Maximum phylogenetic endemism objective__: Maximize the phylogenetic endemism of the features represented in the solution subject to a budget [inspired by @r13; @r14; @r32]. This objective is similar to the maximum phylogenetic diversity except that emphasis is placed conserving features that are associated with geographically restricted periods of evolutionary history rather than a diverse range of evolutionary histories. -```{r} -# load simulated phylogeny data -data(sim_phylogeny) +## Problem formulation -# create a new problem that has the maximum phylogenetic diversity -# objective and a budget of 5000 -p9 <- problem(sim_pu_raster, sim_features) %>% - add_max_phylo_end_objective(budget = 5000, tree = sim_phylogeny) +Now we will formulate a conservation planing problem. To achieve this, we first specify which objects contain the planning unit and feature data (using the `problem()` function). Next, we specify that we want to use the minimum set objective function (using the `add_min_set_objective()` function). This objective function indicates that we wish to minimize the total cost of planning units selected by the prioritization. We then specify boundary penalties reduce spatial fragmentation in the resulting prioritization (using the `add_boundary_penalties()` function; see the [_Calibrating trade-offs_ vignette](calibrating_trade-offs.html) for details on calibrating the penalty value). We also specify representation targets to ensure the resulting prioritization provides adequate coverage of each vegetation community (using the `add_relative_targets()` function). Specifically, we specify targets to ensure at least 17% of the spatial extent of each vegetation community (based on the [Aichi Target 11](https://www.cbd.int/sp/targets/)). Additionally, we set constraints to ensure that planning units predominately covered by existing protected areas are selected by the prioritization (using the `add_locked_in_constraints()` function). Finally, we specify that the prioritization should either select -- or not select -- planning units for prioritization (using the `add_binary_decisions()` function). -# print the problem -print(p9) -``` -* __Maximum utility objective__: Secure as much of the features as possible without exceeding a budget. This objective is functionally equivalent to selecting the planning units with the greatest amounts of each feature (e.g. species richness). Generally, we don't encourage the use of this objective because it will only rarely identify complementary solutions---solutions which adequately conserve a range of different features---except perhaps to explore trade-offs or provide a baseline solution with which to compare other solutions. -```{r} -# create a new problem that has the maximum utility objective and a budget -# of 5000 -p10 <- problem(sim_pu_raster, sim_features) %>% - add_max_utility_objective(budget = 5000) +```{r, fig.width = w, fig.height = h} +# build problem +p1 <- problem(tas_pu, tas_features, cost_column = "cost") %>% + add_min_set_objective() %>% + add_boundary_penalties(penalty = 0.005) %>% + add_relative_targets(0.17) %>% + add_locked_in_constraints("locked_in") %>% + add_binary_decisions() # print the problem -print(p10) -``` - -### Add targets - -Most conservation planning problems require targets. Targets are used to specify the minimum amount or proportion of a feature's distribution that needs to be protected in the solution. For example, we may want to develop a reserve network that will secure 20% of the distribution for each feature for minimal cost. - -There are four ways for specifying targets in the _prioritizr R_ package: - -* __Absolute targets__: Targets are expressed as the total amount of each feature in the study area that need to be secured. For example, if we had binary feature data that showed the absence or presence of suitable habitat across the study area, we could set an absolute target as 5 to mean that we require 5 planning units with suitable habitat in the solution. -```{r} -# create a problem with targets which specify that the solution must conserve -# a need a sum total of 3 units of suitable habitat for each feature -p11 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_absolute_targets(3) - -# print problem -print(p11) -``` -* __Relative targets__: Targets are set as a proportion (between 0 and 1) of the total amount of each feature in the study area. For example, if we had binary feature data and the feature occupied a total of 20 planning units in the study area, we could set a relative target of 50 % to specify that the solution must secure 10 planning units for the feature. We could alternatively specify an absolute target of 10 to achieve the same result, but sometimes proportions are easier to work with. -```{r} -# create a problem with the minimum set objective and relative targets of 10 % -# for each feature -p12 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) - -# print problem -print(p12) - -# create a problem with targets which specify that we need 10 % of the habitat -# for the first feature, 15 % for the second feature, 20 % for the third feature -# 25 % for the fourth feature and 30 % of the habitat for the fifth feature -targets <- c(0.1, 0.15, 0.2, 0.25, 0.3) -p13 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(targets) - -# print problem -print(p13) -``` -* __Log-linear targets__: Targets are expressed using scaling factors and log-linear interpolation. This method for specifying targets is commonly used for global prioritization analyses [@r15]. -```{r} -# create problem with added log-linear targets -p14 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_loglinear_targets(10, 0.9, 100, 0.2) - -# print problem -print(p14) -``` -* __Manual targets__: Targets are manually specified. This is only really recommended for advanced users or problems that involve multiple management zones. See the [zones vignette](zones.html) for more information on these targets. - -As with the functions for specifying the objective of a problem, if we try adding multiple targets to a problem, only the most recently added set of targets are used. - -### Add constraints - -A constraint can be added to a conservation planning problem to ensure that all solutions exhibit a specific property. For example, they can be used to make sure that all solutions select a specific planning unit or that all selected planning units in the solution follow a certain configuration. - -The following constraints can be added to conservation planning problems in the _prioritizr R_ package. - -* __Locked in constraints__: Add constraints to ensure that certain planning units are prioritized in the solution. For example, it may be desirable to lock in planning units that are inside existing protected areas so that the solution fills in the gaps in the existing reserve network. -```{r} -# create problem with constraints which specify that the first planning unit -# must be selected in the solution -p15 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_locked_in_constraints(1) - -# print problem -print(p15) -``` -* __Locked out constraints__: Add constraints to ensure that certain planning units are not prioritized in the solution. For example, it may be useful to lock out planning units that have been degraded and are not suitable for conserving species. -```{r} -# create problem with constraints which specify that the second planning unit -# must not be selected in the solution -p16 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_locked_out_constraints(2) - -# print problem -print(p16) -``` -* __Neighbor constraints__: Add constraints to a conservation problem to ensure that all selected planning units have at least a certain number of neighbors. -```{r} -# create problem with constraints which specify that all selected planning units -# in the solution must have at least 1 neighbor -p17 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_neighbor_constraints(1) - -# print problem -print(p17) -``` -* __Contiguity constraints__: Add constraints to a conservation problem to ensure that all selected planning units are spatially connected to each other and form spatially contiguous unit. -```{r} -# create problem with constraints which specify that all selected planning units -# in the solution must form a single contiguous unit -p18 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_contiguity_constraints() - -# print problem -print(p18) -``` -* __Feature contiguity constraints__: Add constraints to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of those implemented in the `add_contiguity_constraints` function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit. -```{r} -# create problem with constraints which specify that the planning units used -# to conserve each feature must form a contiguous unit -p19 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_feature_contiguity_constraints() - -# print problem -print(p19) -``` - -* __Linear constraints__: Add constraints to ensure that all selected planning units meet certain criteria. For example, they can be used to add multiple budgets, or limit the number of planning units selected in different administrative areas within a study region (e.g. different countries). - -```{r} -# create problem with constraints which specify that the sum of -# values in sim_features[[1]] among selected planning units must not exceed a -#' threshold value of 190. -p20 <- problem(sim_pu_raster, sim_features) %>% - add_min_shortfall_objective(budget = 1800) %>% - add_relative_targets(0.1) %>% - add_linear_constraints(190, "<=", sim_features[[1]]) - -# print problem -print(p20) +print(p1) ``` -* __Mandatory allocation constraints__: Add constraints to ensure that every planning unit is allocated to a management zone in the solution. Please note that this function can only be used with problems that contain multiple zones. For more information on problems with multiple zones and an example using this function, see the Management Zones vignette. +## Prioritization -In particular, The `add_locked_in_constraints` and `add_locked_out_constraints` functions are incredibly useful for real-world conservation planning exercises, so it's worth pointing out that there are several ways we can specify which planning units should be locked in or out of the solutions. If we use raster planning unit data, we can also use raster data to specify which planning units should be locked in our locked out. +We can now solve the problem formulation (`p1`) to generate a prioritization (using the `solve()` function). The _prioritizr_ R package supports a range of different exact algorithm solvers, including _Gurobi_, _IBM CPLEX_, _CBC_, _Rsymphony_, and _lpsymphony_. Although there are benefits and limitations associated with each of these different solvers, they should return similar results. Note that you will need at least one solver installed on your system to generate prioritizations. Since we did not specify a solver when building the problem, the _prioritizr R_ package will automatically select the best available solver installed. We recommend using the _Gurobi_ solver if possible, and have used it for this tutorial (see the _Gurobi Installation Guide_ vignette for installation instructions). After solving the problem, the prioritization will be stored in the `solution_1` column of the `s1` object. -```{r, fig.width = 6.5, fig.height = 2.5} -# load data to lock in or lock out planning units -data(sim_locked_in_raster) -data(sim_locked_out_raster) +```{r, fig.width = w, fig.height = h} +# solve problem +s1 <- solve(p1) -# plot the locked data -plot(stack(sim_locked_in_raster, sim_locked_out_raster), - main = c("Locked In", "Locked Out")) - -# create a problem using raster planning unit data and use the locked raster -# data to lock in some planning units and lock out some other planning units -p21 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_locked_in_constraints(sim_locked_in_raster) %>% - add_locked_out_constraints(sim_locked_out_raster) - -# print problem -print(p21) +# plot map of prioritization +plot(st_as_sf(s1[, "solution_1"]), main = "Prioritization", + pal = c("grey90", "darkgreen")) ``` -If our planning unit data are in a spatial vector format (similar to the `sim_pu_polygons` data) or a tabular format (similar to `pu_dat`), we can use the field names in the data to refer to which planning units should be locked in and / or out. For example, the `sim_pu_polygons` object has `TRUE` / `FALSE` values in the "locked_in" field which indicate which planning units should be selected in the solution. We could use the data in this field to specify that those planning units with `TRUE` values should be locked in using the following methods. - -```{r} -# preview first six rows of the attribute table for sim_pu_polygons -head(sim_pu_polygons@data) +## Feature representation -# specify locked in data using the field name -p22 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_locked_in_constraints("locked_in") +Let's examine how well the vegetation communities are represented by existing protected areas and the prioritization. -# print problem -print(p22) +```{r, fig.width = 7} +# create column with existing protected areas +tas_pu$pa <- round(tas_pu$locked_in) -# specify locked in data using the values in the field -p23 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_locked_in_constraints(which(sim_pu_polygons$locked_in)) +# calculate feature representation statistics based on existing protected areas +tc_pa <- eval_target_coverage_summary(p1, tas_pu[, "pa"]) +print(tc_pa) -# print problem -print(p23) -``` +# calculate feature representation statistics based on the prioritization +tc_s1 <- eval_target_coverage_summary(p1, s1[, "solution_1"]) +print(tc_s1) -### Add penalties +# explore representation by existing protected areas +## calculate number of features adequately represented by existing protected +## areas +sum(tc_pa$met) -We can also add penalties to a problem to favor or penalize solutions according to a secondary objective. Unlike the constraint functions, these functions will add extra information to the objective function of the optimization function to penalize solutions that do not exhibit specific characteristics. For example, penalties can be added to a problem to avoid highly fragmented solutions at the expense of accepting slightly more expensive solutions. All penalty functions have a `penalty` argument that controls the relative importance of the secondary penalty function compared to the primary objective function. It is worth noting that incredibly low or incredibly high `penalty` values---relative to the main objective function---can cause problems to take a very long time to solve, so when trying out a range of different penalty values it can be helpful to limit the solver to run for a set period of time. +## summarize representation (values show percent coverage) +summary(tc_pa$relative_held * 100) -The _prioritizr R_ package currently offers only two methods for adding penalties to a conservation planning problem. +## visualize representation (values show percent coverage) +hist(tc_pa$relative_held * 100, + main = "Feature representation by existing protected areas", + xlim = c(0, 100), + xlab = "Percent coverage of features (%)") -* __Boundary penalties__: Add penalties to penalize solutions that are excessively fragmented. These penalties are similar to those used in _Marxan_ [@r3; @r1]. -```{r} -# create problem with penalties that penalize fragmented solutions with a -# penalty factor of 0.01 -p24 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_boundary_penalties(penalty = 0.01) -# print problem -print(p24) -``` -* __Connectivity penalties__: Add penalties to favor solutions that select combinations of planning units with high connectivity between them. These penalties are similar to those used in _Marxan with Zones_ [@r2; @r1]. This function supports both symmetric and asymmetric connectivities among planning units. -```{r} -# create problem with penalties that favor combinations of planning units with -# high connectivity, here we will use only the first four layers in -# sim_features for the features and we will use the fifth layer in sim_features -# to represent the connectivity data, where the connectivity_matrix function -# will create a matrix showing the average strength of connectivity between -# adjacent planning units using the data in the fifth layer of sim_features -p25 <- problem(sim_pu_raster, sim_features[[1:4]]) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_boundary_penalties( - penalty = 5, - data = connectivity_matrix(sim_pu_raster, sim_features[[5]])) +# explore representation by prioritization +## summarize representation (values show percent coverage) +summary(tc_s1$relative_held * 100) -# print problem -print(p25) -``` -* __Linear penalties__: Add penalties to penalize solutions that select planning units according to a certain variable (e.g. anthropogenic pressure). -```{r} -# create data for penalizing planning units -# (note this requires the RandomFields package to be installed) -pen_raster <- simulate_cost(sim_pu_raster) - -# create problem with penalties that penalize solutions that select -# planning units with high values in the pen_raster object, -# here we will use a penalty value of 5 to indicate the trade-off (scaling) -# between the penalty values (in the sim_pu_raster) and the main objective -# (i.e. the cost of the solution) -p26 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_linear_penalties(penalty = 5, data = pen_raster) +## calculate number of features adequately represented by the prioritization +sum(tc_s1$met) -# print problem -print(p26) +## visualize representation (values show percent coverage) +hist(tc_s1$relative_held * 100, + main = "Feature representation by prioritization", + xlim = c(0, 100), + xlab = "Percent coverage of features (%)") ``` -### Add the decision types +We can see that representation of the vegetation communities by existing protected areas is remarkably poor. For example, many of the vegetation communities have nearly zero coverage by existing protected areas. In other words, are almost entirely absent from existing protected areas. We can also see that all vegetation communities have at least 17% coverage by the prioritization -- meaning that it meets the representation targets for all of the features. -Conservation planning problems involve making decisions on how planning units will be managed. These decisions are then associated with management actions (e.g. turning a planning unit into a protected area). The type of decision describes how the action is applied to planning units. For instance, the default decision-type is a binary decision type, meaning that we are either selecting or not selecting planning units for management. +## Irreplaceability -The _prioritizr R_ package currently offers the following types of decisions for customizing problems. +After generating the prioritization, we can examine the relative importance of planning units selected by the prioritization. This can be useful to identify critically important planning units for conservation -- in other words, places that contain biodiversity features which cannot be represented anywhere else -- and schedule implementation of the prioritization. To achieve this, we will use the Ferrier metric [@r34]. -* __Binary decisions__: Add a binary decision to a conservation planning problem. This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem object, then this decision class will be used by default. -```{r} -# add binary decisions to a problem -p27 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() - -# print problem -print(p27) -``` -* __Proportion decisions__: Add a proportion decision to a problem. This is a relaxed decision where a part of a planning unit can be prioritized, as opposed to the default of the entire planning unit. Typically, this decision has the assumed action of buying a fraction of a planning unit to include in a protected area network. Generally, problems can be solved much faster with proportion-type decisions than binary-type decisions, so they can be very useful when commercial solvers are not available. -```{r} -# add proportion decisions to a problem -p28 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_proportion_decisions() +```{r, fig.width = w, fig.height = h} +# calculate irreplaceability +irrep_s1 <- eval_ferrier_importance(p1, s1["solution_1"]) +print(irrep_s1) -# print problem -print(p28) -``` -* __Semi-continuous decisions__: Add a semi-continuous decision to a problem. This decision is similar to proportion decisions except that it has an upper bound parameter. By default, the decision can range from prioritizing none (0%) to all (100%) of a planning unit. However, a upper bound can be specified to ensure that at most only a fraction (e.g. 80%) of a planning unit can be purchased. This type of decision may be useful when it is not practical to conserve the entire area indicated by a planning unit. -```{r} -# add semi-continuous decisions to a problem, where we can only manage at most -# 50 % of the area encompassed by a planning unit -p29 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_semicontinuous_decisions(0.5) +# manually coerce values for planning units not selected in prioritization +# to NA, so that they are shown in white +irrep_s1$plot_total <- irrep_s1$total +irrep_s1$plot_total[s1$solution_1 < 0.5] <- NA_real_ -# print problem -print(p29) +# plot map of overall importance scores +plot(st_as_sf(irrep_s1[, "plot_total"]), main = "Overall importance") ``` -### Add a solver - -Next, after specifying the mathematical formulation that underpins your conservation planning problem, you can specify how the problem should be solved. If you do not specify this information, the _prioritizr R_ package will automatically use the best solver currently installed on your system with some reasonable defaults. __We strongly recommend installing the [Gurobi software suite and the _gurobi_ _R_ package](https://www.gurobi.com/) to solve problems, and for more information on this topic please refer to the [Gurobi Installation Guide](gurobi_installation.html)__. - -Currently, the _prioritizr R_ package supports five different solvers. - -* __*Gurobi* solver__: [_Gurobi_](https://www.gurobi.com/) is a state of the art commercial optimization software. It is by far the fastest of the solvers that can be used to solve conservation problems. However, it is not freely available. That said, special licenses are available to academics at no cost. -```{r} -# create a problem and specify that Gurobi should be used to solve the problem -# and specify an optimality gap of zero to obtain the optimal solution -p30 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_gurobi_solver(gap = 0) - -# print problem -print(p30) -``` -* __*IBM CPLEX* solver__: [_IBM CPLEX_](https://www.ibm.com/analytics/cplex-optimizer) is a commercial optimization software. It is faster than the open source solvers available for generating prioritizations (see below), however, it is not freely available. Similar to the _Gurobi_ software, special licenses are available to academics at no cost. -```{r} -# create a problem and specify that IBM CPLEX should be used to solve the -# problem and specify an optimality gap of zero to obtain the optimal solution -p31 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_cplex_solver(gap = 0) +## Portfolios -# print problem -print(p31) -``` -* __*CBC* solver__: [*CBC*](https://projects.coin-or.org/Cbc) is an -open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. Although formal benchmarks have yet to be completed, preliminary analyses suggest that it is -the fastest open-source solver available for generating prioritizations. It requires the _rcbc R_ package, which is currently only available on [GitHub](https://github.com/dirkschumacher/rcbc). -```{r} -# create a problem and specify that CBC should be used to solve the -# problem and specify an optimality gap of zero to obtain the optimal solution -p32 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_cbc_solver(gap = 0) +Conservation planning exercises often involve generating multiple different prioritizations. This can help decision makers consider different options, and provide starting points for building consensus among stakeholders. To generate a range of different prioritizations given the same problem formulation, we can use portfolio functions. Here we will use the gap portfolio to generate 1000 solutions that are within 30% of optimality. Please note that you will need to have the *Gurobi* solver installed to use this specific portfolio. If you don'thave access to *Gurobi*, you could try using the shuffle portfolio instead (using the `add_shuffle_portfolio()` function). -# print problem -print(p32) -``` -* __*lpsymphony* solver__: [_SYMPHONY_](https://projects.coin-or.org/SYMPHONY) is an open-source integer programming solver that is also part of the COIN-OR project. This solver uses the _lpsymphony R_ package (available on [Bioconductor](http://bioconductor.org/packages/release/bioc/html/lpsymphony.html)) to interface with the _SYMPHONY_ software. ```{r} -# create a problem and specify that lpsymphony should be used to solve the -# problem and specify an optimality gap of zero to obtain the optimal solution -p33 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_lpsymphony_solver(gap = 0) +# create new problem with a portfolio added to it +p2 <- p1 %>% + add_gap_portfolio(number_solutions = 1000, pool_gap = 0.2) # print problem -print(p33) -``` -* __*Rsymphony* solver__: This solver provides a different interface to the [_SYMPHONY_](https://projects.coin-or.org/SYMPHONY) software. It uses the _Rsymphony R_ package which is available on The Comprehensive R Archive Network (CRAN). This solver is generally slower than the other solvers, because it cannot use parallel processing. -```{r} -# create a problem and specify that Rsymphony should be used to solve the -# problem and specify an optimality gap of zero to obtain the optimal solution -p34 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_rsymphony_solver(gap = 0) +print(p2) -# print problem -print(p34) +# generate prioritizations +prt <- solve(p2) +print(prt) ``` -### Add a portfolio - -Many conservation planning exercises require a portfolio of solutions. For example, real-world exercises can involve presenting decision makers with a range of near-optimal decisions. Additionally, the number of times that different planning units are selected in different solutions can provide insight into their relative importance. - -The following methods are available for generating a portfolio of solutions. - -* __Extra portfolio__: Generate a portfolio of solutions by storing feasible solutions found during the optimization process. Note that this method requires that the _Gurobi_ optimization software is used to generate solutions. -```{r} -# create a problem and specify that a portfolio should be created using -# extra solutions found while solving the problem -p35 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_extra_portfolio() - -# print problem -print(p35) -``` -* __Top portfolio__: Generate a portfolio of solutions by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions). Note that this method requires that the _Gurobi_ optimization software is used to generate solutions. -```{r} -# create a problem and specify that a portfolio should be created using -# the top five solutions -p36 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_top_portfolio(number_solutions = 5) +After generating all these prioritizations, we now want some way to visualize them. Because it would be onerous to look at each and every prioritization individually, we will use statistical analyses to help us. We can visualize the differences between these different prioritizations -- based on which planning units they selected -- using a hierarchical cluster analysis [@r35]. -# print problem -print(p36) -``` -* __Gap portfolio__: Generate a portfolio of solutions by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is especially useful for generating multiple solutions that can used be to calculate selection frequencies (similar to _Marxan_). Note that this method requires that the _Gurobi_ optimization software is used to generate solutions. -```{r} -# create a problem and specify that a portfolio should be created by -# finding five solutions within 10% of optimality -p37 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_gap_portfolio(number_solutions = 5, pool_gap = 0.2) +```{r, fig.height = 4.5, fig.width = 7, fig.show = "hold"} +# extract solutions +prt_results <- prt@data[, startsWith(names(prt), "solution_"), ] -# print problem -print(p37) -``` -* __Cuts portfolio__: Generate a portfolio of distinct solutions within a pre-specified optimality gap. This method is only recommended if the _Gurobi_ optimization solver is not available. -```{r} -# create a problem and specify that a portfolio containing 10 solutions -# should be created using using Bender's cuts -p38 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_cuts_portfolio(number_solutions = 10) +# calculate pair-wise distances between different prioritizations for analysis +prt_dists <- vegan::vegdist(t(prt_results), method = "jaccard", binary = TRUE) -# print problem -print(p38) -``` -* __Shuffle portfolio__: Generate a portfolio of solutions by randomly reordering the data prior to attempting to solve the problem. If the _Gurobi_ optimization solver is not available, this method is the fastest method for generating a set number of solutions within a specified distance from optimality. -```{r} -# create a problem and specify a portfolio should be created that contains -# 10 solutions and that any duplicate solutions should not be removed -p39 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() %>% - add_shuffle_portfolio(number_solutions = 10, remove_duplicates = FALSE) +# run cluster analysis +prt_clust <- hclust(as.dist(prt_dists), method = "average") -# print problem -print(p39) +# visualize clusters +opar <- par() +par(oma = c(0, 0, 0, 0), mar= c(0, 4.1, 1.5, 2.1)) +plot(prt_clust, labels = FALSE, sub = NA, xlab = "", + main = "Different prioritizations in portfolio") +suppressWarnings(par(opar)) ``` -### Solve the problem +We can see that there are approximately six main groups of prioritizations in the portfolio. To explore these different groups, let's conduct another cluster analysis (i.e., a _k_-medoids analysis) to extract the most representative prioritization from each of these groups. In other words, we will run another statistical analysis to find the most central prioritization within each group. -Finally, after formulating our conservation planning problem and specifying how the problem should be solved, we can use the `solve` function to obtain a solution. Note that the solver will typically print out some information describing the size of the problem and report its progress when searching for a suitable solution. +```{r, fig.width = 7, fig.height = 5} +# run k-medoids analysis +prt_med <- pam(prt_dists, k = 6) -```{r, fig.height = h, fig.width = w} -# formulate the problem -p40 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_boundary_penalties(penalty = 500, edge_factor = 0.5) %>% - add_binary_decisions() +# extract names of prioritizations that are most central for each group. +prt_med_names <- prt_med$medoids +print(prt_med_names) -# solve the problem (using the default solver) -s40 <- solve(p40) +# create a copy of prt and set values for locked in planning units to -1 +# so we can easily visualize differences between prioritizations +prt2 <- prt[, prt_med_names] +prt2@data[which(tas_pu$locked_in > 0.5), prt_med_names] <- -1 -# plot solution -plot(s40, col = c("grey90", "darkgreen"), main = "Solution", - xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1)) +# plot a map showing main different prioritizations +# dark grey: locked in planning units +# grey: planning units not selected +# green: selected planning units +plot(st_as_sf(prt2), pal = c("grey60", "grey90", "darkgreen")) ``` -We can plot this solution because the planning unit input data are spatially referenced in a raster format. The output format will always match the planning unit data used to initialize the problem. For example, the solution to a problem with planning units in a spatial vector (shapefile) format would also be in a spatial vector format. Similarly, if the planning units were in a tabular format (i.e. `data.frame`), the solution would also be returned in a tabular format. - -We can also extract attributes from the solution that describe the quality of the solution and the optimization process. - -```{r} -# extract the objective (numerical value being minimized or maximized) -print(attr(s40, "objective")) - -# extract time spent solving solution -print(attr(s40, "runtime")) +## _Marxan_ compatibility -# extract state message from the solver that describes why this specific -# solution was returned -print(attr(s40, "status")) -``` - -### Evaluate the performance of a solution +The _prioritizr R_ package provides functionality to help _Marxan_ users generate prioritizations. Specifically, it can import conservation planning data prepared for _Marxan_, and can generate prioritizations using a similar problem formulation as _Marxan_ [based on @r1]. Indeed, the problem formulation presented earlier in this vignette is very similar to that used by _Marxan_. The key difference is that the problem formulation we specified earlier uses "hard constraints" for feature representation, and _Marxan_ uses "soft constraints" for feature representation. This means that prioritization we generated earlier was mathematically guaranteed to reach the targets for all features. However, if we used _Marxan_ to generate the prioritization, then we could have produced a prioritization that would fail to reach targets (depending the _Species Penalty Factors_ used to generate the prioritization). In addition to these differences in terms problem formulation, the _prioritizr R_ package uses exact algorithms -- instead of the simulated annealing algorithm -- which ensures that we obtain prioritizations that are near optimal. -After obtaining a solution to a conservation planning problem, it can be useful to calculate various summary statistics to understand its performance. The following functions are available to summarize a solution: +Here we will show the _prioritizr R_ package can import _Marxan_ data and generate a prioritization. To begin with, let's import a conservation planning data prepared for _Marxan_. -* Calculate the number of planning units selected within a solution. -```{r} -# calculate statistic -eval_n_summary(p40, s40) -``` -* Calculate the total cost of a solution. -```{r} -# calculate statistic -eval_cost_summary(p40, s40) -``` -* Calculate how well features are represented by a solution. This function can be used for problems that are built using targets and those that are not built using targets. -```{r} -# calculate statistics -eval_feature_representation_summary(p40, s40) -``` -* Calculate how well feature representation targets are met by a solution. This function can only be used with problems contain targets. ```{r} -# calculate statistics -eval_target_coverage_summary(p40, s40) -``` -* Calculate the exposed boundary length (perimeter) associated with a solution. -```{r} -# calculate statistic -eval_boundary_summary(p40, s40) -``` -* Calculate the connectivity held within a solution. -```{r} -# calculate statistic -# here we use the raster data for the first feature as an example -# to parametrize pair-wise connectivity between different planning units -eval_connectivity_summary( - p40, s40, data = connectivity_matrix(sim_pu_raster, sim_features[[1]])) -``` - -### _Marxan_ problems - -Although users are encouraged to build and tailor conservation planning problems to suit their own needs using the `problem` function, sometimes it just simply easier to use a more familiar formulation. The `marxan_problem` function is provided as a convenient wrapper for building and solving _Marxan_-style conservation problems. If users already have their conservation planning data formatted for use with _Marxan_, this function can also read _Marxan_ data files and solve the _Marxan_-style problems using exact algorithm solvers. __Please note that problems built using the `marxan_problem` function are still solved the same way as a problem initialized using the `problem` function, and therefore still require the installation of one of the solver packages.__ - -Here is a short example showing how the `marxan_problem` function can be used to read _Marxan_ input files and the `solve` function can be used to solve the problem. -```{r, results = "hide"} -# set file path for Marxan input file -minput <- system.file("extdata/input.dat", package = "prioritizr") - -# read Marxan input file -mp <- marxan_problem(minput) +# import data +## planning unit data +pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr") +pu_data <- read.csv(pu_path, header = TRUE, stringsAsFactors = FALSE) +print(head(pu_data)) -# print problem -print(mp) +## feature data +spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr") +spec_data <- read.csv(spec_path, header = TRUE, stringsAsFactors = FALSE) +print(head(spec_data)) -# solve the problem -ms <- solve(mp) +## amount of each feature within each planning unit data +puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr") +puvspr_data <- read.csv(puvspr_path, header = TRUE, stringsAsFactors = FALSE) +print(head(puvspr_data)) -# since the Marxan data was in a tabular format, the solution is also returned -# in a tabular format, so we will print the first six rows of the table -# containing the solution -head(ms) +## boundary data +bound_path <- system.file("extdata/input/bound.dat", package = "prioritizr") +bound_data <- read.table(bound_path, header = TRUE, stringsAsFactors = FALSE) +print(head(bound_data)) ``` -Alternatively, rather then using a _Marxan_ input file to construct the problem, we can manually read in the _Marxan_ data files and input these to the `marxan_problem` function. +After importing the data, we can now generate a prioritization based on the _Marxan_ problem formulation (using the `marxan_problem()` function). **Please note that this function does not generate prioritizations using _Marxan_.** Instead, it uses the data to create an optimization problem formulation similar to _Marxan_ -- using hard constraints instead of soft constraints -- and uses an exact algorithm solver to generate a prioritization. ```{r} -# load data -pu <- system.file("extdata/input/pu.dat", package = "prioritizr") %>% - read.table(sep = ",", header = TRUE) -features <- system.file("extdata/input/spec.dat", package = "prioritizr") %>% - read.table(sep = ",", header = TRUE) -bound <- system.file("extdata/input/bound.dat", package = "prioritizr") %>% - read.table(sep = "\t", header = TRUE) -rij <- system.file("extdata/input/puvspr.dat", package = "prioritizr") %>% - read.table(sep = ",", header = TRUE) - -# build Marxan problem using data.frame objects -mp2 <- marxan_problem(x = pu, spec = features, puvspr = rij, bound = bound, - blm = 0) +# create problem +p2 <- marxan_problem(pu_data, spec_data, puvspr_data, bound_data, + blm = 0.0005) # print problem -print(mp2) -``` - -### Importance (irreplaceability) - -Conservation plans can take a long time to implement. Since funding availability and habitat quality can decline over time, it is critical that the most important places in a prioritization are scheduled for protection as early as possible. For instance, some planning units in a solution might contain many rare species which do not occur in any other planning units. Alternatively, some planning units might offer an especially high return on investment that reduces costs considerably. As a consequence, conservation planners often need information on which planning units selected in a prioritization are most important to the overall success of the prioritization. To achieve this, conservation planners can use importance (irreplaceability) scores for each planning unit selected in a solution. - -The _prioritizr R_ package offers multiple methods for assessing importance. These includes scores calculated based on replacement costs [`eval_replacement_importance()`; @r31], Ferrier _et al._ [-@r34] (`eval_ferrier_importance()`), and rarity weighted richness scores [`eval_rare_richness_importance()`; @r33]. The replacement cost scores quantify the change in the objective function (e.g. additional costs required to meet feature targets) of the optimal solution if a given planning unit in a solution cannot be acquired. They can (i) account for the cost of different planning units, (ii) account for multiple management zones, (iii) apply to any objective function, and (iv) identify truly irreplaceable planning units (denoted with infinite values). The Ferrier scores quantify the importance of planning units for meeting feature targets. They can only be applied to conservation problems with a minimum set objective and a single zone (i.e. the classic _Marxan_-type problem). Furthermore---unlike the replacement cost scores---the Ferrier scores provide a score for each feature within each planning unit, providing insight into why certain planning units are more important than other planning units. The rarity weighted richness scores are simply a measure of biological diversity. They do not account for planning costs, multiple management zones, objective functions, or feature targets (or weightings). They merely describe the spatial patterns of biodiversity, and do not account for many of the factors needed to quantify the importance of a planning unit for achieving conservation goals. - -We recommend using replacement cost scores for small and moderate sized problems (e.g. less than 30,000 planning units) when it is feasible to do so. It can take a very long time to compute replacement cost scores, and so it is simply not feasible to compute these scores for particularly large problems. For moderate and large sized problems (e.g. more than 30,000 planning units), we recommend using the Ferrier method. This is because it explicitly accounts for representation targets, unlike the rarity weighted richness scores. - -Below we will generate a solution, and then calculate importance scores for the planning units selected in the solution using the three different methods. - -```{r, fig.height = h, fig.width = w} -# formulate the problem -p41 <- problem(sim_pu_raster, sim_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.1) %>% - add_binary_decisions() - -# solve the problem -s41 <- solve(p41) - -# plot solution -plot(s41, col = c("grey90", "darkgreen"), main = "Solution", - xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1)) - -# calculate replacement cost scores and make the solver quiet -rc41 <- p41 %>% - add_default_solver(gap = 0, verbose = FALSE) %>% - eval_replacement_importance(s41) - -# plot replacement cost scores -plot(rc41, main = "replacement cost") -``` - -```{r, fig.height = h, fig.width = w} -# calculate Ferrier scores and extract total score -fs41 <- eval_ferrier_importance(p40, s40)[["total"]] - -# plot Ferrier scores -plot(fs41, main = "Ferrier scores") -``` +print(p2) -```{r, fig.height = h, fig.width = w} -# calculate rarity weighted richness scores -rwr41 <- eval_rare_richness_importance(p40, s40) +# solve problem +s2 <- solve(p2) -# plot replacement cost scores -plot(rwr41, main = "rarity weighted richness") +# print first six rows of solution object +print(head(s2)) ``` -Although rarity weighted richness scores can approximate scores derived from the other two methods in certain conservation planning exercises, we can see that the rarity weighted richness scores provide completely different results in this case. - ## Conclusion -Hopefully, this vignette has provided an informative introduction to the _prioritizr R_ package. For more worked examples using the _prioritizr R_ package, check out the [Tasmania](tasmania.html) and [Salt Spring Island](saltspring.html) vignettes. Perhaps, one of the best ways to learn a new piece of software is to just try it out. Test it, try breaking it, make mistakes, and learn from them. We would recommend trying to build conservation planning problems that resemble those you face in your own work---but using the built-in example data sets. This way you can quickly verify that the problems you build actually mean what you think they mean. For instance, you can try playing around with the targets and see what effect they have on the solutions, or try playing around with penalties and see what effect they have on the solutions. Finally, if you have any questions about using the _prioritizr R_ package or suggestions for it, please file an issue on the package's online coding repository (https://github.com/prioritizr/prioritizr/issues). +This tutorial shows how the _prioritizr R_ package can be used to build a conservation problem, generate a prioritization, and evaluate it. Although we explored just a few functions, the package provides many different functions so that you can build and custom-tailor conservation planning problems to suit your needs. To learn more about the package, please see the package vignettes for [an overview of the package](package_overview.html), [instructions for installing the _Gurobi_ optimization suite](gurobi_installation_guide.html), [benchmarks comparing the performance of different solvers](solver_benchmarks.html), and [a record of publications that have cited the package](publication_record.html). In addition to this tutorial, the package also provides tutorials on [incorporating connectivity into prioritizations](connectivity_tutorial.html), [calibrating trade-offs between different criteria](calibrating_trade-offs.html) (e.g., total cost and spatial fragmentation), and [creating prioritizations that have multiple management zones or management actions](management_zones_tutorial.html). ## References diff --git a/inst/doc/prioritizr.html b/inst/doc/prioritizr.html index fe7517b0f..c8a893e75 100644 --- a/inst/doc/prioritizr.html +++ b/inst/doc/prioritizr.html @@ -12,7 +12,7 @@ -prioritizr: Systematic Conservation Prioritization in R +Getting started @@ -159,1354 +159,498 @@ -

      prioritizr: Systematic Conservation Prioritization in R

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      Getting started

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      Summary

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      The prioritizr R package uses integer linear programming (ILP) techniques to provide a flexible interface for building and solving conservation planning problems (Rodrigues et al. 2000; Billionnet 2013). It supports a broad range of objectives, constraints, and penalties that can be used to custom-tailor conservation planning problems to the specific needs of a conservation planning exercise. Once built, conservation planning problems can be solved using a variety of commercial and open-source exact algorithm solvers. In contrast to the algorithms conventionally used to solve conservation problems, such as heuristics or simulated annealing (Ball et al. 2009), the exact algorithms used here are guaranteed to find optimal solutions. Furthermore, conservation problems can be constructed to optimize the spatial allocation of different management zone (or actions), meaning that conservation practitioners can identify solutions that benefit multiple stakeholders. Finally, this package has the functionality to read input data formatted for the Marxan conservation planning program (Ball et al. 2009), and find much cheaper solutions in a much shorter period of time than Marxan (Beyer et al. 2016).

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      Introduction

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      Systematic conservation planning is a rigorous, repeatable, and structured approach to designing new protected areas that efficiently meet conservation objectives (Margules & Pressey 2000). Historically, conservation decision-making has often evaluated parcels opportunistically as they became available for purchase, donation, or under threat. Although purchasing such areas may improve the status quo, such decisions may not substantially enhance the long-term persistence of target species or communities. Faced with this realization, conservation planners began using decision support tools to help simulate alternative reserve designs over a range of different biodiversity and management goals and, ultimately, guide protected area acquisitions and management actions. Due to the systematic, evidence-based nature of these tools, conservation prioritization can help contribute to a transparent, inclusive, and more defensible decision making process.

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      A conservation planning exercise typically starts by defining a study area. This study area should encompass all the areas relevant to the decision maker or the hypothesis being tested. The extent of a study area could encompass a few important localities (e.g. Stigner et al. 2016), a single state (e.g. Kirkpatrick 1983), an entire country (Fuller et al. 2010), or the entire planet (Butchart et al. 2015). Next, the study area is divided into a set of discrete areas termed planning units. Each planning unit represents a discrete locality in the study area that can be managed independently of other areas. The general idea is that some combination of the planning units can be selected for conservation actions (e.g. protected area establishment, habitat restoration). Planning units are often created as square or hexagon cells that are sized according to the scale of the conservation actions, and the resolution of the data that underpin the planning exercise (but see Klein et al. 2009).

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      Cost data (or a surrogate thereof) are needed to inform the prioritization process. Specifically, these cost data describe the relative expenditure associated with managing each planning unit for conservation. For example, if the goal of the conservation planning exercise is to identify priority areas for expanding a local protected area system, then the cost data could represent the physical cost of purchasing the land. Alternatively, if such data are not available, then surrogate data could are often used instead (e.g. human population density, opportunity cost of foregone commercial activities, or planning unit size).

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      Conservation planning exercises also require data on the biodiversity elements that are of conservation interest (termed conservation features). These features could be species (e.g. Neofelis nebulosa, the Clouded Leopard), populations, or habitats (e.g. mangroves or cloud forest). After identifying the set of relevant conservation features for a conservation planning exercise, spatially explicit data need to be obtained for each and every feature to describe their spatial distribution (e.g. habitat suitability data, probability of occurrence data, presence/absence data). This is important to ensure that conservation features are adequately covered (represented) by prioritizations. After assembling all the data, the next step is to define the conservation planning problem.

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      The prioritizr R package is designed to help you build and solve conservation planning problems. Specifically, prioritizations are generated by using formulating a mathematical optimization problem and then solving it to generate a solution. These mathematical optimization problems are formulated using the planning unit data, cost data, and feature data, and with information related to the overarching aim of the prioritization process. In general, the goal of an optimization problem is to minimize (or maximize) an objective function that is calculated using a set of decision variables, subject to a series of constraints to ensure that solution exhibits specific properties. The objective function describes the quantity which we are trying to minimize (e.g. cost of the solution) or maximize (e.g. number of features conserved). The decision variables describe the entities that we can control, and indicate which planning units are selected for conservation management and which of those are not. The constraints can be thought of as rules that the need decision variables need to follow. For example, a commonly used constraint is specifying that the solution must not exceed a certain budget.

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      A wide variety of approaches have been developed for solving optimization problems. Reserve design problems are frequently solved using simulated annealing (Kirkpatrick et al. 1983) or heuristics (Nicholls & Margules 1993; Moilanen 2007). These methods are conceptually simple and can be applied to a wide variety of optimization problems. However, they do not scale well for large or complex problems (Beyer et al. 2016). Additionally, these methods cannot tell you how close any given solution is to the optimal solution. The prioritizr R package uses exact algorithms to efficiently solve conservation planning problems to within a pre-specified a optimality gap. In other words, you can specify that you need the optimal solution (i.e. a gap of 0%) and the algorithms will, given enough time, find a solution that meets this criteria. In the past, exact algorithms have been too slow for conservation planning exercises (Pressey et al. 1996). However, improvements over the last decade mean that they are now much faster (Achterberg & Wunderling 2013; Beyer et al. 2016).

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      In this package, optimization problems are expressed using integer linear programming (ILP) so that they can be solved using (linear) exact algorithm solvers. The general form of an integer programming problem can be expressed in matrix notation using the following equation.

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      \[\text{Minimize} \space \boldsymbol{c}^\text{T} \boldsymbol{x} \space -\space \text{subject to} \space A\boldsymbol{x} -\space \Box \space \boldsymbol{b}\]

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      Here, where \(x\) is a vector of decision variables, \(c\) and \(b\) are vectors of known coefficients, and \(A\) is the constraint matrix. The final term specifies a series of structural constants and the \(\Box\) symbol is used to indicate that the relational operators for the constraints can be either \(\geq\), \(=\), or \(\leq\). In the context of a conservation planning problem, \(c\) could be used to represent the planning unit costs, \(A\) could be used to store the data showing the presence / absence (or amount) of each feature in each planning unit, \(b\) could be used to represent minimum amount of habitat required for each species in the solution, the \(\Box\) could be set to \(\geq\) symbols to indicate that the total amount of each feature in the solution must exceed the quantities in \(b\). But there are many other ways of formulating the reserve selection problem (Rodrigues et al. 2000).

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      Package overview

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      The prioritizr R package contains eight main types of functions. These functions are used to:

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      • create a new conservation planning problem by specifying the planning units, features, and management zones of conservation interest (e.g. species, ecosystems).
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      • add an objective to a conservation planning problem.
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      • add targets to a problem to specify how much of each feature is desired or required to be conserved in the solutions.
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      • add constraints to a conservation planning problem to ensure that solutions exhibit specific properties (e.g. select specific planning units for protection).
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      • add penalties to a problem to penalize solutions according to specific metric (e.g. connectivity).
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      • add decisions to a problem to specify the nature of the decisions in the problem.
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      • add methods to generate a portfolio of solutions.
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      • add a solver to a conservation problem to specify which software should be used to generate solutions and customize the optimization process.
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      • solve a conservation problem.
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      • evaluate a solution by computing summary statistics.
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      • evaluate the relative importance (irreplaceability) of planning units selected in a solution.
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      Package workflow

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      The general workflow when using the prioritizr R package starts with creating a new conservation planning problem object using data. Specifically, the problem object should be constructed using data that specify the planning units, biodiversity features, management zones (if applicable), and costs. After creating a new problem object, it can be customized—by adding objectives, penalties, constraints, and other information—to build a precise representation of the conservation planning problem required, and then solved to obtain a solutions.

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      All conservation planning problems require an objective. An objective specifies the property which is used to compare different feasible solutions. Simply put, the objective is the property of the solution which should be maximized or minimized during the optimization process. For instance, with the minimum set objective (specified using add_min_set_objective), we are seeking to minimize the cost of the solution (similar to Marxan). On the other hand, with the maximum coverage objective (specified using add_max_cover_objective), we are seeking to maximize the number of different features represented in the solution.

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      Many objectives require targets (e.g. the minimum set objective). Targets are a specialized set of constraints that relate to the total quantity of each feature secured in the solution (e.g. amount of suitable habitat or number of individuals). In the case of the minimum set objective ( add_min_set_objective), they are used to ensure that solutions secure a sufficient quantity of each feature, and in other objectives, such as the maximum features objective ( add_max_features_objective) they are used to assess whether a feature has been adequately conserved by a candidate solution. Targets can be expressed numerically as the total amount required for a given feature (using add_absolute_targets), or as a proportion of the total amount found in the planning units (using add_relative_targets). Note that not all objectives require targets, and a warning will be thrown if an attempt is made to add targets to a problem with an objective that does not use them.

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      Constraints and penalties can be added to a conservation planning problem to ensure that solutions exhibit a specific property or penalize solutions which don’t exhibit a specific property (respectively). The difference between constraints and penalties, strictly speaking, is constraints are used to rule out potential solutions that don’t exhibit a specific property. For instance, constraints can be used to ensure that specific planning units are selected in the solution for prioritization (using add_locked_in_constraints) or not selected in the solution for prioritization (using add_locked_out_constraints). On the other hand, penalties are combined with the objective of a problem, with a penalty factor, and the overall objective of the problem then becomes to minimize (or maximize) the primary objective function and the penalty function. For example, penalties can be added to a problem to penalize solutions that are excessively fragmented (using add_boundary_penalties). These penalties have a penalty argument that specifies the relative importance of having spatially clustered solutions. When the argument to penalty is high, then solutions which are less fragmented are valued more highly—even if they cost more—and when the argument to penalty is low, then the solutions which are more fragmented are valued less highly.

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      After building a conservation problem, it can then be solved to obtain a solution (or portfolio of solutions if desired). The solution is returned in the same format as the planning unit data used to construct the problem. This means that if raster or shapefile / vector data was used when initializing the problem, then the solution will also be in raster or shapefile / vector data. This can be very helpful when it comes to interpreting and visualizing solutions because it means that the solution data does not first have to be merged with spatial data before they can be plotted on a map.

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      Usage

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      Here we will provide an introduction to using the prioritizr R package to build and solve a conservation planning problem. Please note that we will not discuss conservation planning with multiple zones in this vignette, for more information on working with multiple management zones please see the zones vignette.

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      First, we will load the prioritizr package.

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      # load package
-library(prioritizr)
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-# set default options for printing tabular data
-options(tibble.width = Inf)
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      Data

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      Now we will load some built-in data sets that are distributed with the prioritizr R package. This package contains several different planning unit data sets. To provide a comprehensive overview of the different ways that we can initialize a conservation planning problem, we will load each of them.

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      First, we will load the raster planning unit data (sim_pu_raster). Here, the planning units are represented as a raster (i.e. a RasterLayer object) and each pixel corresponds to the spatial extent of each panning unit. The pixel values correspond to the acquisition costs of each planning unit.

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      # load raster planning unit data
-data(sim_pu_raster)
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-# print description of the data
-print(sim_pu_raster)
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      ## class      : RasterLayer 
-## dimensions : 10, 10, 100  (nrow, ncol, ncell)
-## resolution : 0.1, 0.1  (x, y)
-## extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-## crs        : NA 
-## source     : memory
-## names      : layer 
-## values     : 190.1328, 215.8638  (min, max)
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      # plot the data
-plot(sim_pu_raster)
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      Secondly, we will load one of the spatial vector planning unit data sets (sim_pu_polygons). Here, each polygon (i.e. feature using ArcGIS terminology) corresponds to a different planning unit. This data set has an attribute table that contains additional information about each polygon. Namely, the cost field (column) in the attribute table contains the acquisition cost for each planning unit.

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      # load polygon planning unit data
-data(sim_pu_polygons)
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-# print first six rows of attribute table
-head(sim_pu_polygons@data)
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      ##       cost locked_in locked_out
-## 1 215.8638     FALSE      FALSE
-## 2 212.7823     FALSE      FALSE
-## 3 207.4962     FALSE      FALSE
-## 4 208.9322     FALSE       TRUE
-## 5 214.0419     FALSE      FALSE
-## 6 213.7636     FALSE      FALSE
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      # plot the planning units
-spplot(sim_pu_polygons, zcol = "cost")
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      Thirdly, we will load some planning unit data stored in tabular format (i.e. data.frame format). For those familiar with Marxan or dealing with very large conservation planning problems (> 10 million planning units), it may be useful to work with data in this format because it does not contain any spatial information which will reduce computational burden. When using tabular data to initialize conservation planning problems, the data must follow the conventions used by Marxan. Specifically, each row in the planning unit table must correspond to a different planning unit. The table must also have an “id” column to provide a unique integer identifier for each planning unit, and it must also have a column that indicates the cost of each planning unit. For more information, please see the official Marxan documentation.

      -
      # specify file path for planning unit data
-pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr")
-
-# load in the tabular planning unit data
-# note that we use the data.table::fread function, as opposed to the read.csv
-# function, because it is much faster
-pu_dat <- data.table::fread(pu_path, data.table = FALSE)
-
-# preview first six rows of the tabular planning unit data
-# note that it has some extra columns other than id and cost as per the
-# Marxan format
-head(pu_dat)
      -
      ##   id       cost status    xloc     yloc
-## 1  3        0.0      0 1116623 -4493479
-## 2 30   752727.5      3 1110623 -4496943
-## 3 56  3734907.5      0 1092623 -4500408
-## 4 58  1695902.1      0 1116623 -4500408
-## 5 84  3422025.6      0 1098623 -4503872
-## 6 85 17890758.4      0 1110623 -4503872
      -

      Finally, we will load data showing the spatial distribution of the conservation features. Our conservation features (sim_features) are represented as a stack of raster objects (i.e. a RasterStack object) where each layer corresponds to a different feature (e.g. a multi-band GeoTIFF where each band corresponds to a different feature). The pixel values in each layer correspond to the amount of suitable habitat available in a given planning unit. Note that our planning unit raster layer and our conservation feature stack have exactly the same spatial properties (i.e. resolution, extent, coordinate reference system) so their pixels line up perfectly.

      -
      # load feature data
-data(sim_features)
-
-# plot the distribution of suitable habitat for each feature
-plot(sim_features, main = paste("Feature", seq_len(nlayers(sim_features))),
-     nr = 2, box = FALSE, axes = FALSE)
      -

      -
      -
      -

      Initialize a problem

      -

      After having loaded our planning unit and feature data, we will now try initializing the some conservation planning problems. There are a lot of different ways to initialize a conservation planning problem, so here we will just showcase a few of the more commonly used methods. For an exhaustive description of all the ways you can initialize a conservation problem, see the help file for the problem function (which you can open using the code ?problem). First off, we will initialize a conservation planning problem using the raster data.

      -
      # create problem
-p1 <- problem(sim_pu_raster, sim_features)
-
-# print problem
-print(p1)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      none
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
      # print number of planning units
-number_of_planning_units(p1)
      -
      ## [1] 90
      -
      # print number of features
-number_of_features(p1)
      -
      ## [1] 5
      -

      Generally, we recommend initializing problems using raster data where possible. This is because the problem function needs to calculate the amount of each feature in each planning unit, and by providing both the planning unit and feature data in raster format with the same spatial resolution, extents, and coordinate systems, this means that the problem function does not need to do any geo-processing behind the scenes. But sometimes we can’t use raster planning unit data because our planning units aren’t equal-sized grid cells. So, below is an example showing how we can initialize a conservation planning problem using planning units that are formatted as spatial vector data. Note that if we had pre-computed the amount of each feature in each planning unit and stored the data in the attribute table, we could pass in the names of the columns as an argument to the problem function.

      -
      # create problem with spatial vector data
-# note that we have to specify which column in the attribute table contains
-# the cost data
-p2 <- problem(sim_pu_polygons, sim_features, cost_column = "cost")
-
-# print problem
-print(p2)
      -
      ## Conservation Problem
-##   planning units: SpatialPolygonsDataFrame (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      none
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -

      We can also initialize a conservation planning problem using tabular planning unit data (i.e. a data.frame). Since the tabular planning unit data does not contain any spatial information, we also have to provide the feature data in tabular format (i.e. a data.frame) and data showing the amount of each feature in each planning unit in tabular format (i.e. a data.frame). The feature data must have an “id” column containing a unique integer identifier for each feature, and the planning unit by feature data must contain the following three columns: “pu” corresponding to the planning unit identifiers, “species” corresponding to the feature identifiers, and “amount” showing the amount of a given feature in a given planning unit.

      -
      # set file path for feature data
-spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr")
-
-# load in feature data
-spec_dat <- data.table::fread(spec_path, data.table = FALSE)
-
-# print first six rows of the data
-# note that it contains extra columns
-head(spec_dat)
      -
      ##   id prop spf   name
-## 1 10  0.3   1  bird1
-## 2 11  0.3   1  nvis2
-## 3 12  0.3   1  nvis8
-## 4 13  0.3   1  nvis9
-## 5 14  0.3   1 nvis14
-## 6 15  0.3   1 nvis20
      -
      # set file path for planning unit vs. feature data
-puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr")
-
-# load in planning unit vs feature data
-puvspr_dat <- data.table::fread(puvspr_path, data.table = FALSE)
-
-# print first six rows of the data
-head(puvspr_dat)
      -
      ##   species  pu     amount
-## 1      26  56 1203448.84
-## 2      26  58  451670.10
-## 3      26  84  680473.75
-## 4      26  85   97356.24
-## 5      26  86   78034.76
-## 6      26 111 4783274.17
      -
      # create problem
-p3 <- problem(pu_dat, spec_dat, cost_column = "cost", rij = puvspr_dat)
-
-# print problem
-print(p3)
      -
      ## Conservation Problem
-##   planning units: data.frame (1751 units)
-##   cost:           min: 0, max: 41569219.38232
-##   features:       bird1, nvis2, nvis8, ... (17 features)
-##   objective:      none
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -

      For more information on initializing problems, please see the help page for the problem function (which you can open using the code ?problem). Now that we have initialized a conservation planning problem, we will show you how you can customize it to suit the exact needs of your conservation planning scenario. Although we initialized the conservation planning problems using several different methods, moving forward, we will only use raster-based planning unit data to keep things simple.

      -
      -
      -

      Add an objective

      -

      The next step is to add an objective to the problem. A problem objective is used to specify the primary goal of the problem (i.e. the quantity that is to be maximized or minimized). All conservation planning problems involve minimizing or maximizing some kind of objective. For instance, we might require a solution that conserves enough habitat for each species while minimizing the overall cost of the reserve network. Alternatively, we might require a solution that maximizes the number of conserved species while ensuring that the cost of the reserve network does not exceed the budget. Please note that objectives are added in the same way regardless of the type of data used to initialize the problem.

      -

      The prioritizr R package supports a variety of different objective functions.

      -
        -
      • Minimum set objective: Minimize the cost of the solution whilst ensuring that all targets are met (Rodrigues et al. 2000). This objective is similar to that used in Marxan (Ball et al. 2009). For example, we can add a minimum set objective to a problem using the following code.
        • -
      -
      # create a new problem that has the minimum set objective
-p3 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective()
-
-# print the problem
-print(p3)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Maximum cover objective: Represent at least one instance of as many features as possible within a given budget (Church et al. 1996).
        • -
      -
      # create a new problem that has the maximum coverage objective and a budget
-# of 5000
-p4 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_cover_objective(5000)
-
-# print the problem
-print(p4)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Maximum coverage objective [budget (5000)]
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Maximum features objective: Fulfill as many targets as possible while ensuring that the cost of the solution does not exceed a budget (inspired by Cabeza & Moilanen 2001). This object is similar to the maximum cover objective except that we have the option of later specifying targets for each feature. In practice, this objective is more useful than the maximum cover objective because features often require a certain amount of area for them to persist and simply capturing a single instance of habitat for each feature is generally unlikely to enhance their long-term persistence.
        • -
      -
      # create a new problem that has the maximum features objective and a budget
-# of 5000
-p5 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_features_objective(budget = 5000)
-
-# print the problem
-print(p5)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Maximum representation objective [budget (5000)]
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Minimum shortfall objective: Minimize the overall (weighted sum) shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when there is a large amount of left-over budget when using the maximum feature representation objective and the remaining funds need to be allocated to places that will enhance the representation of features with unmet targets.
        • -
      -
      # create a new problem that has the minimum shortfall objective and a budget
-# of 5000
-p6 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_shortfall_objective(budget = 5000)
-
-# print the problem
-print(p6)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum shortfall objective [budget (5000)]
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Minimum largest shortfall objective: Minimize the largest (maximum) shortfall while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when the minimum shortfall objective returns solutions that focus too much on representing a small number of features (e.g. because they occur in much cheaper planning units), and solutions are needed to spread conservation effort out more evenly amongst all features—even if it means that all features will have (relatively) poor representation.
        • -
      -
      # create a new problem that has the minimum largest shortfall objective and a
-# budget of 5000
-p7 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_largest_shortfall_objective(budget = 5000)
-
-# print the problem
-print(p7)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum largest shortfall objective [budget (5000)]
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Maximum phylogenetic diversity objective: Maximize the phylogenetic diversity of the features represented in the solution subject to a budget (inspired by Faith 1992; Rodrigues & Gaston 2002). This objective is similar to the maximum features objective except that emphasis is placed on protecting features which are associated with a diverse range of evolutionary histories. The prioritizr R package contains a simulated phylogeny that can be used with the simulated feature data (sim_phylogny).
        • -
      -
      # load simulated phylogeny data
-data(sim_phylogeny)
-
-# create a new problem that has the maximum phylogenetic diversity
-# objective and a budget of 5000
-p8 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_phylo_div_objective(budget = 5000, tree = sim_phylogeny)
-
-# print the problem
-print(p8)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Phylogenetic diversity objective [budget (5000)]
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Maximum phylogenetic endemism objective: Maximize the phylogenetic endemism of the features represented in the solution subject to a budget (inspired by Faith 1992; Rodrigues & Gaston 2002; Rosauer et al. 2009). This objective is similar to the maximum phylogenetic diversity except that emphasis is placed conserving features that are associated with geographically restricted periods of evolutionary history rather than a diverse range of evolutionary histories.
        • -
      -
      # load simulated phylogeny data
-data(sim_phylogeny)
-
-# create a new problem that has the maximum phylogenetic diversity
-# objective and a budget of 5000
-p9 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_phylo_end_objective(budget = 5000, tree = sim_phylogeny)
-
-# print the problem
-print(p9)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Phylogenetic endemism objective [budget (5000)]
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Maximum utility objective: Secure as much of the features as possible without exceeding a budget. This objective is functionally equivalent to selecting the planning units with the greatest amounts of each feature (e.g. species richness). Generally, we don’t encourage the use of this objective because it will only rarely identify complementary solutions—solutions which adequately conserve a range of different features—except perhaps to explore trade-offs or provide a baseline solution with which to compare other solutions.
        • -
      -
      # create a new problem that has the maximum utility objective and a budget
-# of 5000
-p10 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_utility_objective(budget = 5000)
-
-# print the problem
-print(p10)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Maximum utility objective [budget (5000)]
-##   targets:        none
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
      -
      -

      Add targets

      -

      Most conservation planning problems require targets. Targets are used to specify the minimum amount or proportion of a feature’s distribution that needs to be protected in the solution. For example, we may want to develop a reserve network that will secure 20% of the distribution for each feature for minimal cost.

      -

      There are four ways for specifying targets in the prioritizr R package:

      -
        -
      • Absolute targets: Targets are expressed as the total amount of each feature in the study area that need to be secured. For example, if we had binary feature data that showed the absence or presence of suitable habitat across the study area, we could set an absolute target as 5 to mean that we require 5 planning units with suitable habitat in the solution.
        • -
      -
      # create a problem with targets which specify that the solution must conserve
-# a need a sum total of 3 units of suitable habitat for each feature
-p11 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_absolute_targets(3)
-
-# print problem
-print(p11)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Absolute targets [targets (min: 3, max: 3)]
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Relative targets: Targets are set as a proportion (between 0 and 1) of the total amount of each feature in the study area. For example, if we had binary feature data and the feature occupied a total of 20 planning units in the study area, we could set a relative target of 50 % to specify that the solution must secure 10 planning units for the feature. We could alternatively specify an absolute target of 10 to achieve the same result, but sometimes proportions are easier to work with.
        • -
      -
      # create a problem with the minimum set objective and relative targets of 10 %
-# for each feature
-p12 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1)
-
-# print problem
-print(p12)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
      # create a problem with targets which specify that we need 10 % of the habitat
-# for the first feature, 15 % for the second feature, 20 % for the third feature
-# 25 % for the fourth feature and 30 % of the habitat for the fifth feature
-targets <- c(0.1, 0.15, 0.2, 0.25, 0.3)
-p13 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(targets)
-
-# print problem
-print(p13)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.3)]
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Log-linear targets: Targets are expressed using scaling factors and log-linear interpolation. This method for specifying targets is commonly used for global prioritization analyses (Rodrigues et al. 2004).
        • -
      -
      # create problem with added log-linear targets
-p14 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_loglinear_targets(10, 0.9, 100, 0.2)
-
-# print problem
-print(p14)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Absolute targets [targets (min: 17.290505409161, max: 21.5906174426385)]
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Manual targets: Targets are manually specified. This is only really recommended for advanced users or problems that involve multiple management zones. See the zones vignette for more information on these targets.
        • -
      -

      As with the functions for specifying the objective of a problem, if we try adding multiple targets to a problem, only the most recently added set of targets are used.

      -
      -
      -

      Add constraints

      -

      A constraint can be added to a conservation planning problem to ensure that all solutions exhibit a specific property. For example, they can be used to make sure that all solutions select a specific planning unit or that all selected planning units in the solution follow a certain configuration.

      -

      The following constraints can be added to conservation planning problems in the prioritizr R package.

      -
        -
      • Locked in constraints: Add constraints to ensure that certain planning units are prioritized in the solution. For example, it may be desirable to lock in planning units that are inside existing protected areas so that the solution fills in the gaps in the existing reserve network.
        • -
      -
      # create problem with constraints which specify that the first planning unit
-# must be selected in the solution
-p15 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_in_constraints(1)
-
-# print problem
-print(p15)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <Locked in planning units [1 locked units]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Locked out constraints: Add constraints to ensure that certain planning units are not prioritized in the solution. For example, it may be useful to lock out planning units that have been degraded and are not suitable for conserving species.
        • -
      -
      # create problem with constraints which specify that the second planning unit
-# must not be selected in the solution
-p16 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_out_constraints(2)
-
-# print problem
-print(p16)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <Locked out planning units [1 locked units]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Neighbor constraints: Add constraints to a conservation problem to ensure that all selected planning units have at least a certain number of neighbors.
        • -
      -
      # create problem with constraints which specify that all selected planning units
-# in the solution must have at least 1 neighbor
-p17 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_neighbor_constraints(1)
-
-# print problem
-print(p17)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <Neighbor constraint [number of neighbors (1), zones]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Contiguity constraints: Add constraints to a conservation problem to ensure that all selected planning units are spatially connected to each other and form spatially contiguous unit.
        • -
      -
      # create problem with constraints which specify that all selected planning units
-# in the solution must form a single contiguous unit
-p18 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_contiguity_constraints()
-
-# print problem
-print(p18)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <Contiguity constraints [apply constraints? (1), zones]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Feature contiguity constraints: Add constraints to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of those implemented in the add_contiguity_constraints function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit.
        • -
      -
      # create problem with constraints which specify that the planning units used
-# to conserve each feature must form a contiguous unit
-p19 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_feature_contiguity_constraints()
-
-# print problem
-print(p19)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <Feature contiguity constraints [apply constraints? (1), layer.1 zones, layer.2 zones, layer.3 zones, layer.4 zones, layer.5 zones]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Linear constraints: Add constraints to ensure that all selected planning units meet certain criteria. For example, they can be used to add multiple budgets, or limit the number of planning units selected in different administrative areas within a study region (e.g. different countries).
        • -
      -
      # create problem with constraints which specify that the sum of
-# values in sim_features[[1]] among selected planning units must not exceed a
-#' threshold value of 190.
-p20 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_shortfall_objective(budget = 1800) %>%
-       add_relative_targets(0.1) %>%
-       add_linear_constraints(190, "<=", sim_features[[1]])
-
-# print problem
-print(p20)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum shortfall objective [budget (1800)]
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <Linear constraints [threshold (190)]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Mandatory allocation constraints: Add constraints to ensure that every planning unit is allocated to a management zone in the solution. Please note that this function can only be used with problems that contain multiple zones. For more information on problems with multiple zones and an example using this function, see the Management Zones vignette.
        • -
      -

      In particular, The add_locked_in_constraints and add_locked_out_constraints functions are incredibly useful for real-world conservation planning exercises, so it’s worth pointing out that there are several ways we can specify which planning units should be locked in or out of the solutions. If we use raster planning unit data, we can also use raster data to specify which planning units should be locked in our locked out.

      -
      # load data to lock in or lock out planning units
-data(sim_locked_in_raster)
-data(sim_locked_out_raster)
-
-# plot the locked data
-plot(stack(sim_locked_in_raster, sim_locked_out_raster),
-     main = c("Locked In", "Locked Out"))
      -

      -
      # create a problem using raster planning unit data and use the locked raster
-# data to lock in some planning units and lock out some other planning units
-p21 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_in_constraints(sim_locked_in_raster) %>%
-       add_locked_out_constraints(sim_locked_out_raster)
-
-# print problem
-print(p21)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <Locked out planning units [10 locked units]
-##                    Locked in planning units [10 locked units]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -

      If our planning unit data are in a spatial vector format (similar to the sim_pu_polygons data) or a tabular format (similar to pu_dat), we can use the field names in the data to refer to which planning units should be locked in and / or out. For example, the sim_pu_polygons object has TRUE / FALSE values in the “locked_in” field which indicate which planning units should be selected in the solution. We could use the data in this field to specify that those planning units with TRUE values should be locked in using the following methods.

      -
      # preview first six rows of the attribute table for sim_pu_polygons
-head(sim_pu_polygons@data)
      -
      ##       cost locked_in locked_out
-## 1 215.8638     FALSE      FALSE
-## 2 212.7823     FALSE      FALSE
-## 3 207.4962     FALSE      FALSE
-## 4 208.9322     FALSE       TRUE
-## 5 214.0419     FALSE      FALSE
-## 6 213.7636     FALSE      FALSE
      -
      # specify locked in data using the field name
-p22 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_in_constraints("locked_in")
-
-# print problem
-print(p22)
      -
      ## Conservation Problem
-##   planning units: SpatialPolygonsDataFrame (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <Locked in planning units [10 locked units]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
      # specify locked in data using the values in the field
-p23 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_in_constraints(which(sim_pu_polygons$locked_in))
-
-# print problem
-print(p23)
      -
      ## Conservation Problem
-##   planning units: SpatialPolygonsDataFrame (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <Locked in planning units [10 locked units]>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
      -
      -

      Add penalties

      -

      We can also add penalties to a problem to favor or penalize solutions according to a secondary objective. Unlike the constraint functions, these functions will add extra information to the objective function of the optimization function to penalize solutions that do not exhibit specific characteristics. For example, penalties can be added to a problem to avoid highly fragmented solutions at the expense of accepting slightly more expensive solutions. All penalty functions have a penalty argument that controls the relative importance of the secondary penalty function compared to the primary objective function. It is worth noting that incredibly low or incredibly high penalty values—relative to the main objective function—can cause problems to take a very long time to solve, so when trying out a range of different penalty values it can be helpful to limit the solver to run for a set period of time.

      -

      The prioritizr R package currently offers only two methods for adding penalties to a conservation planning problem.

      -
        -
      • Boundary penalties: Add penalties to penalize solutions that are excessively fragmented. These penalties are similar to those used in Marxan (Ball et al. 2009; Beyer et al. 2016).
        • -
      -
      # create problem with penalties that penalize fragmented solutions with a
-# penalty factor of 0.01
-p24 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_boundary_penalties(penalty = 0.01)
-
-# print problem
-print(p24)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (0.01), zones]>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Connectivity penalties: Add penalties to favor solutions that select combinations of planning units with high connectivity between them. These penalties are similar to those used in Marxan with Zones (Watts et al. 2009; Beyer et al. 2016). This function supports both symmetric and asymmetric connectivities among planning units.
        • -
      -
      # create problem with penalties that favor combinations of planning units with
-# high connectivity, here we will use only the first four layers in
-# sim_features for the features and we will use the fifth layer in sim_features
-# to represent the connectivity data, where the connectivity_matrix function
-# will create a matrix showing the average strength of connectivity between
-# adjacent planning units using the data in the fifth layer of sim_features
-p25 <- problem(sim_pu_raster, sim_features[[1:4]]) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_boundary_penalties(
-         penalty = 5,
-         data = connectivity_matrix(sim_pu_raster, sim_features[[5]]))
-
-# print problem
-print(p25)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, layer.4 (4 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (5), zones]>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Linear penalties: Add penalties to penalize solutions that select planning units according to a certain variable (e.g. anthropogenic pressure).
        • -
      -
      # create data for penalizing planning units
-# (note this requires the RandomFields package to be installed)
-pen_raster <- simulate_cost(sim_pu_raster)
-
-# create problem with penalties that penalize solutions that select
-# planning units with high values in the pen_raster object,
-# here we will use a penalty value of 5 to indicate the trade-off (scaling)
-# between the penalty values (in the sim_pu_raster) and the main objective
-# (i.e. the cost of the solution)
-p26 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_linear_penalties(penalty = 5, data = pen_raster)
-
-# print problem
-print(p26)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      default
-##   constraints:    <none>
-##   penalties:      <Linear penalties [penalty (5)]>
-##   portfolio:      default
-##   solver:         default
      -
      -
      -

      Add the decision types

      -

      Conservation planning problems involve making decisions on how planning units will be managed. These decisions are then associated with management actions (e.g. turning a planning unit into a protected area). The type of decision describes how the action is applied to planning units. For instance, the default decision-type is a binary decision type, meaning that we are either selecting or not selecting planning units for management.

      -

      The prioritizr R package currently offers the following types of decisions for customizing problems.

      -
        -
      • Binary decisions: Add a binary decision to a conservation planning problem. This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem object, then this decision class will be used by default.
        • -
      -
      # add binary decisions to a problem
-p27 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions()
-
-# print problem
-print(p27)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
+
      The aim of this tutorial is to provide a short introduction to the prioritizr R package. It is also intended for helping conservation planners familiar the Marxan decision support tool (Ball et al. 2009) to start using the package for their work.
      
+
      +
      +

      Data

      +

      Let’s load the packages and data used in this tutorial. Since this tutorial uses data from the prioritizrdata R package, please ensure that it is installed. The data used in this tutorial were obtained from the Introduction to Marxan course. Specifically, the data were originally a subset of a larger spatial prioritization project performed under contract to Australia’s Department of Environment and Water Resources (Klein et al. 2007).

      +
      # load packages
+library(prioritizrdata)
+library(prioritizr)
+library(vegan)
+library(cluster)
+
+# load planning unit data
+data(tas_pu)
+
+# load feature data
+data(tas_features)
      +

      The tas_pu object contains planning units represented as spatial polygons (i.e., a SpatialPolygonsDataFrame object). This object has three columns that denote the following information for each planning unit: a unique identifier (id), unimproved land value (cost), and current conservation status (locked_in). Planning units that have at least half of their area overlapping with existing protected areas are denoted with a locked in value of 1, otherwise they are denoted with a value of 0. If you are familiar with the Marxan decision support tool, then you will notice that some of these columns are formatted similar conventions.

      +

      Now, let’s have a look at the planning unit data. We can see that the planning units correspond to hexagonal land parcels. We can also see that is a clear spatial pattern in the cost and conservation status the planning units.

      +
      # print planning unit data
+print(tas_pu)
      +
      ## class       : SpatialPolygonsDataFrame 
+## features    : 1130 
+## extent      : 298809.6, 613818.8, 5167775, 5502544  (xmin, xmax, ymin, ymax)
+## crs         : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## variables   : 5
+## names       :   id,              cost, status, locked_in, locked_out 
+## min values  :    1, 0.192488262910798,      0,         0,          0 
+## max values  : 1130,  61.9272727272727,      2,         1,          0
      +
      # plot map of planning unit costs
+plot(st_as_sf(tas_pu[, "cost"]), main = "Planning unit costs")
      +

      +
      # plot map of planning unit coverage by protected areas
+plot(st_as_sf(tas_pu[, "locked_in"]), main = "Protected area coverage")
      +

      +

      The tas_features object describes the spatial distribution of the features. Specifically, the feature data are expressed as a stack of 62 rasters (i.e., a RasterStack object). Each layer in the stack corresponds to one of 62 different vegetation communities. To describe the spatial distribution of a given vegetation community, each layer contains a spatially referenced grid of rectangular cells and each of these grid cells is associated with information on the distribution of the a given vegetation community. Specifically, these grid cells are assigned values that indicate if a given vegetation community is present (using value of 1) or absent (using value of 0) within the spatial extent of each grid cell.

      +

      Next, let’s examine the feature data. Here we will only plot the first four features as an example. The pixel values denote the presence (denoted by a value of 1) or absence (denoted by a value of zero) of each feature within the extent of the study area.

      +
      # print planning unit data
+print(tas_features)
      +
      ## class      : RasterStack 
+## dimensions : 398, 359, 142882, 62  (nrow, ncol, ncell, nlayers)
+## resolution : 1000, 1000  (x, y)
+## extent     : 288801.7, 647801.7, 5142976, 5540976  (xmin, xmax, ymin, ymax)
+## crs        : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## names      : tas_features.1, tas_features.2, tas_features.3, tas_features.4, tas_features.5, tas_features.6, tas_features.7, tas_features.8, tas_features.9, tas_features.10, tas_features.11, tas_features.12, tas_features.13, tas_features.14, tas_features.15, ... 
+## min values :              0,              0,              0,              0,              0,              0,              0,              0,              0,               0,               0,               0,               0,               0,               0, ... 
+## max values :              1,              1,              1,              1,              1,              1,              1,              1,              1,               1,               1,               1,               1,               1,               1, ...
      +
      # plot map of the first four vegetation classes
+plot(tas_features[[1:4]], main = paste("Feature", 1:4))
      +

      +

      The planning units in this tutorial are stored as spatial polygons. Although spatial polygons provide considerable flexibility in the shape and size of the planning units, such flexibility comes at a cost. This is because the spatial data processing routines needed to combine spatial polygon data and raster data for optimization can be very computationally expensive (e.g., calculating zonal statistics). As a consequence, we generally recommend using raster-based planning unit data where possible to reduce processing time. Another strategy is to complete spatial data processing routines manually using other software (e.g., ESRI ArcGIS) and use the pre-processed data directly with the prioritizr R package.

      +
      +
      +

      Problem formulation

      +

      Now we will formulate a conservation planing problem. To achieve this, we first specify which objects contain the planning unit and feature data (using the problem() function). Next, we specify that we want to use the minimum set objective function (using the add_min_set_objective() function). This objective function indicates that we wish to minimize the total cost of planning units selected by the prioritization. We then specify boundary penalties reduce spatial fragmentation in the resulting prioritization (using the add_boundary_penalties() function; see the Calibrating trade-offs vignette for details on calibrating the penalty value). We also specify representation targets to ensure the resulting prioritization provides adequate coverage of each vegetation community (using the add_relative_targets() function). Specifically, we specify targets to ensure at least 17% of the spatial extent of each vegetation community (based on the Aichi Target 11). Additionally, we set constraints to ensure that planning units predominately covered by existing protected areas are selected by the prioritization (using the add_locked_in_constraints() function). Finally, we specify that the prioritization should either select – or not select – planning units for prioritization (using the add_binary_decisions() function).

      +
      # build problem
+p1 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 0.005) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# print the problem
+print(p1)
      +
      ## Conservation Problem
+##   planning units: SpatialPolygonsDataFrame (1130 units)
+##   cost:           min: 0.19249, max: 61.92727
+##   features:       tas_features.1, tas_features.2, tas_features.3, ... (62 features)
 ##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
 ##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Proportion decisions: Add a proportion decision to a problem. This is a relaxed decision where a part of a planning unit can be prioritized, as opposed to the default of the entire planning unit. Typically, this decision has the assumed action of buying a fraction of a planning unit to include in a protected area network. Generally, problems can be solved much faster with proportion-type decisions than binary-type decisions, so they can be very useful when commercial solvers are not available.
        • -
      -
      # add proportion decisions to a problem
-p28 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_proportion_decisions()
-
-# print problem
-print(p28)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Proportion decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         default
      -
        -
      • Semi-continuous decisions: Add a semi-continuous decision to a problem. This decision is similar to proportion decisions except that it has an upper bound parameter. By default, the decision can range from prioritizing none (0%) to all (100%) of a planning unit. However, a upper bound can be specified to ensure that at most only a fraction (e.g. 80%) of a planning unit can be purchased. This type of decision may be useful when it is not practical to conserve the entire area indicated by a planning unit.
        • -
      -
      # add semi-continuous decisions to a problem, where we can only manage at most
-# 50 % of the area encompassed by a planning unit
-p29 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_semicontinuous_decisions(0.5)
-
-# print problem
-print(p29)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Semicontinuous decision [upper limit (0.5)]
-##   constraints:    <none>
-##   penalties:      <none>
+##   constraints:    <Locked in planning units [257 locked units]>
+##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (0.005), zones]>
 ##   portfolio:      default
 ##   solver:         default
      -
      -

      Add a solver

      -

      Next, after specifying the mathematical formulation that underpins your conservation planning problem, you can specify how the problem should be solved. If you do not specify this information, the prioritizr R package will automatically use the best solver currently installed on your system with some reasonable defaults. We strongly recommend installing the Gurobi software suite and the gurobi R package to solve problems, and for more information on this topic please refer to the Gurobi Installation Guide.

      -

      Currently, the prioritizr R package supports five different solvers.

      -
        -
      • Gurobi solver: Gurobi is a state of the art commercial optimization software. It is by far the fastest of the solvers that can be used to solve conservation problems. However, it is not freely available. That said, special licenses are available to academics at no cost.
        • -
      -
      # create a problem and specify that Gurobi should be used to solve the problem
-# and specify an optimality gap of zero to obtain the optimal solution
-p30 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_gurobi_solver(gap = 0)
-
-# print problem
-print(p30)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         Gurobi [first_feasible (0), gap (0), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (1)]
      -
        -
      • IBM CPLEX solver: IBM CPLEX is a commercial optimization software. It is faster than the open source solvers available for generating prioritizations (see below), however, it is not freely available. Similar to the Gurobi software, special licenses are available to academics at no cost.
        • -
      -
      # create a problem and specify that IBM CPLEX should be used to solve the
-# problem and specify an optimality gap of zero to obtain the optimal solution
-p31 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_cplex_solver(gap = 0)
-
-# print problem
-print(p31)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         CPLEX [gap (0), presolve (1), threads (1), time_limit (2147483647), verbose (1)]
      -
        -
      • CBC solver: CBC is an open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. Although formal benchmarks have yet to be completed, preliminary analyses suggest that it is the fastest open-source solver available for generating prioritizations. It requires the rcbc R package, which is currently only available on GitHub.
        • -
      -
      # create a problem and specify that CBC should be used to solve the
-# problem and specify an optimality gap of zero to obtain the optimal solution
-p32 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_cbc_solver(gap = 0)
-
-# print problem
-print(p32)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         CBC [first_feasible (0), gap (0), presolve (1), threads (1), time_limit (2147483647), verbose (1)]
      -
        -
      • lpsymphony solver: SYMPHONY is an open-source integer programming solver that is also part of the COIN-OR project. This solver uses the lpsymphony R package (available on Bioconductor) to interface with the SYMPHONY software.
        • -
      -
      # create a problem and specify that lpsymphony should be used to solve the
-# problem and specify an optimality gap of zero to obtain the optimal solution
-p33 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_lpsymphony_solver(gap = 0)
-
-# print problem
-print(p33)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         Lpsymphony [first_feasible (0), gap (0), time_limit (2147483647), verbose (1)]
      -
        -
      • Rsymphony solver: This solver provides a different interface to the SYMPHONY software. It uses the Rsymphony R package which is available on The Comprehensive R Archive Network (CRAN). This solver is generally slower than the other solvers, because it cannot use parallel processing.
        • -
      -
      # create a problem and specify that Rsymphony should be used to solve the
-# problem and specify an optimality gap of zero to obtain the optimal solution
-p34 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_rsymphony_solver(gap = 0)
-
-# print problem
-print(p34)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         Rsymphony [first_feasible (0), gap (0), time_limit (2147483647), verbose (1)]
      -
      -
      -

      Add a portfolio

      -

      Many conservation planning exercises require a portfolio of solutions. For example, real-world exercises can involve presenting decision makers with a range of near-optimal decisions. Additionally, the number of times that different planning units are selected in different solutions can provide insight into their relative importance.

      -

      The following methods are available for generating a portfolio of solutions.

      -
        -
      • Extra portfolio: Generate a portfolio of solutions by storing feasible solutions found during the optimization process. Note that this method requires that the Gurobi optimization software is used to generate solutions.
        • -
      -
      # create a problem and specify that a portfolio should be created using
-# extra solutions found while solving the problem
-p35 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_extra_portfolio()
-
-# print problem
-print(p35)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      Extra portfolio
-##   solver:         default
      -
        -
      • Top portfolio: Generate a portfolio of solutions by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions). Note that this method requires that the Gurobi optimization software is used to generate solutions.
        • -
      -
      # create a problem and specify that a portfolio should be created using
-# the top five solutions
-p36 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_top_portfolio(number_solutions = 5)
-
-# print problem
-print(p36)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      Top portfolio [number_solutions (5)]
-##   solver:         default
      -
        -
      • Gap portfolio: Generate a portfolio of solutions by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is especially useful for generating multiple solutions that can used be to calculate selection frequencies (similar to Marxan). Note that this method requires that the Gurobi optimization software is used to generate solutions.
        • -
      -
      # create a problem and specify that a portfolio should be created by
-# finding five solutions within 10% of optimality
-p37 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_gap_portfolio(number_solutions = 5, pool_gap = 0.2)
-
-# print problem
-print(p37)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      Gap portfolio [number_solutions (5), pool_gap (0.2)]
-##   solver:         default
      -
        -
      • Cuts portfolio: Generate a portfolio of distinct solutions within a pre-specified optimality gap. This method is only recommended if the Gurobi optimization solver is not available.
        • -
      -
      # create a problem and specify that a portfolio containing 10 solutions
-# should be created using using Bender's cuts
-p38 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_cuts_portfolio(number_solutions = 10)
-
-# print problem
-print(p38)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      Cuts portfolio [number_solutions (10)]
-##   solver:         default
      -
        -
      • Shuffle portfolio: Generate a portfolio of solutions by randomly reordering the data prior to attempting to solve the problem. If the Gurobi optimization solver is not available, this method is the fastest method for generating a set number of solutions within a specified distance from optimality.
        • -
      -
      # create a problem and specify a portfolio should be created that contains
-# 10 solutions and that any duplicate solutions should not be removed
-p39 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_shuffle_portfolio(number_solutions = 10, remove_duplicates = FALSE)
-
-# print problem
-print(p39)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (90 units)
-##   cost:           min: 190.13276, max: 215.86384
-##   features:       layer.1, layer.2, layer.3, ... (5 features)
+
      
+
      Prioritization
      
+
      We can now solve the problem formulation (p1) to generate a prioritization (using the solve() function). The prioritizr R package supports a range of different exact algorithm solvers, including Gurobi, IBM CPLEX, CBC, Rsymphony, and lpsymphony. Although there are benefits and limitations associated with each of these different solvers, they should return similar results. Note that you will need at least one solver installed on your system to generate prioritizations. Since we did not specify a solver when building the problem, the prioritizr R package will automatically select the best available solver installed. We recommend using the Gurobi solver if possible, and have used it for this tutorial (see the Gurobi Installation Guide vignette for installation instructions). After solving the problem, the prioritization will be stored in the solution_1 column of the s1 object.
      
+
      # solve problem
+s1 <- solve(p1)
      
+
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
+## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
+## Optimize a model with 6358 rows, 4278 columns and 14496 nonzeros
+## Model fingerprint: 0xc7d1c688
+## Variable types: 0 continuous, 4278 integer (4278 binary)
+## Coefficient statistics:
+##   Matrix range     [2e-06, 4e+01]
+##   Objective range  [5e-01, 1e+03]
+##   Bounds range     [1e+00, 1e+00]
+##   RHS range        [1e-01, 1e+02]
+## Found heuristic solution: objective 37703.827706
+## Found heuristic solution: objective 27817.085072
+## Presolve removed 2077 rows and 1375 columns
+## Presolve time: 0.04s
+## Presolved: 4281 rows, 2903 columns, 9594 nonzeros
+## Found heuristic solution: objective 24454.499456
+## Variable types: 0 continuous, 2903 integer (2903 binary)
+## Found heuristic solution: objective 23413.987477
+## Root relaxation presolved: 4281 rows, 2903 columns, 9594 nonzeros
+## 
+## 
+## Root relaxation: objective 1.955605e+04, 1793 iterations, 0.09 seconds (0.19 work units)
+## 
+##     Nodes    |    Current Node    |     Objective Bounds      |     Work
+##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
+## 
+##      0     0 19556.0531    0 1615 23413.9875 19556.0531  16.5%     -    0s
+## H    0     0                    23045.733138 19556.0531  15.1%     -    0s
+## H    0     0                    22977.771015 19556.0531  14.9%     -    0s
+##      0     0 19836.0586    0 1855 22977.7710 19836.0586  13.7%     -    0s
+## H    0     0                    21702.297403 19836.0586  8.60%     -    0s
+## 
+## Cutting planes:
+##   Gomory: 2
+##   Cover: 5
+##   MIR: 4
+##   GUB cover: 1
+##   Zero half: 2
+##   RLT: 10
+## 
+## Explored 1 nodes (2393 simplex iterations) in 0.34 seconds (0.60 work units)
+## Thread count was 1 (of 8 available processors)
+## 
+## Solution count 7: 21702.3 22977.8 23045.7 ... 37703.8
+## 
+## Optimal solution found (tolerance 1.00e-01)
+## Best objective 2.170229740250e+04, best bound 1.983605855899e+04, gap 8.5993%
      
+
      # plot map of prioritization
+plot(st_as_sf(s1[, "solution_1"]), main = "Prioritization",
+     pal = c("grey90", "darkgreen"))
      
+
      
+
      
+
      
+
      Feature representation
      
+
      Let’s examine how well the vegetation communities are represented by existing protected areas and the prioritization.
      
+
      # create column with existing protected areas
+tas_pu$pa <- round(tas_pu$locked_in)
+
+# calculate feature representation statistics based on existing protected areas
+tc_pa <- eval_target_coverage_summary(p1, tas_pu[, "pa"])
+print(tc_pa)
      
+
      ## # A tibble: 62 × 9
+##    feature         met   total_amount absolute_target absolute_held
+##    <chr>           <lgl>        <dbl>           <dbl>         <dbl>
+##  1 tas_features.1  FALSE         33.9            5.77         0.556
+##  2 tas_features.2  FALSE        170.            28.9         13.5  
+##  3 tas_features.3  FALSE         24.0            4.08         2.00 
+##  4 tas_features.4  FALSE         32.8            5.57         1.37 
+##  5 tas_features.5  FALSE         24.8            4.21         0    
+##  6 tas_features.6  FALSE         22.0            3.74         0    
+##  7 tas_features.7  FALSE         16.4            2.78         0    
+##  8 tas_features.8  FALSE         43.0            7.31         5.12 
+##  9 tas_features.9  FALSE        388.            66.0         22.4  
+## 10 tas_features.10 FALSE         14.5            2.47         0    
+##    absolute_shortfall relative_target relative_held relative_shortfall
+##                 <dbl>           <dbl>         <dbl>              <dbl>
+##  1               5.21            0.17        0.0164             0.154 
+##  2              15.4             0.17        0.0796             0.0904
+##  3               2.08            0.17        0.0832             0.0868
+##  4               4.19            0.17        0.0420             0.128 
+##  5               4.21            0.17        0                  0.17  
+##  6               3.74            0.17        0                  0.17  
+##  7               2.78            0.17        0                  0.17  
+##  8               2.19            0.17        0.119              0.0510
+##  9              43.5             0.17        0.0578             0.112 
+## 10               2.47            0.17        0                  0.17  
+## # … with 52 more rows
      
+
      # calculate  feature representation statistics based on the prioritization
+tc_s1 <- eval_target_coverage_summary(p1, s1[, "solution_1"])
+print(tc_s1)
      
+
      ## # A tibble: 62 × 9
+##    feature         met   total_amount absolute_target absolute_held
+##    <chr>           <lgl>        <dbl>           <dbl>         <dbl>
+##  1 tas_features.1  TRUE          33.9            5.77          5.97
+##  2 tas_features.2  TRUE         170.            28.9          43.8 
+##  3 tas_features.3  TRUE          24.0            4.08          4.25
+##  4 tas_features.4  TRUE          32.8            5.57          6.37
+##  5 tas_features.5  TRUE          24.8            4.21          4.98
+##  6 tas_features.6  TRUE          22.0            3.74          7.00
+##  7 tas_features.7  TRUE          16.4            2.78          3.00
+##  8 tas_features.8  TRUE          43.0            7.31          8.12
+##  9 tas_features.9  TRUE         388.            66.0          70.8 
+## 10 tas_features.10 TRUE          14.5            2.47          2.91
+##    absolute_shortfall relative_target relative_held relative_shortfall
+##                 <dbl>           <dbl>         <dbl>              <dbl>
+##  1                  0            0.17         0.176                  0
+##  2                  0            0.17         0.258                  0
+##  3                  0            0.17         0.177                  0
+##  4                  0            0.17         0.195                  0
+##  5                  0            0.17         0.201                  0
+##  6                  0            0.17         0.318                  0
+##  7                  0            0.17         0.183                  0
+##  8                  0            0.17         0.189                  0
+##  9                  0            0.17         0.182                  0
+## 10                  0            0.17         0.200                  0
+## # … with 52 more rows
      
+
      # explore representation by existing protected areas
+## calculate number of features adequately represented by existing protected
+## areas
+sum(tc_pa$met)
      
+
      ## [1] 16
      
+
      ## summarize representation (values show percent coverage)
+summary(tc_pa$relative_held * 100)
      
+
      ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
+##   0.000   0.000   4.845  13.909  16.995  58.488
      
+
      ## visualize representation  (values show percent coverage)
+hist(tc_pa$relative_held * 100,
+     main = "Feature representation by existing protected areas",
+     xlim = c(0, 100),
+     xlab = "Percent coverage of features (%)")
      
+
      
+
      # explore representation by prioritization
+## summarize representation (values show percent coverage)
+summary(tc_s1$relative_held * 100)
      
+
      ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
+##   17.14   20.18   25.56   33.83   43.19  100.00
      
+
      ## calculate number of features adequately represented by the prioritization
+sum(tc_s1$met)
      
+
      ## [1] 62
      
+
      ## visualize representation  (values show percent coverage)
+hist(tc_s1$relative_held * 100,
+     main = "Feature representation by prioritization",
+     xlim = c(0, 100),
+     xlab = "Percent coverage of features (%)")
      
+
      
+
      We can see that representation of the vegetation communities by existing protected areas is remarkably poor. For example, many of the vegetation communities have nearly zero coverage by existing protected areas. In other words, are almost entirely absent from existing protected areas. We can also see that all vegetation communities have at least 17% coverage by the prioritization – meaning that it meets the representation targets for all of the features.
      
+
      
+
      
+
      Irreplaceability
      
+
      After generating the prioritization, we can examine the relative importance of planning units selected by the prioritization. This can be useful to identify critically important planning units for conservation – in other words, places that contain biodiversity features which cannot be represented anywhere else – and schedule implementation of the prioritization. To achieve this, we will use the Ferrier metric (Ferrier et al. 2000).
      
+
      # calculate irreplaceability
+irrep_s1 <- eval_ferrier_importance(p1, s1["solution_1"])
+print(irrep_s1)
      
+
      ## class       : SpatialPolygonsDataFrame 
+## features    : 1130 
+## extent      : 298809.6, 613818.8, 5167775, 5502544  (xmin, xmax, ymin, ymax)
+## crs         : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## variables   : 63
+## names       :      tas_features.1,     tas_features.2,      tas_features.3,      tas_features.4,      tas_features.5,    tas_features.6,      tas_features.7,      tas_features.8,      tas_features.9,     tas_features.10,   tas_features.11,     tas_features.12,    tas_features.13,   tas_features.14,     tas_features.15, ... 
+## min values  :                   0,                  0,                   0,                   0,                   0,                 0,                   0,                   0,                   0,                   0,                 0,                   0,                  0,                 0,                   0, ... 
+## max values  : 0.00701698358267939, 0.0066775439067078, 0.00248592654648536, 0.00594796984735507, 0.00219848915242862, 0.221777713215686, 0.00352460472775105, 0.00362070014565918, 0.00736044135306282, 0.00691379490000091, 0.225419698234888, 0.00465456428213494, 0.0025318990590772, 0.010045386228309, 0.00609443943530227, ...
      
+
      # manually coerce values for planning units not selected in prioritization
+# to NA, so that they are shown in white
+irrep_s1$plot_total <- irrep_s1$total
+irrep_s1$plot_total[s1$solution_1 < 0.5] <- NA_real_
+
+# plot map of overall importance scores
+plot(st_as_sf(irrep_s1[, "plot_total"]), main = "Overall importance")
      
+
      
+
      
+
      
+
      Portfolios
      
+
      Conservation planning exercises often involve generating multiple different prioritizations. This can help decision makers consider different options, and provide starting points for building consensus among stakeholders. To generate a range of different prioritizations given the same problem formulation, we can use portfolio functions. Here we will use the gap portfolio to generate 1000 solutions that are within 30% of optimality. Please note that you will need to have the Gurobi solver installed to use this specific portfolio. If you don’thave access to Gurobi, you could try using the shuffle portfolio instead (using the add_shuffle_portfolio() function).
      
+
      # create new problem with a portfolio added to it
+p2 <- p1 %>%
+      add_gap_portfolio(number_solutions = 1000, pool_gap = 0.2)
+
+# print problem
+print(p2)
      
+
      ## Conservation Problem
+##   planning units: SpatialPolygonsDataFrame (1130 units)
+##   cost:           min: 0.19249, max: 61.92727
+##   features:       tas_features.1, tas_features.2, tas_features.3, ... (62 features)
 ##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
 ##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      Shuffle portfolio [number_solutions (10), remove_duplicates (0), threads (1)]
+##   constraints:    <Locked in planning units [257 locked units]>
+##   penalties:      <Boundary penalties [edge factor (min: 0.5, max: 0.5), penalty (0.005), zones]>
+##   portfolio:      Gap portfolio [number_solutions (1000), pool_gap (0.2)]
 ##   solver:         default
      
-
      
-
      
-
      Solve the problem
      
-
      Finally, after formulating our conservation planning problem and specifying how the problem should be solved, we can use the solve function to obtain a solution. Note that the solver will typically print out some information describing the size of the problem and report its progress when searching for a suitable solution.
      
-
      # formulate the problem
-p40 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_boundary_penalties(penalty = 500, edge_factor = 0.5) %>%
-       add_binary_decisions()
-
-# solve the problem (using the default solver)
-s40 <- solve(p40)
      
+
      # generate prioritizations
+prt <- solve(p2)
      
 
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
 ## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 293 rows, 234 columns and 1026 nonzeros
-## Model fingerprint: 0xbd38144b
-## Variable types: 0 continuous, 234 integer (234 binary)
+## Optimize a model with 6358 rows, 4278 columns and 14496 nonzeros
+## Model fingerprint: 0xc7d1c688
+## Variable types: 0 continuous, 4278 integer (4278 binary)
 ## Coefficient statistics:
-##   Matrix range     [2e-01, 1e+00]
-##   Objective range  [1e+02, 4e+02]
+##   Matrix range     [2e-06, 4e+01]
+##   Objective range  [5e-01, 1e+03]
 ##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [3e+00, 8e+00]
-## Found heuristic solution: objective 20287.196992
-## Found heuristic solution: objective 3087.9617505
-## Presolve time: 0.00s
-## Presolved: 293 rows, 234 columns, 1026 nonzeros
-## Variable types: 0 continuous, 234 integer (234 binary)
-## Root relaxation presolved: 293 rows, 234 columns, 1026 nonzeros
+##   RHS range        [1e-01, 1e+02]
+## Found heuristic solution: objective 37703.827706
+## Found heuristic solution: objective 27817.085072
+## Presolve removed 1434 rows and 258 columns
+## Presolve time: 0.02s
+## Presolved: 4924 rows, 4020 columns, 10889 nonzeros
+## Variable types: 0 continuous, 4020 integer (4020 binary)
+## Found heuristic solution: objective 27660.082384
+## Root relaxation presolved: 4924 rows, 4020 columns, 10889 nonzeros
 ## 
 ## 
-## Root relaxation: objective 2.265862e+03, 220 iterations, 0.00 seconds (0.00 work units)
+## Root relaxation: objective 1.954728e+04, 1905 iterations, 0.10 seconds (0.18 work units)
 ## 
 ##     Nodes    |    Current Node    |     Objective Bounds      |     Work
 ##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
 ## 
-##      0     0 2265.86242    0  234 3087.96175 2265.86242  26.6%     -    0s
-##      0     0 2325.53449    0  232 3087.96175 2325.53449  24.7%     -    0s
-##      0     0 2361.03063    0  223 3087.96175 2361.03063  23.5%     -    0s
-##      0     0 2371.27288    0  222 3087.96175 2371.27288  23.2%     -    0s
-##      0     0 2371.27288    0  222 3087.96175 2371.27288  23.2%     -    0s
-## H    0     0                    2790.8740409 2371.27288  15.0%     -    0s
-## H    0     0                    2730.9524342 2371.27288  13.2%     -    0s
-##      0     2 2372.02804    0  222 2730.95243 2372.02804  13.1%     -    0s
-## H    6     6                    2604.7426048 2375.46233  8.80%  21.0    0s
+##      0     0 19547.2818    0 1731 27660.0824 19547.2818  29.3%     -    0s
+## H    0     0                    26145.941445 19547.2818  25.2%     -    0s
+## H    0     0                    24520.062189 19547.2818  20.3%     -    0s
+##      0     0 19820.3758    0 1966 24520.0622 19820.3758  19.2%     -    0s
+## H    0     0                    24498.644854 19820.3758  19.1%     -    0s
+## H    0     0                    23263.485453 19820.3758  14.8%     -    0s
+## H    0     0                    22049.956515 19820.3758  10.1%     -    0s
+##      0     0 19847.8388    0 1956 22049.9565 19847.8388  10.0%     -    0s
+##      0     0 19854.3259    0 1960 22049.9565 19854.3259  10.0%     -    0s
+##      0     0 19854.3439    0 1958 22049.9565 19854.3439  10.0%     -    0s
+##      0     0 19924.6889    0 1682 22049.9565 19924.6889  9.64%     -    0s
+##      0     0 19936.2410    0 1978 22049.9565 19936.2410  9.59%     -    0s
+##      0     0 19937.4882    0 2005 22049.9565 19937.4882  9.58%     -    0s
+##      0     0 19937.6761    0 2005 22049.9565 19937.6761  9.58%     -    0s
+##      0     0 19968.7333    0 1691 22049.9565 19968.7333  9.44%     -    0s
+##      0     0 19970.0998    0 1714 22049.9565 19970.0998  9.43%     -    0s
+##      0     0 19970.4702    0 1714 22049.9565 19970.4702  9.43%     -    0s
+##      0     0 19983.7957    0 1748 22049.9565 19983.7957  9.37%     -    0s
+##      0     0 19984.9623    0 1754 22049.9565 19984.9623  9.37%     -    0s
+##      0     0 19985.0928    0 1754 22049.9565 19985.0928  9.36%     -    0s
+##      0     0 19990.8490    0 2040 22049.9565 19990.8490  9.34%     -    1s
+##      0     0 19991.1771    0 2041 22049.9565 19991.1771  9.34%     -    1s
+##      0     0 19991.9721    0 2039 22049.9565 19991.9721  9.33%     -    1s
+##      0     0 19992.1795    0 2040 22049.9565 19992.1795  9.33%     -    1s
+##      0     0 19995.3797    0 1784 22049.9565 19995.3797  9.32%     -    1s
+##      0     0 19995.3847    0 1788 22049.9565 19995.3847  9.32%     -    1s
+##      0     0 19995.5716    0 2038 22049.9565 19995.5716  9.32%     -    1s
+##      0     0 19995.8374    0 2037 22049.9565 19995.8374  9.32%     -    1s
+##      0     0 19996.1519    0 2039 22049.9565 19996.1519  9.31%     -    1s
+##      0     0 19996.1519    0 2039 22049.9565 19996.1519  9.31%     -    1s
+##      0     2 19996.6237    0 2039 22049.9565 19996.6237  9.31%     -    1s
+## H   27    27                    21471.431466 19996.6237  6.87%   117    2s
+## H   52    52                    21371.814002 19996.6237  6.43%   115    2s
+## H   54    54                    21254.060213 19996.6237  5.92%   117    2s
+## H  108   108                    21204.105802 19996.6237  5.69%   123    3s
+## H  162   162                    21202.636805 19996.6237  5.69%   104    4s
+## H  286   286                    21166.904542 19996.6237  5.53%  69.2    4s
+## H  606   599                    20993.604430 19996.6237  4.75%  32.8    5s
+##    631    15 20993.6044  182 1965 20993.6044 20027.8276  4.60%  31.5   10s
+##    652     7 20993.6044  492 1964 20993.6044 20029.9069  4.59%  37.6   15s
+##    673    15 20091.4377   24 1974 20993.6044 20082.6816  4.34%  45.4   20s
+## H  750    81                    20939.026645 20082.6816  4.09%  61.7   24s
+##    818   151 21249.5497  111   22 20939.0266 20082.6816  4.09%  64.7   25s
+## H 1231   560                    20924.385117 20082.6816  4.02%  44.7   27s
+##   1308   639 20794.8335   63 1319 20924.3851 20084.4398  4.01%  57.3   30s
+## H 1975  1297                    20813.687049 20092.6890  3.46%  50.6   32s
+##   2454  1776 20457.8715   40 1754 20813.6870 20099.7124  3.43%  45.6   35s
+##   3179  2499 21128.9121   88  183 20813.6870 20109.8128  3.38%  46.0   40s
+##   4699  3645 20485.1487   37 1861 20813.6870 20148.3760  3.20%  38.3   45s
+##   5194  3776 20246.3125   28 1773 20813.6870 20155.9610  3.16%  40.3   50s
+##   6021  4504 20367.1172   32 1919 20813.6870 20167.5494  3.10%  40.7   55s
+##   6667  4755 20279.8697   29 1791 20813.6870 20193.4219  2.98%  42.1   60s
+##   7228  4711 20514.1843   33 1904 20813.6870 20195.9413  2.97%  43.7   65s
 ## 
 ## Cutting planes:
-##   Gomory: 3
+##   Gomory: 7
+##   Cover: 4
+##   MIR: 33
+##   StrongCG: 1
+##   Flow cover: 10
+##   GUB cover: 2
+##   Zero half: 22
+##   RLT: 24
 ## 
-## Explored 7 nodes (489 simplex iterations) in 0.08 seconds (0.10 work units)
+## Explored 7780 nodes (344017 simplex iterations) in 68.14 seconds (80.68 work units)
 ## Thread count was 1 (of 8 available processors)
 ## 
-## Solution count 5: 2604.74 2730.95 2790.87 ... 20287.2
+## Solution count 1000: 20813.7 20924.4 20939 ... 22439.4
 ## 
 ## Optimal solution found (tolerance 1.00e-01)
-## Best objective 2.604742604847e+03, best bound 2.375462328932e+03, gap 8.8024%
      
-
      # plot solution
-plot(s40, col = c("grey90", "darkgreen"), main = "Solution",
-     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
      
-
      
-
      We can plot this solution because the planning unit input data are spatially referenced in a raster format. The output format will always match the planning unit data used to initialize the problem. For example, the solution to a problem with planning units in a spatial vector (shapefile) format would also be in a spatial vector format. Similarly, if the planning units were in a tabular format (i.e. data.frame), the solution would also be returned in a tabular format.
      
-
      We can also extract attributes from the solution that describe the quality of the solution and the optimization process.
      
-
      # extract the objective (numerical value being minimized or maximized)
-print(attr(s40, "objective"))
      
-
      ## solution_1 
-##   2604.743
      
-
      # extract time spent solving solution
-print(attr(s40, "runtime"))
      
-
      ## solution_1 
-##      0.099
      
-
      # extract state message from the solver that describes why this specific
-# solution was returned
-print(attr(s40, "status"))
      
-
      ## solution_1 
-##  "OPTIMAL"
      
-
      
-
      
-
      Evaluate the performance of a solution
      
-
      After obtaining a solution to a conservation planning problem, it can be useful to calculate various summary statistics to understand its performance. The following functions are available to summarize a solution:
      
-
        
-
      • Calculate the number of planning units selected within a solution.
        • 
-
      
-
      # calculate statistic
-eval_n_summary(p40, s40)
      
-
      ## # A tibble: 1 × 2
-##   summary  cost
-##   <chr>   <dbl>
-## 1 overall    10
      
-
        
-
      • Calculate the total cost of a solution.
        • 
-
      
-
      # calculate statistic
-eval_cost_summary(p40, s40)
      
-
      ## # A tibble: 1 × 2
-##   summary  cost
-##   <chr>   <dbl>
-## 1 overall 2005.
      
-
        
-
      • Calculate how well features are represented by a solution. This function can be used for problems that are built using targets and those that are not built using targets.
        • 
-
      
-
      # calculate statistics
-eval_feature_representation_summary(p40, s40)
      
-
      ## # A tibble: 5 × 5
-##   summary feature total_amount absolute_held relative_held
-##   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-## 1 overall layer.1         83.3          8.95         0.107
-## 2 overall layer.2         31.2          3.22         0.103
-## 3 overall layer.3         72.0          7.59         0.106
-## 4 overall layer.4         42.7          4.34         0.102
-## 5 overall layer.5         56.7          5.89         0.104
      
-
        
-
      • Calculate how well feature representation targets are met by a solution. This function can only be used with problems contain targets.
        • 
-
      
-
      # calculate statistics
-eval_target_coverage_summary(p40, s40)
      
-
      ## # A tibble: 5 × 9
-##   feature met   total_amount absolute_target absolute_held absolute_shortfall
-##   <chr>   <lgl>        <dbl>           <dbl>         <dbl>              <dbl>
-## 1 layer.1 TRUE          83.3            8.33          8.95                  0
-## 2 layer.2 TRUE          31.2            3.12          3.22                  0
-## 3 layer.3 TRUE          72.0            7.20          7.59                  0
-## 4 layer.4 TRUE          42.7            4.27          4.34                  0
-## 5 layer.5 TRUE          56.7            5.67          5.89                  0
-##   relative_target relative_held relative_shortfall
-##             <dbl>         <dbl>              <dbl>
-## 1             0.1         0.107                  0
-## 2             0.1         0.103                  0
-## 3             0.1         0.106                  0
-## 4             0.1         0.102                  0
-## 5             0.1         0.104                  0
      
-
        
-
      • Calculate the exposed boundary length (perimeter) associated with a solution.
        • 
-
      
-
      # calculate statistic
-eval_boundary_summary(p40, s40)
      
-
      ## # A tibble: 1 × 2
-##   summary boundary
-##   <chr>      <dbl>
-## 1 overall      1.2
      
-
        
-
      • Calculate the connectivity held within a solution.
        • 
-
      
-
      # calculate statistic
-# here we use the raster data for the first feature as an example
-# to parametrize pair-wise connectivity between different planning units
-eval_connectivity_summary(
-  p40, s40, data = connectivity_matrix(sim_pu_raster, sim_features[[1]]))
      
-
      ## # A tibble: 1 × 2
-##   summary connectivity
-##   <chr>          <dbl>
-## 1 overall         1.97
      
-
      
-
      
-
      Marxan problems
      
-
      Although users are encouraged to build and tailor conservation planning problems to suit their own needs using the problem function, sometimes it just simply easier to use a more familiar formulation. The marxan_problem function is provided as a convenient wrapper for building and solving Marxan-style conservation problems. If users already have their conservation planning data formatted for use with Marxan, this function can also read Marxan data files and solve the Marxan-style problems using exact algorithm solvers. Please note that problems built using the marxan_problem function are still solved the same way as a problem initialized using the problem function, and therefore still require the installation of one of the solver packages.
      
-
      Here is a short example showing how the marxan_problem function can be used to read Marxan input files and the solve function can be used to solve the problem.
      
-
      # set file path for Marxan input file
-minput <- system.file("extdata/input.dat", package = "prioritizr")
-
-# read Marxan input file
-mp <- marxan_problem(minput)
-
-# print problem
-print(mp)
      
-
      ## Conservation Problem
-##   planning units: data.frame (1751 units)
-##   cost:           min: 0, max: 41569219.38232
-##   features:       bird1, nvis2, nvis8, ... (17 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.3, max: 0.3)]
-##   decisions:      default
-##   constraints:    <Locked in planning units [317 locked units]
-##                    Locked out planning units [1 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (1), zones]>
-##   portfolio:      default
-##   solver:         default
      
-
      # solve the problem
-ms <- solve(mp)
-
-# since the Marxan data was in a tabular format, the solution is also returned
-# in a tabular format, so we will print the first six rows of the table
-# containing the solution
-head(ms)
      
-
      Alternatively, rather then using a Marxan input file to construct the problem, we can manually read in the Marxan data files and input these to the marxan_problem function.
      
-
      # load data
-pu <- system.file("extdata/input/pu.dat", package = "prioritizr") %>%
-      read.table(sep = ",", header = TRUE)
-features <- system.file("extdata/input/spec.dat", package = "prioritizr") %>%
-            read.table(sep = ",", header = TRUE)
-bound <- system.file("extdata/input/bound.dat", package = "prioritizr") %>%
-         read.table(sep = "\t", header = TRUE)
-rij <- system.file("extdata/input/puvspr.dat", package = "prioritizr") %>%
-       read.table(sep = ",", header = TRUE)
-
-# build Marxan problem using data.frame objects
-mp2 <- marxan_problem(x = pu, spec = features, puvspr = rij, bound = bound,
-                      blm = 0)
-
-# print problem
-print(mp2)
      
+## Best objective 2.081368704941e+04, best bound 2.019762823706e+04, gap 2.9599%
      +
      print(prt)
      +
      ## class       : SpatialPolygonsDataFrame 
+## features    : 1130 
+## extent      : 298809.6, 613818.8, 5167775, 5502544  (xmin, xmax, ymin, ymax)
+## crs         : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
+## variables   : 1005
+## names       :   id,              cost, status, locked_in, locked_out, solution_1, solution_2, solution_3, solution_4, solution_5, solution_6, solution_7, solution_8, solution_9, solution_10, ... 
+## min values  :    1, 0.192488262910798,      0,         0,          0,          0,          0,          0,          0,          0,          0,          0,          0,          0,           0, ... 
+## max values  : 1130,  61.9272727272727,      2,         1,          0,          1,          1,          1,          1,          1,          1,          1,          1,          1,           1, ...
      +

      After generating all these prioritizations, we now want some way to visualize them. Because it would be onerous to look at each and every prioritization individually, we will use statistical analyses to help us. We can visualize the differences between these different prioritizations – based on which planning units they selected – using a hierarchical cluster analysis (Harris et al. 2014).

      +
      # extract solutions
+prt_results <- prt@data[, startsWith(names(prt), "solution_"), ]
+
+# calculate pair-wise distances between different prioritizations for analysis
+prt_dists <- vegan::vegdist(t(prt_results), method = "jaccard", binary = TRUE)
+
+# run cluster analysis
+prt_clust <- hclust(as.dist(prt_dists), method = "average")
+
+# visualize clusters
+opar <- par()
+par(oma = c(0, 0, 0, 0), mar= c(0, 4.1, 1.5, 2.1))
+plot(prt_clust, labels = FALSE, sub = NA, xlab = "",
+     main = "Different prioritizations in portfolio")
+suppressWarnings(par(opar))
      +

      +

      We can see that there are approximately six main groups of prioritizations in the portfolio. To explore these different groups, let’s conduct another cluster analysis (i.e., a k-medoids analysis) to extract the most representative prioritization from each of these groups. In other words, we will run another statistical analysis to find the most central prioritization within each group.

      +
      # run k-medoids analysis
+prt_med <- pam(prt_dists, k = 6)
+
+# extract names of prioritizations that are most central for each group.
+prt_med_names <- prt_med$medoids
+print(prt_med_names)
      +
      ## [1] "solution_29"  "solution_228" "solution_41"  "solution_242" "solution_663"
+## [6] "solution_447"
      +
      # create a copy of prt and set values for locked in planning units to -1
+# so we can easily visualize differences between prioritizations
+prt2 <- prt[, prt_med_names]
+prt2@data[which(tas_pu$locked_in > 0.5), prt_med_names] <- -1
+
+# plot a map showing main different prioritizations
+# dark grey: locked in planning units
+# grey: planning units not selected
+# green: selected planning units
+plot(st_as_sf(prt2), pal = c("grey60", "grey90", "darkgreen"))
      +

      +
      +
      +

      Marxan compatibility

      +

      The prioritizr R package provides functionality to help Marxan users generate prioritizations. Specifically, it can import conservation planning data prepared for Marxan, and can generate prioritizations using a similar problem formulation as Marxan (based on Beyer et al. 2016). Indeed, the problem formulation presented earlier in this vignette is very similar to that used by Marxan. The key difference is that the problem formulation we specified earlier uses “hard constraints” for feature representation, and Marxan uses “soft constraints” for feature representation. This means that prioritization we generated earlier was mathematically guaranteed to reach the targets for all features. However, if we used Marxan to generate the prioritization, then we could have produced a prioritization that would fail to reach targets (depending the Species Penalty Factors used to generate the prioritization). In addition to these differences in terms problem formulation, the prioritizr R package uses exact algorithms – instead of the simulated annealing algorithm – which ensures that we obtain prioritizations that are near optimal.

      +

      Here we will show the prioritizr R package can import Marxan data and generate a prioritization. To begin with, let’s import a conservation planning data prepared for Marxan.

      +
      # import data
+## planning unit data
+pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr")
+pu_data <- read.csv(pu_path, header = TRUE, stringsAsFactors = FALSE)
+print(head(pu_data))
      +
      ##   id       cost status    xloc     yloc
+## 1  3        0.0      0 1116623 -4493479
+## 2 30   752727.5      3 1110623 -4496943
+## 3 56  3734907.5      0 1092623 -4500408
+## 4 58  1695902.1      0 1116623 -4500408
+## 5 84  3422025.6      0 1098623 -4503872
+## 6 85 17890758.4      0 1110623 -4503872
      +
      ## feature data
+spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr")
+spec_data <- read.csv(spec_path, header = TRUE, stringsAsFactors = FALSE)
+print(head(spec_data))
      +
      ##   id prop spf   name
+## 1 10  0.3   1  bird1
+## 2 11  0.3   1  nvis2
+## 3 12  0.3   1  nvis8
+## 4 13  0.3   1  nvis9
+## 5 14  0.3   1 nvis14
+## 6 15  0.3   1 nvis20
      +
      ## amount of each feature within each planning unit data
+puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr")
+puvspr_data <- read.csv(puvspr_path, header = TRUE, stringsAsFactors = FALSE)
+print(head(puvspr_data))
      +
      ##   species  pu     amount
+## 1      26  56 1203448.84
+## 2      26  58  451670.10
+## 3      26  84  680473.75
+## 4      26  85   97356.24
+## 5      26  86   78034.76
+## 6      26 111 4783274.17
      +
      ## boundary data
+bound_path <- system.file("extdata/input/bound.dat", package = "prioritizr")
+bound_data <- read.table(bound_path, header = TRUE, stringsAsFactors = FALSE)
+print(head(bound_data))
      +
      ##   id1 id2 boundary
+## 1   3   3    16000
+## 2   3  30     4000
+## 3   3  58     4000
+## 4  30  30    12000
+## 5  30  58     4000
+## 6  30  85     4000
      +

      After importing the data, we can now generate a prioritization based on the Marxan problem formulation (using the marxan_problem() function). Please note that this function does not generate prioritizations using Marxan. Instead, it uses the data to create an optimization problem formulation similar to Marxan – using hard constraints instead of soft constraints – and uses an exact algorithm solver to generate a prioritization.

      +
      # create problem
+p2 <- marxan_problem(pu_data, spec_data, puvspr_data, bound_data,
+                     blm = 0.0005)
+
+# print problem
+print(p2)
      ## Conservation Problem
 ##   planning units: data.frame (1751 units)
 ##   cost:           min: 0, max: 41569219.38232
@@ -1514,167 +658,80 @@ 
      Marxan problems
      
 ##   objective:      Minimum set objective 
 ##   targets:        Relative targets [targets (min: 0.3, max: 0.3)]
 ##   decisions:      default
-##   constraints:    <Locked in planning units [317 locked units]
-##                    Locked out planning units [1 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (0), zones]>
+##   constraints:    <Locked out planning units [1 locked units]
+##                    Locked in planning units [317 locked units]>
+##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (5e-04), zones]>
 ##   portfolio:      default
 ##   solver:         default
      -
      -
      -

      Importance (irreplaceability)

      -

      Conservation plans can take a long time to implement. Since funding availability and habitat quality can decline over time, it is critical that the most important places in a prioritization are scheduled for protection as early as possible. For instance, some planning units in a solution might contain many rare species which do not occur in any other planning units. Alternatively, some planning units might offer an especially high return on investment that reduces costs considerably. As a consequence, conservation planners often need information on which planning units selected in a prioritization are most important to the overall success of the prioritization. To achieve this, conservation planners can use importance (irreplaceability) scores for each planning unit selected in a solution.

      -

      The prioritizr R package offers multiple methods for assessing importance. These includes scores calculated based on replacement costs [eval_replacement_importance(); Cabeza & Moilanen (2006)], Ferrier et al. (2000) (eval_ferrier_importance()), and rarity weighted richness scores [eval_rare_richness_importance(); Williams et al. (1996)]. The replacement cost scores quantify the change in the objective function (e.g. additional costs required to meet feature targets) of the optimal solution if a given planning unit in a solution cannot be acquired. They can (i) account for the cost of different planning units, (ii) account for multiple management zones, (iii) apply to any objective function, and (iv) identify truly irreplaceable planning units (denoted with infinite values). The Ferrier scores quantify the importance of planning units for meeting feature targets. They can only be applied to conservation problems with a minimum set objective and a single zone (i.e. the classic Marxan-type problem). Furthermore—unlike the replacement cost scores—the Ferrier scores provide a score for each feature within each planning unit, providing insight into why certain planning units are more important than other planning units. The rarity weighted richness scores are simply a measure of biological diversity. They do not account for planning costs, multiple management zones, objective functions, or feature targets (or weightings). They merely describe the spatial patterns of biodiversity, and do not account for many of the factors needed to quantify the importance of a planning unit for achieving conservation goals.

      -

      We recommend using replacement cost scores for small and moderate sized problems (e.g. less than 30,000 planning units) when it is feasible to do so. It can take a very long time to compute replacement cost scores, and so it is simply not feasible to compute these scores for particularly large problems. For moderate and large sized problems (e.g. more than 30,000 planning units), we recommend using the Ferrier method. This is because it explicitly accounts for representation targets, unlike the rarity weighted richness scores.

      -

      Below we will generate a solution, and then calculate importance scores for the planning units selected in the solution using the three different methods.

      -
      # formulate the problem
-p41 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions()
-
-# solve the problem
-s41 <- solve(p41)
      +
      # solve problem
+s2 <- solve(p2)
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
 ## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 5 rows, 90 columns and 450 nonzeros
-## Model fingerprint: 0x6442bf6e
-## Variable types: 0 continuous, 90 integer (90 binary)
+## Optimize a model with 10075 rows, 6780 columns and 24778 nonzeros
+## Model fingerprint: 0x2652a1c2
+## Variable types: 0 continuous, 6780 integer (6780 binary)
 ## Coefficient statistics:
-##   Matrix range     [2e-01, 9e-01]
-##   Objective range  [2e+02, 2e+02]
+##   Matrix range     [5e-01, 4e+07]
+##   Objective range  [4e+00, 4e+07]
 ##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [3e+00, 8e+00]
-## Found heuristic solution: objective 2337.9617505
-## Presolve time: 0.00s
-## Presolved: 5 rows, 90 columns, 450 nonzeros
-## Variable types: 0 continuous, 90 integer (90 binary)
-## Found heuristic solution: objective 2332.1003790
-## Root relaxation presolved: 5 rows, 90 columns, 450 nonzeros
+##   RHS range        [5e+07, 3e+09]
+## Warning: Model contains large rhs
+##          Consider reformulating model or setting NumericFocus parameter
+##          to avoid numerical issues.
+## Found heuristic solution: objective 1.221185e+10
+## Presolve removed 4707 rows and 3103 columns
+## Presolve time: 0.04s
+## Presolved: 5368 rows, 3677 columns, 12704 nonzeros
+## Variable types: 0 continuous, 3677 integer (3677 binary)
+## Found heuristic solution: objective 1.009922e+10
+## Root relaxation presolved: 5368 rows, 3677 columns, 12704 nonzeros
 ## 
 ## 
-## Root relaxation: objective 1.931582e+03, 12 iterations, 0.00 seconds (0.00 work units)
+## Root relaxation: objective 9.564577e+09, 493 iterations, 0.01 seconds (0.01 work units)
 ## 
 ##     Nodes    |    Current Node    |     Objective Bounds      |     Work
 ##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
 ## 
-##      0     0 1931.58191    0    4 2332.10038 1931.58191  17.2%     -    0s
-## H    0     0                    1987.3985265 1931.58191  2.81%     -    0s
+##      0     0 9.5646e+09    0   20 1.0099e+10 9.5646e+09  5.29%     -    0s
 ## 
-## Explored 1 nodes (12 simplex iterations) in 0.00 seconds (0.00 work units)
+## Explored 1 nodes (493 simplex iterations) in 0.06 seconds (0.10 work units)
 ## Thread count was 1 (of 8 available processors)
 ## 
-## Solution count 3: 1987.4 2332.1 2337.96 
+## Solution count 2: 1.00992e+10 1.22118e+10 
 ## 
 ## Optimal solution found (tolerance 1.00e-01)
-## Best objective 1.987398526526e+03, best bound 1.931581908865e+03, gap 2.8085%
      -
      # plot solution
-plot(s41, col = c("grey90", "darkgreen"), main = "Solution",
-     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
      -

      -
      # calculate replacement cost scores and make the solver quiet
-rc41 <- p41 %>%
-        add_default_solver(gap = 0, verbose = FALSE) %>%
-        eval_replacement_importance(s41)
-
-# plot replacement cost scores
-plot(rc41, main = "replacement cost")
      -

      -
      # calculate Ferrier scores and extract total score
-fs41 <- eval_ferrier_importance(p40, s40)[["total"]]
-
-# plot Ferrier scores
-plot(fs41, main = "Ferrier scores")
      -

      -
      # calculate rarity weighted richness scores
-rwr41 <- eval_rare_richness_importance(p40, s40)
-
-# plot replacement cost scores
-plot(rwr41, main = "rarity weighted richness")
      -

      -

      Although rarity weighted richness scores can approximate scores derived from the other two methods in certain conservation planning exercises, we can see that the rarity weighted richness scores provide completely different results in this case.

      -
      +## Best objective 1.009922392231e+10, best bound 9.564577117609e+09, gap 5.2939%       +
      # print first six rows of solution object
+print(head(s2))
      +
      ##   id       cost status    xloc     yloc locked_in locked_out solution_1
+## 1  3        0.0      0 1116623 -4493479     FALSE      FALSE          0
+## 2 30   752727.5      3 1110623 -4496943     FALSE       TRUE          0
+## 3 56  3734907.5      0 1092623 -4500408     FALSE      FALSE          0
+## 4 58  1695902.1      0 1116623 -4500408     FALSE      FALSE          0
+## 5 84  3422025.6      0 1098623 -4503872     FALSE      FALSE          0
+## 6 85 17890758.4      0 1110623 -4503872     FALSE      FALSE          0

      Conclusion

      -

      Hopefully, this vignette has provided an informative introduction to the prioritizr R package. For more worked examples using the prioritizr R package, check out the Tasmania and Salt Spring Island vignettes. Perhaps, one of the best ways to learn a new piece of software is to just try it out. Test it, try breaking it, make mistakes, and learn from them. We would recommend trying to build conservation planning problems that resemble those you face in your own work—but using the built-in example data sets. This way you can quickly verify that the problems you build actually mean what you think they mean. For instance, you can try playing around with the targets and see what effect they have on the solutions, or try playing around with penalties and see what effect they have on the solutions. Finally, if you have any questions about using the prioritizr R package or suggestions for it, please file an issue on the package’s online coding repository (https://github.com/prioritizr/prioritizr/issues).

      +

      This tutorial shows how the prioritizr R package can be used to build a conservation problem, generate a prioritization, and evaluate it. Although we explored just a few functions, the package provides many different functions so that you can build and custom-tailor conservation planning problems to suit your needs. To learn more about the package, please see the package vignettes for an overview of the package, instructions for installing the Gurobi optimization suite, benchmarks comparing the performance of different solvers, and a record of publications that have cited the package. In addition to this tutorial, the package also provides tutorials on incorporating connectivity into prioritizations, calibrating trade-offs between different criteria (e.g., total cost and spatial fragmentation), and creating prioritizations that have multiple management zones or management actions.

      References

      -
      -Achterberg, T. & Wunderling, R. (2013). Mixed Integer Programming: Analyzing 12 Years of Progress. Facets of combinatorial optimization: Festschrift for martin grötschel (eds M. Jünger & G. Reinelt), pp. 449–481. Springer, Berlin, Heidelberg. -
      Ball, I.R., Possingham, H. & Watts, M.E. (2009). Marxan and relatives: Software for spatial conservation prioritisation. Spatial Conservation Prioritisation: Quantitative Methods & Computational Tools (eds A. Moilanen, K.A. Wilson & H. Possingham), pp. 185–189. Oxford University Press, Oxford, UK.
      Beyer, H.L., Dujardin, Y., Watts, M.E. & Possingham, H.P. (2016). Solving conservation planning problems with integer linear programming. Ecological Modelling, 328, 14–22.
      -
      -Billionnet, A. (2013). Mathematical optimization ideas for biodiversity conservation. European Journal of Operational Research, 231, 514–534. -
      -
      -Butchart, S.H., Clarke, M., Smith, R.J., Sykes, R.E., Scharlemann, J.P., Harfoot, M., Buchanan, G.M., Angulo, A., Balmford, A., Bertzky, B. & others. (2015). Shortfalls and solutions for meeting national and global conservation area targets. Conservation Letters, 8, 329–337. -
      -
      -Cabeza, M. & Moilanen, A. (2001). Design of reserve networks and the persistence of biodiversity. Trends in Ecology & Evolution, 16, 242–248. -
      -
      -Cabeza, M. & Moilanen, A. (2006). Replacement cost: A practical measure of site value for cost-effective reserve planning. Biological Conservation, 132, 336–342. -
      -
      -Church, R.L., Stoms, D.M. & Davis, F.W. (1996). Reserve selection as a maximal covering location problem. Biological conservation, 76, 105–112. -
      -
      -Faith, D.P. (1992). Conservation evaluation and phylogenetic diversity. Biological Conservation, 61, 1–10. -
      Ferrier, S., Pressey, R.L. & Barrett, T.W. (2000). A new predictor of the irreplaceability of areas for achieving a conservation goal, its application to real-world planning, and a research agenda for further refinement. Biological Conservation, 93, 303–325.
      -
      -Fuller, R.A., McDonald-Madden, E., Wilson, K.A., Carwardine, J., Grantham, H.S., Watson, J.E., Klein, C.J., Green, D.C. & Possingham, H.P. (2010). Replacing underperforming protected areas achieves better conservation outcomes. Nature, 466, 365. -
      -
      -Kirkpatrick, J.B. (1983). An iterative method for establishing priorities for the selection of nature reserves: An example from Tasmania. Biological Conservation, 25, 127–134. -
      -
      -Kirkpatrick, S., Gelatt, C.D. & Vecchi, M.P. (1983). Optimization by simulated annealing. Science, 220, 671–680. -
      -
      -Klein, C., Wilson, K., Watts, M., Stein, J., Berry, S., Carwardine, J., Smith, M.S., Mackey, B. & Possingham, H. (2009). Incorporating ecological and evolutionary processes into continental-scale conservation planning. Ecological Applications, 19, 206–217. -
      -
      -Margules, C.R. & Pressey, R.L. (2000). Systematic conservation planning. Nature, 405, 243–253. -
      -
      -Moilanen, A. (2007). Landscape Zonation, benefit functions and target-based planning: Unifying reserve selection strategies. Biological Conservation, 134, 571–579. -
      -
      -Nicholls, A.O. & Margules, C.R. (1993). An upgraded reserve selection algorithm. Biological Conservation, 64, 165–169. -
      -
      -Pressey, R.L., Possingham, H.P. & Margules, C.R. (1996). Optimality in reserve selection algorithms: When does it matter and how much? Biological Conservation, 76, 259–267. -
      -
      -Rodrigues, A.S., Akcakaya, H.R., Andelman, S.J., Bakarr, M.I., Boitani, L., Brooks, T.M., Chanson, J.S., Fishpool, L.D., Da Fonseca, G.A., Gaston, K.J. & others. (2004). Global gap analysis: Priority regions for expanding the global protected-area network. BioScience, 54, 1092–1100. -
      -
      -Rodrigues, A.S. & Gaston, K.J. (2002). Maximising phylogenetic diversity in the selection of networks of conservation areas. Biological Conservation, 105, 103–111. -
      -
      -Rodrigues, A.S., Orestes Cerdeira, J. & Gaston, K.J. (2000). Flexibility, efficiency, and accountability: Adapting reserve selection algorithms to more complex conservation problems. Ecography, 23, 565–574. -
      -
      -Rosauer, D., Laffan, S.W., Crisp, M.D., Donnellan, S.C. & Cook, L.G. (2009). Phylogenetic endemism: A new approach for identifying geographical concentrations of evolutionary history. Molecular Ecology, 18, 4061–4072. -
      -
      -Stigner, M.G., Beyer, H.L., Klein, C.J. & Fuller, R.A. (2016). Reconciling recreational use and conservation values in a coastal protected area. Journal of Applied Ecology, 53, 1206–1214. -
      -
      -Watts, M.E., Ball, I.R., Stewart, R.S., Klein, C.J., Wilson, K., Steinback, C., Lourival, R., Kircher, L. & Possingham, H.P. (2009). Marxan with Zones: Software for optimal conservation based land- and sea-use zoning. Environmental Modelling & Software, 24, 1513–1521. +
      +Harris, L.R., Watts, M.E., Nel, R., Schoeman, D.S. & Possingham, H.P. (2014). Using multivariate statistics to explore trade-offs among spatial planning scenarios (P. Armsworth, Ed.). Journal of Applied Ecology, 51, 1504–1514.
      -
      -Williams, P., Gibbons, D., Margules, C., Rebelo, A., Humphries, C. & Pressey, R. (1996). A comparison of richness hotspots, rarity hotspots, and complementary areas for conserving diversity of British birds. Conservation Biology, 10, 155–174. +
      +Klein, C., Carwardine, J., Wilson, K., Watts, M. & Possingham, H. (2007). Spatial Prioritization Approaches for the Conservation of Biodiversity in Australia: Considering Conservation Costs, Ecological & Evolutionary Processes, and Large-Intact Areas. Report to the Department of Environment; Water Resources.
      diff --git a/inst/doc/publication_record.Rmd b/inst/doc/publication_record.Rmd index 7768b00fc..f7ca8b88d 100644 --- a/inst/doc/publication_record.Rmd +++ b/inst/doc/publication_record.Rmd @@ -1,5 +1,5 @@ --- -title: "Publication Record" +title: "Publication record" output: rmarkdown::html_vignette: toc: true @@ -8,7 +8,7 @@ output: fontsize: 11pt documentclass: article vignette: > - %\VignetteIndexEntry{Publication Record} + %\VignetteIndexEntry{Publication record} %\VignetteEngine{knitr::rmarkdown_notangle} --- diff --git a/inst/doc/publication_record.html b/inst/doc/publication_record.html index 624dc224f..28a637e22 100644 --- a/inst/doc/publication_record.html +++ b/inst/doc/publication_record.html @@ -12,7 +12,7 @@ -Publication Record +Publication record @@ -42,7 +42,7 @@ -

      Publication Record

      +

      Publication record

      diff --git a/inst/doc/saltspring.Rmd b/inst/doc/saltspring.Rmd deleted file mode 100644 index 91284e3d2..000000000 --- a/inst/doc/saltspring.Rmd +++ /dev/null @@ -1,212 +0,0 @@ ---- -title: "Salt Spring Island Tutorial" -output: - rmarkdown::html_vignette: - toc: true - fig_caption: true - self_contained: yes -fontsize: 11pt -documentclass: article -bibliography: references.bib -csl: reference-style.csl -vignette: > - %\VignetteIndexEntry{Salt Spring Island Tutorial} - %\VignetteEngine{knitr::rmarkdown_notangle} ---- - -```{r, include = FALSE} -h <- 3.5 -w <- 3.5 -is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_", - "_R_CHECK_LICENSE_") %in% names(Sys.getenv())) -knitr::opts_chunk$set(fig.align = "center", eval = !is_check) -``` - -## Introduction - -This aim of this tutorial is to show how raster data can used to build conservation problems with the _prioritizr R_ package. The data used here is a subset of a much larger dataset for the Georgia Basin obtained as part of an online _Marxan_-based planning tool created for the Coastal Douglas-fir Conservation Partnership [CDFCP; @r29]. For simplicity, we focus only on Salt Spring Island, British Columbia. Salt Spring Island is central to the region and supports a diverse and globally unique mix of dry forest and savanna habitats. Today, these habitats are critically threatened due to land conversion, invasive species, and altered disturbance regimes. Known broadly as the Georgia Depression-Puget Lowlands, this region includes threatened Coastal Douglas-fir forest and Oak-Savannah habitats, also referred to as Garry oak ecosystems. Please note that this tutorial uses data from the _prioritizrdata R_ package, so ensure that it is installed before trying out the code yourself. For more information on the dataset refer to the [Marxan tool portal](https://arcese.forestry.ubc.ca/marxan-tool/) and the [tool tutorial](https://peter-arcese-lab.sites.olt.ubc.ca/files/2016/09/CDFCP_tutorial_2017_05.pdf). - -
      - -![_Extent of Coastal Douglas-fir Conservation Partnership Tool area and location of Salt Spring Island_](figures/map.jpg) - -
      - -## Exploring the data - -This dataset contains two items. First, a single-band raster planning unit layer where each one hectare pixel represents a planning unit and contains its corresponding cost [@r28]. Second, a raster stack containing ecological community feature data. Field and remote sensed data were used to calculate the probability of occurrence of five key ecological communities found on Salt Spring island. Each layer in the stack represents a different community type. In order these are; Old Forest, Savannah, Wetland, Shrub, and a layer representing the inverse probability of occurrence of human commensal species. For a given layer, the cell value indicates the composite probability of encountering the suite of bird species most commonly associated with that community type. - -First, load the required packages and the data. - -```{r, message = FALSE} -# load packages -library(prioritizrdata) -library(prioritizr) - -# load planning unit data -data(salt_pu) - -# load conservation feature data -data(salt_features) -``` - -Let's have a look at the planning unit data. Note that we log-transformed the raster to better visualize the variation in planning unit cost. - -```{r, fig.width = w, fig.height = h} -# print planning unit data -print(salt_pu) - -# plot histogram of the planning unit costs -hist(values(salt_pu), main = "Distribution of costs", - xlab = "Planning unit costs") -``` - -```{r, fig.width = w, fig.height = h} -# plot map showing the planning units costs on a log-scale -plot(log(salt_pu), main = "Planning unit costs (log)") -``` - -Next, let's look at the feature data. - -```{r, fig.width = 4.5, fig.height = 4.5} -# print features -print(salt_features) - -# plot map showing the distribution of the features -plot(salt_features, main = names(salt_features)) -``` - -## Formulating the Problem - -In this tutorial, we will only cover a few of the different ways that conservation planning problems can be formulated. The examples used here are provided to highlight how different parameters can substantially---or only slightly---alter solutions. Here, we use the minimum set objective to fulfill all targets and constraints for the smallest cost. This objective is similar to that used in the _Marxan_ decision support tool. To keep this simple, we will set biodiversity targets at 17 % to reflect the [Aichi Biodiversity Target 11](https://www.cbd.int/sp/targets/). Because properties on Salt Spring Island can either be acquired in their entirety or not at all, we leave the decision framework as the default; binary decision making. This means that planning units are either selected in the solution or not selected in the solution---planning units cannot be partially acquired. - -Now we will formulate the conservation planning problem. - -```{r} -# create problem -p1 <- problem(salt_pu, salt_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.17) %>% - add_binary_decisions() %>% - add_default_solver() - -# print problem -print(p1) -``` - -Note that the `%>%` notation is used to attach the objectives, targets, and decisions to the problem. Since binary-type decisions are the default decision-type, we don't have to explicitly specify the decision-type, but we specify it here for clarity. - -## Solving the problem - -The _prioritizr R_ package supports three different integer linear programming solvers: _gurobi_ (via the _gurobi_ package), _IBM CPLEX_ (via the _cplexAPI_ package), _SYMPHONY_ (via the _Rsymphony_ and _lpsymphony_ packages) and _CBC_ (via the _rcbc_ package). There are costs and benefits associated with each of these solvers, but the solver itself should have little impact on the actual solution returned (though certain solvers may take longer to return solutions than others). - -First, remember that the solvers must be installed. You can check if these packages are installed by running the code below. Some of these solvers are a bit complicated to install. For instance, the _gurobi_ package is distributed with the [_Gurobi_ commercial software suite](https://www.gurobi.com/) and is not available on the Comprehensive R Archive Network (CRAN). For more information on installing the _gurobi_ package, please refer to the [_Gurobi Installation Guide_](gurobi_installation.html) for more information on installing the _gurobi R_ package. Additionally, the _rcbc_ package is not available on CRAN, and must be installed from GitHub ([please refer to its documentation for installation instructions](https://dirkschumacher.github.io/rcbc/). Furthermore, although the _Rcplex_ package is available on CRAN, it cannot be successfully installed unless the [IBM CPLEX software](https://www.ibm.com/analytics/cplex-optimizer) has [already installed on your system](https://github.com/cran/cplexAPI/blob/master/inst/INSTALL). - -```{r, eval = FALSE} -print(require(gurobi)) -print(require(cplexAPI)) -print(require(Rsymphony)) -print(require(lpsymphony)) -print(require(rcbc)) -``` - -Now we will try solving the problem using the different solvers (see [`?solve`](https://prioritizr.net/reference/solve.html) for more information). We will also experiment with limiting the maximum amount of time that can be spent looking for each solution when solving the problem (using the `time_limit` parameter), and see how this alters the solutions. - -```{r, message = FALSE, results = "hide"} -titles <- c() # create vector to store plot titles -s1 <- stack() # create empty stack to store solutions - -# create new problem object with added solver -if (require("Rsymphony")) { - titles <- c(titles, "Rsymphony (5s)") - p2 <- p1 %>% add_rsymphony_solver(time_limit = 5) - s1 <- addLayer(s1, solve(p2)) -} - -if (require("Rsymphony")) { - titles <- c(titles, "Rsymphony (10s)") - p3 <- p1 %>% add_rsymphony_solver(time_limit = 10) - s1 <- addLayer(s1, solve(p3)) -} - -if (require("gurobi")) { - titles <- c(titles, "Gurobi (5s)") - p4 <- p1 %>% add_gurobi_solver(time_limit = 5) - s1 <- addLayer(s1, solve(p4)) -} - -if (require("cplexAPI")) { - titles <- c(titles, "IBM CPLEX (5s)") - p5 <- p1 %>% add_cplex_solver(time_limit = 5) - s1 <- addLayer(s1, solve(p5)) -} - -if (require("lpsymphony")) { - titles <- c(titles, "lpsymphony (10s)") - p6 <- p1 %>% add_lpsymphony_solver(time_limit = 10) - s1 <- addLayer(s1, solve(p6)) -} - -if (require("rcbc")) { - titles <- c(titles, "CBC (10s)") - p7 <- p1 %>% add_cbc_solver(time_limit = 10) - s1 <- addLayer(s1, solve(p7)) -} -``` - -Now let's visualize the solutions. - -```{r, fig.height = 5.5, fig.width = 5} -plot(s1, main = titles, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")) -``` - -We can see that all of the solutions are very similar. Therefore it would appear that for this particular problem, the solution is not highly sensitive to solver choice. For larger and more complex problems, however, we would expect the solution from _Gurobi_ to be far superior when setting time limits. At a glance, it also appears that the time limit settings did not largely impact the solutions (5 seconds vs. 10 seconds), but a more rigorous analysis is needed to investigate this. - -## Adding connectivity - -Isolated and fragmented populations are often more vulnerable to extinction. As a consequence, landscape connectivity is a key focus of many conservation planning exercises. There are a number of methods that can be used to increase connectivity in prioritizations. These methods typically involve adding constraints to a problem to ensure that solutions exhibit a specific property (e.g. selected planning units that form a contiguous reserve), or adding penalties to a problem to penalize solutions that exhibit specific properties (e.g. high levels of fragmentation). Here we will explore a couple different strategies for increasing connectivity in solutions. For brevity, we will use default solver which is automatically added to a problem if a solver is not manually specified. - -```{r} -# basic problem formulation -p6 <- problem(salt_pu, salt_features) %>% - add_min_set_objective() %>% - add_relative_targets(0.17) %>% - add_binary_decisions() %>% - add_default_solver() - -# print problem -print(p6) -``` - -```{r, results = "hide"} -titles2 <- c() # create vector to store plot titles -s2 <- stack() # create empty stack to store solutions - -# no connectivity requirement -titles2 <- c(titles2, "No connectivity") -s2 <- addLayer(s2, solve(p6)) - -# require at least two for each selected planning unit -titles2 <- c(titles2, "Neighbor constraints (two)") -p7 <- p6 %>% add_neighbor_constraints(2) -s2 <- addLayer(s2, solve(p7)) - -# impose small penalty for fragmented solutions -titles2 <- c(titles2, "Boundary penalty (low)") -p8 <- p6 %>% add_boundary_penalties(0.0005, 0.5) -s2 <- addLayer(s2, solve(p8)) - -# impose high penalty for fragmented solutions -titles2 <- c(titles2, "Boundary penalty (high)") -p9 <- p6 %>% add_boundary_penalties(0.05, 0.5) -s2 <- addLayer(s2, solve(p9)) -``` - -```{r, fig.height = 5.5, fig.width = 5} -# plot solutions -plot(s2, main = titles2, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")) -``` - -Here we can see that adding the constraints and penalties to the problem has a small, but noticeable effect on the solutions. We would expect to see larger difference between the solutions for problems that contain more than five conservation features. You may also wish to explore the `add_connectivity_penalties` and `add_feature_contiguity_constraints` functions. These functions use additional data on landscape resistance to provide a more accurate parametrization of connectivity and, in turn, deliver more effective solutions. - -## References diff --git a/inst/doc/saltspring.html b/inst/doc/saltspring.html deleted file mode 100644 index 02c199cd5..000000000 --- a/inst/doc/saltspring.html +++ /dev/null @@ -1,390 +0,0 @@ - - - - - - - - - - - - - - -Salt Spring Island Tutorial - - - - - - - - - - - - - - - - - - - - - - - - - - -

      Salt Spring Island Tutorial

      - - - - -
      -

      Introduction

      -

      This aim of this tutorial is to show how raster data can used to build conservation problems with the prioritizr R package. The data used here is a subset of a much larger dataset for the Georgia Basin obtained as part of an online Marxan-based planning tool created for the Coastal Douglas-fir Conservation Partnership [CDFCP; Morrell et al. (2017)]. For simplicity, we focus only on Salt Spring Island, British Columbia. Salt Spring Island is central to the region and supports a diverse and globally unique mix of dry forest and savanna habitats. Today, these habitats are critically threatened due to land conversion, invasive species, and altered disturbance regimes. Known broadly as the Georgia Depression-Puget Lowlands, this region includes threatened Coastal Douglas-fir forest and Oak-Savannah habitats, also referred to as Garry oak ecosystems. Please note that this tutorial uses data from the prioritizrdata R package, so ensure that it is installed before trying out the code yourself. For more information on the dataset refer to the Marxan tool portal and the tool tutorial.

      -
      -
      - -

      Extent of Coastal Douglas-fir Conservation Partnership Tool area and location of Salt Spring Island

      -
      -
      -
      -
      -

      Exploring the data

      -

      This dataset contains two items. First, a single-band raster planning unit layer where each one hectare pixel represents a planning unit and contains its corresponding cost (BC Assessment 2015). Second, a raster stack containing ecological community feature data. Field and remote sensed data were used to calculate the probability of occurrence of five key ecological communities found on Salt Spring island. Each layer in the stack represents a different community type. In order these are; Old Forest, Savannah, Wetland, Shrub, and a layer representing the inverse probability of occurrence of human commensal species. For a given layer, the cell value indicates the composite probability of encountering the suite of bird species most commonly associated with that community type.

      -

      First, load the required packages and the data.

      -
      # load packages
-library(prioritizrdata)
-library(prioritizr)
-
-# load planning unit data
-data(salt_pu)
-
-# load conservation feature data
-data(salt_features)
      -

      Let’s have a look at the planning unit data. Note that we log-transformed the raster to better visualize the variation in planning unit cost.

      -
      # print planning unit data
-print(salt_pu)
      -
      ## class      : RasterLayer 
-## dimensions : 280, 200, 56000  (nrow, ncol, ncell)
-## resolution : 100, 100  (x, y)
-## extent     : 454589.9, 474589.9, 5394614, 5422614  (xmin, xmax, ymin, ymax)
-## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
-## source     : memory
-## names      : salt_pu 
-## values     : 0.02552, 10000  (min, max)
      -
      # plot histogram of the planning unit costs
-hist(values(salt_pu), main = "Distribution of costs",
-     xlab = "Planning unit costs")
      -

      -
      # plot map showing the planning units costs on a log-scale
-plot(log(salt_pu), main = "Planning unit costs (log)")
      -

      -

      Next, let’s look at the feature data.

      -
      # print features
-print(salt_features)
      -
      ## class      : RasterStack 
-## dimensions : 280, 200, 56000, 5  (nrow, ncol, ncell, nlayers)
-## resolution : 100, 100  (x, y)
-## extent     : 454589.9, 474589.9, 5394614, 5422614  (xmin, xmax, ymin, ymax)
-## crs        : +proj=utm +zone=10 +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
-## names      : salt_features.1, salt_features.2, salt_features.3, salt_features.4, salt_features.5 
-## min values :       0.3595050,       0.2979212,       0.1132785,       0.4013101,       0.3703639 
-## max values :       0.9312289,       0.6608167,       0.6434712,       0.8249719,       0.9032656
      -
      # plot map showing the distribution of the features
-plot(salt_features, main = names(salt_features))
      -

      -
      -
      -

      Formulating the Problem

      -

      In this tutorial, we will only cover a few of the different ways that conservation planning problems can be formulated. The examples used here are provided to highlight how different parameters can substantially—or only slightly—alter solutions. Here, we use the minimum set objective to fulfill all targets and constraints for the smallest cost. This objective is similar to that used in the Marxan decision support tool. To keep this simple, we will set biodiversity targets at 17 % to reflect the Aichi Biodiversity Target 11. Because properties on Salt Spring Island can either be acquired in their entirety or not at all, we leave the decision framework as the default; binary decision making. This means that planning units are either selected in the solution or not selected in the solution—planning units cannot be partially acquired.

      -

      Now we will formulate the conservation planning problem.

      -
      # create problem
-p1 <- problem(salt_pu, salt_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_binary_decisions() %>%
-      add_default_solver()
-
-# print problem
-print(p1)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (19794 units)
-##   cost:           min: 0.02552, max: 10000
-##   features:       salt_features.1, salt_features.2, salt_features.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (1)]
      -

      Note that the %>% notation is used to attach the objectives, targets, and decisions to the problem. Since binary-type decisions are the default decision-type, we don’t have to explicitly specify the decision-type, but we specify it here for clarity.

      -
      -
      -

      Solving the problem

      -

      The prioritizr R package supports three different integer linear programming solvers: gurobi (via the gurobi package), IBM CPLEX (via the cplexAPI package), SYMPHONY (via the Rsymphony and lpsymphony packages) and CBC (via the rcbc package). There are costs and benefits associated with each of these solvers, but the solver itself should have little impact on the actual solution returned (though certain solvers may take longer to return solutions than others).

      -

      First, remember that the solvers must be installed. You can check if these packages are installed by running the code below. Some of these solvers are a bit complicated to install. For instance, the gurobi package is distributed with the Gurobi commercial software suite and is not available on the Comprehensive R Archive Network (CRAN). For more information on installing the gurobi package, please refer to the Gurobi Installation Guide for more information on installing the gurobi R package. Additionally, the rcbc package is not available on CRAN, and must be installed from GitHub (please refer to its documentation for installation instructions. Furthermore, although the Rcplex package is available on CRAN, it cannot be successfully installed unless the IBM CPLEX software has already installed on your system.

      -
      print(require(gurobi))
-print(require(cplexAPI))
-print(require(Rsymphony))
-print(require(lpsymphony))
-print(require(rcbc))
      -

      Now we will try solving the problem using the different solvers (see ?solve for more information). We will also experiment with limiting the maximum amount of time that can be spent looking for each solution when solving the problem (using the time_limit parameter), and see how this alters the solutions.

      -
      titles <- c() # create vector to store plot titles
-s1 <- stack()  # create empty stack to store solutions
-
-# create new problem object with added solver
-if (require("Rsymphony")) {
-  titles <- c(titles, "Rsymphony (5s)")
-  p2 <- p1 %>% add_rsymphony_solver(time_limit = 5)
-  s1 <- addLayer(s1, solve(p2))
-}
      -
      ## Warning in res(x, ...): overwriting previously defined solver
      -
      if (require("Rsymphony")) {
-  titles <- c(titles, "Rsymphony (10s)")
-  p3 <- p1 %>% add_rsymphony_solver(time_limit = 10)
-  s1 <- addLayer(s1, solve(p3))
-}
      -
      ## Warning in res(x, ...): overwriting previously defined solver
      -
      if (require("gurobi")) {
-  titles <- c(titles, "Gurobi (5s)")
-  p4 <- p1 %>% add_gurobi_solver(time_limit = 5)
-  s1 <- addLayer(s1, solve(p4))
-}
      -
      ## Warning in res(x, ...): overwriting previously defined solver
      -
      if (require("cplexAPI")) {
-  titles <- c(titles, "IBM CPLEX (5s)")
-  p5 <- p1 %>% add_cplex_solver(time_limit = 5)
-  s1 <- addLayer(s1, solve(p5))
-}
      -
      ## Warning in res(x, ...): overwriting previously defined solver
      -
      if (require("lpsymphony")) {
-  titles <- c(titles, "lpsymphony (10s)")
-  p6 <- p1 %>% add_lpsymphony_solver(time_limit = 10)
-  s1 <- addLayer(s1, solve(p6))
-}
      -
      ## Warning in res(x, ...): overwriting previously defined solver
      -
      if (require("rcbc")) {
-  titles <- c(titles, "CBC (10s)")
-  p7 <- p1 %>% add_cbc_solver(time_limit = 10)
-  s1 <- addLayer(s1, solve(p7))
-}
      -
      ## Warning in res(x, ...): overwriting previously defined solver
      -

      Now let’s visualize the solutions.

      -
      plot(s1, main = titles, breaks = c(0, 0.5, 1),  col = c("grey70", "darkgreen"))
      -

      -

      We can see that all of the solutions are very similar. Therefore it would appear that for this particular problem, the solution is not highly sensitive to solver choice. For larger and more complex problems, however, we would expect the solution from Gurobi to be far superior when setting time limits. At a glance, it also appears that the time limit settings did not largely impact the solutions (5 seconds vs. 10 seconds), but a more rigorous analysis is needed to investigate this.

      -
      -
      -

      Adding connectivity

      -

      Isolated and fragmented populations are often more vulnerable to extinction. As a consequence, landscape connectivity is a key focus of many conservation planning exercises. There are a number of methods that can be used to increase connectivity in prioritizations. These methods typically involve adding constraints to a problem to ensure that solutions exhibit a specific property (e.g. selected planning units that form a contiguous reserve), or adding penalties to a problem to penalize solutions that exhibit specific properties (e.g. high levels of fragmentation). Here we will explore a couple different strategies for increasing connectivity in solutions. For brevity, we will use default solver which is automatically added to a problem if a solver is not manually specified.

      -
      # basic problem formulation
-p6 <- problem(salt_pu, salt_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_binary_decisions() %>%
-      add_default_solver()
-
-# print problem
-print(p6)
      -
      ## Conservation Problem
-##   planning units: RasterLayer (19794 units)
-##   cost:           min: 0.02552, max: 10000
-##   features:       salt_features.1, salt_features.2, salt_features.3, ... (5 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      Binary decision 
-##   constraints:    <none>
-##   penalties:      <none>
-##   portfolio:      default
-##   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (1)]
      -
      titles2 <- c() # create vector to store plot titles
-s2 <- stack()  # create empty stack to store solutions
-
-# no connectivity requirement
-titles2 <- c(titles2, "No connectivity")
-s2 <- addLayer(s2, solve(p6))
-
-# require at least two for each selected planning unit
-titles2 <- c(titles2, "Neighbor constraints (two)")
-p7 <- p6 %>% add_neighbor_constraints(2)
-s2 <- addLayer(s2, solve(p7))
-
-# impose small penalty for fragmented solutions
-titles2 <- c(titles2, "Boundary penalty (low)")
-p8 <- p6 %>% add_boundary_penalties(0.0005, 0.5)
-s2 <- addLayer(s2, solve(p8))
-
-# impose high penalty for fragmented solutions
-titles2 <- c(titles2, "Boundary penalty (high)")
-p9 <- p6 %>% add_boundary_penalties(0.05, 0.5)
-s2 <- addLayer(s2, solve(p9))
      -
      # plot solutions
-plot(s2, main = titles2, breaks = c(0, 0.5, 1),  col = c("grey70", "darkgreen"))
      -

      -

      Here we can see that adding the constraints and penalties to the problem has a small, but noticeable effect on the solutions. We would expect to see larger difference between the solutions for problems that contain more than five conservation features. You may also wish to explore the add_connectivity_penalties and add_feature_contiguity_constraints functions. These functions use additional data on landscape resistance to provide a more accurate parametrization of connectivity and, in turn, deliver more effective solutions.

      -
      -
      -

      References

      -
      -
      -BC Assessment. (2015). Property Information Services. URL https://info.bcassessment.ca/ [accessed 13 June 2016]. -
      -
      -Morrell, N., Schuster, R., Crombie, M. & Arcese, P. (2017). A Prioritization Tool for the Conservation of Coastal Douglas-fir Forest and Savannah Habitats of the Georgia Basin. The Nature Trust of British Colombia, Coastal Douglas Fir Conservation Partnership, and the Department of Forest and Conservation Sciences, University of British Colombia, URL https://peter-arcese-lab.sites.olt.ubc.ca/files/2016/09/CDFCP_tutorial_2017_05.pdf [accessed 9 October 2017]. -
      -
      -
      - - - - - - - - - - - diff --git a/inst/doc/solver_benchmark.Rmd b/inst/doc/solver_benchmarks.Rmd similarity index 77% rename from inst/doc/solver_benchmark.Rmd rename to inst/doc/solver_benchmarks.Rmd index a91dafadc..f0c6cd3e3 100644 --- a/inst/doc/solver_benchmark.Rmd +++ b/inst/doc/solver_benchmarks.Rmd @@ -1,5 +1,5 @@ --- -title: "Solver Benchmarks" +title: "Solver benchmarks" output: rmarkdown::html_vignette: toc: true @@ -10,7 +10,7 @@ documentclass: article bibliography: references.bib csl: reference-style.csl vignette: > - %\VignetteIndexEntry{Solver Benchmarks} + %\VignetteIndexEntry{Solver benchmarks} %\VignetteEngine{knitr::rmarkdown_notangle} --- @@ -35,17 +35,17 @@ boundary_penalty_values <- list( devtools::load_all() ``` -# Introduction +## Introduction -The _prioritizr R_ package supports a variety of optimization solvers for generating prioritizations. Specifically, the following functions can be used: [`add_gurobi_solver()`](https://prioritizr.net/reference/add_gurobi_solver.html) (interfaces with the [_Gurobi_ software](https://www.gurobi.com/)), [`add_cplex_solver()`](https://prioritizr.net/reference/add_cplex_solver.html) (interfaces with the [_IBM CPLEX_ software](https://www.ibm.com/analytics/cplex-optimizer)), [`add_cbc_solver()`](https://prioritizr.net/reference/add_cbc_solver.html) (interfaces with the [_CBC_ software](https://projects.coin-or.org/Cbc) using the [_rcbc R_ package](https://dirkschumacher.github.io/rcbc/)), [`add_rsymphony_solver()`](https://prioritizr.net/reference/add_rsymphony_solver.html) (interfaces with the [_SYMPHONY_ software](https://projects.coin-or.org/SYMPHONY) using the [_Rsymphony R_ package](https://CRAN.R-project.org/package=Rsymphony)), and the [`add_lpsymphony_solver()`](https://prioritizr.net/reference/add_lsymphony_solver.html) function (interfaces with the [_SYMPHONY_ software](https://projects.coin-or.org/SYMPHONY) using the [_lpsymphony R_ package](https://www.bioconductor.org/packages/release/bioc/html/lpsymphony.html)). Broadly speaking, _IBM CPLEX_ and _Gurobi_ tend to be the fastest among the supported solvers. Although they are both commercial software, special academic licenses are available at no cost. +The _prioritizr R_ package supports a variety of optimization solvers for generating prioritizations. Specifically, the following functions can be used: `add_gurobi_solver()` (interfaces with the [_Gurobi_ software](https://www.gurobi.com/)), `add_cplex_solver()` (interfaces with the [_IBM CPLEX_ software](https://www.ibm.com/analytics/cplex-optimizer)), `add_cbc_solver()` (interfaces with the [_CBC_ software](https://projects.coin-or.org/Cbc) using the [_rcbc R_ package](https://dirkschumacher.github.io/rcbc/)), `add_rsymphony_solver()` (interfaces with the [_SYMPHONY_ software](https://projects.coin-or.org/SYMPHONY) using the [_Rsymphony R_ package](https://CRAN.R-project.org/package=Rsymphony)), and the `add_lpsymphony_solver()` function (interfaces with the [_SYMPHONY_ software](https://projects.coin-or.org/SYMPHONY) using the [_lpsymphony R_ package](https://www.bioconductor.org/packages/release/bioc/html/lpsymphony.html)). Broadly speaking, _IBM CPLEX_ and _Gurobi_ tend to be the fastest among the supported solvers. Although they are both commercial software, special academic licenses are available at no cost. -In this vignette, we will explore the performance of different solvers. Using a benchmark analysis, we will see how well they can tackle problems of varying size (e.g. number of planning units) and complexity (e.g. adding boundary length penalties to reduce spatial fragmentation). Since users working in governmental and non-governmental organizations may need to purchase licenses for _IBM CPLEX_ or _Gurobi_ to use them, this vignette also aims to provide insight into whether the potential benefits of purchasing such licenses is worthwhile. Indeed -- depending on the size and complexity of a given conservation planning problem -- solvers based on open source software may only take slightly longer than commercial solvers. +In this vignette, we will explore the performance of different solvers. Using a benchmark analysis, we will see how well they can tackle problems of varying size (e.g., number of planning units) and complexity (e.g., adding boundary length penalties to reduce spatial fragmentation). Since users working in governmental and non-governmental organizations may need to purchase licenses for _IBM CPLEX_ or _Gurobi_ to use them, this vignette also aims to provide insight into whether the potential benefits of purchasing such licenses is worthwhile. Indeed -- depending on the size and complexity of a given conservation planning problem -- solvers based on open source software may only take slightly longer than commercial solvers. -# Methods +## Methods -This vignette will report the results of a benchmark analysis. To reduce computational burden, we previously completed the benchmark analysis and [uploaded the results to an online repository](https://github.com/prioritizr/benchmark/releases) ([code available online](https://github.com/prioritizr/benchmark)). This analysis involved generating prioritizations using different solvers and recording how long it took for the solvers to finish. To help understand the factors that influence how long it takes for solvers to generate a prioritization, we examined a suite of conservation planning problems with varying size (i.e. number of planning units), complexity (i.e. varying penalties to reduce spatial fragmentation), and with different objective functions (i.e. [metric used to evaluate competing solutions](https://prioritizr.net/reference/objectives.html)). In this section, we will download the results for the previously completed benchmark analysis and examine the parameters used to conduct it. +This vignette will report the results of a benchmark analysis. To reduce computational burden, we previously completed the benchmark analysis and [uploaded the results to an online repository](https://github.com/prioritizr/benchmark/releases) ([code available online](https://github.com/prioritizr/benchmark)). This analysis involved generating prioritizations using different solvers and recording how long it took for the solvers to finish. To help understand the factors that influence how long it takes for solvers to generate a prioritization, we examined a suite of conservation planning problems with varying size (i.e., number of planning units), complexity (i.e., varying penalties to reduce spatial fragmentation), and with different objective functions (i.e., [metric used to evaluate competing solutions](https://prioritizr.net/reference/objectives.html)). In this section, we will download the results for the previously completed benchmark analysis and examine the parameters used to conduct it. -## Set up +### Set up To start off, we will the load packages used in this vignette. @@ -58,7 +58,7 @@ library(units) library(dplyr) ``` -## Download benchmark results +### Download benchmark results Let's download the results of the benchmark analysis. This code will save the results to a temporary folder on your computer. Please note that downloading the results might take several minutes to complete depending on your Internet connection. If you are unable to download the results onto your computer, you can view the graphs shown in this vignette. You only need to run the code in this vignette if you wish to explore certain aspects of the results yourself. @@ -73,7 +73,7 @@ pb_download( load(file.path(tempdir(), "results.rda")) ``` -## Benchmark parameters +### Benchmark parameters After downloading the benchmark results, let's have a look at the parameters that were used to conduct it. Note that all benchmark scenarios have 72 features. @@ -82,11 +82,11 @@ After downloading the benchmark results, let's have a look at the parameters tha n_planning_units <- unique(benchmark_results$number_of_planning_units) print(n_planning_units) -# number of features (e.g. number of different species examined) +# number of features (e.g., number of different species examined) unique(benchmark_results$number_features) # representation targets, -# units are proportion of the total amount of each feature (e.g. 0.1 = 10%) +# units are proportion of the total amount of each feature (e.g., 0.1 = 10%) unique(benchmark_results$relative_target) # number of planning units @@ -107,7 +107,7 @@ boundary_penalty_values$add_min_set_objective ## boundary penalty values for min shortfall objective function boundary_penalty_values$add_min_shortfall_objective -# budgets examined for budget-limited objectives (e.g. 0.1 = 10% of total cost) +# budgets examined for budget-limited objectives (e.g., 0.1 = 10% of total cost) ## note that the min set objective function does not use a budget, ## and thus it has a NA value tibble(objective = unique(benchmark_results$objective), @@ -115,7 +115,7 @@ tibble(objective = unique(benchmark_results$objective), ``` -## Helper function +### Helper function Now we will define a helper function to quickly plot the results from the benchmark analysis. This will be helpful for interpreting the results of the benchmark analysis in the following section. @@ -208,9 +208,9 @@ plot_benchmark <- function( } ``` -# Results +## Results -We will now inspect the results of the benchmark analysis. The `benchmark_results` object is a table (i.e. `tibble()`) containing information for each benchmark run (e.g. run time), and the `solution_raster_data` object (i.e. `RasterStack`) contains the prioritizations generated for each benchmark run. +We will now inspect the results of the benchmark analysis. The `benchmark_results` object is a table (i.e., `tibble()`) containing information for each benchmark run (e.g., run time), and the `solution_raster_data` object (i.e., `RasterStack`) contains the prioritizations generated for each benchmark run. ```{r "preview_results"} # preview results @@ -233,7 +233,7 @@ theme(axis.text.x = element_text(size = 7)) + labs(x = "Solver", y = "Run time (hours)") ``` -## Minimum set results (no boundary penalty) +### Minimum set results (no boundary penalty) Now, let's investigate the solver behavior in more detail. Specifically, we will examine the benchmark results generated for the minimum set objective function. This is because the minimum set objective function is the most commonly used objective function in systematic conservation, due to the fact that it is used by the [_Marxan_ decision support software](https://marxansolutions.org/). To begin with, let's examine the results for the smallest and simplest conservation planning problems examined in the benchmark analysis. Here, all prioritizations were generated using problems that involved `r formatC(n_planning_units[1], big.mark = ",")` planning units and did not contain any boundary length penalties. Since all benchmark scenarios have 72 features -- as mentioned earlier -- all of these prioritizations were generated with 72 features. When looking at the results, we can see that all solvers solve the problem in a comparable amount of time across all targets investigated. @@ -244,7 +244,7 @@ plot_benchmark( boundary_penalty = 0) ``` -Next, let's look at the results for a more realistic problem involving `r formatC(n_planning_units[2], big.mark = ",")` planning units and see how the timing of the different solvers used compares. Note that all other factors (e.g. absence of boundary length penalties) are the same as for the previous graph. +Next, let's look at the results for a more realistic problem involving `r formatC(n_planning_units[2], big.mark = ",")` planning units and see how the timing of the different solvers used compares. Note that all other factors (e.g., absence of boundary length penalties) are the same as for the previous graph. ```{r "min_set_pu_n_2"} plot_benchmark( @@ -271,7 +271,7 @@ plot_benchmark( boundary_penalty = 0) ``` -To get a better sense of how the faster solvers (i.e. based on _CBC_, _IBM CPLEX_, _Gurobi_) compare for such a large problem, let's take a closer look at these three solvers. Interestingly, we can see that the solver based on the open source _CBC_ software is slightly faster -- by a few minutes -- than the other solvers. +To get a better sense of how the faster solvers (i.e., based on _CBC_, _IBM CPLEX_, _Gurobi_) compare for such a large problem, let's take a closer look at these three solvers. Interestingly, we can see that the solver based on the open source _CBC_ software is slightly faster -- by a few minutes -- than the other solvers. ```{r "min_set_pu_n_4_fast_only"} plot_benchmark( @@ -282,9 +282,9 @@ plot_benchmark( ``` -## Minimum set results with low boundary penalty +### Minimum set results with low boundary penalty -Now let's at the same problem types, but this time with a low boundary length penalty value added to the problem formulation. To start with, we will look at scenarios with a low `boundary_penalty` value (i.e. $`r boundary_penalty_values$add_min_set_objective[2]`$). Let's start again with the smallest problem size we've benchmarked. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. +Now let's at the same problem types, but this time with a low boundary length penalty value added to the problem formulation. To start with, we will look at scenarios with a low `boundary_penalty` value (i.e., $`r boundary_penalty_values$add_min_set_objective[2]`$). Let's start again with the smallest problem size we've benchmarked. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. ```{r "min_set_pu_n_1_with_low_boundary_penalty"} plot_benchmark( @@ -330,9 +330,9 @@ plot_benchmark( solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver")) ``` -## Minimum set results with high boundary penalty +### Minimum set results with high boundary penalty -Now let's look at the same problem types, but this time with a high boundary length penalty parameter added to the problem formulation (i.e. $`r boundary_penalty_values$add_min_set_objective[3]`$). Let's start again with the smallest problem size we've benchmarked. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. Although there are some differences between the solvers, they all have very similar run times (i.e. all less than one second). +Now let's look at the same problem types, but this time with a high boundary length penalty parameter added to the problem formulation (i.e., $`r boundary_penalty_values$add_min_set_objective[3]`$). Let's start again with the smallest problem size we've benchmarked. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. Although there are some differences between the solvers, they all have very similar run times (i.e., all less than one second). ```{r "min_set_pu_n_1_with_high_boundary_penalty"} plot_benchmark( @@ -378,7 +378,7 @@ plot_benchmark( solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver")) ``` -## Minimize shortfall results (no boundary penalty) +### Minimize shortfall results (no boundary penalty) Now, let's investigate the solver behavior for the minimum shortfall objective function. Let's start with the smallest problem size examined. All benchmark scenarios have 72 features. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. We can see that all solvers solve the problem in a comparable amount of time across all targets investigated. @@ -407,7 +407,7 @@ plot_benchmark( boundary_penalty = 0) ``` -Finally, let's look at timing comparisons for a large problem with `r formatC(n_planning_units[4], big.mark = ",")` planning units. We can see that all the open source solvers (i.e. _CBC_, _Rsymphony_ and _lpsymphony_) take a lot longer than the commercial solvers (i.e. _IBM CPLEX_ and _Guorbi_). +Finally, let's look at timing comparisons for a large problem with `r formatC(n_planning_units[4], big.mark = ",")` planning units. We can see that all the open source solvers (i.e., _CBC_, _Rsymphony_ and _lpsymphony_) take a lot longer than the commercial solvers (i.e., _IBM CPLEX_ and _Guorbi_). ```{r "min_short_pu_n_4"} plot_benchmark( @@ -416,9 +416,9 @@ plot_benchmark( boundary_penalty = 0) ``` -## Minimize shortfall results with low boundary penalty +### Minimize shortfall results with low boundary penalty -Now let's look at the same problem type, but this time with a low `boundary_penalty` parameter added to the problem formulation (i.e. $`r boundary_penalty_values$add_min_shortfall_objective[2]`$). Let's start again with the smallest problem size examined. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. +Now let's look at the same problem type, but this time with a low `boundary_penalty` parameter added to the problem formulation (i.e., $`r boundary_penalty_values$add_min_shortfall_objective[2]`$). Let's start again with the smallest problem size examined. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. ```{r "min_short_pu_n_1_with_low_boundary_penalty"} plot_benchmark( @@ -454,7 +454,7 @@ plot_benchmark( boundary_penalty = boundary_penalty_values$add_min_shortfall_objective[2]) ``` -To get a better sense of how the faster solvers compare (i.e. _CBC_, _IBM CPLEX_, and _Gurobi_), let's take a closer look at these three solvers. We can see that the _CBC_ solver takes a lot longer to generate prioritizations than the _IBM CPLEX_ and _Gurobi_ solvers. This result suggests that _IBM CPLEX_ and _Gurobi_ could be really beneficial for large-scale conservation planning problems with boundary length penalties and the minimum shortfall objective function. +To get a better sense of how the faster solvers compare (i.e., _CBC_, _IBM CPLEX_, and _Gurobi_), let's take a closer look at these three solvers. We can see that the _CBC_ solver takes a lot longer to generate prioritizations than the _IBM CPLEX_ and _Gurobi_ solvers. This result suggests that _IBM CPLEX_ and _Gurobi_ could be really beneficial for large-scale conservation planning problems with boundary length penalties and the minimum shortfall objective function. ```{r "min_short_pu_n_4_and_boundary_penalty_and_fast_solvers"} plot_benchmark( @@ -464,7 +464,7 @@ plot_benchmark( solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver")) ``` -## Minimize shortfall results with high boundary penalty +### Minimize shortfall results with high boundary penalty Now let's look at the same problem types, but this time with a higher `boundary_penalty` parameter added to the problem formulation ($`r boundary_penalty_values$add_min_shortfall_objective[3]`$). Let's start again with the smallest problem size examined. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. @@ -475,7 +475,7 @@ plot_benchmark( boundary_penalty = boundary_penalty_values$add_min_shortfall_objective[3]) ``` -Next, let's look at the results for a greater number of planning units (i.e. `r formatC(n_planning_units[2], big.mark = ",")` planning units) and see how the timings compare. All the solvers have a similar run time now. Interestingly, the _Gurobi_ solver is the slowest -- but only by a couple of minutes -- for these benchmark parameters. +Next, let's look at the results for a greater number of planning units (i.e., `r formatC(n_planning_units[2], big.mark = ",")` planning units) and see how the timings compare. All the solvers have a similar run time now. Interestingly, the _Gurobi_ solver is the slowest -- but only by a couple of minutes -- for these benchmark parameters. ```{r "min_short_pu_n_2 with boundary penalty"} plot_benchmark( @@ -502,6 +502,6 @@ plot_benchmark( boundary_penalty = boundary_penalty_values$add_min_shortfall_objective[3]) ``` -# Conclusion +## Conclusion -The benchmark results demonstrate that the time required to solve a conservation planning problem can vary considerably depending on the size and complexity of the problem, and also the solver used to generate the prioritization. Indeed, some solvers (e.g. _Rsymphony_ solver) may require many hours to solve a problem that other solvers (e.g. _CBC_ or _Gurobi_ solvers) can solve within minutes. Broadly speaking, we recommend using the _Gurobi_ and _IBM CPLEX_ solvers where possible. This is because they often have the best performance. Although academics can obtain a special license to use these solvers at no cost, conservation planners working in governmental or non-governmental organizations may not have access to these solvers. In such cases, we recommend using the _CBC_ solver because it generally has better performance than the other open source solvers (i.e. the _Rsymphony_ and _lpsymphony_ solvers). Since the _CBC_ solver did not always have better performance than the other open source solvers, we recommend trying the _lpsymphony_ solver if the _CBC_ solver is taking a long time to solve a particular problem. +The benchmark results demonstrate that the time required to solve a conservation planning problem can vary considerably depending on the size and complexity of the problem, and also the solver used to generate the prioritization. Indeed, some solvers (e.g., _Rsymphony_ solver) may require many hours to solve a problem that other solvers (e.g., _CBC_ or _Gurobi_ solvers) can solve within minutes. Broadly speaking, we recommend using the _Gurobi_ and _IBM CPLEX_ solvers where possible. This is because they often have the best performance. Although academics can obtain a special license to use these solvers at no cost, conservation planners working in governmental or non-governmental organizations may not have access to these solvers. In such cases, we recommend using the _CBC_ solver because it generally has better performance than the other open source solvers (i.e., the _Rsymphony_ and _lpsymphony_ solvers). Since the _CBC_ solver did not always have better performance than the other open source solvers, we recommend trying the _lpsymphony_ solver if the _CBC_ solver is taking a long time to solve a particular problem. diff --git a/inst/doc/solver_benchmark.html b/inst/doc/solver_benchmarks.html similarity index 99% rename from inst/doc/solver_benchmark.html rename to inst/doc/solver_benchmarks.html index 4ee814d72..6f5f55d6c 100644 --- a/inst/doc/solver_benchmark.html +++ b/inst/doc/solver_benchmarks.html @@ -12,7 +12,7 @@ -Solver Benchmarks +Solver benchmarks @@ -137,7 +137,7 @@ -

      Solver Benchmarks

      +

      Solver benchmarks

      @@ -163,16 +163,16 @@

      Solver Benchmarks

      -
      -

      Introduction

      -

      The prioritizr R package supports a variety of optimization solvers for generating prioritizations. Specifically, the following functions can be used: add_gurobi_solver() (interfaces with the Gurobi software), add_cplex_solver() (interfaces with the IBM CPLEX software), add_cbc_solver() (interfaces with the CBC software using the rcbc R package), add_rsymphony_solver() (interfaces with the SYMPHONY software using the Rsymphony R package), and the add_lpsymphony_solver() function (interfaces with the SYMPHONY software using the lpsymphony R package). Broadly speaking, IBM CPLEX and Gurobi tend to be the fastest among the supported solvers. Although they are both commercial software, special academic licenses are available at no cost.

      -

      In this vignette, we will explore the performance of different solvers. Using a benchmark analysis, we will see how well they can tackle problems of varying size (e.g. number of planning units) and complexity (e.g. adding boundary length penalties to reduce spatial fragmentation). Since users working in governmental and non-governmental organizations may need to purchase licenses for IBM CPLEX or Gurobi to use them, this vignette also aims to provide insight into whether the potential benefits of purchasing such licenses is worthwhile. Indeed – depending on the size and complexity of a given conservation planning problem – solvers based on open source software may only take slightly longer than commercial solvers.

      +
      +

      Introduction

      +

      The prioritizr R package supports a variety of optimization solvers for generating prioritizations. Specifically, the following functions can be used: add_gurobi_solver() (interfaces with the Gurobi software), add_cplex_solver() (interfaces with the IBM CPLEX software), add_cbc_solver() (interfaces with the CBC software using the rcbc R package), add_rsymphony_solver() (interfaces with the SYMPHONY software using the Rsymphony R package), and the add_lpsymphony_solver() function (interfaces with the SYMPHONY software using the lpsymphony R package). Broadly speaking, IBM CPLEX and Gurobi tend to be the fastest among the supported solvers. Although they are both commercial software, special academic licenses are available at no cost.

      +

      In this vignette, we will explore the performance of different solvers. Using a benchmark analysis, we will see how well they can tackle problems of varying size (e.g., number of planning units) and complexity (e.g., adding boundary length penalties to reduce spatial fragmentation). Since users working in governmental and non-governmental organizations may need to purchase licenses for IBM CPLEX or Gurobi to use them, this vignette also aims to provide insight into whether the potential benefits of purchasing such licenses is worthwhile. Indeed – depending on the size and complexity of a given conservation planning problem – solvers based on open source software may only take slightly longer than commercial solvers.

      -
      -

      Methods

      -

      This vignette will report the results of a benchmark analysis. To reduce computational burden, we previously completed the benchmark analysis and uploaded the results to an online repository (code available online). This analysis involved generating prioritizations using different solvers and recording how long it took for the solvers to finish. To help understand the factors that influence how long it takes for solvers to generate a prioritization, we examined a suite of conservation planning problems with varying size (i.e. number of planning units), complexity (i.e. varying penalties to reduce spatial fragmentation), and with different objective functions (i.e. metric used to evaluate competing solutions). In this section, we will download the results for the previously completed benchmark analysis and examine the parameters used to conduct it.

      -
      -

      Set up

      +
      +

      Methods

      +

      This vignette will report the results of a benchmark analysis. To reduce computational burden, we previously completed the benchmark analysis and uploaded the results to an online repository (code available online). This analysis involved generating prioritizations using different solvers and recording how long it took for the solvers to finish. To help understand the factors that influence how long it takes for solvers to generate a prioritization, we examined a suite of conservation planning problems with varying size (i.e., number of planning units), complexity (i.e., varying penalties to reduce spatial fragmentation), and with different objective functions (i.e., metric used to evaluate competing solutions). In this section, we will download the results for the previously completed benchmark analysis and examine the parameters used to conduct it.

      +
      +

      Set up

      To start off, we will the load packages used in this vignette.

      # load packages
 library(prioritizr)
@@ -181,8 +181,8 @@ 
      Set up
      
 library(units)
 library(dplyr)
      -
      -

      Download benchmark results

      +
      +

      Download benchmark results

      Let’s download the results of the benchmark analysis. This code will save the results to a temporary folder on your computer. Please note that downloading the results might take several minutes to complete depending on your Internet connection. If you are unable to download the results onto your computer, you can view the graphs shown in this vignette. You only need to run the code in this vignette if you wish to explore certain aspects of the results yourself.

      # download data to temporary folder
 pb_download(
@@ -193,18 +193,18 @@ 
      Download benchmark results
      
 # load benchmark results
 load(file.path(tempdir(), "results.rda"))
      -
      -

      Benchmark parameters

      +
      +

      Benchmark parameters

      After downloading the benchmark results, let’s have a look at the parameters that were used to conduct it. Note that all benchmark scenarios have 72 features.

      # numbers of planning units examined the benchmark analysis
 n_planning_units <- unique(benchmark_results$number_of_planning_units)
 print(n_planning_units)
      ## [1]   1478  12902 102242 606180
      -
      # number of features (e.g. number of different species examined)
+
      # number of features (e.g., number of different species examined)
 unique(benchmark_results$number_features)
      
 
      ## [1] 72
      
 
      # representation targets,
-# units are proportion of the total amount of each feature (e.g. 0.1 = 10%)
+# units are proportion of the total amount of each feature (e.g., 0.1 = 10%)
 unique(benchmark_results$relative_target)
      
 
      ## [1] 0.10 0.15 0.20 0.30
      
 
      # number of planning units
@@ -225,7 +225,7 @@ 
      Benchmark parameters
      
 
      ## boundary penalty values for min shortfall objective function
 boundary_penalty_values$add_min_shortfall_objective
      
 
      ## [1] 0e+00 1e-14 1e-13
      
-
      # budgets examined for budget-limited objectives (e.g. 0.1 = 10% of total cost)
+
      # budgets examined for budget-limited objectives (e.g., 0.1 = 10% of total cost)
 ## note that the min set objective function does not use a budget,
 ## and thus it has a NA value
 tibble(objective = unique(benchmark_results$objective),
@@ -236,8 +236,8 @@ 
      Benchmark parameters
      
 ## 1 add_min_set_objective         NA  
 ## 2 add_min_shortfall_objective    0.1
      
 
      
-
      
-
      Helper function
      
+
      
+
      Helper function
      
 
      Now we will define a helper function to quickly plot the results from the benchmark analysis. This will be helpful for interpreting the results of the benchmark analysis in the following section.
      
 
      # define helper function to create plots
 plot_benchmark <- function(
@@ -327,9 +327,9 @@ 
      Helper function
      
 }
      
 
      
 
      
-
      
-
      Results
      
-
      We will now inspect the results of the benchmark analysis. The benchmark_results object is a table (i.e. tibble()) containing information for each benchmark run (e.g. run time), and the solution_raster_data object (i.e. RasterStack) contains the prioritizations generated for each benchmark run.
      
+
      
+
      Results
      
+
      We will now inspect the results of the benchmark analysis. The benchmark_results object is a table (i.e., tibble()) containing information for each benchmark run (e.g., run time), and the solution_raster_data object (i.e., RasterStack) contains the prioritizations generated for each benchmark run.
      
 
      # preview results
 print(benchmark_results)
      
 
      ## # A tibble: 480 × 21
@@ -407,15 +407,15 @@ 
      Results
      
 theme(axis.text.x = element_text(size = 7)) +
 labs(x = "Solver", y = "Run time (hours)")
      
 
      
-
      
-
      Minimum set results (no boundary penalty)
      
+
      
+
      Minimum set results (no boundary penalty)
      
 
      Now, let’s investigate the solver behavior in more detail. Specifically, we will examine the benchmark results generated for the minimum set objective function. This is because the minimum set objective function is the most commonly used objective function in systematic conservation, due to the fact that it is used by the Marxan decision support software. To begin with, let’s examine the results for the smallest and simplest conservation planning problems examined in the benchmark analysis. Here, all prioritizations were generated using problems that involved 1,478 planning units and did not contain any boundary length penalties. Since all benchmark scenarios have 72 features – as mentioned earlier – all of these prioritizations were generated with 72 features. When looking at the results, we can see that all solvers solve the problem in a comparable amount of time across all targets investigated.
      
 
      plot_benchmark(
   objective = "add_min_set_objective",
   n_pu = n_planning_units[1],
   boundary_penalty = 0)
      
 
      
-
      Next, let’s look at the results for a more realistic problem involving 12,902 planning units and see how the timing of the different solvers used compares. Note that all other factors (e.g. absence of boundary length penalties) are the same as for the previous graph.
      
+
      Next, let’s look at the results for a more realistic problem involving 12,902 planning units and see how the timing of the different solvers used compares. Note that all other factors (e.g., absence of boundary length penalties) are the same as for the previous graph.
      
 
      plot_benchmark(
   objective = "add_min_set_objective",
   n_pu = n_planning_units[2],
@@ -433,7 +433,7 @@ 
      Minimum set results (no boundary penalty)
      
   n_pu = n_planning_units[4],
   boundary_penalty = 0)
      
 
      
-
      To get a better sense of how the faster solvers (i.e. based on CBC, IBM CPLEX, Gurobi) compare for such a large problem, let’s take a closer look at these three solvers. Interestingly, we can see that the solver based on the open source CBC software is slightly faster – by a few minutes – than the other solvers.
      
+
      To get a better sense of how the faster solvers (i.e., based on CBC, IBM CPLEX, Gurobi) compare for such a large problem, let’s take a closer look at these three solvers. Interestingly, we can see that the solver based on the open source CBC software is slightly faster – by a few minutes – than the other solvers.
      
 
      plot_benchmark(
   objective = "add_min_set_objective",
   n_pu = n_planning_units[4],
@@ -441,9 +441,9 @@ 
      Minimum set results (no boundary penalty)
      
   solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver"))
      
 
      
 
      
-
      
-
      Minimum set results with low boundary penalty
      
-
      Now let’s at the same problem types, but this time with a low boundary length penalty value added to the problem formulation. To start with, we will look at scenarios with a low boundary_penalty value (i.e. \(10^{-5}\)). Let’s start again with the smallest problem size we’ve benchmarked. This problem has only 1,478 planning units.
      
+
      
+
      Minimum set results with low boundary penalty
      
+
      Now let’s at the same problem types, but this time with a low boundary length penalty value added to the problem formulation. To start with, we will look at scenarios with a low boundary_penalty value (i.e., \(10^{-5}\)). Let’s start again with the smallest problem size we’ve benchmarked. This problem has only 1,478 planning units.
      
 
      plot_benchmark(
   objective = "add_min_set_objective",
   n_pu = n_planning_units[1],
@@ -475,9 +475,9 @@ 
      Minimum set results with low boundary penalty
      
   solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver"))
      
 
      
 
      
-
      
-
      Minimum set results with high boundary penalty
      
-
      Now let’s look at the same problem types, but this time with a high boundary length penalty parameter added to the problem formulation (i.e. \(0.001\)). Let’s start again with the smallest problem size we’ve benchmarked. This problem has only 1,478 planning units. Although there are some differences between the solvers, they all have very similar run times (i.e. all less than one second).
      
+
      
+
      Minimum set results with high boundary penalty
      
+
      Now let’s look at the same problem types, but this time with a high boundary length penalty parameter added to the problem formulation (i.e., \(0.001\)). Let’s start again with the smallest problem size we’ve benchmarked. This problem has only 1,478 planning units. Although there are some differences between the solvers, they all have very similar run times (i.e., all less than one second).
      
 
      plot_benchmark(
   objective = "add_min_set_objective",
   n_pu = n_planning_units[1],
@@ -509,8 +509,8 @@ 
      Minimum set results with high boundary penalty
      
   solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver"))
      
 
      
 
      
-
      
-
      Minimize shortfall results (no boundary penalty)
      
+
      
+
      Minimize shortfall results (no boundary penalty)
      
 
      Now, let’s investigate the solver behavior for the minimum shortfall objective function. Let’s start with the smallest problem size examined. All benchmark scenarios have 72 features. This problem has only 1,478 planning units. We can see that all solvers solve the problem in a comparable amount of time across all targets investigated.
      
 
      plot_benchmark(
   objective = "add_min_shortfall_objective",
@@ -529,16 +529,16 @@ 
      Minimize shortfall results (no boundary penalty)
      
   n_pu = n_planning_units[3],
   boundary_penalty = 0)
      
 
      
-
      Finally, let’s look at timing comparisons for a large problem with 606,180 planning units. We can see that all the open source solvers (i.e. CBC, Rsymphony and lpsymphony) take a lot longer than the commercial solvers (i.e. IBM CPLEX and Guorbi).
      
+
      Finally, let’s look at timing comparisons for a large problem with 606,180 planning units. We can see that all the open source solvers (i.e., CBC, Rsymphony and lpsymphony) take a lot longer than the commercial solvers (i.e., IBM CPLEX and Guorbi).
      
 
      plot_benchmark(
   objective = "add_min_shortfall_objective",
   n_pu = n_planning_units[4],
   boundary_penalty = 0)
      
 
      
 
      
-
      
-
      Minimize shortfall results with low boundary penalty
      
-
      Now let’s look at the same problem type, but this time with a low boundary_penalty parameter added to the problem formulation (i.e. \(10^{-14}\)). Let’s start again with the smallest problem size examined. This problem has only 1,478 planning units.
      
+
      
+
      Minimize shortfall results with low boundary penalty
      
+
      Now let’s look at the same problem type, but this time with a low boundary_penalty parameter added to the problem formulation (i.e., \(10^{-14}\)). Let’s start again with the smallest problem size examined. This problem has only 1,478 planning units.
      
 
      plot_benchmark(
   objective = "add_min_shortfall_objective",
   n_pu = n_planning_units[1],
@@ -562,7 +562,7 @@ 
      Minimize shortfall results with low boundary penalty
      
   n_pu = n_planning_units[4],
   boundary_penalty = boundary_penalty_values$add_min_shortfall_objective[2])
      
 
      
-
      To get a better sense of how the faster solvers compare (i.e. CBC, IBM CPLEX, and Gurobi), let’s take a closer look at these three solvers. We can see that the CBC solver takes a lot longer to generate prioritizations than the IBM CPLEX and Gurobi solvers. This result suggests that IBM CPLEX and Gurobi could be really beneficial for large-scale conservation planning problems with boundary length penalties and the minimum shortfall objective function.
      
+
      To get a better sense of how the faster solvers compare (i.e., CBC, IBM CPLEX, and Gurobi), let’s take a closer look at these three solvers. We can see that the CBC solver takes a lot longer to generate prioritizations than the IBM CPLEX and Gurobi solvers. This result suggests that IBM CPLEX and Gurobi could be really beneficial for large-scale conservation planning problems with boundary length penalties and the minimum shortfall objective function.
      
 
      plot_benchmark(
   objective = "add_min_shortfall_objective",
   n_pu = n_planning_units[4],
@@ -570,15 +570,15 @@ 
      Minimize shortfall results with low boundary penalty
      
   solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver"))
      
 
      
 
      
-
      
-
      Minimize shortfall results with high boundary penalty
      
+
      
+
      Minimize shortfall results with high boundary penalty
      
 
      Now let’s look at the same problem types, but this time with a higher boundary_penalty parameter added to the problem formulation (\(10^{-13}\)). Let’s start again with the smallest problem size examined. This problem has only 1,478 planning units.
      
 
      plot_benchmark(
   objective = "add_min_shortfall_objective",
   n_pu = n_planning_units[1],
   boundary_penalty = boundary_penalty_values$add_min_shortfall_objective[3])
      
 
      
-
      Next, let’s look at the results for a greater number of planning units (i.e. 12,902 planning units) and see how the timings compare. All the solvers have a similar run time now. Interestingly, the Gurobi solver is the slowest – but only by a couple of minutes – for these benchmark parameters.
      
+
      Next, let’s look at the results for a greater number of planning units (i.e., 12,902 planning units) and see how the timings compare. All the solvers have a similar run time now. Interestingly, the Gurobi solver is the slowest – but only by a couple of minutes – for these benchmark parameters.
      
 
      plot_benchmark(
   objective = "add_min_shortfall_objective",
   n_pu = n_planning_units[2],
@@ -598,9 +598,9 @@ 
      Minimize shortfall results with high boundary penalty
      
 
      
 
      
 
      
-
      
-
      Conclusion
      
-
      The benchmark results demonstrate that the time required to solve a conservation planning problem can vary considerably depending on the size and complexity of the problem, and also the solver used to generate the prioritization. Indeed, some solvers (e.g. Rsymphony solver) may require many hours to solve a problem that other solvers (e.g. CBC or Gurobi solvers) can solve within minutes. Broadly speaking, we recommend using the Gurobi and IBM CPLEX solvers where possible. This is because they often have the best performance. Although academics can obtain a special license to use these solvers at no cost, conservation planners working in governmental or non-governmental organizations may not have access to these solvers. In such cases, we recommend using the CBC solver because it generally has better performance than the other open source solvers (i.e. the Rsymphony and lpsymphony solvers). Since the CBC solver did not always have better performance than the other open source solvers, we recommend trying the lpsymphony solver if the CBC solver is taking a long time to solve a particular problem.
      
+
      
+
      Conclusion
      
+
      The benchmark results demonstrate that the time required to solve a conservation planning problem can vary considerably depending on the size and complexity of the problem, and also the solver used to generate the prioritization. Indeed, some solvers (e.g., Rsymphony solver) may require many hours to solve a problem that other solvers (e.g., CBC or Gurobi solvers) can solve within minutes. Broadly speaking, we recommend using the Gurobi and IBM CPLEX solvers where possible. This is because they often have the best performance. Although academics can obtain a special license to use these solvers at no cost, conservation planners working in governmental or non-governmental organizations may not have access to these solvers. In such cases, we recommend using the CBC solver because it generally has better performance than the other open source solvers (i.e., the Rsymphony and lpsymphony solvers). Since the CBC solver did not always have better performance than the other open source solvers, we recommend trying the lpsymphony solver if the CBC solver is taking a long time to solve a particular problem.
      
 
      
 
 
diff --git a/inst/doc/tasmania.Rmd b/inst/doc/tasmania.Rmd
deleted file mode 100644
index 62aaddab1..000000000
--- a/inst/doc/tasmania.Rmd
+++ /dev/null
@@ -1,225 +0,0 @@
----
-title: "Tasmania Tutorial"
-output:
-  rmarkdown::html_vignette:
-    toc: true
-    fig_caption: true
-    self_contained: yes
-fontsize: 11pt
-documentclass: article
-bibliography: references.bib
-csl: reference-style.csl
-vignette: >
-  %\VignetteIndexEntry{Tasmania Tutorial}
-  %\VignetteEngine{knitr::rmarkdown_notangle}
----
-
-```{r, include = FALSE}
-h <- 3.5
-w <- 3.5
-is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_",
-             "_R_CHECK_LICENSE_") %in% names(Sys.getenv()))
-knitr::opts_chunk$set(fig.align = "center", eval = !is_check)
-```
-
-## Introduction
-
-The aim of this tutorial is to provide a worked example of how vector-based data can be used to develop conservation prioritizations using the _prioritizr R_ package. It is also written for conservation planners that have used the _Marxan_ decision support tool [@r3] and are interested in applying the _prioritizr R_ package to their own work. The dataset used in this tutorial was obtained from the _Introduction to Marxan_ course. This data was originally a subset of a larger spatial prioritization project performed under contract to Australia's Department of Environment and Water Resources [@r30].
-
-Please note that this tutorial uses data from the _prioritizrdata R_, so ensure that it is installed before trying out the code yourself.
-
-## Exploring the data
-
-This dataset contains two items. First, a spatial planning unit layer that has an attribute table which contains three columns: integer unique identifiers ("id"), unimproved land values ("cost"), and their existing level of protection ("status"). Units with 50 % or more of their area contained in protected areas are associated with a status of 2, otherwise they are associated with a value of 0. If you are familiar with the _Marxan_ decision support tool, then you will notice that these columns are formatted in a similar manner to the input data for _Marxan_. For _Marxan_ input data, planning units must be described in a table containing one row for each planning unit with a unique identifier and the corresponding cost.
-
-The second item in this dataset is the raster-based feature data. Specifically, the feature data is expressed as a stack of rasters (termed a `RasterStack` object). Here each layer in the stack represents the distribution of a different vegetation class in Tasmania, Australia. There are 62 vegetation classes in total. For a given layer, pixel values indicate the presence (value of 1) or absence (value of 0) of the vegetation class in an area.
-
-First, load the required packages and the data.
-
-```{r, message = FALSE}
-# load packages
-library(prioritizrdata)
-library(prioritizr)
-
-# load planning unit data
-data(tas_pu)
-
-# load conservation feature data
-data(tas_features)
-```
-
-Now, let's have a look at the planning unit data.
-
-```{r, fig.width = w, fig.height = h}
-# print planning unit data
-print(tas_pu)
-
-# plot map of planning unit costs
-plot(st_as_sf(tas_pu[, "cost"]), main = "Planning unit costs")
-```
-
-Next, let examine the feature data. Here we will only plot the first four features as an example. The pixel values denote the presence or absence of each feature within the extent of the study area.
-
-```{r, fig.width = 4.5, fig.height = 4.5}
-# print planning unit data
-print(tas_features)
-
-# plot map of the first four vegetation classes
-plot(tas_features[[1:4]], main = paste("Feature", 1:4))
-```
-
-The planning units in this example are a spatial polygon layer---not a raster---and so there can be considerable flexibility in the shape of the planning units. That said, there is a trade-off with the efficiency of data pre-processing in vector-based planning unit data compared to raster-based planning unit data. Vector-based planning unit data generally require more time to complete pre-processing computations (e.g. overlaying the planning unit data with the feature data, or generating boundary data). As a consequence, we generally recommend using raster-based planning unit data where possible to reduce processing time---but note that this is not possible when not all planning units are equal-sized squares. Another strategy is to complete the pre-processing in other software environments (e.g. _ArcGIS_) and use the pre-processed data directly with the _prioritizr_ package.
-
-## _Marxan_ problem formulation
-
-Here, we will provide an example of using the `marxan_problem` function to build and solve a typical _Marxan_ conservation planning problem. Then we will show how this same problem can be built and solved using the fully customizable `problem` function as a comparison.
-
-The dataset used in this example follows many of the conventions used by the _Marxan_ decision support tool. As a consequence, it is not too difficult to format the data for use with the `marxan_problem` function. The `marxan_problem` function is essentially a wrapper to the `problem` function. This means that when we solve problems created using the `marxan_problem` function, we will solve them using exact algorithms and not the simulated annealing algorithm used by _Marxan_.
-
-All problem objects formulated with `marxan_problem` use the minimum set objective. Targets can be either relative or absolute, and planning units can be specified for masking in or out using the `locked_in` and `locked_out` arguments. To favor clumped solutions, use the `penalty` argument to impose a penalty on solutions with high boundary lengths (equivalent to the Boundary Length Modifier (BLM) used in _Marxan_), and the `edge_factor` argument to scale the penalty for edges that do not have neighboring planning units, such as the coastline. For simplicity we set all of the targets at the same level, 17 %, to reflect the [Aichi](https://www.cbd.int/sp/targets/) biodiversity target to "safeguard" at least 17% of terrestrial ecosystems by 2020. For example, to prioritize planning units in Tasmania that meet the 17 % representation target at the least cost.
-
-First, we will convert the vector-based planning unit data and raster-based feature data into the tabular formats required by the `marxan_problem` function. These formats are very similar to the formats used by _Marxan_.
-
-```{r}
-# create table with planning unit data
-pu_data <- tas_pu@data
-
-# print first six rows
-head(pu_data)
-
-# create table with the feature identifiers, names, and targets
-spec_data <- data.frame(id = seq_len(nlayers(tas_features)),
-                        name = paste0("veg", seq_len(nlayers(tas_features))),
-                        prop = 0.17)
-
-# print first six rows
-head(spec_data)
-
-# create table with the planning unit vs. feature data
-puvspr_data <- rij_matrix(tas_pu, tas_features)
-puvspr_data <- as(puvspr_data, "dgTMatrix")
-puvspr_data <- data.frame(pu = puvspr_data@j + 1, species = puvspr_data@i + 1,
-                          amount = puvspr_data@x)
-
-# print first six rows
-head(puvspr_data)
-
-# create table with the boundary data
-bound_data <- boundary_matrix(tas_pu)
-bound_data <- as(bound_data, "dgTMatrix")
-bound_data <- data.frame(id1 = bound_data@i + 1, id2 = bound_data@j + 1,
-                         boundary = bound_data@x)
-# print first six rows
-head(bound_data)
-```
-
-Now that we have converted the data to tabular format, we can use the `marxan_problem` function to create a conservation planning problem.
-
-```{r}
-# create problem
-p1 <- marxan_problem(pu_data, spec_data, puvspr_data, bound_data,
-                     blm = 0.0005)
-
-# print problem
-print(p1)
-```
-
-Next, we can solve the problem (see [`?solve`](https://prioritizr.net/reference/solve.html) for more information). The _prioritizr_ R package supports three different exact algorithm software packages: _gurobi_, _Rsymphony_, and _lpsymphony_. There are costs and benefits associated with each of these different solvers, but each software should return similar results. Note that you will need at least one of these package installed on your system to solve problems. We recommend using the _gurobi_ solver if possible, and have used this solver when building this tutorial. After solving the problem, we will calculate some statistics to describe the solution. Note that the planning unit selections are stored in the "solution_1" column of the solution object.
-
-```{r, fig.width = w, fig.height = h}
-# solve problem
-s1 <- solve(p1)
-
-# print first six rows of solution object
-head(s1)
-
-# count number of planning units in solution
-sum(s1$solution_1)
-
-# proportion of planning units in solution
-mean(s1$solution_1)
-
-# calculate feature representation
-r1 <- eval_feature_representation_summary(p1, s1[, "solution_1", drop = FALSE])
-print(r1)
-
-# visualize the solution by converting the solution to a spatial object
-s1 <- SpatialPolygonsDataFrame(as(tas_pu, "SpatialPolygons"), data = s1)
-s1$solution_1 <- factor(s1$solution_1)
-plot(st_as_sf(s1[, "solution_1"]), pal = c("grey90", "darkgreen"),
-    main = "marxan_problem solution")
-```
-
-## General problem formulation
-
-Now we will formulate the exact same problem using the `problem` function and the spatially referenced data. We recommend using this approach instead of the `marxan_problem` because it is more verbose and you can specify exactly how the conservation planning problem should be formulated.
-
-```{r, fig.width = w, fig.height = h}
-# build problem
-p2 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_locked_in_constraints("locked_in") %>%
-      add_binary_decisions() %>%
-      add_boundary_penalties(penalty = 0.0005, edge_factor = 1)
-
-# print the problem
-print(p2)
-
-# solve problem
-s2 <- solve(p2)
-
-# calculate feature representation
-r2 <- eval_feature_representation_summary(p2, s2[, "solution_1"])
-print(r2)
-
-# visualize solution
-s2$solution_1 <- factor(s2$solution_1)
-plot(st_as_sf(s2[, "solution_1"]), pal = c("grey90", "darkgreen"),
-    main = "problem solution")
-```
-
-## Selection frequencies
-
-Similar to the _Marxan_ decision support tool, we can generate a portfolio of solutions and compute the planning unit selection frequencies to understand their relative importance. This can be useful when trying to understand which planning units in the solution are the most irreplaceable. To do this, we will create a portfolio containing 1000 solutions within 20% of optimality, and calculate the number of times that each planning unit was selected. Note that this requires the _Gurobi_ software to be installed.
-
-```{r}
-# create new problem with a portfolio added to it
-p3 <- p2 %>%
-      add_gap_portfolio(number_solutions = 1000, pool_gap = 0.2)
-
-# print problem
-print(p3)
-```
-
-```{r, message = FALSE, results = "hide"}
-# generate solutions
-s3 <- solve(p3)
-
-# find column numbers with the solutions
-solution_columns <- which(grepl("solution", names(s3)))
-
-# calculate selection frequencies
-s3$selection_frequencies <- rowSums(as.matrix(s3@data[, solution_columns]))
-```
-
-```{r, fig.width = 4.5, fig.height = 4.5}
-# plot first four solutions in the portfolio
-s3$solution_1 <- factor(s3$solution_1)
-s3$solution_2 <- factor(s3$solution_2)
-s3$solution_3 <- factor(s3$solution_3)
-s3$solution_4 <- factor(s3$solution_4)
-plot(st_as_sf(s3[, c("solution_1", "solution_2", "solution_3", "solution_4")]),
-  pal = c("grey90", "darkgreen"))
-```
-
-```{r, fig.width = w, fig.height = h}
-# plot histogram of selection frequencies
-hist(s3$selection_frequencies, main = "Selection frequencies",
-     xlab = "Number of times units were selected")
-
-# plot spatial distribution of the selection frequencies
-plot(st_as_sf(s3[, "selection_frequencies"]), main = "Selection frequencies")
-```
-
-## References
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-Tasmania Tutorial
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-
      Tasmania Tutorial
      
-
-
-
-
-
      
-
      Introduction
      
-
      The aim of this tutorial is to provide a worked example of how vector-based data can be used to develop conservation prioritizations using the prioritizr R package. It is also written for conservation planners that have used the Marxan decision support tool (Ball et al. 2009) and are interested in applying the prioritizr R package to their own work. The dataset used in this tutorial was obtained from the Introduction to Marxan course. This data was originally a subset of a larger spatial prioritization project performed under contract to Australia’s Department of Environment and Water Resources (Klein et al. 2007).
      
-
      Please note that this tutorial uses data from the prioritizrdata R, so ensure that it is installed before trying out the code yourself.
      
-
      
-
      
-
      Exploring the data
      
-
      This dataset contains two items. First, a spatial planning unit layer that has an attribute table which contains three columns: integer unique identifiers (“id”), unimproved land values (“cost”), and their existing level of protection (“status”). Units with 50 % or more of their area contained in protected areas are associated with a status of 2, otherwise they are associated with a value of 0. If you are familiar with the Marxan decision support tool, then you will notice that these columns are formatted in a similar manner to the input data for Marxan. For Marxan input data, planning units must be described in a table containing one row for each planning unit with a unique identifier and the corresponding cost.
      
-
      The second item in this dataset is the raster-based feature data. Specifically, the feature data is expressed as a stack of rasters (termed a RasterStack object). Here each layer in the stack represents the distribution of a different vegetation class in Tasmania, Australia. There are 62 vegetation classes in total. For a given layer, pixel values indicate the presence (value of 1) or absence (value of 0) of the vegetation class in an area.
      
-
      First, load the required packages and the data.
      
-
      # load packages
-library(prioritizrdata)
-library(prioritizr)
-
-# load planning unit data
-data(tas_pu)
-
-# load conservation feature data
-data(tas_features)
      
-
      Now, let’s have a look at the planning unit data.
      
-
      # print planning unit data
-print(tas_pu)
      
-
      ## class       : SpatialPolygonsDataFrame 
-## features    : 1130 
-## extent      : 298809.6, 613818.8, 5167775, 5502544  (xmin, xmax, ymin, ymax)
-## crs         : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
-## variables   : 5
-## names       :   id,              cost, status, locked_in, locked_out 
-## min values  :    1, 0.192488262910798,      0,         0,          0 
-## max values  : 1130,  61.9272727272727,      2,         1,          0
      
-
      # plot map of planning unit costs
-plot(st_as_sf(tas_pu[, "cost"]), main = "Planning unit costs")
      
-
      
-
      Next, let examine the feature data. Here we will only plot the first four features as an example. The pixel values denote the presence or absence of each feature within the extent of the study area.
      
-
      # print planning unit data
-print(tas_features)
      
-
      ## class      : RasterStack 
-## dimensions : 398, 359, 142882, 62  (nrow, ncol, ncell, nlayers)
-## resolution : 1000, 1000  (x, y)
-## extent     : 288801.7, 647801.7, 5142976, 5540976  (xmin, xmax, ymin, ymax)
-## crs        : +proj=utm +zone=55 +south +datum=WGS84 +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0 
-## names      : tas_features.1, tas_features.2, tas_features.3, tas_features.4, tas_features.5, tas_features.6, tas_features.7, tas_features.8, tas_features.9, tas_features.10, tas_features.11, tas_features.12, tas_features.13, tas_features.14, tas_features.15, ... 
-## min values :              0,              0,              0,              0,              0,              0,              0,              0,              0,               0,               0,               0,               0,               0,               0, ... 
-## max values :              1,              1,              1,              1,              1,              1,              1,              1,              1,               1,               1,               1,               1,               1,               1, ...
      
-
      # plot map of the first four vegetation classes
-plot(tas_features[[1:4]], main = paste("Feature", 1:4))
      
-
      
-
      The planning units in this example are a spatial polygon layer—not a raster—and so there can be considerable flexibility in the shape of the planning units. That said, there is a trade-off with the efficiency of data pre-processing in vector-based planning unit data compared to raster-based planning unit data. Vector-based planning unit data generally require more time to complete pre-processing computations (e.g. overlaying the planning unit data with the feature data, or generating boundary data). As a consequence, we generally recommend using raster-based planning unit data where possible to reduce processing time—but note that this is not possible when not all planning units are equal-sized squares. Another strategy is to complete the pre-processing in other software environments (e.g. ArcGIS) and use the pre-processed data directly with the prioritizr package.
      
-
      
-
      
-
      Marxan problem formulation
      
-
      Here, we will provide an example of using the marxan_problem function to build and solve a typical Marxan conservation planning problem. Then we will show how this same problem can be built and solved using the fully customizable problem function as a comparison.
      
-
      The dataset used in this example follows many of the conventions used by the Marxan decision support tool. As a consequence, it is not too difficult to format the data for use with the marxan_problem function. The marxan_problem function is essentially a wrapper to the problem function. This means that when we solve problems created using the marxan_problem function, we will solve them using exact algorithms and not the simulated annealing algorithm used by Marxan.
      
-
      All problem objects formulated with marxan_problem use the minimum set objective. Targets can be either relative or absolute, and planning units can be specified for masking in or out using the locked_in and locked_out arguments. To favor clumped solutions, use the penalty argument to impose a penalty on solutions with high boundary lengths (equivalent to the Boundary Length Modifier (BLM) used in Marxan), and the edge_factor argument to scale the penalty for edges that do not have neighboring planning units, such as the coastline. For simplicity we set all of the targets at the same level, 17 %, to reflect the Aichi biodiversity target to “safeguard” at least 17% of terrestrial ecosystems by 2020. For example, to prioritize planning units in Tasmania that meet the 17 % representation target at the least cost.
      
-
      First, we will convert the vector-based planning unit data and raster-based feature data into the tabular formats required by the marxan_problem function. These formats are very similar to the formats used by Marxan.
      
-
      # create table with planning unit data
-pu_data <- tas_pu@data
-
-# print first six rows
-head(pu_data)
      
-
      ##   id     cost status locked_in locked_out
-## 0  1 60.24638      0     FALSE      FALSE
-## 1  2 19.86301      0     FALSE      FALSE
-## 2  3 59.68051      0     FALSE      FALSE
-## 3  4 32.41614      0     FALSE      FALSE
-## 4  5 26.17706      0     FALSE      FALSE
-## 5  6 51.26218      0     FALSE      FALSE
      
-
      # create table with the feature identifiers, names, and targets
-spec_data <- data.frame(id = seq_len(nlayers(tas_features)),
-                        name = paste0("veg", seq_len(nlayers(tas_features))),
-                        prop = 0.17)
-
-# print first six rows
-head(spec_data)
      
-
      ##   id name prop
-## 1  1 veg1 0.17
-## 2  2 veg2 0.17
-## 3  3 veg3 0.17
-## 4  4 veg4 0.17
-## 5  5 veg5 0.17
-## 6  6 veg6 0.17
      
-
      # create table with the planning unit vs. feature data
-puvspr_data <- rij_matrix(tas_pu, tas_features)
-puvspr_data <- as(puvspr_data, "dgTMatrix")
-puvspr_data <- data.frame(pu = puvspr_data@j + 1, species = puvspr_data@i + 1,
-                          amount = puvspr_data@x)
-
-# print first six rows
-head(puvspr_data)
      
-
      ##   pu species       amount
-## 1  3      54 1.000000e+00
-## 2  3      59 1.165971e+01
-## 3  5      30 1.000000e+00
-## 4  6      27 1.000000e+00
-## 5  6      35 1.000000e+00
-## 6  6      59 3.635182e-05
      
-
      # create table with the boundary data
-bound_data <- boundary_matrix(tas_pu)
-bound_data <- as(bound_data, "dgTMatrix")
-bound_data <- data.frame(id1 = bound_data@i + 1, id2 = bound_data@j + 1,
-                         boundary = bound_data@x)
-# print first six rows
-head(bound_data)
      
-
      ##   id1 id2   boundary
-## 1   1   1  6314.6621
-## 2   3   1  3922.9264
-## 3   6   1   150.3778
-## 4   2   2 23958.6982
-## 5   4   2  3233.3056
-## 6   7   2  4639.9220
      
-
      Now that we have converted the data to tabular format, we can use the marxan_problem function to create a conservation planning problem.
      
-
      # create problem
-p1 <- marxan_problem(pu_data, spec_data, puvspr_data, bound_data,
-                     blm = 0.0005)
-
-# print problem
-print(p1)
      
-
      ## Conservation Problem
-##   planning units: data.frame (1130 units)
-##   cost:           min: 0.19249, max: 61.92727
-##   features:       veg1, veg2, veg3, ... (62 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      default
-##   constraints:    <Locked in planning units [257 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (5e-04), zones]>
-##   portfolio:      default
-##   solver:         default
      
-
      Next, we can solve the problem (see ?solve for more information). The prioritizr R package supports three different exact algorithm software packages: gurobi, Rsymphony, and lpsymphony. There are costs and benefits associated with each of these different solvers, but each software should return similar results. Note that you will need at least one of these package installed on your system to solve problems. We recommend using the gurobi solver if possible, and have used this solver when building this tutorial. After solving the problem, we will calculate some statistics to describe the solution. Note that the planning unit selections are stored in the “solution_1” column of the solution object.
      
-
      # solve problem
-s1 <- solve(p1)
      
-
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 6358 rows, 4278 columns and 14496 nonzeros
-## Model fingerprint: 0x96b70d15
-## Variable types: 0 continuous, 4278 integer (4278 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-06, 4e+01]
-##   Objective range  [5e-02, 2e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [1e-01, 1e+02]
-## Found heuristic solution: objective 30263.129158
-## Found heuristic solution: objective 12512.071934
-## Presolve removed 3428 rows and 2241 columns
-## Presolve time: 0.03s
-## Presolved: 2930 rows, 2037 columns, 6882 nonzeros
-## Found heuristic solution: objective 11751.436316
-## Variable types: 0 continuous, 2037 integer (2037 binary)
-## Found heuristic solution: objective 11425.978431
-## Root relaxation presolved: 2930 rows, 2037 columns, 6882 nonzeros
-## 
-## 
-## Root relaxation: objective 1.081359e+04, 715 iterations, 0.02 seconds (0.03 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 10813.5861    0  135 11425.9784 10813.5861  5.36%     -    0s
-## 
-## Explored 1 nodes (715 simplex iterations) in 0.05 seconds (0.08 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 4: 11426 11751.4 12512.1 30263.1 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 1.142597843052e+04, best bound 1.081358611386e+04, gap 5.3596%
      
-
      # print first six rows of solution object
-head(s1)
      
-
      ##   id     cost status locked_in locked_out solution_1
-## 0  1 60.24638      0     FALSE      FALSE          0
-## 1  2 19.86301      0     FALSE      FALSE          0
-## 2  3 59.68051      0     FALSE      FALSE          0
-## 3  4 32.41614      0     FALSE      FALSE          0
-## 4  5 26.17706      0     FALSE      FALSE          0
-## 5  6 51.26218      0     FALSE      FALSE          0
      
-
      # count number of planning units in solution
-sum(s1$solution_1)
      
-
      ## [1] 315
      
-
      # proportion of planning units in solution
-mean(s1$solution_1)
      
-
      ## [1] 0.2787611
      
-
      # calculate feature representation
-r1 <- eval_feature_representation_summary(p1, s1[, "solution_1", drop = FALSE])
-print(r1)
      
-
      ## # A tibble: 62 × 5
-##    summary feature total_amount absolute_held relative_held
-##    <chr>   <chr>          <dbl>         <dbl>         <dbl>
-##  1 overall veg1            33.9          5.97         0.176
-##  2 overall veg2           170.          42.8          0.252
-##  3 overall veg3            24.0          5.63         0.235
-##  4 overall veg4            32.8          8.37         0.256
-##  5 overall veg5            24.8          4.98         0.201
-##  6 overall veg6            22.0          7.10         0.323
-##  7 overall veg7            16.4          3.06         0.187
-##  8 overall veg8            43.0          8.12         0.189
-##  9 overall veg9           388.          78.9          0.203
-## 10 overall veg10           14.5          4.02         0.277
-## # … with 52 more rows
      
-
      # visualize the solution by converting the solution to a spatial object
-s1 <- SpatialPolygonsDataFrame(as(tas_pu, "SpatialPolygons"), data = s1)
-s1$solution_1 <- factor(s1$solution_1)
-plot(st_as_sf(s1[, "solution_1"]), pal = c("grey90", "darkgreen"),
-    main = "marxan_problem solution")
      
-
      
-
      
-
      
-
      General problem formulation
      
-
      Now we will formulate the exact same problem using the problem function and the spatially referenced data. We recommend using this approach instead of the marxan_problem because it is more verbose and you can specify exactly how the conservation planning problem should be formulated.
      
-
      # build problem
-p2 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_locked_in_constraints("locked_in") %>%
-      add_binary_decisions() %>%
-      add_boundary_penalties(penalty = 0.0005, edge_factor = 1)
-
-# print the problem
-print(p2)
      
-
      ## Conservation Problem
-##   planning units: SpatialPolygonsDataFrame (1130 units)
-##   cost:           min: 0.19249, max: 61.92727
-##   features:       tas_features.1, tas_features.2, tas_features.3, ... (62 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      Binary decision 
-##   constraints:    <Locked in planning units [257 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (5e-04), zones]>
-##   portfolio:      default
-##   solver:         default
      
-
      # solve problem
-s2 <- solve(p2)
      
-
      ## Gurobi Optimizer version 9.5.0 build v9.5.0rc5 (linux64)
-## Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
-## Optimize a model with 6358 rows, 4278 columns and 14496 nonzeros
-## Model fingerprint: 0x96b70d15
-## Variable types: 0 continuous, 4278 integer (4278 binary)
-## Coefficient statistics:
-##   Matrix range     [2e-06, 4e+01]
-##   Objective range  [5e-02, 2e+02]
-##   Bounds range     [1e+00, 1e+00]
-##   RHS range        [1e-01, 1e+02]
-## Found heuristic solution: objective 30263.129158
-## Found heuristic solution: objective 12512.071934
-## Presolve removed 3428 rows and 2241 columns
-## Presolve time: 0.03s
-## Presolved: 2930 rows, 2037 columns, 6882 nonzeros
-## Found heuristic solution: objective 11751.436316
-## Variable types: 0 continuous, 2037 integer (2037 binary)
-## Found heuristic solution: objective 11425.978431
-## Root relaxation presolved: 2930 rows, 2037 columns, 6882 nonzeros
-## 
-## 
-## Root relaxation: objective 1.081359e+04, 715 iterations, 0.02 seconds (0.03 work units)
-## 
-##     Nodes    |    Current Node    |     Objective Bounds      |     Work
-##  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
-## 
-##      0     0 10813.5861    0  135 11425.9784 10813.5861  5.36%     -    0s
-## 
-## Explored 1 nodes (715 simplex iterations) in 0.05 seconds (0.08 work units)
-## Thread count was 1 (of 8 available processors)
-## 
-## Solution count 4: 11426 11751.4 12512.1 30263.1 
-## 
-## Optimal solution found (tolerance 1.00e-01)
-## Best objective 1.142597843052e+04, best bound 1.081358611386e+04, gap 5.3596%
      
-
      # calculate feature representation
-r2 <- eval_feature_representation_summary(p2, s2[, "solution_1"])
-print(r2)
      
-
      ## # A tibble: 62 × 5
-##    summary feature         total_amount absolute_held relative_held
-##    <chr>   <chr>                  <dbl>         <dbl>         <dbl>
-##  1 overall tas_features.1          33.9          5.97         0.176
-##  2 overall tas_features.2         170.          42.8          0.252
-##  3 overall tas_features.3          24.0          5.63         0.235
-##  4 overall tas_features.4          32.8          8.37         0.256
-##  5 overall tas_features.5          24.8          4.98         0.201
-##  6 overall tas_features.6          22.0          7.10         0.323
-##  7 overall tas_features.7          16.4          3.06         0.187
-##  8 overall tas_features.8          43.0          8.12         0.189
-##  9 overall tas_features.9         388.          78.9          0.203
-## 10 overall tas_features.10         14.5          4.02         0.277
-## # … with 52 more rows
      
-
      # visualize solution
-s2$solution_1 <- factor(s2$solution_1)
-plot(st_as_sf(s2[, "solution_1"]), pal = c("grey90", "darkgreen"),
-    main = "problem solution")
      
-
      
-
      
-
      
-
      Selection frequencies
      
-
      Similar to the Marxan decision support tool, we can generate a portfolio of solutions and compute the planning unit selection frequencies to understand their relative importance. This can be useful when trying to understand which planning units in the solution are the most irreplaceable. To do this, we will create a portfolio containing 1000 solutions within 20% of optimality, and calculate the number of times that each planning unit was selected. Note that this requires the Gurobi software to be installed.
      
-
      # create new problem with a portfolio added to it
-p3 <- p2 %>%
-      add_gap_portfolio(number_solutions = 1000, pool_gap = 0.2)
-
-# print problem
-print(p3)
      
-
      ## Conservation Problem
-##   planning units: SpatialPolygonsDataFrame (1130 units)
-##   cost:           min: 0.19249, max: 61.92727
-##   features:       tas_features.1, tas_features.2, tas_features.3, ... (62 features)
-##   objective:      Minimum set objective 
-##   targets:        Relative targets [targets (min: 0.17, max: 0.17)]
-##   decisions:      Binary decision 
-##   constraints:    <Locked in planning units [257 locked units]>
-##   penalties:      <Boundary penalties [edge factor (min: 1, max: 1), penalty (5e-04), zones]>
-##   portfolio:      Gap portfolio [number_solutions (1000), pool_gap (0.2)]
-##   solver:         default
      
-
      # generate solutions
-s3 <- solve(p3)
-
-# find column numbers with the solutions
-solution_columns <- which(grepl("solution", names(s3)))
-
-# calculate selection frequencies
-s3$selection_frequencies <- rowSums(as.matrix(s3@data[, solution_columns]))
      
-
      # plot first four solutions in the portfolio
-s3$solution_1 <- factor(s3$solution_1)
-s3$solution_2 <- factor(s3$solution_2)
-s3$solution_3 <- factor(s3$solution_3)
-s3$solution_4 <- factor(s3$solution_4)
-plot(st_as_sf(s3[, c("solution_1", "solution_2", "solution_3", "solution_4")]),
-  pal = c("grey90", "darkgreen"))
      
-
      
-
      # plot histogram of selection frequencies
-hist(s3$selection_frequencies, main = "Selection frequencies",
-     xlab = "Number of times units were selected")
      
-
      
-
      # plot spatial distribution of the selection frequencies
-plot(st_as_sf(s3[, "selection_frequencies"]), main = "Selection frequencies")
      
-
      
-
      
-
      
-
      References
      
-
      
-
      
-Ball, I.R., Possingham, H. & Watts, M.E. (2009). Marxan and relatives: Software for spatial conservation prioritisation. Spatial Conservation Prioritisation: Quantitative Methods & Computational Tools (eds A. Moilanen, K.A. Wilson & H. Possingham), pp. 185–189. Oxford University Press, Oxford, UK.
-
      
-
      
-Klein, C., Carwardine, J., Wilson, K., Watts, M. & Possingham, H. (2007). Spatial Prioritization Approaches for the Conservation of Biodiversity in Australia: Considering Conservation Costs, Ecological & Evolutionary Processes, and Large-Intact Areas. Report to the Department of Environment; Water Resources.
-
      
-
      
-
      
-
-
-
-
-
-
-
-
-
-
-
diff --git a/man/ConservationProblem-class.Rd b/man/ConservationProblem-class.Rd
index 5afa4fd2c..5605d256b 100644
--- a/man/ConservationProblem-class.Rd
+++ b/man/ConservationProblem-class.Rd
@@ -7,13 +7,13 @@
 \description{
 This class is used to represent conservation planning problems. A
 conservation planning problem has spatially explicit planning units.
-A prioritization involves making a decision on each planning unit (e.g. is
+A prioritization involves making a decision on each planning unit (e.g., is
 the planning unit going to be turned into a protected area?). Each
 planning unit is associated with a cost that represents the cost incurred
 by applying the decision to the planning unit. The problem also has a set
 of representation targets for each feature. Further, it also has
 constraints used to ensure that the solution meets additional
-objectives (e.g. certain areas are locked into the solution). Finally,
+objectives (e.g., certain areas are locked into the solution). Finally,
 a conservation planning problem---unlike an optimization problem---also
 requires a method to solve the problem. \strong{This class represents a
 planning problem, to actually build and then solve a planning problem,
diff --git a/man/Parameter-class.Rd b/man/Parameter-class.Rd
index 8dda4d116..aa80afd78 100644
--- a/man/Parameter-class.Rd
+++ b/man/Parameter-class.Rd
@@ -22,7 +22,7 @@ should interact directly with this class.}
 \item{$default}{\code{numeric} vector of default values.}
 
 \item{$class}{\code{character} name of the class that the values inherit
-from (e.g. \code{"integer"}.}
+from (e.g., \code{"integer"}.}
 
 \item{$lower_limit}{\code{numeric} vector specifying the minimum
 permitted value for each element in \verb{$value}.}
diff --git a/man/ScalarParameter-class.Rd b/man/ScalarParameter-class.Rd
index ae53d73bf..f5ef8e7f8 100644
--- a/man/ScalarParameter-class.Rd
+++ b/man/ScalarParameter-class.Rd
@@ -21,7 +21,7 @@ This prototype is used to represent a parameter has a single value.
 \item{$default}{\code{numeric} scalar default value.}
 
 \item{$class}{\code{character} name of the class that \verb{$value} should
-inherit from (e.g. \code{integer}).}
+inherit from (e.g., \code{integer}).}
 
 \item{$lower_limit}{\code{numeric} scalar value that is the minimum value
 that \verb{$value} is permitted to be.}
diff --git a/man/add_absolute_targets.Rd b/man/add_absolute_targets.Rd
index cf24c57a6..d66423387 100644
--- a/man/add_absolute_targets.Rd
+++ b/man/add_absolute_targets.Rd
@@ -17,13 +17,13 @@ add_absolute_targets(x, targets)
 \S4method{add_absolute_targets}{ConservationProblem,character}(x, targets)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{targets}{Object that specifies the targets for each feature.
 See the Targets format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the targets added
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the targets added
 to it.
 }
 \description{
diff --git a/man/add_binary_decisions.Rd b/man/add_binary_decisions.Rd
index 3bb2daaff..4a643a91b 100644
--- a/man/add_binary_decisions.Rd
+++ b/man/add_binary_decisions.Rd
@@ -7,10 +7,10 @@
 add_binary_decisions(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the decisions added
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the decisions added
 to it.
 }
 \description{
@@ -22,7 +22,7 @@ added to a problem then this decision class will be used by default.
 }
 \details{
 Conservation planning problems involve making decisions on planning
-units. These decisions are then associated with actions (e.g. turning a
+units. These decisions are then associated with actions (e.g., turning a
 planning unit into a protected area). Only a
 single decision should be added to a \code{ConservationProblem} object.
 Note that if multiple decisions are added to a problem object, then the
diff --git a/man/add_boundary_penalties.Rd b/man/add_boundary_penalties.Rd
index b4631aca5..cdac0205b 100644
--- a/man/add_boundary_penalties.Rd
+++ b/man/add_boundary_penalties.Rd
@@ -13,11 +13,11 @@ add_boundary_penalties(
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{penalty}{\code{numeric} penalty that is used to scale the importance
 of selecting planning units that are spatially clumped together compared
-to the main problem objective (e.g. solution cost when the argument to
+to the main problem objective (e.g., solution cost when the argument to
 \code{x} has a minimum set objective per \code{\link[=add_min_set_objective]{add_min_set_objective()}}).
 Higher \code{penalty} values prefer solutions with a higher degree of spatial
 clumping, and smaller \code{penalty} values prefer solutions with a smaller
@@ -42,23 +42,23 @@ represent the relative importance of clumping planning units that are
 allocated to the same zone. Cell values must range between 1 and -1, where
 negative values favor solutions that spread out planning units. The default
 argument to \code{zones} is an identity
-matrix (i.e. a matrix with ones along the matrix diagonal and zeros
+matrix (i.e., a matrix with ones along the matrix diagonal and zeros
 elsewhere), so that penalties are incurred when neighboring planning units
 are not assigned to the same zone. If the cells along
 the matrix diagonal contain markedly smaller values than those found
 elsewhere in the matrix, then solutions are preferred that surround
 planning units with those allocated to different zones
-(i.e. greater spatial fragmentation).}
+(i.e., greater spatial fragmentation).}
 
 \item{data}{\code{NULL}, \code{data.frame}, \code{matrix}, or \code{Matrix}
 object containing the boundary data. These data describe the total
 amount of boundary (perimeter) length  for each planning unit,
 and the amount of boundary (perimeter) length shared between different
-planning units (i.e. planning units that are adjacent to each other).
+planning units (i.e., planning units that are adjacent to each other).
 See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the penalties
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the penalties
 added to it.
 }
 \description{
@@ -91,14 +91,14 @@ This argument is the default.
 Note that the boundary data must be supplied
 using one of the other formats below if the planning unit data
 in the argument to \code{x} do not explicitly contain spatial information
-(e.g. planning unit data are a \code{data.frame} or \code{numeric} class).}
+(e.g., planning unit data are a \code{data.frame} or \code{numeric} class).}
 
 \item{\code{data} as a \code{matrix}/\code{Matrix} object}{where rows and columns represent
 different planning units and the value of each cell represents the
 amount of shared boundary length between two different planning units.
 Cells that occur along the matrix diagonal represent the amount of
 exposed boundary associated with each planning unit that has
-no neighbor (e.g. these value might pertain to boundaries along a
+no neighbor (e.g., these value might pertain to boundaries along a
 coastline).}
 
 \item{\code{data} as a \code{data.frame} object}{with the columns \code{"id1"},
@@ -107,7 +107,7 @@ identifiers (indices) for a pair of planning units, and the \code{"boundary"}
 column contains the amount of shared boundary length between these
 two planning units.
 This format follows the the standard \emph{Marxan} format for boundary
-data (i.e. per the "bound.dat" file).}
+data (i.e., per the "bound.dat" file).}
 
 }
 }
@@ -119,11 +119,11 @@ The boundary penalties are implemented using the following equations. Let
 (indexed by \eqn{i} or \eqn{j}), \eqn{Z} represent
 the set of management zones (indexed by \eqn{z} or \eqn{y}), and
 \eqn{X_{iz}}{Xiz} represent the decision
-variable for planning unit \eqn{i} for in zone \eqn{z} (e.g. with binary
+variable for planning unit \eqn{i} for in zone \eqn{z} (e.g., with binary
 values one indicating if planning unit is allocated or not). Also, let
 \eqn{p} represent the argument to \code{penalty}, \eqn{E_z}{Ez} represent the
 argument to \code{edge_factor}, \eqn{B_{ij}}{Bij} represent the matrix argument
-to \code{data} (e.g. generated using \code{\link[=boundary_matrix]{boundary_matrix()}}), and
+to \code{data} (e.g., generated using \code{\link[=boundary_matrix]{boundary_matrix()}}), and
 \eqn{W_{zz}}{Wzz} represent the matrix argument to \code{zones}.
 
 \deqn{
@@ -215,7 +215,7 @@ p9 <- p5 \%>\% add_boundary_penalties(500, zone = zm9)
 
 # create zone matrix which favors clumping planning units in zones 1 and 2
 # together, and favors planning units in zone 3 being spread out
-# (i.e. negative clumping)
+# (i.e., negative clumping)
 zm10 <- diag(3)
 zm10[3, 3] <- -1
 print(zm10)
diff --git a/man/add_cbc_solver.Rd b/man/add_cbc_solver.Rd
index 811a9c528..cd7c60c43 100644
--- a/man/add_cbc_solver.Rd
+++ b/man/add_cbc_solver.Rd
@@ -16,7 +16,7 @@ add_cbc_solver(
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{gap}{\code{numeric} gap to optimality. This gap is relative
 and expresses the acceptable deviance from the optimal objective.
@@ -24,12 +24,12 @@ For example, a value of 0.01 will result in the solver stopping when
 it has found a solution within 1\% of optimality.
 Additionally, a value of 0 will result in the solver stopping
 when it has found an optimal solution.
-The default value is 0.1 (i.e. 10\% from optimality).}
+The default value is 0.1 (i.e., 10\% from optimality).}
 
 \item{time_limit}{\code{numeric} time limit (seconds) for generating solutions.
 The solver will return the current best solution when this time limit is
 exceeded. The default value is the largest integer value
-(i.e. \code{.Machine$integer.max}), effectively meaning that solver
+(i.e., \code{.Machine$integer.max}), effectively meaning that solver
 will keep running until a solution within the optimality gap is found.}
 
 \item{presolve}{\code{logical} attempt to simplify the
@@ -49,7 +49,7 @@ Defaults to \code{FALSE}.}
 \item{start_solution}{\code{NULL} or object containing the starting solution
 for the solver. Defaults to \code{NULL} such that no starting solution is used.
 To specify a starting solution, the argument to \code{start_solution} should
-be in the same format as the planning units (i.e. a \code{NULL}, \code{numeric},
+be in the same format as the planning units (i.e., a \code{NULL}, \code{numeric},
 \code{matrix}, \code{data.frame}, \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
 or \code{\link[sf:sf]{sf::sf()}} object).
 See the Start solution format section for more information.}
@@ -58,7 +58,7 @@ See the Start solution format section for more information.}
 optimization problems? Defaults to \code{TRUE}.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the solver
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the solver
 added to it.
 }
 \description{
@@ -78,7 +78,7 @@ Computational Infrastructure for Operations Research (COIN-OR) project.
 Although formal benchmarks examining the performance of this solver for
 conservation planning problems have yet to be completed, preliminary
 analyses suggest that it performs much faster than the other open-source
-solvers (i.e. \code{\link[=add_rsymphony_solver]{add_rsymphony_solver()}}, \code{\link[=add_rsymphony_solver]{add_rsymphony_solver()}}), and
+solvers (i.e., \code{\link[=add_rsymphony_solver]{add_rsymphony_solver()}}, \code{\link[=add_rsymphony_solver]{add_rsymphony_solver()}}), and
 so we recommend using this solver if the \emph{Gurobi} and \emph{IBM CPLEX} solvers
 are unavailable.
 }
diff --git a/man/add_connectivity_penalties.Rd b/man/add_connectivity_penalties.Rd
index e3ca33d9e..0c2e7880c 100644
--- a/man/add_connectivity_penalties.Rd
+++ b/man/add_connectivity_penalties.Rd
@@ -20,11 +20,11 @@
 \S4method{add_connectivity_penalties}{ConservationProblem,ANY,ANY,array}(x, penalty, zones, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{penalty}{\code{numeric} penalty that is used to scale the importance
 of selecting planning units with strong connectivity between them compared
-to the main problem objective (e.g. solution cost when the argument to
+to the main problem objective (e.g., solution cost when the argument to
 \code{x} has a minimum set objective set using
 \code{\link[=add_min_set_objective]{add_min_set_objective()}}). Higher \code{penalty} values
 can be used to obtain solutions with a high degree of connectivity,
@@ -40,7 +40,7 @@ of zones. Cell values along the diagonal of the matrix represent
 the level of connectivity between planning units allocated to the
 same zone. Cell values must lay between 1 and -1, where negative
 values favor solutions with weak connectivity. The default argument to
-\code{zones} is an identity matrix (i.e. a matrix with ones along the
+\code{zones} is an identity matrix (i.e., a matrix with ones along the
 matrix diagonal and zeros elsewhere), so that planning units are
 only considered to be connected when they are allocated to the same zone.
 This argument is required when the argument to \code{data} is a
@@ -56,7 +56,7 @@ that are associated with higher values are more favorable in the solution.
 See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the penalties
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the penalties
 added to it.
 }
 \description{
@@ -95,7 +95,7 @@ denotes the connectivity between two planning units following the
 \emph{Marxan} format. The data can be used to denote symmetric or
 asymmetric relationships between planning units. By default,
 input data is assumed to be symmetric unless asymmetric data is
-also included (e.g. if data is present for planning units 2 and 3, then
+also included (e.g., if data is present for planning units 2 and 3, then
 the same amount of connectivity is expected for planning units 3 and 2,
 unless connectivity data is also provided for planning units 3 and 2).
 If the argument to \code{x} contains multiple zones, then the columns
@@ -109,7 +109,7 @@ allocated to specific zones. If the columns \code{"zone1"} and
 containing four-dimensions where cell values
 indicate the strength of connectivity between planning units
 when they are assigned to specific management zones. The first two
-dimensions (i.e. rows and columns) indicate the strength of
+dimensions (i.e., rows and columns) indicate the strength of
 connectivity between different planning units and the second two
 dimensions indicate the different management zones. Thus
 the \code{data[1, 2, 3, 4]} indicates the strength of
@@ -126,7 +126,7 @@ Let \eqn{I} represent the set of planning units
 (indexed by \eqn{i} or \eqn{j}), \eqn{Z} represent the set
 of management zones (indexed by \eqn{z} or \eqn{y}), and \eqn{X_{iz}}{Xiz}
 represent the decision variable for planning unit \eqn{i} for in zone
-\eqn{z} (e.g. with binary
+\eqn{z} (e.g., with binary
 values one indicating if planning unit is allocated or not). Also, let
 \eqn{p} represent the argument to \code{penalty}, \eqn{D} represent the
 argument to \code{data}, and \eqn{W} represent the argument
@@ -191,7 +191,7 @@ image(b_matrix)
 }
 # create a symmetric connectivity matrix where the connectivity between
 # two planning units corresponds to their spatial proximity
-# i.e. planning units that are further apart share less connectivity
+# i.e., planning units that are further apart share less connectivity
 centroids <- rgeos::gCentroid(sim_pu_polygons, byid = TRUE)
 d_matrix <- (1 / (as(dist(centroids@coords), "Matrix") + 1))
 
@@ -234,7 +234,7 @@ for (i in seq_len(length(sim_pu_polygons))) {
     # find if planning units are adjacent
     if (adjacent_units[i, j]) {
       # find if planning units lay north and south of each other
-      # i.e. they have the same x-coordinate
+      # i.e., they have the same x-coordinate
       if (centroids@coords[i, 1] == centroids@coords[j, 1]) {
         if (centroids@coords[i, 2] > centroids@coords[j, 2]) {
           # if i is north of j add 10 units of connectivity
diff --git a/man/add_contiguity_constraints.Rd b/man/add_contiguity_constraints.Rd
index 7dda85d75..5f29e02f6 100644
--- a/man/add_contiguity_constraints.Rd
+++ b/man/add_contiguity_constraints.Rd
@@ -14,12 +14,12 @@
 \S4method{add_contiguity_constraints}{ConservationProblem,ANY,matrix}(x, zones, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{zones}{\code{matrix} or \code{Matrix} object describing the
 connection scheme for different zones. Each row and column corresponds
 to a different zone in the argument to \code{x}, and cell values must
-contain binary \code{numeric} values (i.e. one or zero) that indicate
+contain binary \code{numeric} values (i.e., one or zero) that indicate
 if connected planning units (as specified in the argument to
 \code{data}) should be still considered connected if they are allocated to
 different zones. The cell values along the diagonal
@@ -28,7 +28,7 @@ contiguity constraints when they are allocated to a given zone. Note
 arguments to \code{zones} must be symmetric, and that a row or column has
 a value of one then the diagonal element for that row or column must also
 have a value of one. The default argument to \code{zones} is an identity
-matrix (i.e. a matrix with ones along the matrix diagonal and zeros
+matrix (i.e., a matrix with ones along the matrix diagonal and zeros
 elsewhere), so that planning units are only considered connected if they
 are both allocated to the same zone.}
 
@@ -40,7 +40,7 @@ connection data is calculated automatically using the
 See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the constraints
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the constraints
 added to it.
 }
 \description{
@@ -65,13 +65,13 @@ calculated automatically using the \code{\link[=adjacency_matrix]{adjacency_matr
 This is the default argument.
 Note that the connection data must be manually defined
 using one of the other formats below when the planning unit data
-in the argument to \code{x} is not spatially referenced (e.g.
+in the argument to \code{x} is not spatially referenced (e.g.,
 in \code{data.frame} or \code{numeric} format).}
 
 \item{\code{data} as a \code{matrix}/\code{Matrix} object}{where rows and columns represent
 different planning units and the value of each cell indicates if the
 two planning units are connected or not. Cell values should be binary
-\code{numeric} values (i.e. one or zero). Cells that occur along the
+\code{numeric} values (i.e., one or zero). Cells that occur along the
 matrix diagonal have no effect on the solution at all because each
 planning unit cannot be a connected with itself.}
 
@@ -84,7 +84,7 @@ specified in the fields \code{"id1"} and \code{"id2"} are connected
 or not. This data can be used to describe symmetric or
 asymmetric relationships between planning units. By default,
 input data is assumed to be symmetric unless asymmetric data is
-also included (e.g. if data is present for planning units 2 and 3, then
+also included (e.g., if data is present for planning units 2 and 3, then
 the same amount of connectivity is expected for planning units 3 and 2,
 unless connectivity data is also provided for planning units 3 and 2).}
 
diff --git a/man/add_cplex_solver.Rd b/man/add_cplex_solver.Rd
index fd8ef5c2b..e8f04eeaa 100644
--- a/man/add_cplex_solver.Rd
+++ b/man/add_cplex_solver.Rd
@@ -14,7 +14,7 @@ add_cplex_solver(
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{gap}{\code{numeric} gap to optimality. This gap is relative
 and expresses the acceptable deviance from the optimal objective.
@@ -22,12 +22,12 @@ For example, a value of 0.01 will result in the solver stopping when
 it has found a solution within 1\% of optimality.
 Additionally, a value of 0 will result in the solver stopping
 when it has found an optimal solution.
-The default value is 0.1 (i.e. 10\% from optimality).}
+The default value is 0.1 (i.e., 10\% from optimality).}
 
 \item{time_limit}{\code{numeric} time limit (seconds) for generating solutions.
 The solver will return the current best solution when this time limit is
 exceeded. The default value is the largest integer value
-(i.e. \code{.Machine$integer.max}), effectively meaning that solver
+(i.e., \code{.Machine$integer.max}), effectively meaning that solver
 will keep running until a solution within the optimality gap is found.}
 
 \item{presolve}{\code{logical} attempt to simplify the
@@ -40,7 +40,7 @@ optimization algorithm. The default value is 1.}
 optimization problems? Defaults to \code{TRUE}.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the solver
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the solver
 added to it.
 }
 \description{
@@ -54,12 +54,12 @@ It requires the \pkg{cplexAPI} package to be installed
 \details{
 \href{https://www.ibm.com/analytics/cplex-optimizer}{\emph{IBM CPLEX}} is a
 commercial optimization software. It is faster than
-the available open source solvers (e.g. \code{\link[=add_lpsymphony_solver]{add_lpsymphony_solver()}} and
+the available open source solvers (e.g., \code{\link[=add_lpsymphony_solver]{add_lpsymphony_solver()}} and
 \code{\link[=add_rsymphony_solver]{add_rsymphony_solver()}}.
 Although formal benchmarks examining the performance of this solver for
 conservation planning problems have yet to be completed, preliminary
 analyses suggest that it performs slightly slower than the \emph{Gurobi}
-solver (i.e. \code{\link[=add_gurobi_solver]{add_gurobi_solver()}}).
+solver (i.e., \code{\link[=add_gurobi_solver]{add_gurobi_solver()}}).
 We recommend using this solver if the \emph{Gurobi} solver is not available.
 Licenses are available for the \emph{IBM CPLEX} software to academics at no cost
 (see \url{https://www.ibm.com/products/ilog-cplex-optimization-studio}).
@@ -75,7 +75,7 @@ this variable can be specified by adding the following text to the
 }
 
 Note that you may need to change the version
-number in the file path (i.e. \code{"CPLEX_Studio128"}). For more information
+number in the file path (i.e., \code{"CPLEX_Studio128"}). For more information
 on installing the pkg{cplexAPI} package, please see the
 \href{https://github.com/cran/cplexAPI/blob/master/inst/INSTALL}{official installation instructions for the package}.
 }
diff --git a/man/add_cuts_portfolio.Rd b/man/add_cuts_portfolio.Rd
index 30d286082..0c22832bc 100644
--- a/man/add_cuts_portfolio.Rd
+++ b/man/add_cuts_portfolio.Rd
@@ -7,13 +7,13 @@
 add_cuts_portfolio(x, number_solutions = 10L)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{number_solutions}{\code{integer} number of attempts to generate
 different solutions. Defaults to 10.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the portfolio
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the portfolio
 added to it.
 }
 \description{
@@ -33,7 +33,7 @@ having multiple threads allocated for solving an individual problem.
 \section{Notes}{
 
 In early versions (< 4.0.1), this function was only compatible with
-\emph{Gurobi} (i.e. \code{\link[=add_gurobi_solver]{add_gurobi_solver()}}). To provide functionality with
+\emph{Gurobi} (i.e., \code{\link[=add_gurobi_solver]{add_gurobi_solver()}}). To provide functionality with
 exact algorithm solvers, this function now adds constraints to the
 problem formulation to generate multiple solutions.
 }
diff --git a/man/add_default_decisions.Rd b/man/add_default_decisions.Rd
index 9a2b71201..21d009d67 100644
--- a/man/add_default_decisions.Rd
+++ b/man/add_default_decisions.Rd
@@ -7,10 +7,10 @@
 add_default_decisions(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the decisions added
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the decisions added
 to it.
 }
 \description{
diff --git a/man/add_default_solver.Rd b/man/add_default_solver.Rd
index 275b561cc..c542952d9 100644
--- a/man/add_default_solver.Rd
+++ b/man/add_default_solver.Rd
@@ -7,12 +7,12 @@
 add_default_solver(x, ...)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{...}{arguments passed to the solver.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the solver
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the solver
 added to it.
 }
 \description{
diff --git a/man/add_extra_portfolio.Rd b/man/add_extra_portfolio.Rd
index e2af932ea..8dcde81da 100644
--- a/man/add_extra_portfolio.Rd
+++ b/man/add_extra_portfolio.Rd
@@ -7,10 +7,10 @@
 add_extra_portfolio(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the portfolio
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the portfolio
 added to it.
 }
 \description{
@@ -23,7 +23,7 @@ the quality of solutions.
 }
 \details{
 This strategy for generating a portfolio requires problems to
-be solved using the \emph{Gurobi} software suite (i.e. using
+be solved using the \emph{Gurobi} software suite (i.e., using
 \code{\link[=add_gurobi_solver]{add_gurobi_solver()}}. Specifically, version 8.0.0 (or greater)
 of the \pkg{gurobi} package must be installed.
 }
diff --git a/man/add_feature_contiguity_constraints.Rd b/man/add_feature_contiguity_constraints.Rd
index c976c2c39..d6f1a446d 100644
--- a/man/add_feature_contiguity_constraints.Rd
+++ b/man/add_feature_contiguity_constraints.Rd
@@ -17,13 +17,13 @@
 \S4method{add_feature_contiguity_constraints}{ConservationProblem,ANY,ANY}(x, zones, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{zones}{\code{matrix}, \code{Matrix} or \code{list} object describing
 the connection scheme for different zones. For \code{matrix} or
 and \code{Matrix} arguments, each row and column corresponds
 to a different zone in the argument to \code{x}, and cell values must
-contain binary \code{numeric} values (i.e. one or zero) that indicate
+contain binary \code{numeric} values (i.e., one or zero) that indicate
 if connected planning units (as specified in the argument to
 \code{data}) should be still considered connected if they are allocated to
 different zones. The cell values along the diagonal
@@ -36,7 +36,7 @@ should differ among the features, then the argument to \code{zones} should
 be a \code{list} of \code{matrix} or \code{Matrix} objects that shows the
 specific scheme for each feature using the conventions described above.
 The default argument to \code{zones} is an identity
-matrix (i.e. a matrix with ones along the matrix diagonal and zeros
+matrix (i.e., a matrix with ones along the matrix diagonal and zeros
 elsewhere), so that planning units are only considered connected if they
 are both allocated to the same zone.}
 
@@ -54,7 +54,7 @@ all adjacent planning units are treated as being connected for all
 features. See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the constraints
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the constraints
 added to it.
 }
 \description{
@@ -94,13 +94,13 @@ argument and means that all adjacent planning units are treated
 as potentially dispersible for all features.
 Note that the connection data must be manually defined
 using one of the other formats below when the planning unit data
-in the argument to \code{x} is not spatially referenced (e.g.
+in the argument to \code{x} is not spatially referenced (e.g.,
 in \code{data.frame} or \code{numeric} format).}
 
 \item{\code{data} as a\code{matrix}/\code{Matrix} object}{where rows and columns represent
 different planning units and the value of each cell indicates if the
 two planning units are connected or not. Cell values should be binary
-\code{numeric} values (i.e. one or zero). Cells that occur along the
+\code{numeric} values (i.e., one or zero). Cells that occur along the
 matrix diagonal have no effect on the solution at all because each
 planning unit cannot be a connected with itself. Note that pairs
 of connected planning units are treated as being potentially dispersible
@@ -115,7 +115,7 @@ specified in the fields \code{"id1"} and \code{"id2"} are connected
 or not. This data can be used to describe symmetric or
 asymmetric relationships between planning units. By default,
 input data is assumed to be symmetric unless asymmetric data is
-also included (e.g. if data is present for planning units 2 and 3, then
+also included (e.g., if data is present for planning units 2 and 3, then
 the same amount of connectivity is expected for planning units 3 and 2,
 unless connectivity data is also provided for planning units 3 and 2).
 Note that pairs of connected planning units are treated as being
diff --git a/man/add_feature_weights.Rd b/man/add_feature_weights.Rd
index fbf2b1c0b..5ade29f2d 100644
--- a/man/add_feature_weights.Rd
+++ b/man/add_feature_weights.Rd
@@ -11,13 +11,13 @@
 \S4method{add_feature_weights}{ConservationProblem,matrix}(x, weights)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{weights}{\code{numeric} or \code{matrix} of weights.
 See the Weights format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the weights
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the weights
 added to it.
 }
 \description{
@@ -32,7 +32,7 @@ about how the budget should be allocated.
 }
 \details{
 Weights can only be applied to problems that have an objective
-that is budget limited (e.g. \code{\link[=add_max_cover_objective]{add_max_cover_objective()}}).
+that is budget limited (e.g., \code{\link[=add_max_cover_objective]{add_max_cover_objective()}}).
 They can be applied to problems that aim to maximize phylogenetic
 representation (\code{\link[=add_max_phylo_div_objective]{add_max_phylo_div_objective()}}) to favor the
 representation of specific features over the representation of
@@ -95,7 +95,7 @@ p2 <- p1 \%>\% add_feature_weights(w2)
 
 # create manually specified weights that assign higher importance to
 # certain features. These weights could be based on a pre-calculated index
-# (e.g. an index measuring extinction risk where higher values
+# (e.g., an index measuring extinction risk where higher values
 # denote higher extinction risk)
 w3 <- c(0, 0, 0, 100, 200)
 p3 <- p1 \%>\% add_feature_weights(w3)
@@ -137,18 +137,18 @@ plot(sim_phylogeny, main = "represented features",
      tip.color = replace(rep("black", nlayers(sim_features)),
                          which(r4$met), "red"))
 }
-# we can see here that the third feature ("layer.3", i.e.
+# we can see here that the third feature ("layer.3", i.e.,
 # sim_features[[3]]) is not represented in the solution. Let us pretend
 # that it is absolutely critical this feature is adequately conserved
 # in the solution. For example, this feature could represent a species
 # that plays important role in the ecosystem, or a species that is
-# important commercial activities (e.g. eco-tourism). So, to generate
+# important commercial activities (e.g., eco-tourism). So, to generate
 # a solution that conserves the third feature whilst also aiming to
 # maximize phylogenetic diversity, we will create a set of weights that
 # assign a particularly high weighting to the third feature
 w5 <- c(0, 0, 1000, 0, 0)
 
-# we can see that this weighting (i.e. w5[3]) has a much higher value than
+# we can see that this weighting (i.e., w5[3]) has a much higher value than
 # the branch lengths in the phylogeny so solutions that represent this
 # feature be much closer to optimality
 print(sim_phylogeny$edge.length)
diff --git a/man/add_gap_portfolio.Rd b/man/add_gap_portfolio.Rd
index 2388d8403..14222b022 100644
--- a/man/add_gap_portfolio.Rd
+++ b/man/add_gap_portfolio.Rd
@@ -7,7 +7,7 @@
 add_gap_portfolio(x, number_solutions, pool_gap = 0.1)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{number_solutions}{\code{integer} number of solutions required.}
 
@@ -15,12 +15,12 @@ add_gap_portfolio(x, number_solutions, pool_gap = 0.1)
 This relative gap specifies a threshold worst-case performance for
 solutions in the portfolio. For example, value of 0.1 will result in the
 portfolio returning solutions that are within 10\% of an optimal solution.
-Note that the gap specified in the solver (i.e.
+Note that the gap specified in the solver (i.e.,
 \code{\link[=add_gurobi_solver]{add_gurobi_solver()}} must be less than or equal to the gap
 specified to generate the portfolio. Defaults to 0.1.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the portfolio
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the portfolio
 added to it.
 }
 \description{
@@ -33,14 +33,15 @@ frequencies for moderate and large-sized problems (similar to
 }
 \details{
 This strategy for generating a portfolio requires problems to
-be solved using the \emph{Gurobi} software suite (i.e. using
+be solved using the \emph{Gurobi} software suite (i.e., using
 \code{\link[=add_gurobi_solver]{add_gurobi_solver()}}. Specifically, version 9.0.0 (or greater)
 of the \pkg{gurobi} package must be installed.
 Note that the number of solutions returned may be less than the argument to
 \code{number_solutions}, if the total number of solutions that
 meet the optimality gap is less than the number of solutions requested.
 Also, note that this portfolio function only works with problems
-that have binary decisions (i.e. specified using \code{\link[=add_binary_decisions]{add_binary_decisions()}}).
+that have binary decisions (i.e., specified using
+\code{\link[=add_binary_decisions]{add_binary_decisions()}}).
 }
 \examples{
 \dontrun{
diff --git a/man/add_gurobi_solver.Rd b/man/add_gurobi_solver.Rd
index b6380ecf6..6a9b63f92 100644
--- a/man/add_gurobi_solver.Rd
+++ b/man/add_gurobi_solver.Rd
@@ -18,7 +18,7 @@ add_gurobi_solver(
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{gap}{\code{numeric} gap to optimality. This gap is relative
 and expresses the acceptable deviance from the optimal objective.
@@ -26,12 +26,12 @@ For example, a value of 0.01 will result in the solver stopping when
 it has found a solution within 1\% of optimality.
 Additionally, a value of 0 will result in the solver stopping
 when it has found an optimal solution.
-The default value is 0.1 (i.e. 10\% from optimality).}
+The default value is 0.1 (i.e., 10\% from optimality).}
 
 \item{time_limit}{\code{numeric} time limit (seconds) for generating solutions.
 The solver will return the current best solution when this time limit is
 exceeded. The default value is the largest integer value
-(i.e. \code{.Machine$integer.max}), effectively meaning that solver
+(i.e., \code{.Machine$integer.max}), effectively meaning that solver
 will keep running until a solution within the optimality gap is found.}
 
 \item{presolve}{\code{integer} number indicating how intensively the
@@ -65,7 +65,7 @@ the optimization problem exceeds this parameter value, the solver
 will begin storing this information on disk
 (using the *Gurobi( \code{NodeFileStart} parameter).
 This functionality is useful if the system has insufficient memory to
-solve a given problem (e.g. solving the problem with default settings
+solve a given problem (e.g., solving the problem with default settings
 yields the \verb{OUT OF MEMORY} error message) and a system with more memory is
 not readily available.
 For example, a value of 4 indicates that the solver will start using
@@ -77,7 +77,7 @@ to store information on disk when solving a given problem.}
 \item{start_solution}{\code{NULL} or object containing the starting solution
 for the solver. Defaults to \code{NULL} such that no starting solution is used.
 To specify a starting solution, the argument to \code{start_solution} should
-be in the same format as the planning units (i.e. a \code{NULL}, \code{numeric},
+be in the same format as the planning units (i.e., a \code{NULL}, \code{numeric},
 \code{matrix}, \code{data.frame}, \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
 or \code{\link[sf:sf]{sf::sf()}} object).
 See the Start solution format section for more information.}
@@ -86,7 +86,7 @@ See the Start solution format section for more information.}
 optimization problems? Defaults to \code{TRUE}.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the solver
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the solver
 added to it.
 }
 \description{
diff --git a/man/add_linear_constraints.Rd b/man/add_linear_constraints.Rd
index 5879154b9..09eabb799 100644
--- a/man/add_linear_constraints.Rd
+++ b/man/add_linear_constraints.Rd
@@ -23,7 +23,7 @@
 \S4method{add_linear_constraints}{ConservationProblem,ANY,ANY,dgCMatrix}(x, threshold, sense, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{threshold}{\code{numeric} value.
 This threshold value is also known as a "right-hand-side" value
@@ -40,7 +40,7 @@ per integer programming terminology.
 See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the constraints
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the constraints
 added to it.
 }
 \description{
@@ -53,12 +53,12 @@ ensure that solutions meet certain criteria
 (see Examples section below for details).
 For example, these constraints can be used to add multiple budgets.
 They can also be used to ensure that the total number of planning units
-allocated to a certain administrative area (e.g. country) does not exceed
-a certain threshold (e.g. 30\% of its total area). Furthermore,
+allocated to a certain administrative area (e.g., country) does not exceed
+a certain threshold (e.g., 30\% of its total area). Furthermore,
 they can also be used to ensure that features have a minimal level
-of representation (e.g. 30\%) when using an objective
+of representation (e.g., 30\%) when using an objective
 function that aims to enhance feature representation given a budget
-(e.g. \code{\link[=add_min_shortfall_objective]{add_min_shortfall_objective()}}).
+(e.g., \code{\link[=add_min_shortfall_objective]{add_min_shortfall_objective()}}).
 }
 \section{Mathematical formulation}{
 
@@ -67,13 +67,13 @@ equation.
 Let \eqn{I} denote the set of planning units
 (indexed by \eqn{i}), \eqn{Z} the set of management zones (indexed by
 \eqn{z}), and \eqn{X_{iz}}{Xiz} the decision variable for allocating
-planning unit \eqn{i} to zone \eqn{z} (e.g. with binary
+planning unit \eqn{i} to zone \eqn{z} (e.g., with binary
 values indicating if each planning unit is allocated or not). Also, let
 \eqn{D_{iz}}{Diz} denote the constraint data associated with
 planning units \eqn{i \in I}{i in I} for zones \eqn{z \in Z}{z in Z}
 (argument to \code{data}, if supplied as a \code{matrix} object),
 \eqn{\theta} denote the constraint sense
-(argument to \code{sense}, e.g. \eqn{<=}), and \eqn{t} denote the constraint
+(argument to \code{sense}, e.g., \eqn{<=}), and \eqn{t} denote the constraint
 threshold (argument to \code{threshold}).
 
 \deqn{
@@ -216,7 +216,7 @@ plot(stack(s0, s2), main = c("s1", "s2"), axes = FALSE, box = FALSE)
 # third, let's create a modified version of p0 that contains
 # additional constraints to ensure that the solution equitably
 # distributes conservation effort across different administrative areas
-# (e.g. countries) within the study region
+# (e.g., countries) within the study region
 
 # to begin with, we will simulate a dataset describing the spatial extent of
 # four different administrative areas across the study region
diff --git a/man/add_linear_penalties.Rd b/man/add_linear_penalties.Rd
index 064e49d21..82c3815cf 100644
--- a/man/add_linear_penalties.Rd
+++ b/man/add_linear_penalties.Rd
@@ -23,7 +23,7 @@
 \S4method{add_linear_penalties}{ConservationProblem,ANY,dgCMatrix}(x, penalty, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{penalty}{\code{numeric} penalty value that is used to scale the
 importance not selecting planning units with high \code{data} values.
@@ -44,15 +44,15 @@ associated with higher data values are penalized more strongly
 in the solution. See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the penalties
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the penalties
 added to it.
 }
 \description{
 Add penalties to a conservation planning \code{\link[=problem]{problem()}} to penalize
 solutions that select planning units with higher values from a specific
-data source (e.g. anthropogenic impact). These penalties assume
+data source (e.g., anthropogenic impact). These penalties assume
 a linear trade-off between the penalty values and the primary
-objective of the conservation planning \code{\link[=problem]{problem()}} (e.g.
+objective of the conservation planning \code{\link[=problem]{problem()}} (e.g.,
 solution cost for minimum set problems; \code{\link[=add_min_set_objective]{add_min_set_objective()}}.
 }
 \details{
@@ -116,7 +116,7 @@ equations.
 Let \eqn{I} denote the set of planning units
 (indexed by \eqn{i}), \eqn{Z} the set of management zones (indexed by
 \eqn{z}), and \eqn{X_{iz}}{Xiz} the decision variable for allocating
-planning unit \eqn{i} to zone \eqn{z} (e.g. with binary
+planning unit \eqn{i} to zone \eqn{z} (e.g., with binary
 values indicating if each planning unit is allocated or not). Also, let
 \eqn{P_z} represent the penalty scaling value for zones
 \eqn{z \in Z}{z in Z} (argument to \code{penalty}), and
@@ -143,7 +143,7 @@ set.seed(600)
 data(sim_pu_polygons, sim_pu_zones_stack, sim_features, sim_features_zones)
 
 # add a column to contain the penalty data for each planning unit
-# e.g. these values could indicate the level of habitat
+# e.g., these values could indicate the level of habitat
 sim_pu_polygons$penalty_data <- runif(nrow(sim_pu_polygons))
 
 # plot the penalty data to visualise its spatial distribution
@@ -174,7 +174,7 @@ s1 <- solve(p1)
 s2 <- solve(p2)
 
 # plot the solutions and compare them,
-# since we supplied a very high penalty value (i.e. 100), relative
+# since we supplied a very high penalty value (i.e., 100), relative
 # to the range of values in the penalty data and the objective function,
 # the solution in s2 is very sensitive to values in the penalty data
 spplot(s1, zcol = "solution_1", main = "solution without penalties",
@@ -183,7 +183,7 @@ spplot(s2, zcol = "solution_1", main = "solution with penalties",
        axes = FALSE, box = FALSE)
 
 # for real conservation planning exercises,
-# it would be worth exploring a range of penalty values (e.g. ranging
+# it would be worth exploring a range of penalty values (e.g., ranging
 # from 1 to 100 increments of 5) to explore the trade-offs
 }
 
diff --git a/man/add_locked_in_constraints.Rd b/man/add_locked_in_constraints.Rd
index e07a82c48..b994cab4e 100644
--- a/man/add_locked_in_constraints.Rd
+++ b/man/add_locked_in_constraints.Rd
@@ -28,13 +28,13 @@ add_locked_in_constraints(x, locked_in)
 \S4method{add_locked_in_constraints}{ConservationProblem,Raster}(x, locked_in)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{locked_in}{Object that determines which planning units that should be
 locked in. See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the constraints
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the constraints
 added to it.
 }
 \description{
@@ -45,7 +45,7 @@ lock in planning units that are inside existing protected areas so that the
 solution fills in the gaps in the existing reserve network. If specific
 planning units should be locked out of a solution, use
 \code{\link[=add_locked_out_constraints]{add_locked_out_constraints()}}. For problems with non-binary
-planning unit allocations (e.g. proportions), the
+planning unit allocations (e.g., proportions), the
 \code{\link[=add_manual_locked_constraints]{add_manual_locked_constraints()}} function can be used to lock
 planning unit allocations to a specific value.
 }
@@ -87,7 +87,7 @@ This format is only
 compatible if the planning units in the argument to \code{x} are a
 \code{\linkS4class{Spatial}}, \code{\link[sf:sf]{sf::sf()}}, or
 \code{data.frame} object. The fields
-(columns) must have \code{logical} (i.e. \code{TRUE} or \code{FALSE})
+(columns) must have \code{logical} (i.e., \code{TRUE} or \code{FALSE})
 values indicating if the planning unit is to be locked for the solution.
 For problems that contain a single zone, the argument to \code{data} must
 contain a single field name. Otherwise, for problems that
diff --git a/man/add_locked_out_constraints.Rd b/man/add_locked_out_constraints.Rd
index fb703f7bd..d8429ddba 100644
--- a/man/add_locked_out_constraints.Rd
+++ b/man/add_locked_out_constraints.Rd
@@ -28,13 +28,13 @@ add_locked_out_constraints(x, locked_out)
 \S4method{add_locked_out_constraints}{ConservationProblem,Raster}(x, locked_out)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{locked_out}{Object that determines which planning units that should be
 locked out. See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the constraints
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the constraints
 added to it.
 }
 \description{
@@ -44,7 +44,7 @@ that specific planning units are not selected
 useful to lock out planning units that have been degraded and are not
 suitable for conserving species. If specific planning units should be locked
 in to the solution, use \code{\link[=add_locked_out_constraints]{add_locked_out_constraints()}}. For
-problems with non-binary planning unit allocations (e.g. proportions), the
+problems with non-binary planning unit allocations (e.g., proportions), the
 \code{\link[=add_manual_locked_constraints]{add_manual_locked_constraints()}} function can be used to lock
 planning unit allocations to a specific value.
 }
@@ -86,7 +86,7 @@ This format is only
 compatible if the planning units in the argument to \code{x} are a
 \code{\linkS4class{Spatial}}, \code{\link[sf:sf]{sf::sf()}}, or
 \code{data.frame} object. The fields
-(columns) must have \code{logical} (i.e. \code{TRUE} or \code{FALSE})
+(columns) must have \code{logical} (i.e., \code{TRUE} or \code{FALSE})
 values indicating if the planning unit is to be locked for the solution.
 For problems that contain a single zone, the argument to \code{data} must
 contain a single field name. Otherwise, for problems that
diff --git a/man/add_loglinear_targets.Rd b/man/add_loglinear_targets.Rd
index b8fc3279c..d1fdbd6da 100644
--- a/man/add_loglinear_targets.Rd
+++ b/man/add_loglinear_targets.Rd
@@ -17,7 +17,7 @@ add_loglinear_targets(
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{lower_bound_amount}{\code{numeric} threshold.}
 
@@ -43,7 +43,7 @@ use when calculating the targets. Defaults to the feature abundances in the
 study area (calculated using the \code{\link[=feature_abundances]{feature_abundances()}} function.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the targets added
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the targets added
 to it.
 }
 \description{
@@ -76,7 +76,7 @@ that should be used when calculating the targets.
 
 The target calculations do not account for the
 size of each planning unit. Therefore, the feature data should account for
-the size of each planning unit if this is important (e.g. pixel values in
+the size of each planning unit if this is important (e.g., pixel values in
 the argument to \code{features} in the function \code{\link[=problem]{problem()}} could
 correspond to amount of land occupied by the feature in \eqn{km^2} units).
 Additionally, the function can only be applied to
diff --git a/man/add_lsymphony_solver.Rd b/man/add_lsymphony_solver.Rd
index 84c00253b..332721a20 100644
--- a/man/add_lsymphony_solver.Rd
+++ b/man/add_lsymphony_solver.Rd
@@ -14,7 +14,7 @@ add_lpsymphony_solver(
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{gap}{\code{numeric} gap to optimality. This gap is relative
 and expresses the acceptable deviance from the optimal objective.
@@ -22,12 +22,12 @@ For example, a value of 0.01 will result in the solver stopping when
 it has found a solution within 1\% of optimality.
 Additionally, a value of 0 will result in the solver stopping
 when it has found an optimal solution.
-The default value is 0.1 (i.e. 10\% from optimality).}
+The default value is 0.1 (i.e., 10\% from optimality).}
 
 \item{time_limit}{\code{numeric} time limit (seconds) for generating solutions.
 The solver will return the current best solution when this time limit is
 exceeded. The default value is the largest integer value
-(i.e. \code{.Machine$integer.max}), effectively meaning that solver
+(i.e., \code{.Machine$integer.max}), effectively meaning that solver
 will keep running until a solution within the optimality gap is found.}
 
 \item{first_feasible}{\code{logical} should the first feasible solution be
@@ -42,7 +42,7 @@ Defaults to \code{FALSE}.}
 optimization problems? Defaults to \code{TRUE}.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the solver
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the solver
 added to it.
 }
 \description{
diff --git a/man/add_mandatory_allocation_constraints.Rd b/man/add_mandatory_allocation_constraints.Rd
index f9bba43b1..3086865f1 100644
--- a/man/add_mandatory_allocation_constraints.Rd
+++ b/man/add_mandatory_allocation_constraints.Rd
@@ -8,10 +8,10 @@
 \S4method{add_mandatory_allocation_constraints}{ConservationProblem}(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the constraints
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the constraints
 added to it.
 }
 \description{
@@ -27,11 +27,11 @@ developing land-use plans, some decision makers may require that each and
 every single parcel of land has been allocated a specific land-use type.
 In other words are no "left over" areas. Although it might seem tempting
 to simply solve the problem and manually assign "left over" planning units
-to a default zone afterwards (e.g. an "other", "urban", or "grazing"
+to a default zone afterwards (e.g., an "other", "urban", or "grazing"
 land-use), this could result in highly sub-optimal solutions if there
 penalties for siting the default land-use adjacent to other zones.
 Instead, this function can be used to specify that all planning units in a
-problem with multiple zones must be allocated to a management zone (i.e.
+problem with multiple zones must be allocated to a management zone (i.e.,
 zone allocation is mandatory).
 }
 \examples{
diff --git a/man/add_manual_bounded_constraints.Rd b/man/add_manual_bounded_constraints.Rd
index f86be9bf1..3a89d9504 100644
--- a/man/add_manual_bounded_constraints.Rd
+++ b/man/add_manual_bounded_constraints.Rd
@@ -13,18 +13,18 @@ add_manual_bounded_constraints(x, data)
 \S4method{add_manual_bounded_constraints}{ConservationProblem,tbl_df}(x, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{data}{\code{data.frame} or \code{\link[tibble:tibble]{tibble::tibble()}} object.
 See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the constraints
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the constraints
 added to it.
 }
 \description{
 Add constraints to a conservation planning \code{\link[=problem]{problem()}} to ensure
-that the planning unit values (e.g. proportion, binary) in a solution
+that the planning unit values (e.g., proportion, binary) in a solution
 range between specific lower and upper bounds. This function offers more
 fine-grained control than the \code{\link[=add_manual_locked_constraints]{add_manual_locked_constraints()}}
 function and is is most useful for problems involving proportion-type
diff --git a/man/add_manual_locked_constraints.Rd b/man/add_manual_locked_constraints.Rd
index 1b6e19e1b..4716e9d3b 100644
--- a/man/add_manual_locked_constraints.Rd
+++ b/man/add_manual_locked_constraints.Rd
@@ -13,13 +13,13 @@ add_manual_locked_constraints(x, data)
 \S4method{add_manual_locked_constraints}{ConservationProblem,tbl_df}(x, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{data}{\code{data.frame} or \code{\link[tibble:tibble]{tibble::tibble()}} object.
 See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the constraints
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the constraints
 added to it.
 }
 \description{
@@ -44,10 +44,10 @@ zone.}
 
 \item{status}{\code{numeric} values indicating how much
 of each planning unit should be allocated to each zone in the solution.
-For example, the \code{numeric} values could be binary values (i.e. zero
+For example, the \code{numeric} values could be binary values (i.e., zero
 or one) for problems containing binary-type decision variables
 (using the \code{\link[=add_binary_decisions]{add_binary_decisions()}} function). Alternatively,
-the \code{numeric} values could be proportions (e.g. 0.5) for problems
+the \code{numeric} values could be proportions (e.g., 0.5) for problems
 containing proportion-type decision variables (using the
 \code{\link[=add_proportion_decisions]{add_proportion_decisions()}}).}
 
diff --git a/man/add_manual_targets.Rd b/man/add_manual_targets.Rd
index 185bbcfdf..d2784e95e 100644
--- a/man/add_manual_targets.Rd
+++ b/man/add_manual_targets.Rd
@@ -15,13 +15,13 @@ add_manual_targets(x, targets)
 \S4method{add_manual_targets}{ConservationProblem,tbl_df}(x, targets)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{targets}{\code{data.frame} or \code{\link[tibble:tibble]{tibble::tibble()}} object.
 See the Target data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the targets added
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the targets added
 to it.
 }
 \description{
@@ -33,7 +33,7 @@ most cases, targets can be specified using the
 functions. However, this function can be used to (i) mix absolute and
 relative targets for different features and zones, (ii) set targets that
 pertain to the allocations of planning units in multiple zones, and (iii)
-set targets that require different senses (e.g. targets which specify the
+set targets that require different senses (e.g., targets which specify the
 solution should not exceed a certain quantity using \code{"<="} values).
 }
 \details{
diff --git a/man/add_max_cover_objective.Rd b/man/add_max_cover_objective.Rd
index 15b60a5b9..9103a477e 100644
--- a/man/add_max_cover_objective.Rd
+++ b/man/add_max_cover_objective.Rd
@@ -7,7 +7,7 @@
 add_max_cover_objective(x, budget)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{budget}{\code{numeric} value specifying the maximum expenditure of
 the prioritization. For problems with multiple zones, the argument
@@ -16,7 +16,7 @@ for the entire solution or a \code{numeric} vector to specify
 a budget for each each management zone.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the objective
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the objective
 added to it.
 }
 \description{
@@ -31,10 +31,10 @@ The maximum coverage objective seeks to find the set of planning units that
 maximizes the number of represented features, while keeping cost within a
 fixed budget. Here, features are treated as being represented if
 the reserve system contains at least a single instance of a feature
-(i.e. an amount greater than 1). This formulation has often been
+(i.e., an amount greater than 1). This formulation has often been
 used in conservation planning problems dealing with binary biodiversity
 data that indicate the presence/absence of suitable habitat
-(e.g. Church & Velle 1974). Additionally, weights can be used to favor the
+(e.g., Church & Velle 1974). Additionally, weights can be used to favor the
 representation of certain features over other features (see
 \code{\link[=add_feature_weights]{add_feature_weights()}}). Check out the
 \code{\link[=add_max_features_objective]{add_max_features_objective()}} for a more
@@ -58,7 +58,7 @@ Maximize sum_i^I (-s * ci * xi) + sum_j^J (yj * wj) subject to
 sum_i^I (xi * rij) >= (yj * 1) for all j in J &
 sum_i^I (xi * ci) <= B}
 
-Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.
+Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.,
 specifying whether planning unit \eqn{i}{i} has been selected (1) or not
 (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning
 unit \eqn{i}{i}, \eqn{y_j}{yj} indicates if the solution has meet
diff --git a/man/add_max_features_objective.Rd b/man/add_max_features_objective.Rd
index e8a95f3d8..9f9cbd607 100644
--- a/man/add_max_features_objective.Rd
+++ b/man/add_max_features_objective.Rd
@@ -7,7 +7,7 @@
 add_max_features_objective(x, budget)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{budget}{\code{numeric} value specifying the maximum expenditure of
 the prioritization. For problems with multiple zones, the argument
@@ -16,7 +16,7 @@ for the entire solution or (ii) a \code{numeric} vector to specify
 a separate budget for each management zone.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the objective
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the objective
 added to it.
 }
 \description{
@@ -51,7 +51,7 @@ Maximize sum_i^I (-s * ci * xi) + sum_j^J (yj * wj) subject to
 sum_i^I (xi * rij) >= (yj tj) for all j in J &
 sum_i^I (xi * ci) <= B}
 
-Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.
+Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.,
 specifying whether planning unit \eqn{i}{i} has been selected (1) or not
 (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning
 unit \eqn{i}{i}, \eqn{t_j}{tj} is the representation target for feature
diff --git a/man/add_max_phylo_div_objective.Rd b/man/add_max_phylo_div_objective.Rd
index 7c21107cc..8403f5dd0 100644
--- a/man/add_max_phylo_div_objective.Rd
+++ b/man/add_max_phylo_div_objective.Rd
@@ -8,7 +8,7 @@
 add_max_phylo_div_objective(x, budget, tree)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{budget}{\code{numeric} value specifying the maximum expenditure of
 the prioritization. For problems with multiple zones, the argument
@@ -20,7 +20,7 @@ a separate budget for each management zone.}
 for the conservation features.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the objective
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the objective
 added to it.
 }
 \description{
@@ -76,7 +76,7 @@ Maximize sum_i^I (-s * ci * xi) + sum_j^J (mb * lb) subject to sum_i^I
 (xi * rij) >= (yj * tj) for all j in J & mb <= yj for all j in T(b) &
 sum_i^I (xi * ci) <= B}
 
-Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.
+Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.,
 specifying whether planning unit \eqn{i}{i} has been selected (1) or not
 (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning
 unit \eqn{i}{i}, \eqn{t_j}{tj} is the representation target for feature
diff --git a/man/add_max_phylo_end_objective.Rd b/man/add_max_phylo_end_objective.Rd
index 607e87fb2..6d47978da 100644
--- a/man/add_max_phylo_end_objective.Rd
+++ b/man/add_max_phylo_end_objective.Rd
@@ -7,7 +7,7 @@
 add_max_phylo_end_objective(x, budget, tree)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{budget}{\code{numeric} value specifying the maximum expenditure of
 the prioritization. For problems with multiple zones, the argument
@@ -19,7 +19,7 @@ a separate budget for each management zone.}
 for the conservation features.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the objective
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the objective
 added to it.
 }
 \description{
@@ -75,7 +75,7 @@ Maximize sum_i^I (-s * ci * xi) + sum_j^J (mb * lb * (1 / ab))
 subject to sum_i^I (xi * rij) >= (yj * tj) for all j in J &
 mb <= yj for all j in T(b) & sum_i^I (xi * ci) <= B}
 
-Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.
+Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.,
 specifying whether planning unit \eqn{i}{i} has been selected (1) or not
 (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning
 unit \eqn{i}{i}, \eqn{t_j}{tj} is the representation target for feature
diff --git a/man/add_max_utility_objective.Rd b/man/add_max_utility_objective.Rd
index 24c2537bd..f662400d6 100644
--- a/man/add_max_utility_objective.Rd
+++ b/man/add_max_utility_objective.Rd
@@ -7,7 +7,7 @@
 add_max_utility_objective(x, budget)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{budget}{\code{numeric} value specifying the maximum expenditure of
 the prioritization. For problems with multiple zones, the argument
@@ -16,7 +16,7 @@ for the entire solution or (ii) a \code{numeric} vector to specify
 a separate budget for each management zone.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the objective
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the objective
 added to it.
 }
 \description{
@@ -50,7 +50,7 @@ by \eqn{j}{j}) as:
 Maximize sum_i^I (-s * ci * xi) + sum_j^J (aj * wj) subject to
 aj = sum_i^I (xi * rij) for all j in J & sum_i^I (xi * ci) <= B}
 
-Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.
+Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.,
 specifying whether planning unit \eqn{i}{i} has been selected (1) or not
 (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning
 unit \eqn{i}{i}, \eqn{A_j}{Aj} is the amount of feature \eqn{j}{j}
diff --git a/man/add_min_largest_shortfall_objective.Rd b/man/add_min_largest_shortfall_objective.Rd
index 44da36f9c..9d07759a2 100644
--- a/man/add_min_largest_shortfall_objective.Rd
+++ b/man/add_min_largest_shortfall_objective.Rd
@@ -7,7 +7,7 @@
 add_min_largest_shortfall_objective(x, budget)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{budget}{\code{numeric} value specifying the maximum expenditure of
 the prioritization. For problems with multiple zones, the argument
@@ -16,7 +16,7 @@ for the entire solution or (ii) a \code{numeric} vector to specify
 a separate budget for each management zone.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the objective
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the objective
 added to it.
 }
 \description{
@@ -24,7 +24,7 @@ Set the objective of a conservation planning \code{\link[=problem]{problem()}} t
 minimize the largest target shortfall while ensuring that
 the cost of the solution does not exceed a budget. Note that if the
 target shortfall for a single feature cannot be decreased beyond a certain
-point (e.g. because all remaining planning units occupied by that feature
+point (e.g., because all remaining planning units occupied by that feature
 are too costly or are locked out), then solutions may only use a small
 proportion of the specified budget.
 }
@@ -57,7 +57,7 @@ sum_i^I (xi * rij) + yj >= tj for all j in J &
 l >= (yj / tj) for all j in J &
 sum_i^I (xi * ci) <= B}
 
-Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.
+Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.,
 specifying whether planning unit \eqn{i}{i} has been selected (1) or not
 (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning
 unit \eqn{i}{i}, and \eqn{t_j}{tj} is the representation target for feature
diff --git a/man/add_min_set_objective.Rd b/man/add_min_set_objective.Rd
index 832d400ad..878580294 100644
--- a/man/add_min_set_objective.Rd
+++ b/man/add_min_set_objective.Rd
@@ -7,10 +7,10 @@
 add_min_set_objective(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the objective
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the objective
 added to it.
 }
 \description{
@@ -41,7 +41,7 @@ mathematically for a set of planning units (\eqn{I}{I} indexed by
 Minimize sum_i^I (xi * ci) subject to sum_i^I (xi * rij) >= Tj for all
 j in J}
 
-Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.
+Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.,
 specifying whether planning unit \eqn{i}{i} has been selected (1) or not
 (0)), \eqn{c_i}{ci} is the cost of planning unit \eqn{i}{i},
 \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning unit
diff --git a/man/add_min_shortfall_objective.Rd b/man/add_min_shortfall_objective.Rd
index 67493dae9..1cf22bdc4 100644
--- a/man/add_min_shortfall_objective.Rd
+++ b/man/add_min_shortfall_objective.Rd
@@ -7,7 +7,7 @@
 add_min_shortfall_objective(x, budget)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{budget}{\code{numeric} value specifying the maximum expenditure of
 the prioritization. For problems with multiple zones, the argument
@@ -16,7 +16,7 @@ for the entire solution or (ii) a \code{numeric} vector to specify
 a separate budget for each management zone.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the objective
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the objective
 added to it.
 }
 \description{
@@ -49,7 +49,7 @@ Minimize sum_j^J wj * (yj / tj) subject to
 sum_i^I (xi * rij) + yj >= tj for all j in J &
 sum_i^I (xi * ci) <= B}
 
-Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.
+Here, \eqn{x_i}{xi} is the \link{decisions} variable (e.g.,
 specifying whether planning unit \eqn{i}{i} has been selected (1) or not
 (0)), \eqn{r_{ij}}{rij} is the amount of feature \eqn{j}{j} in planning
 unit \eqn{i}{i}, \eqn{t_j}{tj} is the representation target for feature
diff --git a/man/add_neighbor_constraints.Rd b/man/add_neighbor_constraints.Rd
index 36789a6e3..7ce7a5663 100644
--- a/man/add_neighbor_constraints.Rd
+++ b/man/add_neighbor_constraints.Rd
@@ -17,7 +17,7 @@
 \S4method{add_neighbor_constraints}{ConservationProblem,ANY,ANY,array}(x, k, zones, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{k}{\code{integer} minimum number of neighbors for selected
 planning units in the solution. For problems with multiple zones,
@@ -26,13 +26,13 @@ the argument to \code{k} must have an element for each zone.}
 \item{zones}{\code{matrix} or \code{Matrix} object describing the
 neighborhood scheme for different zones. Each row and column corresponds
 to a different zone in the argument to \code{x}, and cell values must
-contain binary \code{numeric} values (i.e. one or zero) that indicate
+contain binary \code{numeric} values (i.e., one or zero) that indicate
 if neighboring planning units (as specified in the argument to
 \code{data}) should be considered neighbors if they are allocated to
 different zones. The cell values along the diagonal
 of the matrix indicate if planning units that are allocated to the same
 zone should be considered neighbors or not. The default argument to
-\code{zones} is an identity matrix (i.e. a matrix with ones along the
+\code{zones} is an identity matrix (i.e., a matrix with ones along the
 matrix diagonal and zeros elsewhere), so that planning units are
 only considered neighbors if they are both allocated to the same zone.}
 
@@ -44,7 +44,7 @@ neighborhood data is calculated automatically using the
 See the Data format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the constraints
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the constraints
 added to it.
 }
 \description{
@@ -69,13 +69,13 @@ automatically
 using the \code{\link[=adjacency_matrix]{adjacency_matrix()}} function. This is the default
 argument. Note that the neighborhood data must be manually defined
 using one of the other formats below when the planning unit data
-in the argument to \code{x} is not spatially referenced (e.g.
+in the argument to \code{x} is not spatially referenced (e.g.,
 in \code{data.frame} or \code{numeric} format).}
 
 \item{\code{data} as a \code{matrix}/\code{Matrix} object}{where rows and columns represent
 different planning units and the value of each cell indicates if the
 two planning units are neighbors or not. Cell values should be binary
-\code{numeric} values (i.e. one or zero). Cells that occur along the
+\code{numeric} values (i.e., one or zero). Cells that occur along the
 matrix diagonal have no effect on the solution at all because each
 planning unit cannot be a neighbor with itself.}
 
@@ -88,7 +88,7 @@ specified in the fields \code{"id1"} and \code{"id2"} are neighbors
 or not. This data can be used to describe symmetric or
 asymmetric relationships between planning units. By default,
 input data is assumed to be symmetric unless asymmetric data is
-also included (e.g. if data is present for planning units 2 and 3, then
+also included (e.g., if data is present for planning units 2 and 3, then
 the same amount of connectivity is expected for planning units 3 and 2,
 unless connectivity data is also provided for planning units 3 and 2).
 If the argument to \code{x} contains multiple zones, then the columns
@@ -102,7 +102,7 @@ are present, then the argument to \code{zones} must be \code{NULL}.}
 \code{numeric} values indicate if planning unit should be treated
 as being neighbors with every other planning unit when they
 are allocated to every combination of management zone. The first two
-dimensions (i.e. rows and columns) correspond to the planning units,
+dimensions (i.e., rows and columns) correspond to the planning units,
 and second two dimensions correspond to the management zones. For
 example, if the argument to \code{data} had a value of 1 at the index
 \code{data[1, 2, 3, 4]} this would indicate that planning unit 1 and
diff --git a/man/add_proportion_decisions.Rd b/man/add_proportion_decisions.Rd
index 4d325879f..672662b3d 100644
--- a/man/add_proportion_decisions.Rd
+++ b/man/add_proportion_decisions.Rd
@@ -7,10 +7,10 @@
 add_proportion_decisions(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the decisions added
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the decisions added
 to it.
 }
 \description{
@@ -23,7 +23,7 @@ decisions
 }
 \details{
 Conservation planning problems involve making decisions on planning
-units. These decisions are then associated with actions (e.g. turning a
+units. These decisions are then associated with actions (e.g., turning a
 planning unit into a protected area). Only a
 single decision should be added to a \code{ConservationProblem} object.
 Note that if multiple decisions are added to a problem object, then the
diff --git a/man/add_relative_targets.Rd b/man/add_relative_targets.Rd
index ff4e3f939..3b599b7ff 100644
--- a/man/add_relative_targets.Rd
+++ b/man/add_relative_targets.Rd
@@ -18,13 +18,13 @@ add_relative_targets(x, targets)
 \S4method{add_relative_targets}{ConservationProblem,character}(x, targets)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{targets}{Object that specifies the targets for each feature.
 See the Targets format section for more information.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the targets added
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the targets added
 to it.
 }
 \description{
diff --git a/man/add_rsymphony_solver.Rd b/man/add_rsymphony_solver.Rd
index 64119808b..d511ada10 100644
--- a/man/add_rsymphony_solver.Rd
+++ b/man/add_rsymphony_solver.Rd
@@ -13,7 +13,7 @@ add_rsymphony_solver(
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{gap}{\code{numeric} gap to optimality. This gap is relative
 and expresses the acceptable deviance from the optimal objective.
@@ -21,12 +21,12 @@ For example, a value of 0.01 will result in the solver stopping when
 it has found a solution within 1\% of optimality.
 Additionally, a value of 0 will result in the solver stopping
 when it has found an optimal solution.
-The default value is 0.1 (i.e. 10\% from optimality).}
+The default value is 0.1 (i.e., 10\% from optimality).}
 
 \item{time_limit}{\code{numeric} time limit (seconds) for generating solutions.
 The solver will return the current best solution when this time limit is
 exceeded. The default value is the largest integer value
-(i.e. \code{.Machine$integer.max}), effectively meaning that solver
+(i.e., \code{.Machine$integer.max}), effectively meaning that solver
 will keep running until a solution within the optimality gap is found.}
 
 \item{first_feasible}{\code{logical} should the first feasible solution be
@@ -41,7 +41,7 @@ Defaults to \code{FALSE}.}
 optimization problems? Defaults to \code{TRUE}.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the solver
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the solver
 added to it.
 }
 \description{
diff --git a/man/add_semicontinuous_decisions.Rd b/man/add_semicontinuous_decisions.Rd
index 4eab94a76..3017b3694 100644
--- a/man/add_semicontinuous_decisions.Rd
+++ b/man/add_semicontinuous_decisions.Rd
@@ -7,13 +7,13 @@
 add_semicontinuous_decisions(x, upper_limit)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{upper_limit}{\code{numeric} value specifying the maximum proportion
-of a planning unit that can be reserved (e.g. set to 0.8 for 80\%).}
+of a planning unit that can be reserved (e.g., set to 0.8 for 80\%).}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the decisions added
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the decisions added
 to it.
 }
 \description{
@@ -25,13 +25,13 @@ This decision is similar to the \code{\link[=add_proportion_decisions]{add_propo
 function except that it has an upper bound parameter. By default, the
 decision can range from prioritizing none (0\%) to all (100\%) of a
 planning unit. However, an upper bound can be specified to ensure that at
-most only a fraction (e.g. 80\%) of a planning unit can be preserved. This
+most only a fraction (e.g., 80\%) of a planning unit can be preserved. This
 type of decision may be useful when it is not practical to conserve entire
 planning units.
 }
 \details{
 Conservation planning problems involve making decisions on planning
-units. These decisions are then associated with actions (e.g. turning a
+units. These decisions are then associated with actions (e.g., turning a
 planning unit into a protected area). Only a
 single decision should be added to a \code{ConservationProblem} object.
 Note that if multiple decisions are added to a problem object, then the
diff --git a/man/add_shuffle_portfolio.Rd b/man/add_shuffle_portfolio.Rd
index 548c6a34d..2cd7f8d2a 100644
--- a/man/add_shuffle_portfolio.Rd
+++ b/man/add_shuffle_portfolio.Rd
@@ -12,7 +12,7 @@ add_shuffle_portfolio(
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{number_solutions}{\code{integer} number of attempts to generate
 different solutions. Defaults to 10.}
@@ -24,7 +24,7 @@ the solution portfolio. Defaults to 1.}
 be removed? Defaults to \code{TRUE}.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the portfolio
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the portfolio
 added to it.
 }
 \description{
diff --git a/man/add_top_portfolio.Rd b/man/add_top_portfolio.Rd
index 83b6bed38..a5c91e3f1 100644
--- a/man/add_top_portfolio.Rd
+++ b/man/add_top_portfolio.Rd
@@ -7,12 +7,12 @@
 add_top_portfolio(x, number_solutions)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{number_solutions}{\code{integer} number of solutions required.}
 }
 \value{
-Object (i.e. \code{\linkS4class{ConservationProblem}}) with the portfolio
+Object (i.e., \code{\linkS4class{ConservationProblem}}) with the portfolio
 added to it.
 }
 \description{
@@ -22,7 +22,7 @@ are closest to optimality (i.e the top solutions).
 }
 \details{
 This strategy for generating a portfolio requires problems to
-be solved using the \emph{Gurobi} software suite (i.e. using
+be solved using the \emph{Gurobi} software suite (i.e., using
 \code{\link[=add_gurobi_solver]{add_gurobi_solver()}}. Specifically, version 9.0.0 (or greater)
 of the \pkg{gurobi} package must be installed.
 Note that the number of solutions returned may be less than the argument to
diff --git a/man/boundary_matrix.Rd b/man/boundary_matrix.Rd
index 2d21c7ec1..64936b74c 100644
--- a/man/boundary_matrix.Rd
+++ b/man/boundary_matrix.Rd
@@ -38,7 +38,7 @@ to pre-process data? If \code{TRUE}, then the experimental
 will be used to pre-compute which planning units are adjacent to
 each other and potentially reduce the processing time required to
 generate the boundary matrices. This argument is only used when
-the planning unit data are vector-based polygons (i.e.
+the planning unit data are vector-based polygons (i.e.,
 \code{\link[sp:SpatialPolygons]{sp::SpatialPolygonsDataFrame()}} objects). \strong{Note that
 using \code{TRUE} may crash Mac OSX systems.} The default argument
 is \code{FALSE}.}
@@ -59,11 +59,11 @@ This function returns a \code{\linkS4class{dsCMatrix}}
 symmetric sparse matrix. Cells on the off-diagonal indicate the length of
 the shared boundary between two different planning units. Cells on the
 diagonal indicate length of a given planning unit's edges that have no
-neighbors (e.g. for edges of planning units found along the
+neighbors (e.g., for edges of planning units found along the
 coastline). \strong{This function assumes the data are in a coordinate
 system where Euclidean distances accurately describe the proximity
 between two points on the earth}. Thus spatial data in a longitude/latitude
-coordinate system (i.e.
+coordinate system (i.e.,
 \href{https://spatialreference.org/ref/epsg/wgs-84/}{WGS84})
 should be reprojected to another coordinate system before using this
 function. Note that for \code{\linkS4class{Raster}} objects
diff --git a/man/compile.Rd b/man/compile.Rd
index d5bd21c8f..bc31583eb 100644
--- a/man/compile.Rd
+++ b/man/compile.Rd
@@ -10,7 +10,7 @@ compile(x, ...)
 \method{compile}{ConservationProblem}(x, compressed_formulation = NA, ...)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{...}{not used.}
 
diff --git a/man/connectivity_matrix.Rd b/man/connectivity_matrix.Rd
index 7d156320f..dbf6de9e0 100644
--- a/man/connectivity_matrix.Rd
+++ b/man/connectivity_matrix.Rd
@@ -39,7 +39,7 @@ the conductance values. Note that argument to \code{y} can only be a
 Also, note that if the argument to \code{x} is a
 \code{\linkS4class{Raster}} object then
 argument to \code{y} must have the same spatial properties as it
-(i.e. coordinate system, extent, resolution).}
+(i.e., coordinate system, extent, resolution).}
 
 \item{...}{additional arguments passed to \code{\link[=fast_extract]{fast_extract()}} for
 extracting and calculating the conductance values for each planning unit.
@@ -112,7 +112,7 @@ plot(clamp(raster(as.matrix(cm_ply)), lower = 1e-5, useValues = FALSE),
 # create connectivity matrix using habitat suitability data for each feature,
 # this could be useful if prioritisations should spatially clump
 # together adjacent planning units that have suitable habitat
-# for the same species (e.g. to maintain functional connectivity)
+# for the same species (e.g., to maintain functional connectivity)
 
 ## let's use the raster data for this example, and we can generate the
 ## connectivity matrix that we would use in the prioritization by
@@ -131,7 +131,7 @@ plot(clamp(raster(as.matrix(cm_sum)), lower = 1e-5, useValues = FALSE),
 
 ## we could take this example one step further, and use weights to indicate
 ## relative importance of maintaining functional connectivity
-## for each feature (i.e. use the weighted sum instead of the sum)
+## for each feature (i.e., use the weighted sum instead of the sum)
 
 ## let's pretend that the first feature is 20 times more important
 ## than all the other species
@@ -151,7 +151,7 @@ plot(clamp(raster(as.matrix(cm_wsum)), lower = 1e-5, useValues = FALSE),
 }
 
 ## since the statistical distribution of the connectivity values
-## for each feature (e.g. the mean and standard deviation of the
+## for each feature (e.g., the mean and standard deviation of the
 ## connectivity values) are different, it might make sense -- depending
 ## on the goal of the conservation planning exercise and the underlying
 ## data -- to first normalize the conductance values before applying the
diff --git a/man/constraints.Rd b/man/constraints.Rd
index 558328909..f7c659580 100644
--- a/man/constraints.Rd
+++ b/man/constraints.Rd
@@ -58,7 +58,7 @@ Add constraints to ensure that all selected planning units meet certain
 criteria. For example, they can be used to add
 multiple budgets, or limit the number of
 planning units selected in different administrative areas within a study
-region (e.g. different countries).}
+region (e.g., different countries).}
 
 \item{\code{\link[=add_mandatory_allocation_constraints]{add_mandatory_allocation_constraints()}}}{
 Add constraints to ensure that every planning unit is allocated to a
diff --git a/man/decisions.Rd b/man/decisions.Rd
index a5bc4657f..739e71e58 100644
--- a/man/decisions.Rd
+++ b/man/decisions.Rd
@@ -41,7 +41,7 @@ similar to \code{add_proportion_decision} except that it has an upper
 bound parameter. By default, the decision can range from prioritizing
 none (0\%) to all (100\%) of a planning unit. However, a upper
 bound can be specified to ensure that at most only a fraction
-(e.g. 80\%) of a planning unit can be preserved. This type of
+(e.g., 80\%) of a planning unit can be preserved. This type of
 decision may be useful when it is not practical to conserve the
 entire area encompassed by any single planning unit.}
 
diff --git a/man/eval_boundary_summary.Rd b/man/eval_boundary_summary.Rd
index 0beccae98..de09d3126 100644
--- a/man/eval_boundary_summary.Rd
+++ b/man/eval_boundary_summary.Rd
@@ -20,7 +20,7 @@ eval_boundary_summary(x, ...)
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{...}{not used.}
 
@@ -47,19 +47,19 @@ represent the relative importance of clumping planning units that are
 allocated to the same zone. Cell values must range between 1 and -1, where
 negative values favor solutions that spread out planning units. The default
 argument to \code{zones} is an identity
-matrix (i.e. a matrix with ones along the matrix diagonal and zeros
+matrix (i.e., a matrix with ones along the matrix diagonal and zeros
 elsewhere), so that penalties are incurred when neighboring planning units
 are not assigned to the same zone. If the cells along
 the matrix diagonal contain markedly smaller values than those found
 elsewhere in the matrix, then solutions are preferred that surround
 planning units with those allocated to different zones
-(i.e. greater spatial fragmentation).}
+(i.e., greater spatial fragmentation).}
 
 \item{data}{\code{NULL}, \code{data.frame}, \code{matrix}, or \code{Matrix}
 object containing the boundary data. These data describe the total
 amount of boundary (perimeter) length  for each planning unit,
 and the amount of boundary (perimeter) length shared between different
-planning units (i.e. planning units that are adjacent to each other).
+planning units (i.e., planning units that are adjacent to each other).
 See the Data format section for more information.}
 }
 \value{
@@ -96,7 +96,7 @@ This summary statistic is equivalent to the \code{Connectivity_Edge} metric
 reported by the \href{https://marxansolutions.org}{\emph{Marxan} software}
 (Ball \emph{et al.} 2009).
 It is calculated using the same equations used to penalize solutions
-according to their total exposed boundary (i.e. \code{\link[=add_boundary_penalties]{add_boundary_penalties()}}).
+according to their total exposed boundary (i.e., \code{\link[=add_boundary_penalties]{add_boundary_penalties()}}).
 See the Examples section for examples on how differences \code{zone} arguments
 can be used to calculate boundaries for different combinations of zones.
 }
@@ -114,14 +114,14 @@ This argument is the default.
 Note that the boundary data must be supplied
 using one of the other formats below if the planning unit data
 in the argument to \code{x} do not explicitly contain spatial information
-(e.g. planning unit data are a \code{data.frame} or \code{numeric} class).}
+(e.g., planning unit data are a \code{data.frame} or \code{numeric} class).}
 
 \item{\code{data} as a \code{matrix}/\code{Matrix} object}{where rows and columns represent
 different planning units and the value of each cell represents the
 amount of shared boundary length between two different planning units.
 Cells that occur along the matrix diagonal represent the amount of
 exposed boundary associated with each planning unit that has
-no neighbor (e.g. these value might pertain to boundaries along a
+no neighbor (e.g., these value might pertain to boundaries along a
 coastline).}
 
 \item{\code{data} as a \code{data.frame} object}{with the columns \code{"id1"},
@@ -130,7 +130,7 @@ identifiers (indices) for a pair of planning units, and the \code{"boundary"}
 column contains the amount of shared boundary length between these
 two planning units.
 This format follows the the standard \emph{Marxan} format for boundary
-data (i.e. per the "bound.dat" file).}
+data (i.e., per the "bound.dat" file).}
 
 }
 }
diff --git a/man/eval_connectivity_summary.Rd b/man/eval_connectivity_summary.Rd
index 0a3b3294d..9955a1395 100644
--- a/man/eval_connectivity_summary.Rd
+++ b/man/eval_connectivity_summary.Rd
@@ -20,7 +20,7 @@
 \S4method{eval_connectivity_summary}{ConservationProblem,ANY,ANY,array}(x, solution, zones, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{solution}{\code{numeric}, \code{matrix}, \code{data.frame},
 \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
@@ -37,7 +37,7 @@ of zones. Cell values along the diagonal of the matrix represent
 the level of connectivity between planning units allocated to the
 same zone. Cell values must lay between 1 and -1, where negative
 values favor solutions with weak connectivity. The default argument to
-\code{zones} is an identity matrix (i.e. a matrix with ones along the
+\code{zones} is an identity matrix (i.e., a matrix with ones along the
 matrix diagonal and zeros elsewhere), so that planning units are
 only considered to be connected when they are allocated to the same zone.
 This argument is required when the argument to \code{data} is a
@@ -86,7 +86,7 @@ This summary statistic is comparable to the \code{Connectivity_In} metric
 reported by the
 \href{https://marxansolutions.org}{\emph{Marxan} software} (Ball \emph{et al.} 2009).
 It is calculated using the same equations used to penalize solutions
-with connectivity data (i.e. \code{\link[=add_connectivity_penalties]{add_connectivity_penalties()}}).
+with connectivity data (i.e., \code{\link[=add_connectivity_penalties]{add_connectivity_penalties()}}).
 Specifically, it is calculated as the sum of the pair-wise connectivity
 values in the argument to \code{data}, weighted by the value of the planning
 units in the solution.
@@ -193,7 +193,7 @@ denotes the connectivity between two planning units following the
 \emph{Marxan} format. The data can be used to denote symmetric or
 asymmetric relationships between planning units. By default,
 input data is assumed to be symmetric unless asymmetric data is
-also included (e.g. if data is present for planning units 2 and 3, then
+also included (e.g., if data is present for planning units 2 and 3, then
 the same amount of connectivity is expected for planning units 3 and 2,
 unless connectivity data is also provided for planning units 3 and 2).
 If the argument to \code{x} contains multiple zones, then the columns
@@ -207,7 +207,7 @@ allocated to specific zones. If the columns \code{"zone1"} and
 containing four-dimensions where cell values
 indicate the strength of connectivity between planning units
 when they are assigned to specific management zones. The first two
-dimensions (i.e. rows and columns) indicate the strength of
+dimensions (i.e., rows and columns) indicate the strength of
 connectivity between different planning units and the second two
 dimensions indicate the different management zones. Thus
 the \code{data[1, 2, 3, 4]} indicates the strength of
diff --git a/man/eval_cost_summary.Rd b/man/eval_cost_summary.Rd
index 200a08d23..8d4f9b6e0 100644
--- a/man/eval_cost_summary.Rd
+++ b/man/eval_cost_summary.Rd
@@ -13,7 +13,7 @@ eval_cost_summary(x, solution)
 \method{eval_cost_summary}{ConservationProblem}(x, solution)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{solution}{\code{numeric}, \code{matrix}, \code{data.frame},
 \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
@@ -58,7 +58,7 @@ This metric is equivalent to the \code{Cost} metric reported by the
 \href{https://marxansolutions.org}{\emph{Marxan} software} (Ball \emph{et al.} 2009).
 Specifically, the cost of a solution is defined as the sum of the cost
 values, supplied when creating a \code{\link[=problem]{problem()}} object
-(e.g. using the \code{cost_column} argument),
+(e.g., using the \code{cost_column} argument),
 weighted by the status of each planning unit in the solution.
 }
 \section{Solution format}{
diff --git a/man/eval_feature_representation_summary.Rd b/man/eval_feature_representation_summary.Rd
index 39d6ac744..78233cc08 100644
--- a/man/eval_feature_representation_summary.Rd
+++ b/man/eval_feature_representation_summary.Rd
@@ -25,7 +25,7 @@ eval_feature_representation_summary(x, solution)
 \S4method{eval_feature_representation_summary}{ConservationProblem,Raster}(x, solution)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{solution}{\code{numeric}, \code{matrix}, \code{data.frame},
 \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
@@ -37,7 +37,7 @@ See the Solution format section for more information.}
 \value{
 \code{\link[tibble:tibble]{tibble::tibble()}} object describing feature representation.
 Here, each row describes a specific summary statistic
-(e.g. different management zone) for a specific feature.
+(e.g., different management zone) for a specific feature.
 It contains the following columns:
 
 \describe{
@@ -57,13 +57,14 @@ in the entire conservation planning problem
 (not just planning units selected within the solution).
 It is calculated as the sum of the feature data,
 supplied when creating a \code{\link[=problem]{problem()}} object
-(e.g. presence/absence values).}
+(e.g., presence/absence values).}
 
 \item{absolute_held}{\code{numeric} total amount of each feature secured within
 the solution. It is calculated as the sum of the feature data,
 supplied when creating a \code{\link[=problem]{problem()}} object
-(e.g. presence/absence values), weighted by the status of each
-planning unit in the solution (e.g. selected or not for prioritization).}
+(e.g., presence/absence values), weighted by the status of each
+planning unit in the solution (e.g., selected or not for
+prioritization).}
 
 \item{relative_held}{\code{numeric} proportion of
 each feature secured within the solution. It is calculated
diff --git a/man/eval_ferrier_importance.Rd b/man/eval_ferrier_importance.Rd
index 82ba13172..684e40775 100644
--- a/man/eval_ferrier_importance.Rd
+++ b/man/eval_ferrier_importance.Rd
@@ -25,7 +25,7 @@ eval_ferrier_importance(x, solution)
 \S4method{eval_ferrier_importance}{ConservationProblem,Raster}(x, solution)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{solution}{\code{numeric}, \code{matrix}, \code{data.frame},
 \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
diff --git a/man/eval_n_summary.Rd b/man/eval_n_summary.Rd
index 0af0d9441..6a9add7cd 100644
--- a/man/eval_n_summary.Rd
+++ b/man/eval_n_summary.Rd
@@ -13,7 +13,7 @@ eval_n_summary(x, solution)
 \method{eval_n_summary}{ConservationProblem}(x, solution)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{solution}{\code{numeric}, \code{matrix}, \code{data.frame},
 \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
@@ -48,8 +48,8 @@ to a conservation planning \code{\link[=problem]{problem()}}.
 \details{
 This summary statistic is calculated as the sum of the values in
 the solution. As a consequence, this metric can produce a
-non-integer value (e.g. 4.3) for solutions containing proportion values
-(e.g. generated by solving a \code{\link[=problem]{problem()}} built using the
+non-integer value (e.g., 4.3) for solutions containing proportion values
+(e.g., generated by solving a \code{\link[=problem]{problem()}} built using the
 \code{\link[=add_proportion_decisions]{add_proportion_decisions()}} function).
 }
 \section{Solution format}{
diff --git a/man/eval_rare_richness_importance.Rd b/man/eval_rare_richness_importance.Rd
index ccedc5f84..035b5d3fc 100644
--- a/man/eval_rare_richness_importance.Rd
+++ b/man/eval_rare_richness_importance.Rd
@@ -25,7 +25,7 @@ eval_rare_richness_importance(x, solution, ...)
 \S4method{eval_rare_richness_importance}{ConservationProblem,Raster}(x, solution, rescale, ...)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{solution}{\code{numeric}, \code{matrix}, \code{data.frame},
 \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
@@ -51,7 +51,7 @@ same format as the planning unit data in the argument to \code{x}.
 Calculate importance scores for planning units selected in a solution
 using rarity weighted richness scores (based on Williams \emph{et al.} 1996).
 This method is only recommended for large-scaled conservation
-planning exercises (i.e. more than 100,000 planning units) where
+planning exercises (i.e., more than 100,000 planning units) where
 importance scores cannot be calculated using other methods in a feasible
 period of time. This is because rarity weighted richness scores cannot (i)
 account for the cost of different planning units, (ii) account for multiple
diff --git a/man/eval_replacement_importance.Rd b/man/eval_replacement_importance.Rd
index 593172fc5..313372e20 100644
--- a/man/eval_replacement_importance.Rd
+++ b/man/eval_replacement_importance.Rd
@@ -25,7 +25,7 @@ eval_replacement_importance(x, solution, ...)
 \S4method{eval_replacement_importance}{ConservationProblem,Raster}(x, solution, rescale, run_checks, force, threads, ...)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{solution}{\code{numeric}, \code{matrix}, \code{data.frame},
 \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
@@ -84,19 +84,19 @@ objective function (\code{\link[=add_max_utility_objective]{add_max_utility_obje
 replacement cost scores correspond to the reduction in the utility when
 each planning unit is locked out. Infinite values mean that no feasible
 solution exists when planning units are locked out---they are
-absolutely essential for obtaining a solution (e.g. they contain rare
+absolutely essential for obtaining a solution (e.g., they contain rare
 species that are not found in any other planning units or were locked in).
 Zeros values mean that planning units can swapped with other planning units
 and this will have no effect on the performance of the solution at all
-(e.g. because they were only selected due to spatial fragmentation
+(e.g., because they were only selected due to spatial fragmentation
 penalties).
 
 These calculations can take a long time to complete for large
 or complex conservation planning problems. As such, we using this
 method for small or moderate-sized conservation planning problems
-(e.g. < 30,000 planning units). To reduce run time, we
-recommend calculating these scores without additional penalties (e.g.
-\code{\link[=add_boundary_penalties]{add_boundary_penalties()}}) or spatial constraints (e.g.
+(e.g., < 30,000 planning units). To reduce run time, we
+recommend calculating these scores without additional penalties (e.g.,
+\code{\link[=add_boundary_penalties]{add_boundary_penalties()}}) or spatial constraints (e.g.,
 \code{\link[=add_contiguity_constraints]{add_contiguity_constraints()}}). To further reduce run time,
 we recommend using proportion-type decisions when calculating the scores
 (see below for an example).
diff --git a/man/eval_target_coverage_summary.Rd b/man/eval_target_coverage_summary.Rd
index 00204ac0c..aae7e607d 100644
--- a/man/eval_target_coverage_summary.Rd
+++ b/man/eval_target_coverage_summary.Rd
@@ -24,7 +24,7 @@ eval_target_coverage_summary(x, solution, include_zone, include_sense)
 )
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{solution}{\code{numeric}, \code{matrix}, \code{data.frame},
 \code{\linkS4class{Raster}}, \code{\linkS4class{Spatial}},
@@ -60,16 +60,16 @@ is \code{TRUE}.}
 
 \item{sense}{\code{character} sense associated with each target.
 Sense values specify the nature of the target.
-Typically (e.g. when using the \code{\link[=add_absolute_targets]{add_absolute_targets()}} or
+Typically (e.g., when using the \code{\link[=add_absolute_targets]{add_absolute_targets()}} or
 \code{\link[=add_relative_targets]{add_relative_targets()}} functions), targets are specified using sense
 values indicating that the total amount of a feature held within a
 solution (ideally) be greater than or equal to a threshold amount
-(i.e. a  sense value of \code{">="}).
-Additionally, targets (i.e. using the \code{\link[=add_manual_targets]{add_manual_targets()}} function)
+(i.e., a  sense value of \code{">="}).
+Additionally, targets (i.e., using the \code{\link[=add_manual_targets]{add_manual_targets()}} function)
 can also be specified using sense values indicating that the total
 amount of a feature held within a solution must be equal to a
-threshold amount (i.e. a sense value of \code{"="}) or smaller than or equal
-to a threshold amount (i.e. a sense value of \code{"<="}).
+threshold amount (i.e., a sense value of \code{"="}) or smaller than or equal
+to a threshold amount (i.e., a sense value of \code{"<="}).
 This column is only included if the argument to \code{include_sense} is
 \code{TRUE}.}
 
@@ -93,44 +93,45 @@ the feature and (if relevant) zones associated with each target (per the
 \code{"feature"} and \code{"zone"} columns, respectively).
 This column is calculated as the sum of the feature data,
 supplied when creating a \code{\link[=problem]{problem()}} object
-(e.g. presence/absence values), weighted by the status of each
-planning unit in the solution (e.g. selected or not for prioritization).}
+(e.g., presence/absence values), weighted by the status of each
+planning unit in the solution (e.g., selected or not for
+prioritization).}
 
 \item{absolute_shortfall}{ \code{numeric} total amount by which the solution
 fails to meet each target.
 This column is calculated as the difference between the total amount
 held within the solution for the feature and (if relevant) zones
-associated with the target (i.e. \code{"absolute_held"} column) and the
-target total threshold amount (i.e. \code{"absolute_target"} column), with
+associated with the target (i.e., \code{"absolute_held"} column) and the
+target total threshold amount (i.e., \code{"absolute_target"} column), with
 values set to zero depending on the sense specified for the target
-(e.g. if the target sense is \code{>=} then the difference is
+(e.g., if the target sense is \code{>=} then the difference is
 set to zero if the value in the \code{"absolute_held"} is smaller than
 that in the \code{"absolute_target"} column).}
 
 \item{relative_target}{\code{numeric} proportion threshold amount associated
 with each target.
 This column is calculated by dividing the total threshold amount
-associated with each target (i.e. \code{"absolute_target"} column) by
+associated with each target (i.e., \code{"absolute_target"} column) by
 the total amount associated with each target
-(i.e. \code{"total_amount"} column).}
+(i.e., \code{"total_amount"} column).}
 
 \item{relative_held}{\code{numeric} proportion held within the solution for the
 feature and (if relevant) zones associated with each target (per the
 \code{"feature"} and \code{"zone"} columns, respectively).
 This column is calculated by dividing the total amount held
-for each target (i.e. \code{"absolute_held"} column) by the
+for each target (i.e., \code{"absolute_held"} column) by the
 total amount for with each target
-(i.e. \code{"total_amount"} column).}
+(i.e., \code{"total_amount"} column).}
 
 \item{relative_shortfall}{\code{numeric} proportion by which the solution fails
 to meet each target.
 This column is calculated by dividing the total shortfall for
-each target (i.e. \code{"absolute_shortfall"} column) by the
-total amount for each target (i.e. \code{"total_amount"} column).}
+each target (i.e., \code{"absolute_shortfall"} column) by the
+total amount for each target (i.e., \code{"total_amount"} column).}
 
 \item{met}{\code{logical} indicating if each target is met by the solution. This
 column is calculated by checking if the total shortfall associated
-with each target (i.e. \verb{"absolute_shortfall}" column) is equal to
+with each target (i.e., \verb{"absolute_shortfall}" column) is equal to
 zero.}
 
 }
diff --git a/man/feature_abundances.Rd b/man/feature_abundances.Rd
index e8ac74cca..4c42ab573 100644
--- a/man/feature_abundances.Rd
+++ b/man/feature_abundances.Rd
@@ -10,7 +10,7 @@ feature_abundances(x, na.rm)
 \method{feature_abundances}{ConservationProblem}(x, na.rm = FALSE)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{na.rm}{\code{logical} should planning units with \code{NA} cost
 data be excluded from the abundance calculations? The default argument
@@ -51,10 +51,10 @@ of a conservation planning problem.
 }
 \details{
 Planning units can have cost data with finite values
-(e.g. 0.1, 3, 100) and \code{NA} values. This functionality is provided so
+(e.g., 0.1, 3, 100) and \code{NA} values. This functionality is provided so
 that locations which are not available for protected area acquisition can
 be included when calculating targets for conservation features
-(e.g. when targets are specified using \code{\link[=add_relative_targets]{add_relative_targets()}}).
+(e.g., when targets are specified using \code{\link[=add_relative_targets]{add_relative_targets()}}).
 If the total amount of each feature in all the planning units is
 required---including the planning units with \code{NA} cost data---then the
 the \code{na.rm} argument should be set to \code{FALSE}. However, if
@@ -137,8 +137,8 @@ p5 <- p3 \%>\%
 s5 <- solve(p5)
 
 # plot the solution
-# this solution contains all the planning units with finite cost data (i.e.
-# cost data that do not have NA values)
+# this solution contains all the planning units with finite cost data
+# (i.e., cost data that do not have NA values)
 plot(s5)
 }
 }
diff --git a/man/feature_names.Rd b/man/feature_names.Rd
index a6fc7a346..930cba968 100644
--- a/man/feature_names.Rd
+++ b/man/feature_names.Rd
@@ -16,7 +16,7 @@ feature_names(x)
 \S4method{feature_names}{ZonesCharacter}(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) or \code{\link[=Zones]{Zones()}}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) or \code{\link[=Zones]{Zones()}}
 object.}
 }
 \value{
diff --git a/man/importance.Rd b/man/importance.Rd
index bd2a6d74d..2a0c2ad82 100644
--- a/man/importance.Rd
+++ b/man/importance.Rd
@@ -18,7 +18,7 @@ The following methods are available for calculating importance scores:
 Calculate importance scores using replacement costs (based
 on Cabeza and Moilanen 2006).
 These scores quantify the change in the objective
-function (e.g. additional costs required to meet feature targets) of the
+function (e.g., additional costs required to meet feature targets) of the
 optimal solution if a given planning unit in a solution cannot be acquired.
 They can (i) account for the cost of different planning units, (ii) account
 for multiple management zones, (iii) apply to any objective function, and
@@ -29,7 +29,7 @@ values).}
 Calculate importance scores following Ferrier \emph{et al.} (2000).
 These scores measure importance based on how critical
 planning units are for meeting targets. They can only be applied to
-conservation problems with a minimum set objective and a single zone (i.e.
+conservation problems with a minimum set objective and a single zone (i.e.,
 the classic \emph{Marxan}-type problem). Furthermore---unlike the
 replacement cost scores---these scores provide a
 score for each feature within each planning unit, providing insight into
@@ -53,8 +53,8 @@ planning problem -- regardless of the objective function or number of
 zones considered in the problem -- and measure planning unit importance based
 on degradation of the prioritization.
 Although the replacement cost scores can be calculated for small and
-moderate sized problems (e.g. less than 30,000 planning units), they may not
-be feasible for particularly large problems (e.g. more than 100,000 planning
+moderate sized problems (e.g., less than 30,000 planning units), they may not
+be feasible for particularly large problems (e.g., more than 100,000 planning
 units). In such cases, we recommend calculating importance scores using the
 Ferrier method. This is because the Ferrier method can be
 calculated relatively quickly for large-sized problems and it
diff --git a/man/marxan_boundary_data_to_matrix.Rd b/man/marxan_boundary_data_to_matrix.Rd
index b1e4d4e45..15fff2d37 100644
--- a/man/marxan_boundary_data_to_matrix.Rd
+++ b/man/marxan_boundary_data_to_matrix.Rd
@@ -7,7 +7,7 @@
 marxan_boundary_data_to_matrix(x, data)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object that
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object that
 contains planning unit and zone data to ensure that the argument to
 \code{data} is converted correctly. This argument can be set to
 \code{NULL} if checks are not required (not recommended).}
diff --git a/man/marxan_problem.Rd b/man/marxan_problem.Rd
index c05e1886e..bf14f2040 100644
--- a/man/marxan_problem.Rd
+++ b/man/marxan_problem.Rd
@@ -104,13 +104,13 @@ has an effect when argument to \code{x} is a \code{data.frame}. The
 default argument is zero.}
 }
 \value{
-\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.
+\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.
 }
 \description{
 Create a conservation planning \code{\link[=problem]{problem()}} following the
 mathematical formulations used in \emph{Marxan} (detailed in Beyer
 \emph{et al.} 2016). Note that these problems are solved using
-exact algorithms and not simulated annealing (i.e. the \emph{Marxan} software).
+exact algorithms and not simulated annealing (i.e., the \emph{Marxan} software).
 }
 \details{
 This function is provided as a convenient wrapper for solving
diff --git a/man/number_of_features.Rd b/man/number_of_features.Rd
index d1c0b895e..63eb3c7a3 100644
--- a/man/number_of_features.Rd
+++ b/man/number_of_features.Rd
@@ -19,7 +19,7 @@ number_of_features(x)
 \S4method{number_of_features}{ZonesCharacter}(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}),
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}),
 \code{\linkS4class{OptimizationProblem}}, or \code{\link[=Zones]{Zones()}} object.}
 }
 \value{
diff --git a/man/number_of_planning_units.Rd b/man/number_of_planning_units.Rd
index 3260fdb77..df8ae2ca7 100644
--- a/man/number_of_planning_units.Rd
+++ b/man/number_of_planning_units.Rd
@@ -13,7 +13,7 @@ number_of_planning_units(x)
 \S4method{number_of_planning_units}{OptimizationProblem}(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}),
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}),
 \code{\linkS4class{OptimizationProblem}}, or \code{\link[=Zones]{Zones()}} object.}
 }
 \value{
diff --git a/man/number_of_total_units.Rd b/man/number_of_total_units.Rd
index 51f2fb80b..b593b28e7 100644
--- a/man/number_of_total_units.Rd
+++ b/man/number_of_total_units.Rd
@@ -10,7 +10,7 @@ number_of_total_units(x)
 \S4method{number_of_total_units}{ConservationProblem}(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}),
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}),
 \code{\linkS4class{OptimizationProblem}}, or \code{\link[=Zones]{Zones()}} object.}
 }
 \value{
diff --git a/man/number_of_zones.Rd b/man/number_of_zones.Rd
index b91669197..03a1d42d0 100644
--- a/man/number_of_zones.Rd
+++ b/man/number_of_zones.Rd
@@ -19,7 +19,7 @@ number_of_zones(x)
 \S4method{number_of_zones}{ZonesCharacter}(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}),
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}),
 \code{\linkS4class{OptimizationProblem}}, or \code{\link[=Zones]{Zones()}} object.}
 }
 \value{
diff --git a/man/penalties.Rd b/man/penalties.Rd
index 315e9307f..8d076abd8 100644
--- a/man/penalties.Rd
+++ b/man/penalties.Rd
@@ -7,7 +7,7 @@
 A penalty can be applied to a conservation planning \code{\link[=problem]{problem()}} to
 penalize solutions according to a specific metric. Penalties---unlike
 \link{constraints}---act as an explicit trade-off with the objective
-being minimized or maximized (e.g. solution cost when used with
+being minimized or maximized (e.g., solution cost when used with
 \code{\link[=add_min_set_objective]{add_min_set_objective()}}).
 }
 \details{
@@ -33,7 +33,7 @@ planning units with high connectivity between them.}
 \item{\code{\link[=add_linear_penalties]{add_linear_penalties()}}}{Add penalties to a
 conservation problem to favor solutions that avoid selecting
 planning units based on a certain variable
-(e.g. anthropogenic pressure).}
+(e.g., anthropogenic pressure).}
 
 }
 }
diff --git a/man/portfolios.Rd b/man/portfolios.Rd
index 2f5730e54..286459059 100644
--- a/man/portfolios.Rd
+++ b/man/portfolios.Rd
@@ -7,10 +7,10 @@
 Conservation planning exercises rarely have access to all the
 data needed to identify the \emph{truly} perfect solution. This is because
 available data may lack important details
-(e.g. land acquisition costs may be unavailable), contain errors
-(e.g. species presence/absence data may have false positives),
+(e.g., land acquisition costs may be unavailable), contain errors
+(e.g., species presence/absence data may have false positives),
 or key objectives may not be formally incorporated into the
-prioritization process (e.g. future land use requirements).
+prioritization process (e.g., future land use requirements).
 As such, conservation planners can help decision makers by providing
 them with a portfolio of solutions to inform their decision.
 }
diff --git a/man/presolve_check.Rd b/man/presolve_check.Rd
index 0a14ca550..91486f2cb 100644
--- a/man/presolve_check.Rd
+++ b/man/presolve_check.Rd
@@ -13,7 +13,7 @@ presolve_check(x)
 \method{presolve_check}{OptimizationProblem}(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) or
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) or
 \code{\linkS4class{OptimizationProblem}} object.}
 }
 \value{
@@ -37,7 +37,7 @@ locked in, (ii) all planning units are locked out, and (iii) all
 planning units have negative cost values (after applying penalties if any
 were specified). Although such conservation planning problems
 are mathematically valid, they are generally the result of a coding mistake
-when building the problem (e.g. using an absurdly high
+when building the problem (e.g., using an absurdly high
 penalty value or using the wrong dataset to lock in planning units).
 Thus such issues, if they are indeed issues and not false positives, can
 be fixed by carefully checking the code, data, and parameters used to build
@@ -46,15 +46,15 @@ the conservation planning problem.
 This function then checks for values that may lead to numerical instability
 issues when solving the problem. Specifically, it checks if the range of
 values in certain components of the optimization problem are over a
-certain threshold (i.e. \eqn{1 \times 10 ^9}{1e+9}) or if the values
+certain threshold (i.e., \eqn{1 \times 10 ^9}{1e+9}) or if the values
 themselves exceed a certain threshold
-(i.e. \eqn{1 \times 10^{10}}{1e+10}).
+(i.e., \eqn{1 \times 10^{10}}{1e+10}).
 In most cases, such issues will simply cause an exact
 algorithm solver to take a very long time to generate a solution. In rare
 cases, such issues can cause incorrect calculations which can lead
 to exact algorithm solvers returning infeasible solutions
-(e.g. a solution to the minimum set problem where not all targets are met)
-or solutions that exceed the specified optimality gap (e.g. a suboptimal
+(e.g., a solution to the minimum set problem where not all targets are met)
+or solutions that exceed the specified optimality gap (e.g., a suboptimal
 solution when a zero optimality gap is specified).
 
 What can you do if a conservation planning problem fails to pass these
@@ -72,7 +72,7 @@ planning unit cost values are too large. For example, if you express the
 costs of the planning units in terms of USD then you might have
 some planning units that cost over one billion dollars in large-scale
 planning exercises. This can be fixed by rescaling the values so that they
-are smaller (e.g. multiplying the values by a number smaller than one, or
+are smaller (e.g., multiplying the values by a number smaller than one, or
 expressing them as a fraction of the maximum cost). Let's consider another
 common issue, let's pretend that you used habitat suitability models to
 predict the amount of suitable habitat
@@ -99,7 +99,7 @@ unit(s) is causing this infeasibility and set its cost to zero. After
 solving the problem, you will need to manually recalculate the cost
 of the solutions but at least now you can be confident that you have the
 optimal solution. Now let's pretend that you are using the maximum features
-objective (i.e. \code{\link[=add_max_features_objective]{add_max_features_objective()}}) and assigned some
+objective (i.e., \code{\link[=add_max_features_objective]{add_max_features_objective()}}) and assigned some
 really high weights to the targets for some features to ensure that their
 targets were met in the optimal solution. If you set the weights for
 these features to one billion then you will probably run into numerical
@@ -107,7 +107,7 @@ instability issues. Instead, you can calculate minimum weight needed to
 guarantee that these features will be represented in the optimal solution
 and use this value instead of one billion. This minimum weight value
 can be calculated as the sum of the weight values for the other features
-and adding a small number to it (e.g. 1). Finally, if you're running out
+and adding a small number to it (e.g., 1). Finally, if you're running out
 of ideas for addressing numerical stability issues you have one remaining
 option: you can use the \code{numeric_focus} argument in the
 \code{\link[=add_gurobi_solver]{add_gurobi_solver()}} function to tell the solver to pay extra
diff --git a/man/prioritizr-deprecated.Rd b/man/prioritizr-deprecated.Rd
index b1ecd4db1..29871e48f 100644
--- a/man/prioritizr-deprecated.Rd
+++ b/man/prioritizr-deprecated.Rd
@@ -51,7 +51,7 @@ package, we have listed alternatives for deprecated the functions
 (where applicable).
 If a function is described as being renamed, then this means
 that only the name of the function has changed
-(i.e. the inputs, outputs, and underlying code remain the same).
+(i.e., the inputs, outputs, and underlying code remain the same).
 }
 \details{
 The following functions have been deprecated:
diff --git a/man/prioritizr.Rd b/man/prioritizr.Rd
index e567fbc50..fc624f28c 100644
--- a/man/prioritizr.Rd
+++ b/man/prioritizr.Rd
@@ -30,7 +30,7 @@ for more information.
 This package contains several vignettes that are designed to
 showcase its functionality. To view them, please use the code
 \code{vignette("name", package = "prioritizr")} where \code{"name"} is the
-name of the desired vignette (e.g. \code{"gurobi_installation"}).
+name of the desired vignette (e.g., \code{"gurobi_installation"}).
 
 \describe{
 
diff --git a/man/problem.Rd b/man/problem.Rd
index c9ed379d6..c9b938542 100644
--- a/man/problem.Rd
+++ b/man/problem.Rd
@@ -66,7 +66,7 @@ the study area. To exclude planning units, set the cost for those raster
 cells to \code{NA}, or use the \code{add_locked_out_constraint} function.}
 
 \item{features}{The feature data can be specified in a variety of ways.
-The specific formats that can be used depend on the cost data format (i.e.
+The specific formats that can be used depend on the cost data format (i.e.,
 argument to \code{x}) and whether the problem should have a single zone or
 multiple zones. If the problem should have a single zone, then the feature
 data can be specified following:
@@ -76,7 +76,7 @@ data can be specified following:
 \code{\link[sf:sf]{x = sf::st_sf()}}:
 \code{\link[raster:Raster-classes]{y = Raster-class}}
 object showing the distribution of conservation features. Missing
-values (i.e. \code{NA} values) can be used to indicate the absence of
+values (i.e., \code{NA} values) can be used to indicate the absence of
 a feature in a particular cell instead of explicitly setting these
 cells to zero. Note that this argument type for \code{features} can
 only be used to specify data for problems involving a single zone.
@@ -117,7 +117,7 @@ data can be specified following:
 \code{\link[sf:sf]{x = sf::st_sf()}}:
 \code{\link[=zones]{y = ZonesRaster}}:
 object showing the distribution of conservation features in multiple
-zones. As above, missing values (i.e. \code{NA} values) can be used to
+zones. As above, missing values (i.e., \code{NA} values) can be used to
 indicate the absence of a feature in a particular cell instead of
 explicitly setting these cells to zero.
 \item \code{\link[sp:Spatial-class]{x = Spatial-class}}, or
@@ -191,7 +191,7 @@ data for a prioritization.
 Create a systematic conservation planning problem. This function is used to
 specify the basic data used in a spatial prioritization problem: the
 spatial distribution of the planning units and their costs, as well as
-the features (e.g. species, ecosystems) that need to be conserved. After
+the features (e.g., species, ecosystems) that need to be conserved. After
 constructing this \code{ConservationProblem-class} object, it can be
 customized to meet specific goals using \link{objectives},
 \link{targets}, \link{constraints}, and
@@ -216,34 +216,34 @@ be incorporated by using multiple zones
 on the management action(s), you can compile the following data.
 
 First, you will need to create a set of planning units
-(i.e. discrete spatial areas) to inform decision making.
+(i.e., discrete spatial areas) to inform decision making.
 Planning units are often created by subdividing a study region
 into a set square or hexagonal cells. They can also be created using
-administrative boundaries (e.g. provinces), land management boundaries
-(e.g. property boundaries derived from cadastral data), or
-ecological boundaries (e.g. based on ecosystem classification data).
-The size (i.e. spatial grain) of the planning units is often determined
+administrative boundaries (e.g., provinces), land management boundaries
+(e.g., property boundaries derived from cadastral data), or
+ecological boundaries (e.g., based on ecosystem classification data).
+The size (i.e., spatial grain) of the planning units is often determined
 based on a compromise between the scale needed to inform decision making, the
 spatial accuracy (resolution) of available datasets, and
 the computational resources available for generating prioritizations
-(e.g. RAM and number of CPUs on your computer).
+(e.g., RAM and number of CPUs on your computer).
 
 Second, you will need data to quantify the cost of implementing
 implementing each management action within each planning unit.
 Critically, the cost data should reflect the management action(s)
 considered in the exercise.
 For example, costs are often specified using data that reflect economic
-expenditure (e.g. land acquisition cost),
-socioeconomic conditions (e.g. human population density),
+expenditure (e.g., land acquisition cost),
+socioeconomic conditions (e.g., human population density),
 opportunity costs of foregone commercial activities
-(e.g. logging or agriculture), or
+(e.g., logging or agriculture), or
 opportunity costs of foregone recreational activities
-(e.g. recreational fishing) activities,
+(e.g., recreational fishing) activities,
 In some cases -- depending on the management action(s) considered --
 it can make sense to use a constant cost value
-(e.g. all planning units are assigned a cost value equal to one)
+(e.g., all planning units are assigned a cost value equal to one)
 or use a cost value based on spatial extent
-(e.g. each planning unit is assigned a cost value based on its total area).
+(e.g., each planning unit is assigned a cost value based on its total area).
 Also, in most cases, you want to avoid negative cost values.
 This because a negative value means that a place is \emph{desirable}
 for implementing a management action, and such places will almost
@@ -254,13 +254,13 @@ management actions within planning units.
 To achieve this, you will need to select a set of conservation features
 that relate to the over-arching goals of the exercise.
 For example, conservation features often include
-species (e.g. Clouded Leopard), habitats (e.g. mangroves or
+species (e.g., Clouded Leopard), habitats (e.g., mangroves or
 cloud forest), or ecosystems.
 The benefit that each feature derives from a planning unit
-can take a variety of forms, but is typically occupancy (i.e.
+can take a variety of forms, but is typically occupancy (i.e.,
 presence or absence), area of occurrence within each planning unit
-(e.g. based on species' geographic range data), or
-a measure of habitat suitability (e.g. estimated using a statistical model).
+(e.g., based on species' geographic range data), or
+a measure of habitat suitability (e.g., estimated using a statistical model).
 After compiling these data, you have the minimal data need to generate
 a prioritization.
 
@@ -314,7 +314,7 @@ If you wish to see exactly how a conservation planning problem is
 formulated as mixed integer linear programming problem, you can use
 the \code{\link[=write_problem]{write_problem()}} function to save the optimization problem
 to a plain-text file on your computer and then view it using a standard
-text editor (e.g. Notepad).
+text editor (e.g., Notepad).
 
 Please note that this function internally computes the amount of each
 feature in each planning unit when this data is not supplied (using the
@@ -365,13 +365,13 @@ p5 <- problem(sim_pu_sf, sim_features, "cost") \%>\%
       add_default_solver(verbose = FALSE)
 
 # since geo-processing can be slow for large spatial vector datasets
-# (e.g. polygons, lines, points), it can be worthwhile to pre-process the
+# (e.g., polygons, lines, points), it can be worthwhile to pre-process the
 # planning unit data so that it contains columns indicating the amount of
 # each feature inside each planning unit
-# (i.e. each column corresponds to a different feature)
+# (i.e., each column corresponds to a different feature)
 
 # calculate the amount of each species within each planning unit
-# (i.e. SpatialPolygonsDataFrame object)
+# (i.e., SpatialPolygonsDataFrame object)
 pre_proc_data <- rij_matrix(sim_pu_polygons, sim_features)
 
 # add extra columns to the polygon (Spatial) planning unit data
@@ -404,7 +404,7 @@ p7 <- problem(sim_pu_sf, features = names(pre_proc_data2), "cost") \%>\%
 
 # in addition to spatially explicit data, pre-processed aspatial data
 # can also be used to create a problem
-# (e.g. data created using external spreadsheet software)
+# (e.g., data created using external spreadsheet software)
 costs <- sim_pu_polygons$cost
 features <- data.frame(id = seq_len(nlayers(sim_features)),
                        name = names(sim_features))
diff --git a/man/rij_matrix.Rd b/man/rij_matrix.Rd
index f4983a96c..1c12de8f9 100644
--- a/man/rij_matrix.Rd
+++ b/man/rij_matrix.Rd
@@ -44,7 +44,7 @@ Generate a matrix showing the amount of each feature in each planning
 unit (also known as an \emph{rij} matrix).
 }
 \details{
-Generally, processing vector (i.e. \code{\linkS4class{Spatial}} or
+Generally, processing vector (i.e., \code{\linkS4class{Spatial}} or
 \code{\link[sf:sf]{sf::sf()}}) data takes much
 longer to process then \code{\linkS4class{Raster}} data,
 so it is recommended to use \code{\linkS4class{Raster}} data
diff --git a/man/run_calculations.Rd b/man/run_calculations.Rd
index 9a7685af9..d3afaf9d8 100644
--- a/man/run_calculations.Rd
+++ b/man/run_calculations.Rd
@@ -7,7 +7,7 @@
 run_calculations(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 }
 \value{
 Invisible \code{TRUE} indicating success.
@@ -16,7 +16,7 @@ Invisible \code{TRUE} indicating success.
 Execute preliminary calculations in a conservation problem and store the
 results for later use. This function is useful when creating slightly
 different versions of the same conservation planning problem that involve
-the same pre-processing steps (e.g. calculating boundary data), because
+the same pre-processing steps (e.g., calculating boundary data), because
 means that the same calculations will not be run multiple times.
 }
 \details{
diff --git a/man/solve.Rd b/man/solve.Rd
index 93a0de3c1..0d36c471a 100644
--- a/man/solve.Rd
+++ b/man/solve.Rd
@@ -11,7 +11,7 @@
 \S4method{solve}{ConservationProblem,missing}(a, b, ..., run_checks = TRUE, force = FALSE)
 }
 \arguments{
-\item{a}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) or
+\item{a}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) or
 \code{\linkS4class{OptimizationProblem}} object.}
 
 \item{b}{\code{\linkS4class{Solver}} object. Not used if \code{a} is an
@@ -36,8 +36,8 @@ Additionally, the returned object will have the following additional
 attributes: \code{"objective"} containing the solution's objective,
 \code{"runtime"} denoting the number of seconds that elapsed while solving
 the problem, and \code{"status"} describing the status of the solution
-(e.g. \code{"OPTIMAL"} indicates that the optimal solution was found).
-In most cases, the first solution (e.g. \code{"solution_1"})
+(e.g., \code{"OPTIMAL"} indicates that the optimal solution was found).
+In most cases, the first solution (e.g., \code{"solution_1"})
 will contain the best solution found by the solver (note that this
 may not be an optimal solution depending on the gap used to solve
 the problem and noting that the default gap is 0.1).
@@ -52,15 +52,15 @@ for available solvers). If no solver has been explicitly specified,
 then the best available exact algorithm solver will be used by default
 (see \code{\link[=add_default_solver]{add_default_solver()}}. Although these exact algorithm
 solvers will often display a lot of information that isn't really that
-helpful (e.g. nodes, cutting planes), they do display information
-about the progress they are making on solving the problem (e.g. the
+helpful (e.g., nodes, cutting planes), they do display information
+about the progress they are making on solving the problem (e.g., the
 performance of the best solution found at a given point in time). If
 potential issues were detected during the
 presolve checks (see \code{\link[=presolve_check]{presolve_check()}})
-and the problem is being forcibly solved (i.e. with \code{force = TRUE}),
+and the problem is being forcibly solved (i.e., with \code{force = TRUE}),
 then it is also worth checking for any warnings displayed by the solver
 to see if these potential issues are actually causing issues
-(e.g. \emph{Gurobi} can display warnings that include
+(e.g., \emph{Gurobi} can display warnings that include
 \code{"Warning: Model contains large matrix coefficient range"} and
 \code{"Warning: Model contains large rhs"}).
 
@@ -108,11 +108,11 @@ If the argument to \code{a} contains a single zone, then the solution object
 will contain fields (columns) that solution the values.
 Specifically, the field name(s) containing the solution values
 be will named as \code{"solution_XXX"} where \code{"XXX"} corresponds to a solution
-identifier (e.g. \code{"solution_1"}).
+identifier (e.g., \code{"solution_1"}).
 If the argument to \code{a} contains multiple zones, then the fields
 containing solutions will be named as \code{"solution_XXX_YYY"} where
 \code{"XXX"} corresponds to the solution identifier and \code{"YYY"} is the name
-of the management zone (e.g. \code{"solution_1_zone1"}).}
+of the management zone (e.g., \code{"solution_1_zone1"}).}
 
 }
 }
diff --git a/man/write_problem.Rd b/man/write_problem.Rd
index a81af070f..b369386bc 100644
--- a/man/write_problem.Rd
+++ b/man/write_problem.Rd
@@ -7,7 +7,7 @@
 write_problem(x, path)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) object.}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) object.}
 
 \item{path}{\code{character} file path to save the problem formulation.
 The argument should contain a \code{".lp"} or \verb{.mps"} file extension
diff --git a/man/zone_names.Rd b/man/zone_names.Rd
index 22c57bf03..f486945af 100644
--- a/man/zone_names.Rd
+++ b/man/zone_names.Rd
@@ -17,7 +17,7 @@ zone_names(x)
 \S4method{zone_names}{ZonesCharacter}(x)
 }
 \arguments{
-\item{x}{\code{\link[=problem]{problem()}} (i.e. \code{\linkS4class{ConservationProblem}}) or \code{\link[=Zones]{Zones()}}}
+\item{x}{\code{\link[=problem]{problem()}} (i.e., \code{\linkS4class{ConservationProblem}}) or \code{\link[=Zones]{Zones()}}}
 }
 \value{
 \code{character} zone names.
diff --git a/man/zones.Rd b/man/zones.Rd
index a60fee953..ca28f3800 100644
--- a/man/zones.Rd
+++ b/man/zones.Rd
@@ -28,7 +28,7 @@ Organize data for multiple features for multiple management zones.
 Specifically, the data should describe the expected amount of each
 feature within each planning unit given each management zone.
 For example, the data could describe the occupancy
-(e.g. presence/absence), probability of occurrence, or
+(e.g., presence/absence), probability of occurrence, or
 abundance expected for each feature when each planning unit
 is allocated to a different zone.
 }
diff --git a/pkgdown/extra.css b/pkgdown/extra.css
index 68e9213f2..d4c532b04 100644
--- a/pkgdown/extra.css
+++ b/pkgdown/extra.css
@@ -2,14 +2,20 @@
   background: #FFFFFF;
 }
 
-[id='prioritizr-'] .page-header {
-  margin-bottom: 0px;
-  padding-bottom: 0px;
+.template-home .contents .section.level1 .page-header {
+  padding-top: 60px;
+  padding-bottom: 0px !important;
+  margin-bottom: 15px !important;
 }
 
-[id='systematic-conservation-prioritization-in-r'] h1 {
-  margin-top: 0px;
-  padding-top: 0px;
+[id='prioritizr-'] {
+  margin-bottom: 0px !important;
+  padding-bottom: 0px !important;
+}
+
+[id='systematic-conservation-prioritization-in-r'] {
+  margin-top: 0px !important;
+  padding-top: 0px !important;
   font-size: 35px;
   padding-bottom: 10px;
 }
diff --git a/vignettes/calibrating_trade-offs_tutorial.Rmd b/vignettes/calibrating_trade-offs_tutorial.Rmd
new file mode 100644
index 000000000..22089a2c7
--- /dev/null
+++ b/vignettes/calibrating_trade-offs_tutorial.Rmd
@@ -0,0 +1,678 @@
+---
+title: "Calibrating trade-offs tutorial"
+output:
+  rmarkdown::html_vignette:
+    toc: true
+    fig_caption: true
+    self_contained: yes
+fontsize: 11pt
+documentclass: article
+bibliography: references.bib
+csl: reference-style.csl
+vignette: >
+  %\VignetteIndexEntry{Calibrating trade-offs tutorial}
+  %\VignetteEngine{knitr::rmarkdown_notangle}
+---
+
+```{r, include = FALSE}
+# define dummy variables so that vignette passes package checks
+prelim_penalty <- rep(NA_real_, 100)
+threshold <- rep(NA_real_, 100)
+topsis_results <- data.frame(
+  alt.row = seq_len(3), score = runif(3), rank = seq_len(3)
+)
+```
+
+```{r, include = FALSE}
+# define variables for vignette figures and code execution
+h <- 3.5
+w <- 3.5
+is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_",
+             "_R_CHECK_LICENSE_") %in% names(Sys.getenv()))
+knitr::opts_chunk$set(fig.align = "center", eval = !is_check)
+```
+
+## Introduction
+
+Systematic conservation planning requires making trade-offs [@r4; @r36]. Since different criteria may conflict with one another -- or not align perfectly -- prioritizations need to make trade-offs between different criteria [@r37]. Although some criteria can easily be accounted for by using locked constraints or representation targets [e.g., @r40; @r39], this is not always the case [e.g., @r38]. For example, prioritizations often need to balance overall cost with the overall level spatial fragmentation among reserves [@r41; @r42]. Additionally, prioritizations often need to balance the overall level of connectivity among reserves against other criteria [@r43]. Since the best trade-off depends on a range of factors -- such as available budgets, species' connectivity requirements, and management capacity -- finding the best balance can be challenging.
+
+The _prioritizr R_ package provides multi-objective optimization methods to help identify the best trade-offs between different criteria. To achieve this, a conservation planning problem can be formulated with a primary objective (e.g., `add_min_set_objective()`) and penalties (e.g., `add_boundary_penalties()`) that relate to such criteria. When building the problem, the nature of the trade-offs can be specified using certain parameters (e.g., the `penalty` parameter of the `add_boundary_penalties()` function). To identify a prioritization that finds the best balance between different criteria, the trade-off parameters can be tuned using a calibration analysis. These analyses -- in the context of systematic conservation planning -- typically involve generating a set of candidate prioritizations based on different parameters, measuring their performance according to each of the criteria, and then selecting a prioritization (or set of prioritizations) based on how well they achieve the criteria [@r41; @r42; @r43]. For example, the _Marxan_ decision support tool has a range of parameters (e.g., species penalty factors, boundary length modifier) that are calibrated to balance cost, species' representation, and spatial fragmentation [@r45].
+
+The aim of this tutorial is to provide guidance on calibrating trade-offs when using the _prioritizr R_ package. Here we will explore a couple of different approaches for generating candidate prioritizations, and methods for finding the best balance between different criteria. Specifically, we will try to generate prioritizations that strike the best balance between total cost and spatial fragmentation (measured as total boundary length). As such, the code used in this vignette will be directly applicable when performing a boundary length calibration analysis.
+
+## Data
+
+Let's load the packages and dataset used in this tutorial. Since this tutorial uses the _prioritizrdata R_ package along with several other _R_ packages (see below), please ensure that they are all installed. This particular dataset comprises two object: `tas_pu` and `tas_features`. Although we will briefly discuss this dataset below, please refer to the _Tasmania Tutorial_ vignette for further details.
+
+```{r, message = FALSE}
+# load packages
+library(prioritizrdata)
+library(prioritizr)
+library(dplyr)
+library(tibble)
+library(scales)
+library(ggplot2)
+library(topsis)
+library(withr)
+
+# load planning unit data
+data(tas_pu)
+
+# convert planning units to sf format
+tas_pu <- st_as_sf(tas_pu)
+
+# load feature data
+data(tas_features)
+
+# print planning unit data
+print(tas_pu)
+
+# print feature data
+print(tas_features)
+```
+
+The `tas_pu` object contains planning units represented as spatial polygons (i.e., converted to a `sf::st_sf()` object). This object has three columns that denote the following information for each planning unit: a unique identifier (`id`), unimproved land value (`cost`), and current conservation status (`locked_in`). Specifically, the conservation status column indicates if at least half the area planning unit is covered by existing protected areas (denoted by a value of 1) or not (denoted by a value of zero).
+
+```{r, fig.width = w, fig.height = h}
+# plot map of planning unit costs
+plot(tas_pu[, "cost"], main = "Planning unit costs")
+
+# plot map of planning unit statuses
+plot(tas_pu[, "locked_in"], main = "Planning unit status")
+```
+
+The `tas_features` object describes the spatial distribution of different vegetation communities (using presence/absence data). We will use the vegetation communities as the biodiversity features for the prioritization.
+
+```{r, fig.width = 4.5, fig.height = 4.5}
+# plot map of the first four vegetation classes
+plot(tas_features[[1:4]], main = paste("Feature", 1:4))
+```
+
+We can use this dataset to generate a prioritization. Specifically, we will use the minimum set objective so that the optimization process minimizes total cost. We will add representation targets to ensure that prioritizations cover 17% of each vegetation community. Additionally, we will add constraints to ensure that planning units covered by existing protected areas are selected (i.e., locked in). Finally, we will specify that the conservation planning exercise involves binary decisions (i.e., selecting or not selecting planning units for protected area establishment).
+
+```{r, fig.width = w, fig.height = h, results = "hide"}
+# define a problem
+p0 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# print problem
+print(p0)
+
+# solve problem
+s0 <- solve(p0)
+
+# print result
+print(s0)
+
+# create column for making a map of the prioritization
+s0$map_1 <- case_when(
+  s0$locked_in > 0.5 ~ "locked in",
+  s0$solution_1 > 0.5 ~ "priority",
+  TRUE ~ "other"
+)
+
+# plot map of prioritization
+plot(
+  s0[, "map_1"], pal = c("purple", "grey90", "darkgreen"),
+  main = NULL, key.pos = 1
+)
+```
+
+We can see that the priority areas identified by the prioritization are scattered across the study area (shown in green). Indeed, none of the priority areas are connect to existing protected areas (shown in purple), and very of them are connect with other priority areas. As such, the prioritization has a high level of spatial fragmentation. If it is important avoid such levels of spatial fragmentation, then we will need to explicitly account spatial fragmentation in the optimization process.
+
+## Preliminary processing
+
+We need to conduct some preliminary processing procedures to prepare the data for subsequent analysis. This is important to help make it easier to find suitable trade-off parameters, and avoid numerical scaling issues that can result in overly long run times (see `presolve_check()` for further information). These processing steps are akin to data scaling (or normalization) procedures that are applied in statistical analysis to improve model convergence.
+
+The first processing procedure involves setting the cost values for all locked in planning units to zero. This is so that the total cost estimates of the prioritization reflects the total cost of establishing new protected areas -- not just total land value. In other words, we want the total cost estimate for a prioritization to reflect the cost of implementing conservation actions. **This procedure is especially important when using the hierarchical approach described below, so that cost thresholds are based on percentage increases in the cost of establishing new protected areas.**
+
+```{r, fig.width = w, fig.height = h}
+
+# set costs for planning units covered by existing protected areas to zero
+tas_pu$cost[tas_pu$locked_in > 0.5] <- 0
+
+# plot map of planning unit costs
+plot(tas_pu[, "cost"], main = "Planning unit cost")
+```
+
+The second procedure involves pre-computing the boundary length data and manually re-scaling the boundary length values. This procedure is important because boundary length values are often very large that, in turn, can cause numerical issues that result in excessive run times (see `presolve_check()` for further details).
+
+```{r}
+# generate boundary length data for the planning units
+tas_bd <- boundary_matrix(tas_pu)
+
+# manually re-scale the boundary length values
+tas_bd@x <- rescale(tas_bd@x, to = c(0.01, 100))
+```
+
+After applying these procedures, our data is ready for subsequent analysis.
+
+## Generating candidate prioritizations
+
+Here we will start the calibration analysis by generating a set of candidate prioritizations. Specifically, these prioritizations will be generated using different parameters to specify different trade-offs between the different criteria. Since this tutorial involves navigating trade-offs between the overall cost of a prioritization and the level of spatial fragmentation associated with a prioritization (as measured by total boundary length), we will generate prioritizations using different parameters related to these criteria. We will examine two approaches for generating candidate prioritizations based on multi-objective optimization procedures.
+**Although we'll be examining both approaches in this tutorial, you would normally only use one of these approaches when conducting your own analysis**
+
+### Blended approach
+
+The blended approach for multi-objective optimization involves combining separate criteria (e.g., total cost and total boundary length) into a single joint criterion. To achieve this, a trade-off (or scaling) parameter is used to specify the relative importance of each criterion. This approach is the default approach provided by the _prioritizr R_ package. Specifically, each of the functions for adding a penalty to a problem formulation (e.g., `add_boundary_penalties()`) contains a parameter to control the relative importance of the penalties (i.e., the `penalty` parameter). For example, when using the `add_boundary_penalties()` function, setting a high `penalty` value will indicate that it is important to reduce the overall exposed boundary (perimeter) of the prioritization.
+
+The main challenge with the blended approach is identifying a range of suitable `penalty` values to generate candidate prioritizations. If we set a `penalty` value that is too low, then the penalties will have no effect (e.g., boundary length penalties would have no effect on the prioritization). If we set a `penalty` value too high, then the prioritization will effectively ignore the primary objective. In such cases, the prioritization will be overly spatially clustered -- because the planning unit cost values have no effect --- and contain a single reserve. Thus we need to find a suitable range of `penalty` values before we can generate a set of candidate prioritizations.
+
+We can find a suitable range of `penalty` values by generating a set of preliminary prioritizations. These preliminary prioritizations will be based on different `penalty` values -- similar to the process for generating the candidate prioritizations -- but solved using customized settings that sacrifice optimality for fast run times (see below for details). This is especially important because specifying a `penalty` value that is too high will cause the optimization process to take a very long time to generate a solutions (due to the numerical scaling issues mentioned previously). To find a suitable range of `penalty` values, we need to identify an upper limit for the `penalty` value (i.e., the highest `penalty` value that result in a prioritization containing a single reserve). Let's create some preliminary `penalty` to identify this upper limit. **Please note that you might need to adjust the `prelim_upper` value to find the upper limit when analyzing different datasets.**
+
+```{r}
+# define a range of different penalty values
+## note that we use a power scale to avoid focusing on very high penalty values
+prelim_lower <- -5   # change this for your own data
+prelim_upper <- 2.8  # change this for your own data
+prelim_penalty <- round(10^seq(prelim_lower, prelim_upper, length.out = 9), 5)
+
+# print penalty values
+print(prelim_penalty)
+```
+
+Next, let's use the preliminary `penalty` values to generate preliminary prioritizations. As mentioned earlier, we will generate these preliminary prioritizations using customized settings to reduce runtime. Specifically, we will set a time limit of 10 minutes per run, and relax the optimality gap to 20%. Although we would not normally use such settings -- because the resulting prioritizations are not guaranteed to be near-optimal (the default gap is 10%) -- this is fine because our goal here is to tune the preliminary `penalty` values. Indeed, none of these preliminary prioritizations will be considered as candidate prioritizations. **Please note that you might need to set a higher time limit, or relax the optimality  gap even further (e.g., 40%) when analyzing larger datasets.**
+
+```{r, results = "hide"}
+# define a problem without boundary penalties
+p0 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# generate preliminary prioritizations based on each penalty
+## note that we specify a relaxed gap and time limit for the solver
+prelim_blended_results <- lapply(prelim_penalty, function(x) {
+  s <-
+    p0 %>%
+    add_boundary_penalties(penalty = x, data = tas_bd) %>%
+    add_default_solver(gap = 0.2, time_limit = 10 * 60) %>%
+    solve()
+  s <- data.frame(s = s$solution_1)
+  names(s) <- with_options(list(scipen = 30), paste0("penalty_", x))
+  s
+})
+
+# format results as a single spatial object
+prelim_blended_results <- cbind(
+  tas_pu, do.call(bind_cols, prelim_blended_results)
+)
+
+# preview results
+print(prelim_blended_results)
+```
+
+After generating the preliminary prioritizations, let's create some maps to visualize them. In particular, we want to understand how different penalty values influence the spatial fragmentation of the prioritizations.
+
+```{r, fig.width = 7, fig.height = 5.0}
+# plot maps of prioritizations
+plot(
+  x =
+    prelim_blended_results %>%
+    dplyr::select(starts_with("penalty_")) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        prelim_blended_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
+```
+
+We can see that as the `penalty` value used to generate the prioritizations increases, the spatial fragmentation of the prioritizations decreases. In particular, we can see that a `penalty` value of `r prelim_penalty[8]` results in a single reserve -- meaning this is our best guess of the upper limit. Using this `penalty` value as an upper limit, we will now generate a second series of prioritizations that will be the candidate prioritizations. Critically, these candidate prioritizations will not be generated using with time limit and be generated using a more suitable gap (i.e., default gap of 10%).
+
+```{r, fig.width = 7, fig.height = 5.0, results = "hide"}
+# define a new set of penalty values
+## note that we use a linear scale to explore both low and high penalty values
+penalty <- round(seq(1e-5, prelim_penalty[8], length.out = 9), 5)
+
+# generate prioritizations based on each penalty
+blended_results <- lapply(penalty, function(x) {
+  ## generate solution
+  s <-
+    p0 %>%
+    add_boundary_penalties(penalty = x, data = tas_bd) %>%
+    solve()
+  ## return data frame with solution
+  s <- data.frame(s = s$solution_1)
+  names(s) <- with_options(list(scipen = 30), paste0("penalty_", x))
+  s
+})
+
+# format results as a single spatial object
+blended_results <- cbind(tas_pu, do.call(bind_cols, blended_results))
+
+# plot maps of prioritizations
+plot(
+  x =
+    blended_results %>%
+    dplyr::select(starts_with("penalty_")) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        blended_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
+```
+
+We now have a set of candidate prioritizations generated using the blended approach. The main advantages of this approach is that it is similar calibration analyses used by other decision support tools for conservation (i.e., _Marxan_) and it is relatively straightforward to implement. However, this approach also has a key disadvantage. Because the `penalty` parameter is a unitless trade-off parameter -- meaning that we can't leverage existing knowledge to specify a suitable range of `penalty` values -- we first have to conduct a preliminary analysis to identify an upper limit. Although finding an upper limit was fairly simple for the example datset, it can be difficult to find for more realistic data. In the next section, we will show how to generate a set of candidate prioritzations using the hierachical approach -- which does not have this disadvantage.
+
+### Hierarchical approach
+
+The hierarchical approach for multi-objective optimization involves generating a series of incremental prioritizations -- using a different objective at each increment to refine the previous solution -- until the final solution achieves all of the objectives. The advantage with this approach is that we can specify trade-off parameters for each objective based on a percentage from optimality. This means that we can leverage our own knowledge -- or that of decision maker -- when to generate a range of suitable trade-off parameters. As such, this approach does not require us to generate a series of preliminary prioritizations.
+
+This approach is slightly more complicated to implement within the _prioritizr R_ package then the blended approach. To start off, we generate an initial prioritization based on a problem formulation that does not consider any penalties. Critically, we will generate this prioritization by solving the problem to optimality (using the `gap` parameter of the `add_default_solver()` function).
+
+```{r, fig.width = w, fig.height = h, results = "hide"}
+# define a problem without boundary penalties
+p1 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0)
+
+# solve problem
+s1 <- solve(p1)
+
+# add column for making a map of the prioritization
+s1$map_1 <- case_when(
+  s1$locked_in > 0.5 ~ "locked in",
+  s1$solution_1 > 0.5 ~ "priority",
+  TRUE ~ "other"
+)
+
+# plot map of prioritization
+plot(
+  s0[, "map_1"], pal = c("purple", "grey90", "darkgreen"),
+  main = NULL, key.pos = 1
+)
+```
+
+Next, we will calculate the total cost of the initial prioritization.
+
+```{r, fig.width = w, fig.height = h}
+# calculate cost
+s1_cost <- eval_cost_summary(p1, s1[, "solution_1"])$cost
+
+# print cost
+print(s1_cost)
+```
+
+Now we will calculate a series of cost thresholds. These cost thresholds will be calculated by inflating the cost of the initial prioritization by a range of percentage values. Since these values are percentages -- and not unitless values unlike those used in the blended approach -- we can use domain knowledge to specify a suitable range of cost thresholds. For this tutorial, let's assume that it would be impractical -- per our domain knowledge -- to expend more than four times the total cost of the initial prioritization to reduce spatial fragmentation.
+
+```{r}
+# calculate cost threshold values
+threshold <- s1_cost + (s1_cost * seq(1e-5, 4, length.out = 9))
+threshold <- ceiling(threshold)
+
+# print cost thresholds
+print(threshold)
+```
+
+After generating the cost thresholds, we can use them to generate prioritizations. Specifically, we will generate prioritizations that aim to minimize total boundary length as much as possible -- ignoring the total cost of the prioritizations -- whilst ensuring that the total cost of the prioritization does not exceed a given cost threshold and the other considerations (e.g., locked in constraints). To achieve this, we create a new column in the `tas_pu` object that contains only zero values (called `zeros`) and use this new column to specify the cost data for the prioritizations.
+**Although we normally recommend against cost data that contain zero values -- because planning units with zero costs are often selected in prioritizations even if they are not needed -- here we use zero cost values so that the prioritization will focus exclusively on spatial fragmentation.** Additionally, when it comes to generating the prioritization, we will add linear constraints to ensure that the total cost of the prioritization does not exceed a given cost threshold (using the `add_linear_constraints()` function).
+
+```{r, fig.width = 7, fig.height = 5.0, results = "hide"}
+# add a column with zeros
+tas_pu$zeros <- 0
+
+# define a problem with zero cost values and boundary penalties
+## note that because all the costs are all zero, it doesn't actually
+## matter what penalty value is used (as long as the value is > 0)
+## and so we just use a value of 1
+p2 <- problem(tas_pu, tas_features, cost_column = "zeros") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 1, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# generate prioritizations based on each cost threshold
+## note that the prioritizations are solved to within 10% of optimality
+## (the default gap) because the gap is not specified
+hierarchical_results <- lapply(threshold, function(x) {
+  ## generate solution by adding a constraint based on the threshold and
+  ## using the "real" cost values (i.e., not zeros)
+  s <-
+    p2 %>%
+    add_linear_constraints(threshold = x, sense = "<=", data = "cost") %>%
+    solve()
+  ## return data frame with solution
+  s <- data.frame(s = s$solution_1)
+  names(s) <- paste0("threshold_", x)
+  s
+})
+
+# format results as a single spatial object
+hierarchical_results <- cbind(tas_pu, do.call(bind_cols, hierarchical_results))
+
+# plot maps of prioritizations
+plot(
+  x =
+    hierarchical_results %>%
+    dplyr::select(starts_with("threshold_")) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        hierarchical_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
+```
+
+We now have a set of candidate prioritizations generated using the hierarchical approach. This approach can be much faster than the blended approach because it does not require generating a set of prioritizations to identify an upper limit for the `penalty` trade-off parameter. After generating a set of candidate prioritizations, we can then calculate performance metrics to compare the prioritizations.
+
+## Calculating performance metrics
+
+Here we will calculate performance metrics to compare the prioritizations. Since we aim to navigate trade-offs between the total cost of a prioritization and the overall level of spatial fragmentation associated with a prioritization (as measured by total boundary length), we will calculate metrics to assess these criteria. Although we generated two sets of candidate prioritizations in the previous section; for brevity, here we will consider the candidate prioritizations generated using the hierarchical approach. **Please note that you could also apply the following procedures to candidate prioritizations generated using the blended approach.**
+
+```{r}
+# calculate metrics for prioritizations
+## note that we use p0 and not p1 so that cost calculations are based
+## on the cost values and not zeros
+hierarchical_metrics <- lapply(
+  grep("threshold_", names(hierarchical_results)), function(x) {
+    x <- hierarchical_results[, x]
+    data.frame(
+      total_cost = eval_cost_summary(p0, x)$cost,
+      total_boundary_length = eval_boundary_summary(p0, x)$boundary
+    )
+  }
+)
+hierarchical_metrics <- do.call(bind_rows, hierarchical_metrics)
+hierarchical_metrics$threshold <- threshold
+hierarchical_metrics <- as_tibble(hierarchical_metrics)
+
+# preview metrics
+print(hierarchical_metrics)
+```
+
+After calculating the metrics, let's we can use them to help select a prioritization.
+
+## Selecting a prioritization
+
+Now we need to decide on which candidate prioritization achieves the best trade-off. There are a range of qualitative and quantitative methods that are available to select a candidate prioritization [@r45]. Here we will consider three different methods. Since some of these methods a set of candidate prioritizations, we will use the candidate prioritizations using the hierarchical approach for these methods. To keep track of the prioritizations selected by different methods, let's create a `results_data` table.
+
+```{r}
+# create data for plotting
+result_data <-
+  hierarchical_metrics %>%
+  ## rename threshold column to value column
+  rename(value = "threshold") %>%
+  ## add column with column names that contain candidate prioritizations
+  mutate(name = grep(
+    "threshold_", names(hierarchical_results), value = TRUE, fixed = TRUE
+  )) %>%
+  ## add column with labels for plotting
+  mutate(label = paste("Threshold =", value)) %>%
+  ## add column to keep track prioritizations selected by different methods
+  mutate(method = "none")
+
+# print table
+print(result_data)
+```
+
+Next, let's examine some different methods for selecting prioritizations.
+
+### Visual method
+
+One qualitative method involves plotting the relationship between the different criteria, and using the plot to visually select a candidate prioritization. This visual method is often used to help calibrate trade-offs among prioritizations generated using the _Marxan_ decision support tool [e.g., @r41; @r42]. So, let's create a plot to select a prioritization.
+
+```{r, fig.width = 7, fig.height = 5.0}
+# create plot to visualize trade-offs and show selected candidate prioritization
+result_plot <-
+  ggplot(
+    data = result_data,
+    aes(x = total_boundary_length, y = total_cost, label = label)
+  ) +
+  geom_line() +
+  geom_point(size = 3) +
+  geom_text(hjust = -0.15) +
+  scale_color_manual(
+    values = c("visual" = "blue", "not selected" ="black")
+  ) +
+  xlab("Total boundary length of prioritization") +
+  ylab("Total cost of prioritization") +
+  scale_x_continuous(expand = expansion(mult = c(0.05, 0.4))) +
+  theme(legend.title = element_blank())
+
+# render plot
+print(result_plot)
+```
+
+We can see that there is a clear relationship between total cost and total boundary length. It would seem that in order to achieve a lower total boundary length -- and thus lower spatial fragmentation -- the prioritization must have a greater cost. Although we might expect the results to show a smoother curve -- in other words, only Pareto dominant solutions -- this result is expected because we generated candidate prioritizations using the default optimality gap of 10%. Typically, the visual method involves selecting a prioritization near the elbow of the plot. So, let's select the prioritization generated using a `threshold` value of `r threshold[3]`. To keep of the prioritizations selected based on different methods, let's create a `method` column in the `result_data` table.
+
+```{r}
+# specify prioritization selected by visual method
+result_data$method[3] <- "visual"
+```
+
+Next, let's consider a quantitative approach.
+
+### TOPSIS method
+
+Multiple-criteria decision analysis is a disciple that uses analytical methods to evaluate trade-offs between multiple criteria [MCDA; reviewed in @r44]. Although this discipline contains many different methods, here we will use the the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method [@r46]. This method requires (i) data describing the performance of each prioritization according the different criteria, (ii) weights to encode the relative importance of each criteria, and (iii) details on whether each criteria should ideally be minimized or maximized. Let's run the analysis, assuming that we equal weighting for total cost and total boundary length.
+
+```{r}
+# calculate TOPSIS scores
+topsis_results <- topsis(
+  decision =
+    hierarchical_metrics %>%
+    dplyr::select(total_cost, total_boundary_length) %>%
+    as.matrix(),
+  weights = c(1, 1),
+  impacts = c("-", "-")
+)
+
+# print results
+print(topsis_results)
+```
+
+The candidate prioritization with the greatest TOPSIS score is considered to represent the best trade-off between total cost and total boundary length. So, based on this method, we would select the prioritization generated using a `threshold` value of `r threshold[which.max(topsis_results$score)]`. Let's update the `result_data` with this information.
+
+```{r}
+# add column indicating prioritization selected by TOPSIS method
+result_data$method[which.max(topsis_results$score)] <- "TOPSIS"
+```
+
+Next, let's consider another quantitative method.
+
+### Cohon *et al.* (1979) method
+
+This method is based on an algorithm that was originally developed by Cohon *et al.* [@r49], and was later adapted for use in systematic conservation planning [@r50]. Specifically, it involves generating two ideal prioritizations -- with each prioritization representing the ideal prioritization for each criteria -- and then using the performance metrics calculated for these prioritizations to automatically derive a trade-off `penalty` value [@r45; @r49]. Thus, unlike the two other methods, this method does not require a set of candidate prioritizations. **As such, this method can be used to find a prioritization that meets multiple criteria in a much shorter period of time than the other methods.** To implement this method, we first need to generate the ideal prioritizations (note that we specify an gap of 0% to ensure optimality).
+
+```{r, results = "hide"}
+# generate ideal prioritization based on cost criteria
+## note that this is simply the same as the s1 prioritization we generated
+## for the hierarchical approach
+p3 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0)
+
+# solve problem
+s3 <- solve(p3)
+
+# generate ideal prioritization based on spatial fragmentation criteria
+## note that any non-zero penalty value would here,
+## so we just use a penalty  of 1
+p4 <- problem(tas_pu, tas_features, cost_column = "zeros") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 1, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions() %>%
+      add_default_solver(gap = 0)
+
+# solve problem
+s4 <- solve(p4)
+```
+
+Next, let's calculate the performance metrics for these prioritizations.
+
+```{r}
+# generate problem formulation with costs and boundary penalties for
+# calculating performance metrics
+p5 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 1, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# calculate performance metrics for ideal cost prioritization
+s3_metrics <- tibble(
+  total_cost = eval_cost_summary(p5, s3[, "solution_1"])$cost,
+  total_boundary_length =
+    eval_boundary_summary(p5, s3[, "solution_1"])$boundary
+)
+
+# calculate performance metrics for ideal boundary length prioritization
+s4_metrics <- tibble(
+  total_cost = eval_cost_summary(p5, s4[, "solution_1"])$cost,
+  total_boundary_length =
+    eval_boundary_summary(p5, s4[, "solution_1"])$boundary
+)
+```
+
+After calculating these performance metrics, we can use them to automatically calculate a `penalty` value.
+
+```{r}
+# calculate penalty value based on Cohon et al. 1979
+cohon_penalty <- abs(
+  (s3_metrics$total_cost - s4_metrics$total_cost) /
+  (s3_metrics$total_boundary_length - s4_metrics$total_boundary_length)
+)
+
+# round to 5 decimal places to avoid numerical issues during optimization
+cohon_penalty <- round(cohon_penalty, 5)
+
+# print penalty value
+print(cohon_penalty)
+```
+
+Now that we have calculated a `penalty` value using this method, we can use it to generate a prioritization.
+
+```{r, results = "hide"}
+# generate prioritization using penalty value calculated using Cohon et al. 1979
+p6 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = cohon_penalty, data = tas_bd) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
+
+# solve problem
+s6 <- solve(p6)
+```
+
+Let's update the `results_data` table with results about the prioritization.
+
+```{r}
+# add new row with data for prioritization generated following Cohon et al. 1979
+result_data <- bind_rows(
+  result_data,
+  tibble(
+    total_cost = eval_cost_summary(p6, s6[, "solution_1"])$cost,
+    total_boundary_length =
+      eval_boundary_summary(p6, s6[, "solution_1"])$boundary,
+    value = cohon_penalty,
+    name = paste0("penalty_", cohon_penalty),
+    label = paste0("Penalty = ",  cohon_penalty),
+    method = "Cohon"
+  )
+)
+```
+
+Next, let's compare the prioritizations selected by different methods.
+
+### Method comparison
+
+Let's create a plot to visualize the results from the different methods.
+
+```{r, fig.width = 7, fig.height = 5.0}
+# create plot to visualize trade-offs and show selected candidate prioritization
+result_plot <-
+  ggplot(
+    data =
+      result_data %>%
+      mutate(vjust = if_else(method == "Cohon", -1, 0.5)),
+    aes(x = total_boundary_length, y = total_cost, label = label)
+  ) +
+  geom_line() +
+  geom_point(aes(color = method), size = 3) +
+  geom_text(aes(vjust = vjust, color = method), hjust = -0.1) +
+  scale_color_manual(
+    name = "Method",
+    values = c(
+      "visual" = "#984ea3",
+      "none" = "#000000",
+      "TOPSIS" = "#e41a1c",
+      "Cohon" = "#377eb8"
+    )
+  ) +
+  xlab("Total boundary length of prioritization") +
+  ylab("Total cost of prioritization") +
+  scale_x_continuous(expand = expansion(mult = c(0.05, 0.4)))
+
+# render plot
+print(result_plot)
+```
+
+We can see that the different method selected different prioritizations. To further compare the results from the different methods, let's create some maps showing the selected prioritizations.
+
+```{r, fig.width = 7.0, fig.height = h}
+# extract column names for creating the prioritizations
+visual_name <- result_data$name[[which(result_data$method == "visual")]]
+topsis_name <- result_data$name[[which(result_data$method == "TOPSIS")]]
+
+# create object with selected prioritizations
+solutions  <- bind_cols(
+  tas_pu,
+  hierarchical_results %>%
+    st_drop_geometry() %>%
+    dplyr::select(all_of(c(visual_name, topsis_name))) %>%
+    setNames(c("Visual", "TOPSIS")),
+  s6 %>%
+    st_drop_geometry() %>%
+    dplyr::select(solution_1) %>%
+    rename(Cohon = "solution_1")
+)
+
+# plot maps of selected prioritizations
+plot(
+  x =
+    solutions %>%
+    dplyr::select(Visual, TOPSIS, Cohon) %>%
+    mutate_if(is.numeric, function(x) {
+      case_when(
+        hierarchical_results$locked_in > 0.5 ~ "locked in",
+        x > 0.5 ~ "priority",
+        TRUE ~ "other"
+      )
+    }),
+  pal = c("purple", "grey90", "darkgreen")
+)
+```
+
+How do we determine which one is best? This is difficult to say. Ideally, additional information could be used to help select a prioritization, such as knowledge on available resources, species' connectivity requirements, and impacts of neighboring land use. However, from a practical perspective, prioritizations generated for academic contexts might find the quantitative approaches more useful because they have greater transparency and reproducibility. Ultimately, all of these methods are designed to support decision making. This means that they are intended to assist the decision making process, not serve as a replacement.
+
+## Conclusion
+
+Hopefully, this vignette has provided a useful introduction for resolving trade-offs in prioritizations. Although we only explored trade-offs between total cost and spatial fragmentation in this tutorial, this analysis could be adapted to explore trade-offs between a wide range of different criteria. For instance, instead of considering total cost as the primary objective, future analyses could explore trade-offs with feature representation (using the `add_min_shortfall_objective()` function). Additionally, instead of spatial fragmentation, future analyses could explore trade-offs that directly relate to connectivity (using the `add_connectivity_penalties()` function) or specific variables of interest -- such as ecosystem intactness or inverse human footprint index [@r47; @r48] -- to inform decision making (using the `add_linear_penalties()` function). Furthermore, after identifying the best `penalty` or `threshold` values to strike a balance between multiple criteria, you could generate a portfolio of prioritizations (e.g., using the `add_gap_portfolio_function()`) to find multiple options for achieving a similar balance. This might be helpful when you need to generate a set of prioritizations that have comparable performance -- in terms of how well they achieve different criteria -- but select different planning units.
+
+## References
diff --git a/vignettes/connectivity_tutorial.Rmd b/vignettes/connectivity_tutorial.Rmd
new file mode 100644
index 000000000..4deb120fc
--- /dev/null
+++ b/vignettes/connectivity_tutorial.Rmd
@@ -0,0 +1,487 @@
+---
+title: "Connectivity tutorial"
+output:
+  rmarkdown::html_vignette:
+    toc: true
+    fig_caption: true
+    self_contained: yes
+fontsize: 11pt
+documentclass: article
+bibliography: references.bib
+csl: reference-style.csl
+vignette: >
+  %\VignetteIndexEntry{Connectivity tutorial}
+  %\VignetteEngine{knitr::rmarkdown_notangle}
+---
+
+```{r, include = FALSE}
+h <- 4.5
+w <- 4.5
+is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_",
+             "_R_CHECK_LICENSE_") %in% names(Sys.getenv()))
+knitr::opts_knit$set(global.par = TRUE)
+knitr::opts_chunk$set(
+  fig.align = "center", eval = !is_check,
+  fig.width = 4.0, fig.height = 3.5
+)
+```
+
+## Introduction
+
+Connectivity is a key consideration in systematic conservation planning [@r4; @r55]. This is because isolated and fragmented populations are often more vulnerable to extinction [@r60; @r61; @r62]. To promote connectivity in prioritizations, a range of different approaches are available [reviewed in @r56]. These approaches can solely on the spatial configuration of a prioritization to enhance structural connectivity [e.g, reducing the spatial fragmentation of a prioritization\; @r2]. They can also leverage data -- such as environmental, river flow, and telemetry data -- to generate prioritizations that promote functional connectivity [e.g., @r43; @r58; @r59].
+
+The aim of this tutorial is to show how connectivity can be incorporated into prioritizations using the _prioritizr R_ package. Here we will explore various approaches for incorporating connectivity, and see how they alter the spatial configuration of prioritizations. As you will discover, many of these approaches involve setting threshold or penalty values to specify the relative importance of connectivity compared to other criteria (e.g., overall cost). For more information on calibrating these values, please see the [_Calibrating trade-offs tutorial_](calibrating_trade-offs-tutorial.html).
+
+## Data
+
+The dataset used in this tutorial was created for the Coastal Douglas-fir Conservation Partnership [CDFCP\; @r29]. Although the original dataset covers a much larger area; for brevity, here we focus only on Salt Spring Island, British Columbia. Briefly, Salt Spring Island supports a diverse and globally unique mix of dry forest and savanna habitats. Today, these habitats are critically threatened due to land conversion, invasive species, and altered disturbance regimes. For more information on the data, please refer to the [Marxan tool portal](https://arcese.forestry.ubc.ca/marxan-tool/) and the [tool tutorial](https://peter-arcese-lab.sites.olt.ubc.ca/files/2016/09/CDFCP_tutorial_2017_05.pdf).
+
+
      
+
+![Extent of Coastal Douglas-fir Conservation Partnership Tool area and location of Salt Spring Island](figures/map.jpg)
+
+
      
+
+Let's begin by loading the packages and data for this tutorial. Since this tutorial requires the _prioritizrdata R_ package, please ensure that it is installed. Specifically, two objects underpin the data for this tutorial. The `salt_pu` object specifies the planning unit data as a raster layer (i.e., `RasterLayer` object), and the `salt_features` object contains biodiversity data represented as a multi-band raster stack (i.e., a `RasterStack` object).
+
+```{r, message = FALSE}
+# load packages
+library(prioritizr)
+library(prioritizrdata)
+library(scales)
+
+# load planning unit data
+data(salt_pu)
+
+# load ecological data
+data(salt_features)
+```
+
+Now we will conduct some preliminary processing. Specifically, we will aggregate from the 100 m resolution to the 300 m resolution. This is to reduce the time needed to generate prioritizations in this tutorial. In practice, we generally recommend consider other criteria too -- such as the spatial scale that is relevant for decision making and the resolution of available datasets -- when deciding on an appropriate scale for planning units.
+
+```{r}
+# aggregate data to coarser resolution
+salt_pu <- aggregate(salt_pu, fact = 3)
+salt_features <- aggregate(salt_features, fact = 3)
+```
+
+Next, let's have a look at the `salt_pu` object. Here each grid cell represents a planning unit, and the grid cell values denote acquisition costs [@r28]. To aid with visualization, we will log-transform the values when plotting them on a map.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r}
+# print planning unit data
+print(salt_pu)
+
+# plot map showing the planning units costs on a log-scale
+plot(log(salt_pu), main = "Planning unit costs (log)", axes = FALSE)
+```
+
+Let's also look at the `salt_features` object. This object is a stack of raster layers, with each layer corresponding to a different variable that describes a particular aspect of biodiversity. The first four layers correspond to different ecological communities (i.e., _Old Forest_, _Savannah_, _Wetland_, and _Shrub_ communities), and their cell values indicate the probability of encountering a bird species associated a given community. The fifth layer describes the inverse probability of occurrence of human commensal species. In this tutorial, we will use the first four layers as biodiversity features, and the fifth layer to help parameterize connectivity (wherein higher values denote greater connectivity). So, let's extract the data and visualize them.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r}
+# print original data
+print(salt_features)
+
+# extract connectivity data
+salt_con <- salt_features[[nlayers(salt_features)]]
+
+# print connectivity data
+print(salt_con)
+
+# plot map showing the connectivity data
+plot(salt_con, main = "Connectivity data", axes = FALSE)
+```
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1), oma = c(0, 0, 0, 0.5))
+```
+
+```{r, fig.width = 7.0, fig.height = 7.0}
+# extract ecological communities and use these as features
+salt_features <- salt_features[[seq_len(4)]]
+
+# assign names to features
+names(salt_features) <- c("Old_Forest", "Savannah", "Wetland", "Shrub")
+
+# print features
+print(salt_features)
+
+# plot map showing the distribution of the features
+plot(salt_features, main = names(salt_features), axes = FALSE)
+```
+
+## Baseline problem
+
+In this tutorial, we will explore a few different ways of incorporating connectivity into prioritizations. To enable comparisons among prioritizations based on different approaches, we will first create a baseline problem formulation that we will subsequently customize to incorporate connectivity. Specifically, we will formulate the baseline problem using the minimum set objective. We will use representation targets of 17% -- based on [Aichi Biodiversity Target 11](https://www.cbd.int/sp/targets/) -- to provide adequate coverage of each ecological community. Additionally, because land properties on Salt Spring Island can either be acquired in their entirety or not at all, we will use binary decision types. This means that planning units are either selected in the solution or not selected in the solution---planning units cannot be partially acquired. Given all these details, let's formulate the baseline problem.
+
+```{r}
+# create problem
+p0 <- problem(salt_pu, salt_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.17) %>%
+      add_binary_decisions() %>%
+      add_default_solver()
+
+# print problem
+print(p0)
+```
+
+After formulating the baseline problem, we can solve it to generate a prioritization.
+
+```{r, results = "hide"}
+# solve problem
+s0 <- solve(p0)
+```
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r}
+# print solution
+print(s0)
+
+# plot solution
+plot(
+  s0, main = "Baseline prioritization", axes = FALSE,
+  breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+Next, let's explore some options for incorporating connectivity.
+
+## Adding constraints
+
+Let's explore approaches for promoting connectivity in prioritizations by adding constraints to the baseline problem formulation. These approaches ensure that prioritizations exhibit certain characteristics [e.g., ensure prioritizations form a contiguous reserve\; @r57]. This means that, regardless of the optimality gap used to generate a prioritization, the prioritization will always exhibit these characteristics.
+
+### Neighbor constraints
+
+Neighbor constraints can be added to ensure that each selected planning unit has a certain number of neighbors surrounding it (using the `add_neighbor_constraints()` function) [based on @r16]. The `k` parameter can be used to specify the required number of neighbors for each selected planning unit. Let's generate a prioritization by specifying that each planning unit requires at least two neighbors.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with added neighbor constraints and solve it
+s1 <- p0 %>%
+      add_neighbor_constraints(k = 2) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s1), main = c("baseline", "neighbors constraints"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+### Contiguity constraints
+
+Contiguity constraints can be added to ensure that all planning units form a single contiguous reserve (using the `add_contiguity_constraints()` function) [similar to @r57]. These constraints are extremely complex. As such, they can only be applied to small conservation planning problems and the _Gurobi_ solver is required to solve them in a feasible period of time. Since it would take a long time to generate a near-optimal prioritization for this dataset with contiguity constraints, we will also tell the solver to simply return the first solution that it finds which meets the representation targets and the contiguity constraints.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with added contiguity constraints and solve it
+s2 <- p0 %>%
+      add_contiguity_constraints() %>%
+      add_gurobi_solver(first_feasible = TRUE) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s2), main = c("baseline", "contiguity constraints"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+There is also an even more complex version of the contiguity constraints that is available. These constraints -- termed feature contiguity constraints [similar to @r64] -- can be added to ensure that all of the selected planning units used to the reach representation targets within a prioritization form a contiguous network for each feature (using the `add_feature_contiguity_constraints()` function). In other words, they ensure that each feature can disperse through the prioritization to access a target threshold amount of habitat. However, these constraints are extraordinarily complex, only feasible for small problems, and require preprocessing routines to identify initial solutions. As such, we will not consider them in this tutorial.
+
+### Linear constraints
+
+Linear constraints can be used to specify that the prioritizations must meet an arbitrary set of criteria. As such, they can be used to ensure that prioritizations provide adequate coverage of planning units that have facilitate a high level of connectivity. Recall that the `salt_con` data are used to describe connectivity across the study area. Since higher values denote planning units with greater connectivity, we could use linear constraints to ensure that the total sum of connectivity values -- based on this dataset -- meets a particular threshold (e.g. cover at least 30% of the total amount). This would effectively be treating connectivity as an additional feature [similar to @r52].
+
+```{r}
+# compute threshold for constraints
+## here we use a threshold of 30% of the total connectivity values
+threshold <- cellStats(salt_con, "sum") * 0.3
+
+# print threshold
+print(threshold)
+```
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with added linear constraints and solve it
+s3 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s3), main = c("baseline", "linear constraints"),
+   axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+Although using continuous values has the advantage that the prioritization process can explicitly account for differences in the relative amount of connectivity facilitated by different planning units, the disadvantage is that the prioritization could potentially focus on selecting lots of planning units with low connectivity values. To avoid this result, one strategy is to convert the continuous values into binary values using a threshold limit [similar to @r53]. By applying such a threshold limit, linear constraints can then be used to ensure that the prioritization selects a minimum amount of planning units with high connectivity values (i.e., those with connectivity values that are equal to or greater than the threshold limit).
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r}
+# calculate threshold limit
+## here we set a threshold limit based on the median
+threshold_limit <- quantile(salt_con, probs = 0.5)
+
+# convert continuous values to binary values
+salt_con_binary <- round(salt_con <= threshold_limit)
+
+# plot binary values
+plot(salt_con_binary, main = "salt_con_binary", axes = FALSE)
+```
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with added linear constraints and solve it
+## note that we use the original threshold computed before,
+## to ensure the prioritization covers at least 30% of the total amount
+## connectivity values
+s4 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con_binary, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s4), main = c("baseline", "linear constraints (binary)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+Another strategy is to clamp the continuous values below a threshold limit are assigned a value of zero [similar to @r54]. This strategy has the advantage that (i) the prioritization won't focus on selecting lots of planning units with low connectivity values to meet the constraint threshold, and (ii) the optimization process can use semi-continuous values to distinguish between places that can facilitate a moderate amount and a high amount of connectivity.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, results = "hide"}
+# clamp continuous values using the threshold limit we computed before
+salt_con_clamp <- salt_con
+salt_con_clamp[Which(salt_con <= threshold_limit)] <- 0
+
+# plot clamped values
+plot(salt_con_clamp, main = "salt_con_clamp", axes = FALSE)
+```
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with added linear constraints and solve it
+## note that we use the original threshold computed before,
+## to ensure the prioritization covers at least 30% of the total amount
+## connectivity values
+s5 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con_clamp, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s5), main = c("baseline", "linear constraints (clamped)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+If we were concerned that the prioritization did not facilitate a high enough level of connectivity, we could increase the `threshold` value or the `threshold_limit` value. For example, let's increase the `threshold_limit` value used to clamp the continuous connectivity values.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, results = "hide"}
+# compute threshold limit
+threshold_limit2 <- quantile(salt_con, probs = 0.7)
+
+# clamp continuous values using the threshold limit we computed before
+salt_con_clamp2 <- salt_con
+salt_con_clamp2[Which(salt_con <= threshold_limit2)] <- 0
+
+# plot clamped values
+plot(salt_con_clamp2, main = "salt_con_clamp", axes = FALSE)
+```
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with added linear constraints and solve it
+## note that we use the original threshold computed before,
+## to ensure the prioritization covers at least 30% of the total amount
+## connectivity values
+s6 <- p0 %>%
+      add_linear_constraints(
+        data = salt_con_clamp2, threshold = threshold, sense = ">="
+      ) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s6), main = c("baseline", "linear constraints (clamped 2)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+Despite the advantages of clamping the connectivity values, we can see that the prioritization has a relatively high level of spatial fragmentation. In fact, all prioritizations generated using the linear constraints can potentially have this issue. This is because linear constraints do not explicitly account for the spatial arrangement of the planning units. As such, we recommend combining the linear constraints approach with another approach [e.g., the boundary penalties approach discussed below; @r53].
+
+## Adding penalties
+
+Now let's explore approaches for promoting connectivity in prioritizations by adding penalties to the baseline problem formulation. These approaches involve penalizing solutions according to exhibit certain [e.g., penalize spatial fragmentation of prioritizations\; @r2]. Unlike constraint-based methods for incorporating connectivity -- if the optimality gap used to generate a prioritization is too high -- they may not necessarily produce prioritizations that exhibit desirable characteristics.
+
+### Boundary penalties
+
+Boundary penalties can be added to used to reduce the spatial fragmentation of prioritizations (using the `add_boundary_penalties()` function). Specifically, these penalties update the problem formulation to penalize solutions that have a high total amount of exposed boundary length [@r3]. Since boundary data often have large values which can degrade solver performance and result in excessive run times (see the [_Calibrating trade-offs tutorial_](calibrating_trade-offs-tutorial.html) for details), we will first precompute rescale the boundry data.
+
+```{r}
+# precompute the boundary data
+salt_boundary_data <- boundary_matrix(salt_pu)
+
+# rescale boundary data
+salt_boundary_data@x <- rescale(salt_boundary_data@x, to = c(0.01, 100))
+```
+
+Next, let's generate a prioritization using boundary penalties. To specify the relative importance reducing spatial fragmentation -- compared with the primary objective of a problem (e.g. minimizing cost) -- we need to a value for the `penalty` parameter is used. Setting a higher value for `penalty` indicates that it is more important to avoid highly fragmented solutions. Let's generate a prioritization with a `penalty` value of 0.001.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with added boundary penalties
+s7 <- p0 %>%
+      add_boundary_penalties(penalty = 0.001, data = salt_boundary_data) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s7), main = c("baseline", "boundary penalties (0.001)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+We can see that the resulting prioritization is still relatively fragmented, so let's try generating another prioritization with a higher `penalty` value.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with increased boundary penalties
+s8 <- p0 %>%
+      add_boundary_penalties(penalty = 10, data = salt_boundary_data) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s8), main = c("baseline", "boundary penalties (10)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+Although the prioritization is now less fragmented, it has also selected a greater number of planning units. Let's calculate the cost of the prioritizations to see how they vary in overall cost.
+
+```{r}
+# calculate cost of baseline prioritization
+eval_cost_summary(p0, s0)
+
+# calculate cost of prioritization with low boundary penalties (i.e., 0.001)
+eval_cost_summary(p0, s7)
+
+# calculate cost of prioritization high low boundary penalties (i.e., 0.1)
+eval_cost_summary(p0, s8)
+```
+
+We can see that the cost of the prioritizations increase with when we use higher `penalty` values. This is because there is a trade-off between the cost of a prioritization and the level of spatial fragmentation. Although it can be challenging to find the best balance, there are qualitative and quantitative methods available to help navigate such trade-offs. Please see the [_Calibrating trade-offs tutorial_](calibrating_trade-offs-tutorial.html) for a details on these methods.
+
+### Connectivity penalties
+
+Connectivity penalties can be used to promote connectivity in prioritizations (using the `add_connectivity_penalties()` function). These penalties use  connectivity scores to parametrize the strength of connectivity between pairs of planning units [@r38]. Thus higher scores denote a greater level of connectivity between different planning units. For example, previous studies have parametrized connectivity scores using habitat quality, environmental, and river flow data [e.g. @r59; @r63; @r43]. Although there are many approaches to calculate connectivity scores, one approach involves using conductance data -- data that describe how much each planning unit facilitates movement (opposite of landscape resistance data) -- and calculating scores for each pair of planning units by averaging their conductance values (implemented using the `connectivity_matrix()` function).
+
+Let's compute connectivity scores by treating the `salt_con` object as conductance data. This means that we assume that neighboring planning units with higher values in the  `salt_con` object are capable of facilitating a greater amount of connectivity. **Note that the data used to compute connectivity scores must conform to the same spatial properties as the planning unit data (e.g., resolution, spatial extent, coordinate reference system).** Also, although we are using raster data here, these scores can also be computed for vector data too (e.g., `sf::st_sf()` objects). Similar to the boundary data, we will also rescale the connectivity scores to avoid numerical issues during optimization.
+
+```{r}
+# compute connectivity scores
+salt_con_scores <- connectivity_matrix(salt_pu, salt_con)
+
+# rescale scores
+salt_con_scores@x <- rescale(salt_con_scores@x, to = c(0.01, 100))
+```
+
+After computing the connectivity scores, we can use them to generate prioritizations using connectivity penalties. Similar to the boundary penalties, we use the `penalty` parameter to specify the relative importance of promoting connectivity relative to the primary objective of a problem (i.e., minimizing overall cost). Let's generate a prioritization with a `penalty` value of 0.001.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with added connectivity penalties
+s9 <- p0 %>%
+      add_connectivity_penalties(penalty = 0.001, data = salt_con_scores) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s9), main = c("baseline", "connectivity penalties (0.001)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+Now let's try generating another prioritization with a higher `penalty` value.
+
+```{r, include = FALSE}
+par(mar = c(1.1, 4.1, 4.1, 2.1))
+```
+
+```{r, fig.width = 7.0, results = "hide"}
+# create problem with increased connectivity penalties
+s10 <- p0 %>%
+      add_connectivity_penalties(penalty = 0.002, data = salt_con_scores) %>%
+      solve()
+
+# plot solutions
+plot(
+  stack(s0, s10), main = c("baseline", "connectivity penalties (0.002)"),
+  axes = FALSE, breaks = c(0, 0.5, 1), col = c("grey70", "darkgreen")
+)
+```
+
+We can see that increasing the `penalty` parameter causes the prioritizations to select planning units in regions with greater connectivity values (i.e., per the `salt_con` object). As discussed with the boundary penalties, increasing the `penalty` value tells the optimization process to focus more on promoting connectivity---meaning that it won't focus as much on the primary objective (i.e., because the primary objective is to minimize overall costs). For details on calibrating these trade-offs please see the [_Calibrating trade-offs tutorial_](calibrating_trade-offs-tutorial.html). **Note that you will need to the use `eval_connectivity_summary()` function -- instead of the `eval_boundary_summary()` function -- when adapting the tutorial code for connectivity penalties.**
+
+## Conclusion
+
+Hopefully, this tutorial has provided a helpful introduction for incorporating connectivity into prioritizations. Broadly speaking, we recommend using the boundary penalties or the connectivity penalties to ensure that prioritizations explicitly account for the spatial configuration of selected planning units. Additionally, though not fully explored here, the connectivity penalties are a very flexible approach for promoting connectivity. For instance, in addition to parameterizing pair-wise connectivity scores for neighboring planning units, they can also be used to parametrize pair-wise connectivity scores between more distant planning units. Thus connectivity penalties could be used to parametrize connectivity across both small scales and large spatial scales (e.g., using a scaling procedure wherein connectivity scores between pairs of planning units decline with the distance between them).
+
+## References
diff --git a/inst/doc/gurobi_installation.Rmd b/vignettes/gurobi_installation_guide.Rmd
similarity index 88%
rename from inst/doc/gurobi_installation.Rmd
rename to vignettes/gurobi_installation_guide.Rmd
index 016dd7dfd..e36fe4832 100644
--- a/inst/doc/gurobi_installation.Rmd
+++ b/vignettes/gurobi_installation_guide.Rmd
@@ -1,5 +1,5 @@
 ---
-title: "Gurobi Installation Guide"
+title: "Gurobi installation guide"
 author: "Richard Schuster"
 date: "`r Sys.Date()`"
 output:
@@ -10,7 +10,7 @@ output:
 fontsize: 11pt
 documentclass: article
 vignette: >
-  %\VignetteIndexEntry{Gurobi Installation Guide}
+  %\VignetteIndexEntry{Gurobi installation guide}
   %\VignetteEngine{knitr::rmarkdown_notangle}
 ---
 
@@ -28,7 +28,7 @@ devtools::load_all()
 
 ## Introduction
 
-_Gurobi_ is the most powerful and fastest solver that the _prioritizr R_ package can use to solve conservation planning problems. This vignette will walk you through the process of setting up _Gurobi_ on your computer so that you can use it to solve conservation planning problems. If you encounter any problems while following the instructions below, check out the [official _Gurobi_ documentation](https://www.gurobi.com/documentation/).
+_Gurobi_ is the most powerful and fastest solver that the _prioritizr R_ package can use to solve conservation planning problems (see the [_Solver benchmarks_](solver_benchmarks.html) vignette for further details). This guide will walk you through the process of setting up _Gurobi_ on your computer so that it can be used to solve conservation planning problems. If you encounter any problems while following the instructions below, please refer to the [official _Gurobi_ documentation](https://www.gurobi.com/documentation/).
 
 ## Obtaining a license
 
@@ -48,7 +48,7 @@ After obtaining a license, you will need to download the _Gurobi_ installer to y
 
 ## Software installation
 
-The process for installing the _Gurobi_ software depends on the operating system on your computer. Fortunately, _Gurobi_ provide platform-specific ["Quick Start Guides"](https://www.gurobi.com/documentation/) for [Windows](https://www.gurobi.com/documentation/9.0/quickstart_windows/software_installation_guid.html#section:Installation), [MacOS](https://www.gurobi.com/documentation/9.0/quickstart_mac/software_installation_guid.html), and [Linux](https://www.gurobi.com/documentation/9.0/quickstart_linux/software_installation_guid.html) systems that should help with this. Briefly, on Windows systems, you just need to double-click on the _Gurobi_ installer, follow the prompts, and the installer will automatically handle everything for you. On Linux and MacOS systems, you will need to manually extract the downloaded file's contents to a folder, move the extracted contents to a suitable location (typically _/opt/gurobi_), and update your system's variables so that it knows where to find _Gurobi_ (i.e. the `PATH` variable).
+The process for installing the _Gurobi_ software depends on the operating system on your computer. Fortunately, _Gurobi_ provide platform-specific ["Quick Start Guides"](https://www.gurobi.com/documentation/) for [Windows](https://www.gurobi.com/documentation/9.0/quickstart_windows/software_installation_guid.html#section:Installation), [MacOS](https://www.gurobi.com/documentation/9.0/quickstart_mac/software_installation_guid.html), and [Linux](https://www.gurobi.com/documentation/9.0/quickstart_linux/software_installation_guid.html) systems that should help with this. Briefly, on Windows systems, you just need to double-click on the _Gurobi_ installer, follow the prompts, and the installer will automatically handle everything for you. On Linux and MacOS systems, you will need to manually extract the downloaded file's contents to a folder, move the extracted contents to a suitable location (typically _/opt/gurobi_), and update your system's variables so that it knows where to find _Gurobi_ (i.e., the `PATH` variable).
 
 Additionally, if you are using [_RStudio_](https://www.rstudio.com/products/rstudio/) on a Linux system, you might need to add the following text to a Rstudio configuration file (located at `/etc/rstudio/rserver.conf`).
 
@@ -64,7 +64,7 @@ Now we will activate the _Gurobi_ software using the license you obtained earlie
 
 
      ![](figures/cmd-windows-success.png){ width=75% }

      
 
-Next, we will now check that the license has been successfully activated. To achieve this, we will try running _Gurobi_ directly from the command line. Note that the following commands assume you are using version 8.0.0 of _Gurobi_, and so you will need to modify the command if you are using a more recent version (e.g. if using version 9.1.2, then use `gurobi912` instead of `gurobi800` below).
+Next, we will now check that the license has been successfully activated. To achieve this, we will try running _Gurobi_ directly from the command line. Note that the following commands assume you are using version 8.0.0 of _Gurobi_, and so you will need to modify the command if you are using a more recent version (e.g., if using version 9.1.2, then use `gurobi912` instead of `gurobi800` below).
 
 On Windows systems, users can type in the following system command to check their license activation.
 
@@ -86,7 +86,7 @@ After activating the license, you now need to install the _gurobi R_ package. Th
 
 ## _R_ package installation
 
-Now we will install the _gurobi R_ package. This package is not available on the Comprehensive R Archive Network and is instead distributed with the _Gurobi_ software suite. Specifically, the _gurobi_ _R_ package should be located within the folder where you installed the _Gurobi_ software suite. We will install the _gurobi_ _R_ package by running the following _R_ code within your _R_ session. Note that the following code assumes that you are using version 8.0.0 of _Gurobi_, and so you will need to modify the code if you are using a more recent version (e.g. if using version 9.1.2, then use `gurobi912` instead of `gurobi800` below).
+Now we will install the _gurobi R_ package. This package is not available on the Comprehensive R Archive Network and is instead distributed with the _Gurobi_ software suite. Specifically, the _gurobi_ _R_ package should be located within the folder where you installed the _Gurobi_ software suite. We will install the _gurobi_ _R_ package by running the following _R_ code within your _R_ session. Note that the following code assumes that you are using version 8.0.0 of _Gurobi_, and so you will need to modify the code if you are using a more recent version (e.g., if using version 9.1.2, then use `gurobi912` instead of `gurobi800` below).
 
 Assuming you installed _Gurobi_ in the default location, Windows users can install _gurobi_ _R_ package using the following code.
 
@@ -102,7 +102,7 @@ install.packages(file.path(Sys.getenv("GUROBI_HOME"),
                  repos = NULL)
 ```
 
-Next, you will need to install the _slam R_ package because the _gurobi_ _R_ package needs this package to work. Users of all platforms (i.e. Windows, Linux, and MacOS) can install the package using the following _R_ code.
+Next, you will need to install the _slam R_ package because the _gurobi_ _R_ package needs this package to work. Users of all platforms (i.e., Windows, Linux, and MacOS) can install the package using the following _R_ code.
 
 ```{r, eval  = FALSE}
 install.packages("slam", repos = "https://cloud.r-project.org")
@@ -136,7 +136,7 @@ If you see the outputs for `result$objval` and `result$x` and you don't see any
 
 ## Solving a _prioritzr_ problem with _Gurobi_
 
-If you successfully installed the _Gurobi_ software suite and the _gurobi_ _R_ package, you can now try solving conservation planning problems using the _prioritzr_ _R_ package. Although the _prioritizr_ _R_ package should automatically detect that _Gurobi_ has been installed, you can use the function `add_gurobi_solver` to manually specify that _Gurobi_ should be used to solve problems. This function is also useful because you can use it to customize the optimization process (e.g. specify the desired optimality gap or set a limit on how much time should be spent searching for a solution).
+If you successfully installed the _Gurobi_ software suite and the _gurobi_ _R_ package, you can now try solving conservation planning problems using the _prioritzr_ _R_ package. Although the _prioritizr_ _R_ package should automatically detect that _Gurobi_ has been installed, you can use the function `add_gurobi_solver()` to manually specify that _Gurobi_ should be used to solve problems. This function is also useful because you can use it to customize the optimization process (e.g., specify the desired optimality gap or set a limit on how much time should be spent searching for a solution).
 
 Finally, to check that everything has been installed correctly, we will use the _Gurobi_ software suite to solve a reserve selection problem created using the _prioritzr_ _R_ package.
 
diff --git a/inst/doc/zones.Rmd b/vignettes/management_zones_tutorial.Rmd
similarity index 70%
rename from inst/doc/zones.Rmd
rename to vignettes/management_zones_tutorial.Rmd
index b28c8541d..48efd1835 100644
--- a/inst/doc/zones.Rmd
+++ b/vignettes/management_zones_tutorial.Rmd
@@ -1,5 +1,5 @@
 ---
-title: "Management Zones"
+title: "Management zones tutorial"
 output:
   rmarkdown::html_vignette:
     toc: true
@@ -10,7 +10,7 @@ documentclass: article
 bibliography: references.bib
 csl: reference-style.csl
 vignette: >
-  %\VignetteIndexEntry{Management Zones}
+  %\VignetteIndexEntry{Management zones tutorial}
   %\VignetteEngine{knitr::rmarkdown_notangle}
 ---
 
@@ -23,21 +23,22 @@ knitr::opts_chunk$set(fig.align = "center", eval = !is_check,
 
 ## Introduction
 
-One of the main aims in conservation planning is to identify the most cost-effective set of areas to manage biodiversity [@r4]. To achieve this, prioritizations are generally created to identify areas for expanding protected area systems. However, many real-world conservation problems do not simply involve deciding if an area should be protected or not [e.g. @r5; @r18]. Instead, many real-world problems involve a range of different management categories and the goal is to determine which areas should be allocated to which management category. For example, a manager might have a range of different methods (e.g. baiting or trapping at various intensities) for controlling invasive pests in a set of different areas [e.g. @r25]. They would need a prioritization that shows which control methods should be implemented in which areas. In this particular case, a binary prioritization showing which areas contain the most biodiversity is simply not helpful. Furthermore, many real-world problems require decisions that meet multiple, and sometimes conflicting, objectives from different stakeholders. For example, a manager might need to implement a set of no-take and partial-take areas to prevent overfishing, but also ensure that there still remain plenty of areas for fishing activities [e.g. @r26; @r27]. Popularized by _Marxan with Zones_ [@r2], this concept has become known as "zones" and is becoming increasingly important in conservation planning.
+One of the main aims in conservation planning is to identify the most cost-effective set of areas to manage biodiversity [@r4]. To achieve this, prioritizations are generally created to identify areas for expanding protected area systems. However, many real-world conservation problems do not simply involve deciding if an area should be protected or not [e.g., @r5; @r18]. Instead, many problems involve a range of different management categories and the goal is to determine which areas should be allocated to which management category. For example, a manager might have a range of different methods (e.g., baiting or trapping at various intensities) for controlling invasive pests in a set of different areas [e.g., @r25]. They would need a prioritization that shows which control methods should be implemented in which areas. In this particular case, a binary prioritization showing which areas contain the most biodiversity is simply not helpful. Furthermore, many real-world problems require decisions that meet multiple, and sometimes conflicting, objectives from different stakeholders. For example, a manager might need to implement a set of no-take and partial-take areas to prevent overfishing, but also ensure that there still remain plenty of areas for fishing activities [e.g., @r26; @r27]. Popularized by the _Marxan with Zones_ decision support tool [@r2], this concept has become known as "zones" and is becoming increasingly important in conservation planning.
 
-The aim of this vignette is to showcase the zones functionality of the _prioritizr R_ package. It will assume a certain level of familiarity with conservation planning terminology and the _prioritizr R_ package. We recommend reading the [_prioritizr_ vignette](prioritizr.html) first if you don't have much experience in either of these topics.
+The aim of this tutorial is to showcase the zones functionality of the _prioritizr R_ package. It will assume a certain level of familiarity with conservation planning terminology and the package. If you don't have much experience in either of these topics, we recommend first reading the [_Package overview_](package_overview.html) vignette.
 
 ## Usage
 
-
 ### Simple minimum set problem
 
-In the _prioritizr R_ package, all conservation planning problems---including those which contain multiple management zones or actions---are initialized using the `problem` function. To refresh our memory on how we can construct problems using the _prioritizr R_ package, let us quickly construct a simple conservation planning problem. This problem will use the simulated built-in planning unit and feature data distributed with the package. It will have a minimum set objective, targets which require that solution secure to 10 % of the habitat in the study area for each feature, and binary decision variables indicating that planning units are selected or not selected for protection.
+In the _prioritizr R_ package, all conservation planning problems -- including those which contain multiple management zones or actions -- are initialized using the `problem` function. To refresh our memory on how we can construct problems, let us quickly construct a simple conservation planning problem. This problem will use the simulated built-in planning unit and feature data distributed with the package. It will have a minimum set objective, targets which require that solution secure to 10 % of the habitat in the study area for each feature, and binary decision variables indicating that planning units are selected or not selected for protection.
 
-```{r}
+```{r, results = "hide"}
 # load prioritizr package
 library(prioritizr)
+```
 
+```{r}
 # load data
 data(sim_pu_raster, sim_features)
 
@@ -66,7 +67,7 @@ plot(s1, main = "solution", axes = FALSE, box = FALSE)
 
 ### Adding management zones
 
-Now let us imagine that instead of having a single management zone (e.g. protected area), we have two management zones. Similar to the example above, we require a solution that secures 10 % of the habitat in the study area for each feature in the first management zone. But we also require a solution that secures 5 % of the habitat in the study area for each feature in the second management zone. Each planning unit must be allocated to either zone or not selected for management at all. In this example, each planning unit costs the same when it is allocated to either of the two zones. We can formulate and solve this problem using the following code.
+Now let us imagine that instead of having a single management zone (e.g., protected area), we have two management zones. Similar to the example above, we require a solution that secures 10 % of the habitat in the study area for each feature in the first management zone. But we also require a solution that secures 5 % of the habitat in the study area for each feature in the second management zone. Each planning unit must be allocated to either zone or not selected for management at all. In this example, each planning unit costs the same when it is allocated to either of the two zones. We can formulate and solve this problem using the following code.
 
 ```{r}
 # create a matrix with the targets
@@ -125,7 +126,7 @@ plot(category_layer(s2), main = "solution", axes = FALSE, box = FALSE)
 
 ### Multiple zones with varying costs
 
-Real-world problems often have different costs for managing planning units under different zones. These problems also tend to have different expected amounts of each feature when planning units are managed differently. So let us consider a slightly more complex example. Similar to before we will have two management zones. But this time, the cost of managing each planning unit is different depending on which management zone it is assigned to in the solution. Furthermore, when we assign a planning unit to the second zone, we only expect to end up with half of the habitat we would get if we managed the unit in the first zone (e.g. because the second zone is a partial-take zone and the first zone is a no-take zone). We will use the same target data as in the previous example.
+Real-world problems often have different costs for managing planning units under different zones. These problems also tend to have different expected amounts of each feature when planning units are managed differently. So let us consider a slightly more complex example. Similar to before we will have two management zones. But this time, the cost of managing each planning unit is different depending on which management zone it is assigned to in the solution. Furthermore, when we assign a planning unit to the second zone, we only expect to end up with half of the habitat we would get if we managed the unit in the first zone (e.g., because the second zone is a partial-take zone and the first zone is a no-take zone). We will use the same target data as in the previous example.
 
 ```{r, fig.width = 4.0}
 # create new planning unit and cost data
@@ -159,7 +160,7 @@ plot(category_layer(s3), main = "solution", axes = FALSE, box = FALSE)
 
 ### Multiple zones with complex targets
 
-So far, we have dealt with problems where each feature has a target that pertains to a single zone. But sometimes we have targets that pertain to multiple zones. For example, what if we were in charge of managing pest control in a set of areas and we had three different pest control methods we could implement in any given planning unit. We could (1) set up a few traps in a given planning unit and make 10 % of the habitat in the unit pest-free, (2) set up a lot of traps and make 50 % of the habitat in the unit pest-free, or (3) drop baits over a given planning unit and make 80 % of the planning unit pest-free. Each of these different actions has a different cost, with a few low intensity trapping costing $100 per planning unit, a high intensity trapping costing $300, and baiting costing $200 (please note these costs aren't meant to be realistic). After defining our management actions and costs, we require a solution that will yield 8 units of pest free habitat per feature. It's important to note that unlike the previous examples, here we don't have targets for each feature in each zone, but rather our targets are for each feature and across multiple zones. In other words, we don't really care which management actions we implement, we just want the set of actions that will meet our targets for minimum expenditure. We can formulate and solve this problem using the following code.
+So far, we have dealt with problems where each feature has a target that pertains to a single zone. But sometimes we have targets that pertain to multiple zones. For example, what if we were in charge of managing pest control in a set of areas and we had three different pest control methods we could implement in any given planning unit. We could (i) set up a few traps in a given planning unit and make 10 % of the habitat in the unit pest-free, (ii) set up a lot of traps and make 50 % of the habitat in the unit pest-free, or (iii) drop baits over a given planning unit and make 80 % of the planning unit pest-free. Each of these different actions has a different cost, with a few low intensity trapping costing $100 per planning unit, a high intensity trapping costing $300, and baiting costing $200 (please note these costs aren't meant to be realistic). After defining our management actions and costs, we require a solution that will yield 8 units of pest free habitat per feature. It's important to note that unlike the previous examples, here we don't have targets for each feature in each zone, but rather our targets are for each feature and across multiple zones. In other words, we don't really care which management actions we implement, we just want the set of actions that will meet our targets for minimum expenditure. We can formulate and solve this problem using the following code.
 
 ```{r, fig.width = 4.5, fig.height = 3}
 # create planning unit data with costs
@@ -318,6 +319,6 @@ plot(category_layer(s7), main = "solution", axes = FALSE, box = FALSE)
 
 ## Conclusion
 
-Hopefully, this vignette has provided an informative introduction to building and solving problems with multiple zones using the _prioritizr R_ package. Although we have examined only a few different functions here, almost every single function for modifying conservation planning problems is compatible with problems that contain zones. It's worth noting that working with multiple zones is a lot trickier than working with a single zone, so we would recommend playing around with the code in the Examples sections of the help pages to get a feel for what different functions do when they are applied to problems with multiple zones.
+Hopefully, this vignette has provided an informative introduction to building and solving problems with multiple zones. Although we have examined only a few different functions here, almost every single function for modifying conservation planning problems is compatible with problems that contain zones. It's worth noting that working with multiple zones is a lot trickier than working with a single zone, so we would recommend playing around with the code in the _Examples_ sections of the package documentation to help understand how functions work when applied to multiple zones.
 
 ## References
diff --git a/vignettes/package_overview.Rmd b/vignettes/package_overview.Rmd
new file mode 100644
index 000000000..eb1d5ddf3
--- /dev/null
+++ b/vignettes/package_overview.Rmd
@@ -0,0 +1,905 @@
+---
+title: "Package overview"
+output:
+  rmarkdown::html_vignette:
+    toc: true
+    fig_caption: true
+    self_contained: yes
+fontsize: 11pt
+documentclass: article
+bibliography: references.bib
+csl: reference-style.csl
+vignette: >
+  %\VignetteIndexEntry{Package overview}
+  %\VignetteEngine{knitr::rmarkdown_notangle}
+---
+
+```{r, include = FALSE}
+h = 3.5
+w = 3.5
+is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_",
+             "_R_CHECK_LICENSE_") %in% names(Sys.getenv()))
+knitr::opts_chunk$set(fig.align = "center", eval = !is_check,
+                      root.dir = normalizePath("../.."))
+```
+
+## Summary
+
+The _prioritizr R_ package uses integer linear programming (ILP) techniques to provide a flexible interface for building and solving conservation planning problems [@r11; @r16]. It supports a broad range of objectives, constraints, and penalties that can be used to custom-tailor conservation planning problems to the specific needs of a conservation planning exercise. Once built, conservation planning problems can be solved using a variety of commercial and open-source exact algorithm solvers. In contrast to the algorithms conventionally used to solve conservation problems, such as heuristics or simulated annealing [@r3], the exact algorithms used here are guaranteed to find optimal solutions. Furthermore, conservation problems can be constructed to optimize the spatial allocation of different management zone (or actions), meaning that conservation practitioners can identify solutions that benefit multiple stakeholders. Finally, this package has the functionality to read input data formatted for the _Marxan_ conservation planning program [@r3], and find much cheaper solutions in a much shorter period of time than _Marxan_ [@r1].
+
+## Introduction
+
+Systematic conservation planning is a rigorous, repeatable, and structured approach to designing new protected areas that efficiently meet conservation objectives [@r4]. Historically, conservation decision-making has often evaluated parcels opportunistically as they became available for purchase, donation, or under threat. Although purchasing such areas may improve the _status quo_, such decisions may not substantially enhance the long-term persistence of target species or communities. Faced with this realization, conservation planners began using decision support tools to help simulate alternative reserve designs over a range of different biodiversity and management goals and, ultimately, guide protected area acquisitions and management actions. Due to the systematic, evidence-based nature of these tools, conservation prioritization can help contribute to a transparent, inclusive, and more defensible decision making process.
+
+A conservation planning exercise typically starts by defining a study area. This study area should encompass all the areas relevant to the decision maker or the hypothesis being tested. The extent of a study area could encompass a few important localities [e.g., @r18], a single state [e.g., @r17], an entire country [@r19], or the entire planet [@r20]. Next, the study area is divided into a set of discrete areas termed _planning units_. Each planning unit represents a discrete locality in the study area that can be managed independently of other areas. The general idea is that some combination of the planning units can be selected for conservation actions (e.g., protected area establishment, habitat restoration). Planning units are often created as square or hexagon cells that are sized according to the scale of the conservation actions, and the resolution of the data that underpin the planning exercise [but see @r5].
+
+Cost data (or a surrogate thereof) are needed to inform the prioritization process. Specifically, these cost data describe the relative expenditure associated with managing each planning unit for conservation. For example, if the goal of the conservation planning exercise is to identify priority areas for expanding a local protected area system, then the cost data could represent the physical cost of purchasing the land. Alternatively, if such data are not available, then surrogate data could are often used instead (e.g., human population density, opportunity cost of foregone commercial activities, or planning unit size).
+
+Conservation planning exercises also require data on the biodiversity elements that are of conservation interest (termed _conservation features_). These features could be species (e.g., _Neofelis nebulosa_, the Clouded Leopard), populations, or habitats (e.g., mangroves or cloud forest). After identifying the set of relevant conservation features for a conservation planning exercise, spatially explicit data need to be obtained for each and every feature to describe their spatial distribution (e.g., habitat suitability data, probability of occurrence data, presence/absence data). This is important to ensure that conservation features are adequately covered (represented) by prioritizations. After assembling all the data, the next step is to define the conservation planning problem.
+
+The _prioritizr R_ package is designed to help you build and solve conservation planning problems. Specifically, prioritizations are generated by using formulating a mathematical optimization problem and then solving it to generate a solution. These mathematical optimization problems are formulated using the planning unit data, cost data, and feature data, and with information related to the overarching aim of the prioritization process. In general, the goal of an optimization problem is to minimize (or maximize) an _objective function_ that is calculated using a set of _decision variables_, subject to a series of constraints to ensure that solution exhibits specific properties. The objective function describes the quantity which we are trying to minimize (e.g., cost of the solution) or maximize (e.g., number of features conserved). The decision variables describe the entities that we can control, and indicate which planning units are selected for conservation management and which of those are not. The constraints can be thought of as rules that the need decision variables need to follow. For example, a commonly used constraint is specifying that the solution must not exceed a certain budget.
+
+A wide variety of approaches have been developed for solving optimization problems. Reserve design problems are frequently solved using simulated annealing [@r6] or heuristics [@r8; @r7]. These methods are conceptually simple and can be applied to a wide variety of optimization problems. However, they do not scale well for large or complex problems [@r1]. Additionally, these methods cannot tell you how close any given solution is to the optimal solution. The package uses exact algorithms to efficiently solve conservation planning problems to within a pre-specified a optimality gap. In other words, you can specify that you need the optimal solution (i.e., a gap of 0%) and the algorithms will, given enough time, find a solution that meets this criteria. In the past, exact algorithms have been too slow for conservation planning exercises [@r9]. However, improvements over the last decade mean that they are now much faster [@r23; @r1].
+
+In this package, optimization problems are expressed using _integer linear programming_ (ILP) so that they can be solved using (linear) exact algorithm solvers. The general form of an integer programming problem can be expressed in matrix notation using the following equation.
+
+$$\text{Minimize} \space \boldsymbol{c}^\text{T} \boldsymbol{x} \space
+\space \text{subject to} \space A\boldsymbol{x}
+\space \Box \space \boldsymbol{b}$$
+
+Here, where $x$ is a vector of decision variables, $c$ and $b$ are vectors of known coefficients, and $A$ is the constraint matrix. The final term specifies a series of structural constants and the $\Box$ symbol is used to indicate that the relational operators for the constraints can be either $\geq$, $=$, or $\leq$. In the context of a conservation planning problem, $c$ could be used to represent the planning unit costs, $A$ could be used to store the data showing the presence / absence (or amount) of each feature in each planning unit, $b$ could be used to represent minimum amount of habitat required for each species in the solution, the $\Box$ could be set to $\geq$ symbols to indicate that the total amount of each feature in the solution must exceed the quantities in $b$. But there are many other ways of formulating the reserve selection problem [@r11].
+
+## A grammar for conservation planning
+
+The _prioritizr R_ package uses a grammar to describe elements of conservation planning. This means that functions are organized into verbs that relate to specific concepts. For example, all of the functions used to specify the primary objective for optimization end with the `_objective` suffix (e.g., `add_min_set_objective()` and `add_min_shortfall_objective()`). By combining multiple functions together, they can be used to formulate a complete conservation planning problem. Specifically, the verbs for formulating problems are described below.
+
+* Create a new conservation planning [problem](https://prioritizr.net/reference/problem.html) by specifying the planning units, features, and management zones of conservation interest.
+* Add a primary [objective](https://prioritizr.net/reference/objectives.html) to a conservation planning problem (e.g., minimize overall cost).
+* Add [penalties](https://prioritizr.net/reference/penalties.html) to a conservation planning problem to penalize solutions according to specific metric (e.g., connectivity).
+* Add [targets](https://prioritizr.net/reference/targets.html) to a conservation planning problem to specify how much of each feature should ideally be represented  solutions.
+* Add [constraints](https://prioritizr.net/reference/constraints.html) to a conservation planning problem to ensure that solutions exhibit specific properties (e.g., select specific planning units for protection).
+* Add [decisions](https://prioritizr.net/reference/decisions.html) to a conservation planning problem to specify the nature of the decisions in the problem (e.g., binary decisions indicate the planning units should be selected or not selected for management).
+* Add a [portfolio](https://prioritizr.net/reference/portfolios.html) to a conservation planning problem to specify a methodological approach for generating multiple solutions (e.g. generate multiple solutions by finding 100 solutions within 10% of optimality).
+* Add a [solver](https://prioritizr.net/reference/solvers.html) to a conservation problem to specify the optimization software (e.g. Gurobi) for generating solutions and customize the optimization settings (e.g. generate an optimal solution).
+
+After building a conservation planning problem, it can be solved to generate a prioritization (using the `solve()` function). There are also verbs available to help evaluate and interpret solutions. These verbs are described below.
+
+* Evaluate performance by computing [summary statistics](https://prioritizr.net/reference/summaries.html) (e.g. overall cost, feature representation, or total boundary length).
+* Evaluate the relative [importance](https://prioritizr.net/reference/importance.html) of planning units selected by a solution (e.g. based on irreplaceability).
+
+## Workflow
+
+The general workflow when using the _prioritizr R_ package starts with creating a new conservation planning `problem()` object using data. Specifically, the `problem()` object should be constructed using data that specify the planning units, biodiversity features, management zones (if applicable), and costs. After creating a new `problem()` object, it can be customized---by adding objectives, penalties, constraints, and other information---to build a precise representation of the conservation planning problem required, and then solved to obtain a solutions.
+
+All conservation planning problems require an objective. An objective specifies the property which is used to compare different feasible solutions. Simply put, the objective is the property of the solution which should be maximized or minimized during the optimization process. For instance, with the minimum set objective (specified using `add_min_set_objective()`), we are seeking to minimize the cost of the solution (similar to _Marxan_). On the other hand, with the minimum shortfall objective (specified using `add_min_shortfall_objective()`), we are seeking to minimize the average target shortfall for all features represented in the solution, subject to a budget.
+
+Many objectives require representation targets (e.g., the minimum set objective). These targets are a specialized set of constraints that relate to the total quantity of each feature secured in the solution (e.g., amount of suitable habitat or number of individuals). In the case of the minimum set objective ( `add_min_set_objective()`), they are used to ensure that solutions secure a sufficient quantity of each feature, and in other objectives, such as the maximum features objective ( `add_max_features_objective()`) they are used to assess whether a feature has been adequately conserved by a candidate solution. Targets can be expressed numerically as the total amount required for a given feature (using `add_absolute_targets()`), or as a proportion of the total amount found in the planning units (using `add_relative_targets()`). Note that not all objectives require targets, and a warning will be thrown if an attempt is made to add targets to a problem with an objective that does not use them.
+
+Constraints and penalties can be added to a conservation planning problem to ensure that solutions exhibit a specific property or penalize solutions which don't exhibit a specific property (respectively). The difference between constraints and penalties, strictly speaking, is constraints are used to rule out potential solutions that don't exhibit a specific property. For instance, constraints can be used to ensure that specific planning units are selected in the solution for prioritization (using `add_locked_in_constraints()`) or not selected in the solution for prioritization (using `add_locked_out_constraints()`). On the other hand, penalties are combined with the objective of a problem, with a penalty factor, and the overall objective of the problem then becomes to minimize (or maximize) the primary objective function and the penalty function. For example, penalties can be added to a problem to penalize solutions that are excessively fragmented (using `add_boundary_penalties()`). These penalties have a `penalty` argument that specifies the relative importance of having spatially clustered solutions. When the argument to `penalty` is high, then solutions which are less fragmented are valued more highly -- even if they cost more -- and when the argument to `penalty` is low, then the solutions which are more fragmented are valued less highly.
+
+After building a conservation problem, it can then be solved to obtain a solution (or portfolio of solutions if desired). The solution is returned in the same format as the planning unit data used to construct the problem. For instance, this means that if raster data was used to initialize the problem, then the solution will also be output in raster format. This can be very helpful when it comes to interpreting and visualizing solutions because it means that the solution data does not first have to be merged with spatial data before they can be plotted on a map.
+
+## Usage
+
+Here we will provide an introduction to using the _prioritizr R_ package to build and solve a conservation planning problem. Please note that we will not discuss conservation planning with multiple zones in this vignette, for more information on working with multiple management zones please see the [zones vignette](zones.html).
+
+First, we will load the _prioritizr_ package.
+
+```{r, results = "hide", message = FALSE}
+# load package
+library(prioritizr)
+
+# set default options for printing tabular data
+options(tibble.width = Inf)
+```
+
+### Data
+
+Now we will load some built-in data sets that are distributed with the _prioritizr R_ package. This package contains several different planning unit data sets. To provide a comprehensive overview of the different ways that we can initialize a conservation planning problem, we will load each of them.
+
+First, we will load the raster planning unit data (`sim_pu_raster`). Here, the planning units are represented as a raster (i.e., a `RasterLayer` object) and each pixel corresponds to the spatial extent of each panning unit. The pixel values correspond to the acquisition costs of each planning unit.
+
+```{r}
+# load raster planning unit data
+data(sim_pu_raster)
+
+# print description of the data
+print(sim_pu_raster)
+
+# plot the data
+plot(sim_pu_raster)
+```
+
+Secondly, we will load one of the spatial vector planning unit data sets (`sim_pu_polygons`). Here, each polygon (i.e., feature using ArcGIS terminology) corresponds to a different planning unit. This data set has an attribute table that contains additional information about each polygon. Namely, the `cost` field (column) in the attribute table contains the acquisition cost for each planning unit.
+
+```{r}
+# load polygon planning unit data
+data(sim_pu_polygons)
+
+# print first six rows of attribute table
+head(sim_pu_polygons@data)
+
+# plot the planning units
+spplot(sim_pu_polygons, zcol = "cost")
+```
+
+Thirdly, we will load some planning unit data stored in tabular format (i.e., `data.frame` format). For those familiar with _Marxan_ or dealing with very large conservation planning problems (> 10 million planning units), it may be useful to work with data in this format because it does not contain any spatial information which will reduce computational burden. When using tabular data to initialize conservation planning problems, the data must follow the conventions used by _Marxan_. Specifically, each row in the planning unit table must correspond to a different planning unit. The table must also have an "id" column to provide a unique integer identifier for each planning unit, and it must also have a column that indicates the cost of each planning unit. For more information, please see the [official _Marxan_ documentation](https://marxansolutions.org/).
+
+```{r}
+# specify file path for planning unit data
+pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr")
+
+# load in the tabular planning unit data
+# note that we use the data.table::fread function, as opposed to the read.csv
+# function, because it is much faster
+pu_dat <- data.table::fread(pu_path, data.table = FALSE)
+
+# preview first six rows of the tabular planning unit data
+# note that it has some extra columns other than id and cost as per the
+# Marxan format
+head(pu_dat)
+```
+
+Finally, we will load data showing the spatial distribution of the conservation features. Our conservation features (`sim_features`) are represented as a stack of raster objects (i.e., a `RasterStack` object) where each layer corresponds to a different feature (e.g., a multi-band GeoTIFF where each band corresponds to a different feature). The pixel values in each layer correspond to the amount of suitable habitat available in a given planning unit. Note that our planning unit raster layer and our conservation feature stack have exactly the same spatial properties (i.e., resolution, extent, coordinate reference system) so their pixels line up perfectly.
+
+```{r, fig.width = 4, fig.height = 3}
+# load feature data
+data(sim_features)
+
+# plot the distribution of suitable habitat for each feature
+plot(sim_features, main = paste("Feature", seq_len(nlayers(sim_features))),
+     nr = 2, box = FALSE, axes = FALSE)
+```
+
+### Initialize a problem
+
+After having loaded our planning unit and feature data, we will now try initializing the some conservation planning problems. There are a lot of different ways to initialize a conservation planning problem, so here we will just showcase a few of the more commonly used methods. For an exhaustive description of all the ways you can initialize a conservation problem, see the help file for the `problem()` function. First off, we will initialize a conservation planning problem using the raster data.
+
+```{r}
+# create problem
+p1 <- problem(sim_pu_raster, sim_features)
+
+# print problem
+print(p1)
+
+# print number of planning units
+number_of_planning_units(p1)
+
+# print number of features
+number_of_features(p1)
+```
+
+Generally, we recommend initializing problems using raster data where possible. This is because the `problem()` function needs to calculate the amount of each feature in each planning unit, and by providing both the planning unit and feature data in raster format with the same spatial resolution, extents, and coordinate systems, this means that the `problem()` function does not need to do any geoprocessing behind the scenes. But sometimes we can't use raster planning unit data because our planning units aren't equal-sized grid cells. So, below is an example showing how we can initialize a conservation planning problem using planning units that are formatted as spatial vector data. Note that if we had precomputed the amount of each feature in each planning unit and stored the data in the attribute table, we could pass in the names of the columns as an argument to the `problem()` function.
+
+```{r}
+# create problem with spatial vector data
+# note that we have to specify which column in the attribute table contains
+# the cost data
+p2 <- problem(sim_pu_polygons, sim_features, cost_column = "cost")
+
+# print problem
+print(p2)
+```
+
+We can also initialize a conservation planning problem using tabular planning unit data (i.e., `data.frame` format). Since the tabular planning unit data does not contain any spatial information, we also have to provide the feature data in tabular format (i.e., `data.frame` format) and data showing the amount of each feature in each planning unit in tabular format (i.e., `data.frame` format). The feature data must have an "id" column containing a unique integer identifier for each feature, and the planning unit by feature data must contain the following three columns: `pu` corresponding to the planning unit identifiers, `species` corresponding to the feature identifiers, and `amount` showing the amount of a given feature in a given planning unit.
+
+```{r}
+# set file path for feature data
+spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr")
+
+# load in feature data
+spec_dat <- data.table::fread(spec_path, data.table = FALSE)
+
+# print first six rows of the data
+# note that it contains extra columns
+head(spec_dat)
+
+# set file path for planning unit vs. feature data
+puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr")
+
+# load in planning unit vs feature data
+puvspr_dat <- data.table::fread(puvspr_path, data.table = FALSE)
+
+# print first six rows of the data
+head(puvspr_dat)
+
+# create problem
+p3 <- problem(pu_dat, spec_dat, cost_column = "cost", rij = puvspr_dat)
+
+# print problem
+print(p3)
+```
+
+For more information on initializing problems, please see the help page for the `problem()` function (which you can open by entering the code: `?problem`). Now that we have initialized a conservation planning problem, we will show you how you can customize it to suit the exact needs of your conservation planning scenario. Although we initialized the conservation planning problems using several different methods, moving forward, we will only use raster-based planning unit data to keep things simple.
+
+### Add an objective
+
+The next step is to add a primary objective to the problem. A problem objective is used to specify the primary goal of the problem (i.e., the quantity that is to be maximized or minimized). All conservation planning problems involve minimizing or maximizing some kind of objective. For instance, we might require a solution that conserves enough habitat for each species while minimizing the overall cost of the reserve network. Alternatively, we might require a solution that maximizes the number of conserved species while ensuring that the cost of the reserve network does not exceed the budget. Please note that objectives are added in the same way regardless of the type of data used to initialize the problem. The following objectives are available.
+
+* __Minimum set objective__: Minimize the cost of the solution whilst ensuring that all targets are met [@r11]. This objective is similar to that used in _Marxan_ [@r3]. For example, we can add a minimum set objective to a problem using the following code.
+```{r}
+# create a new problem that has the minimum set objective
+p3 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective()
+
+# print the problem
+print(p3)
+```
+* __Maximum cover objective__: Represent at least one instance of as many features as possible within a given budget [@r12].
+```{r}
+# create a new problem that has the maximum coverage objective and a budget
+# of 5000
+p4 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_cover_objective(5000)
+
+# print the problem
+print(p4)
+```
+* __Maximum features objective__: Fulfill as many targets as possible while ensuring that the cost of the solution does not exceed a budget [inspired by @r10]. This object is similar to the maximum cover objective except that we have the option of later specifying targets for each feature. In practice, this objective is more useful than the maximum cover objective because features often require a certain amount of area for them to persist and simply capturing a single instance of habitat for each feature is generally unlikely to enhance their long-term persistence.
+```{r}
+# create a new problem that has the maximum features objective and a budget
+# of 5000
+p5 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_features_objective(budget = 5000)
+
+# print the problem
+print(p5)
+```
+* __Minimum shortfall objective__: Minimize the overall (weighted sum) shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when there is a large amount of left-over budget when using the maximum feature representation objective and the remaining funds need to be allocated to places that will enhance the representation of features with unmet targets.
+```{r}
+# create a new problem that has the minimum shortfall objective and a budget
+# of 5000
+p6 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_shortfall_objective(budget = 5000)
+
+# print the problem
+print(p6)
+```
+* __Minimum largest shortfall objective__: Minimize the largest (maximum) shortfall while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when the minimum shortfall objective returns solutions that focus too much on representing a small number of features (e.g., because they occur in much cheaper planning units), and solutions are needed to spread conservation effort out more evenly among all features---even if it means that all features will have (relatively) poor representation.
+```{r}
+# create a new problem that has the minimum largest shortfall objective and a
+# budget of 5000
+p7 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_largest_shortfall_objective(budget = 5000)
+
+# print the problem
+print(p7)
+```
+* __Maximum phylogenetic diversity objective__: Maximize the phylogenetic diversity of the features represented in the solution subject to a budget [inspired by @r13; @r14]. This objective is similar to the maximum features objective except that emphasis is placed on protecting features which are associated with a diverse range of evolutionary histories. The package contains a simulated phylogeny that can be used with the simulated feature data (`sim_phylogny`).
+```{r}
+# load simulated phylogeny data
+data(sim_phylogeny)
+
+# create a new problem that has the maximum phylogenetic diversity
+# objective and a budget of 5000
+p8 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_phylo_div_objective(budget = 5000, tree = sim_phylogeny)
+
+# print the problem
+print(p8)
+```
+* __Maximum phylogenetic endemism objective__: Maximize the phylogenetic endemism of the features represented in the solution subject to a budget [inspired by @r13; @r14; @r32]. This objective is similar to the maximum phylogenetic diversity except that emphasis is placed conserving features that are associated with geographically restricted periods of evolutionary history rather than a diverse range of evolutionary histories.
+```{r}
+# load simulated phylogeny data
+data(sim_phylogeny)
+
+# create a new problem that has the maximum phylogenetic diversity
+# objective and a budget of 5000
+p9 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_phylo_end_objective(budget = 5000, tree = sim_phylogeny)
+
+# print the problem
+print(p9)
+```
+* __Maximum utility objective__: Secure as much of the features as possible without exceeding a budget. This objective is functionally equivalent to selecting the planning units with the greatest amounts of each feature (e.g., species richness). Generally, we don't encourage the use of this objective because it will only rarely identify complementary solutions--solutions which adequately conserve a range of different features---except perhaps to explore trade-offs or provide a baseline solution with which to compare other solutions.
+```{r}
+# create a new problem that has the maximum utility objective and a budget
+# of 5000
+p10 <- problem(sim_pu_raster, sim_features) %>%
+      add_max_utility_objective(budget = 5000)
+
+# print the problem
+print(p10)
+```
+
+### Add targets
+
+Most conservation planning problems require targets. Targets are used to specify the minimum amount or proportion of a feature's distribution that needs to be protected in the solution. For example, we may want to develop a reserve network that will secure 20% of the distribution for each feature for minimal cost. The following methods are available for specifying targets.
+
+* __Absolute targets__: Targets are expressed as the total amount of each feature in the study area that need to be secured. For example, if we had binary feature data that showed the absence or presence of suitable habitat across the study area, we could set an absolute target as 5 to mean that we require 5 planning units with suitable habitat in the solution.
+```{r}
+# create a problem with targets which specify that the solution must conserve
+# a need a sum total of 3 units of suitable habitat for each feature
+p11 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_absolute_targets(3)
+
+# print problem
+print(p11)
+```
+* __Relative targets__: Targets are set as a proportion (between 0 and 1) of the total amount of each feature in the study area. For example, if we had binary feature data and the feature occupied a total of 20 planning units in the study area, we could set a relative target of 50 % to specify that the solution must secure 10 planning units for the feature. We could alternatively specify an absolute target of 10 to achieve the same result, but sometimes proportions are easier to work with.
+```{r}
+# create a problem with the minimum set objective and relative targets of 10 %
+# for each feature
+p12 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1)
+
+# print problem
+print(p12)
+
+# create a problem with targets which specify that we need 10 % of the habitat
+# for the first feature, 15 % for the second feature, 20 % for the third feature
+# 25 % for the fourth feature and 30 % of the habitat for the fifth feature
+targets <- c(0.1, 0.15, 0.2, 0.25, 0.3)
+p13 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(targets)
+
+# print problem
+print(p13)
+```
+* __Log-linear targets__: Targets are expressed using scaling factors and log-linear interpolation. This method for specifying targets is commonly used for global prioritization analyses [@r15].
+```{r}
+# create problem with added log-linear targets
+p14 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_loglinear_targets(10, 0.9, 100, 0.2)
+
+# print problem
+print(p14)
+```
+* __Manual targets__: Targets are manually specified. This is only really recommended for advanced users or problems that involve multiple management zones. See the [zones vignette](zones.html) for more information on these targets.
+
+As with the functions for specifying the objective of a problem, if we try adding multiple targets to a problem, only the most recently added set of targets are used.
+
+### Add constraints
+
+A constraint can be added to a conservation planning problem to ensure that all solutions exhibit a specific property. For example, they can be used to make sure that all solutions select a specific planning unit or that all selected planning units in the solution follow a certain configuration. The following constraints are available.
+
+* __Locked in constraints__: Add constraints to ensure that certain planning units are prioritized in the solution. For example, it may be desirable to lock in planning units that are inside existing protected areas so that the solution fills in the gaps in the existing reserve network.
+```{r}
+# create problem with constraints which specify that the first planning unit
+# must be selected in the solution
+p15 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints(1)
+
+# print problem
+print(p15)
+```
+* __Locked out constraints__: Add constraints to ensure that certain planning units are not prioritized in the solution. For example, it may be useful to lock out planning units that have been degraded and are not suitable for conserving species.
+```{r}
+# create problem with constraints which specify that the second planning unit
+# must not be selected in the solution
+p16 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_out_constraints(2)
+
+# print problem
+print(p16)
+```
+* __Neighbor constraints__: Add constraints to a conservation problem to ensure that all selected planning units have at least a certain number of neighbors.
+```{r}
+# create problem with constraints which specify that all selected planning units
+# in the solution must have at least 1 neighbor
+p17 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_neighbor_constraints(1)
+
+# print problem
+print(p17)
+```
+* __Contiguity constraints__: Add constraints to a conservation problem to ensure that all selected planning units are spatially connected to each other and form spatially contiguous unit.
+```{r}
+# create problem with constraints which specify that all selected planning units
+# in the solution must form a single contiguous unit
+p18 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_contiguity_constraints()
+
+# print problem
+print(p18)
+```
+* __Feature contiguity constraints__: Add constraints to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of those implemented in the `add_contiguity_constraints` function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit.
+```{r}
+# create problem with constraints which specify that the planning units used
+# to conserve each feature must form a contiguous unit
+p19 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_feature_contiguity_constraints()
+
+# print problem
+print(p19)
+```
+
+* __Linear constraints__: Add constraints to ensure that all selected planning units meet certain criteria. For example, they can be used to add multiple budgets, or limit the number of planning units selected in different administrative areas within a study region (e.g., different countries).
+
+```{r}
+# create problem with constraints which specify that the sum of
+# values in sim_features[[1]] among selected planning units must not exceed a
+#' threshold value of 190.
+p20 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_shortfall_objective(budget = 1800) %>%
+       add_relative_targets(0.1) %>%
+       add_linear_constraints(190, "<=", sim_features[[1]])
+
+# print problem
+print(p20)
+```
+
+* __Mandatory allocation constraints__: Add constraints to ensure that every planning unit is allocated to a management zone in the solution. Please note that this function can only be used with problems that contain multiple zones. For more information on problems with multiple zones and an example using this function, see the Management Zones vignette.
+
+In particular, The `add_locked_in_constraints` and `add_locked_out_constraints` functions are incredibly useful for real-world conservation planning exercises, so it's worth pointing out that there are several ways we can specify which planning units should be locked in or out of the solutions. If we use raster planning unit data, we can also use raster data to specify which planning units should be locked in our locked out.
+
+```{r, fig.width = 6.5, fig.height = 2.5}
+# load data to lock in or lock out planning units
+data(sim_locked_in_raster)
+data(sim_locked_out_raster)
+
+# plot the locked data
+plot(stack(sim_locked_in_raster, sim_locked_out_raster),
+     main = c("Locked In", "Locked Out"))
+
+# create a problem using raster planning unit data and use the locked raster
+# data to lock in some planning units and lock out some other planning units
+p21 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints(sim_locked_in_raster) %>%
+       add_locked_out_constraints(sim_locked_out_raster)
+
+# print problem
+print(p21)
+```
+
+If our planning unit data are in a spatial vector format (similar to the `sim_pu_polygons` data) or a tabular format (similar to `pu_dat`), we can use the field names in the data to refer to which planning units should be locked in and / or out. For example, the `sim_pu_polygons` object has `TRUE` / `FALSE` values in the "locked_in" field which indicate which planning units should be selected in the solution. We could use the data in this field to specify that those planning units with `TRUE` values should be locked in using the following methods.
+
+```{r}
+# preview first six rows of the attribute table for sim_pu_polygons
+head(sim_pu_polygons@data)
+
+# specify locked in data using the field name
+p22 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints("locked_in")
+
+# print problem
+print(p22)
+
+# specify locked in data using the values in the field
+p23 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_locked_in_constraints(which(sim_pu_polygons$locked_in))
+
+# print problem
+print(p23)
+```
+
+### Add penalties
+
+We can also add penalties to a problem to favor or penalize solutions according to a secondary objective. Unlike the constraint functions, these functions will add extra information to the objective function of the optimization function to penalize solutions that do not exhibit specific characteristics. For example, penalties can be added to a problem to avoid highly fragmented solutions at the expense of accepting slightly more expensive solutions. All penalty functions have a `penalty` argument that controls the relative importance of the secondary penalty function compared to the primary objective function. It is worth noting that incredibly low or incredibly high `penalty` values -- relative to the main objective function -- can cause problems to take a very long time to solve, so when trying out a range of different penalty values it can be helpful to limit the solver to run for a set period of time. The following penalties are available.
+
+* __Boundary penalties__:  Add penalties to penalize solutions that are excessively fragmented. These penalties are similar to those used in _Marxan_ [@r3; @r1].
+```{r}
+# create problem with penalties that penalize fragmented solutions with a
+# penalty factor of 0.01
+p24 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_boundary_penalties(penalty = 0.01)
+
+# print problem
+print(p24)
+```
+* __Connectivity penalties__: Add penalties to favor solutions that select combinations of planning units with high connectivity between them. These penalties are similar to those used in _Marxan with Zones_ [@r2; @r1]. This function supports both symmetric and asymmetric connectivities among planning units.
+```{r}
+# create problem with penalties that favor combinations of planning units with
+# high connectivity, here we will use only the first four layers in
+# sim_features for the features and we will use the fifth layer in sim_features
+# to represent the connectivity data, where the connectivity_matrix function
+# will create a matrix showing the average strength of connectivity between
+# adjacent planning units using the data in the fifth layer of sim_features
+p25 <- problem(sim_pu_raster, sim_features[[1:4]]) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_boundary_penalties(
+         penalty = 5,
+         data = connectivity_matrix(sim_pu_raster, sim_features[[5]]))
+
+# print problem
+print(p25)
+```
+* __Linear penalties__: Add penalties to penalize solutions that select planning units according to a certain variable (e.g., anthropogenic pressure).
+```{r}
+# create data for penalizing planning units
+# (note this requires the RandomFields package to be installed)
+pen_raster <- simulate_cost(sim_pu_raster)
+
+# create problem with penalties that penalize solutions that select
+# planning units with high values in the pen_raster object,
+# here we will use a penalty value of 5 to indicate the trade-off (scaling)
+# between the penalty values (in the sim_pu_raster) and the main objective
+# (i.e., the cost of the solution)
+p26 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_linear_penalties(penalty = 5, data = pen_raster)
+
+# print problem
+print(p26)
+```
+
+### Add the decision types
+
+Conservation planning problems involve making decisions on how planning units will be managed. These decisions are then associated with management actions (e.g., turning a planning unit into a protected area). The type of decision describes how the action is applied to planning units. For instance, the default decision-type is a binary decision type, meaning that we are either selecting or not selecting planning units for management. The following decision types are available.
+
+* __Binary decisions__: Add a binary decision to a conservation planning problem. This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem object, then this decision class will be used by default.
+```{r}
+# add binary decisions to a problem
+p27 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions()
+
+# print problem
+print(p27)
+```
+* __Proportion decisions__: Add a proportion decision to a problem. This is a relaxed decision where a part of a planning unit can be prioritized, as opposed to the default of the entire planning unit. Typically, this decision has the assumed action of buying a fraction of a planning unit to include in a protected area network. Generally, problems can be solved much faster with proportion-type decisions than binary-type decisions, so they can be very useful when commercial solvers are not available.
+```{r}
+# add proportion decisions to a problem
+p28 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_proportion_decisions()
+
+# print problem
+print(p28)
+```
+* __Semi-continuous decisions__: Add a semi-continuous decision to a problem. This decision is similar to proportion decisions except that it has an upper bound parameter. By default, the decision can range from prioritizing none (0%) to all (100%) of a planning unit. However, a upper bound can be specified to ensure that at most only a fraction (e.g., 80%) of a planning unit can be purchased. This type of decision may be useful when it is not practical to conserve the entire area indicated by a planning unit.
+```{r}
+# add semi-continuous decisions to a problem, where we can only manage at most
+# 50 % of the area encompassed by a planning unit
+p29 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_semicontinuous_decisions(0.5)
+
+# print problem
+print(p29)
+```
+
+### Add a solver
+
+Next, after specifying the mathematical formulation that underpins your conservation planning problem, you can specify how the problem should be solved. If you do not specify this information, the _prioritizr R_ package will automatically use the best solver currently installed on your system with some reasonable defaults. __We strongly recommend installing the [Gurobi software suite and the _gurobi_ _R_ package](https://www.gurobi.com/) to solve problems, and for more information on this topic please refer to the [Gurobi Installation Guide](gurobi_installation.html)__. The following solvers are available.
+
+* __*Gurobi* solver__: [_Gurobi_](https://www.gurobi.com/) is a state of the art commercial optimization software. It is by far the fastest of the solvers that can be used to solve conservation problems. However, it is not freely available. That said, special licenses are available to academics at no cost.
+```{r}
+# create a problem and specify that Gurobi should be used to solve the problem
+# and specify an optimality gap of zero to obtain the optimal solution
+p30 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_gurobi_solver(gap = 0)
+
+# print problem
+print(p30)
+```
+* __*IBM CPLEX* solver__: [_IBM CPLEX_](https://www.ibm.com/analytics/cplex-optimizer) is a commercial optimization software. It is faster than the open source solvers available for generating prioritizations (see below), however, it is not freely available. Similar to the _Gurobi_ software, special licenses are available to academics at no cost.
+```{r}
+# create a problem and specify that IBM CPLEX should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p31 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_cplex_solver(gap = 0)
+
+# print problem
+print(p31)
+```
+* __*CBC* solver__: [*CBC*](https://projects.coin-or.org/Cbc) is an
+open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. Although formal benchmarks have yet to be completed, preliminary analyses suggest that it is
+the fastest open-source solver available for generating prioritizations. It requires the _rcbc R_ package, which is currently only available on [GitHub](https://github.com/dirkschumacher/rcbc).
+```{r}
+# create a problem and specify that CBC should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p32 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_cbc_solver(gap = 0)
+
+# print problem
+print(p32)
+```
+* __*lpsymphony* solver__: [_SYMPHONY_](https://projects.coin-or.org/SYMPHONY) is an open-source integer programming solver that is also part of the COIN-OR project. This solver uses the _lpsymphony R_ package (available on [Bioconductor](http://bioconductor.org/packages/release/bioc/html/lpsymphony.html)) to interface with the _SYMPHONY_ software.
+```{r}
+# create a problem and specify that lpsymphony should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p33 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_lpsymphony_solver(gap = 0)
+
+# print problem
+print(p33)
+```
+* __*Rsymphony* solver__: This solver provides a different interface to the [_SYMPHONY_](https://projects.coin-or.org/SYMPHONY) software. It uses the _Rsymphony R_ package which is available on The Comprehensive R Archive Network (CRAN). This solver is generally slower than the other solvers, because it cannot use parallel processing.
+```{r}
+# create a problem and specify that Rsymphony should be used to solve the
+# problem and specify an optimality gap of zero to obtain the optimal solution
+p34 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_rsymphony_solver(gap = 0)
+
+# print problem
+print(p34)
+```
+
+### Add a portfolio
+
+Many conservation planning exercises require a portfolio of solutions. For example, real-world exercises can involve presenting decision makers with a range of near-optimal decisions. Additionally, the number of times that different planning units are selected in different solutions can provide insight into their relative importance. The following portfolio methods are available.
+
+* __Gap portfolio__: Generate a portfolio of solutions by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is especially useful for generating multiple solutions that can used be to calculate selection frequencies (similar to _Marxan_). Note that this method requires that the _Gurobi_ optimization software is used to generate solutions.
+```{r}
+# create a problem and specify that a portfolio should be created by
+# finding five solutions within 10% of optimality
+p35 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_gap_portfolio(number_solutions = 5, pool_gap = 0.2)
+
+# print problem
+print(p35)
+```
+* __Top portfolio__: Generate a portfolio of solutions by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions). Note that this method requires that the _Gurobi_ optimization software is used to generate solutions.
+```{r}
+# create a problem and specify that a portfolio should be created using
+# the top five solutions
+p36 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_top_portfolio(number_solutions = 5)
+
+# print problem
+print(p36)
+```
+* __Extra portfolio__: Generate a portfolio of solutions by storing feasible solutions found during the optimization process. Note that this method requires that the _Gurobi_ optimization software is used to generate solutions.
+```{r}
+# create a problem and specify that a portfolio should be created using
+# extra solutions found while solving the problem
+p37 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_extra_portfolio()
+
+# print problem
+print(p37)
+```
+* __Cuts portfolio__: Generate a portfolio of distinct solutions within a pre-specified optimality gap. This method is only recommended if the _Gurobi_ optimization solver is not available.
+```{r}
+# create a problem and specify that a portfolio containing 10 solutions
+# should be created using using Bender's cuts
+p38 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_cuts_portfolio(number_solutions = 10)
+
+# print problem
+print(p38)
+```
+* __Shuffle portfolio__: Generate a portfolio of solutions by randomly reordering the data prior to attempting to solve the problem. If the _Gurobi_ optimization solver is not available, this method is the fastest method for generating a set number of solutions within a specified distance from optimality.
+```{r}
+# create a problem and specify a portfolio should be created that contains
+# 10 solutions and that any duplicate solutions should not be removed
+p39 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions() %>%
+       add_shuffle_portfolio(number_solutions = 10, remove_duplicates = FALSE)
+
+# print problem
+print(p39)
+```
+
+### Solve the problem
+
+After formulating our conservation planning problem and specifying how the problem should be solved, we can use the `solve` function to obtain a solution. Note that the solver will typically print out some information describing the size of the problem and report its progress when searching for a suitable solution.
+
+```{r, fig.height = h, fig.width = w}
+# formulate the problem
+p40 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_boundary_penalties(penalty = 500, edge_factor = 0.5) %>%
+       add_binary_decisions()
+
+# solve the problem (using the default solver)
+s40 <- solve(p40)
+
+# plot solution
+plot(s40, col = c("grey90", "darkgreen"), main = "Solution",
+     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
+```
+
+We can plot this solution because the planning unit input data are spatially referenced in a raster format. The output format will always match the planning unit data used to initialize the problem. For example, the solution to a problem with planning units in a spatial vector (shapefile) format would also be in a spatial vector format. Similarly, if the planning units were in a tabular format (i.e., `data.frame`), the solution would also be returned in a tabular format.
+
+We can also extract attributes from the solution that describe the quality of the solution and the optimization process.
+
+```{r}
+# extract the objective (numerical value being minimized or maximized)
+print(attr(s40, "objective"))
+
+# extract time spent solving solution
+print(attr(s40, "runtime"))
+
+# extract state message from the solver that describes why this specific
+# solution was returned
+print(attr(s40, "status"))
+```
+
+## Evaluate the solution
+
+Conservation planning involves making trade-offs between different criteria (e.g. overall cost, feature representation, connectivity). After obtaining a solution to a conservation planning problem, it is important to evaluate it to help understand the trade-offs made by the prioritization. This is also useful to compare different solutions with each other.
+
+### Evaluating performance
+
+Summary statistics can be computed to evaluate the overall performance of a solution based on certain criteria. The following summaries can be computed.
+
+The following functions are available to summarize a solution:
+
+* __Number summary__: Calculate the number of planning units selected by a solution.
+```{r}
+# calculate statistic
+eval_n_summary(p40, s40)
+```
+* __Cost summary__: Calculate the total cost of a solution.
+```{r}
+# calculate statistic
+eval_cost_summary(p40, s40)
+```
+* __Feature representation summary__: Calculate how well features are represented by a solution. This function can be used for any type of problem.
+```{r}
+# calculate statistics
+eval_feature_representation_summary(p40, s40)
+```
+* __Target coverage summary__: Calculate how well representation targets are met by a solution. This function can only be used with problems contain targets.
+```{r}
+# calculate statistics
+eval_target_coverage_summary(p40, s40)
+```
+* __Boundary summary__: Calculate the total exposed boundary length (perimeter) associated with a solution.
+```{r}
+# calculate statistic
+eval_boundary_summary(p40, s40)
+```
+* __Connectivity summary__: Calculate the connectivity facilitated within a solution.
+```{r}
+# calculate statistic
+# here we use the raster data for the first feature as an example
+# to parametrize pair-wise connectivity between different planning units
+eval_connectivity_summary(
+  p40, s40, data = connectivity_matrix(sim_pu_raster, sim_features[[1]]))
+```
+
+### Evaluating relative importance
+
+Conservation plans can take a long time to implement. Since funding availability and habitat quality can decline over time, it is critical that the most important places in a prioritization are scheduled for management as early as possible. For instance, some planning units in a solution might contain many rare species which do not occur in any other planning units. Alternatively, some planning units might offer an especially high return on investment that reduces costs considerably. As a consequence, conservation planners often need information on which planning units selected in a prioritization are most important to the overall success of the prioritization. To achieve this, conservation planners can use importance scores for each planning unit selected by a solution.
+
+Let's generate a prioritization so that can compare the different importance methods.
+
+```{r, fig.height = h, fig.width = w}
+# formulate the problem
+p41 <- problem(sim_pu_raster, sim_features) %>%
+       add_min_set_objective() %>%
+       add_relative_targets(0.1) %>%
+       add_binary_decisions()
+
+# solve the problem
+s41 <- solve(p41)
+
+# plot solution
+plot(s41, col = c("grey90", "darkgreen"), main = "Solution",
+     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
+```
+
+ The following methods are available for computing importance scores.
+
+* __Replacement cost__: Evaluate importance using the replacement cost method [@r31]. This method quantifies the importance of a given planning unit as the decrease in the performance of the solution (based on the objective function) if the planning unit cannot be acquired (e.g., in terms of the additional costs required to meet feature targets). The advantages of this method are that it (i) accounts for the costs of the planning units, (ii) can be applied to multiple management zones, (iii) can be applied to any objective function, and (iv) can identify truly irreplaceable planning units (denoted with infinite values). However, the key disadvantage  of this method, is that can take an infeasible amount of time to complete for large and complex problems.
+```{r, fig.height = h, fig.width = w}
+# calculate replacement cost scores and make the solver quiet
+rc41 <- p41 %>%
+        add_default_solver(gap = 0, verbose = FALSE) %>%
+        eval_replacement_importance(s41)
+
+# plot replacement cost scores
+plot(rc41, main = "Replacement cost scores")
+```
+* __Ferrier method__: Evaluate importance by computing irreplaceability scores following Ferrier *et al.* [@r-34]. The advantages of this method are that it (i) can be computed relatively quickly for moderate and large-sized problems, and (ii) calculates a score for each feature within each planning unit to provide insight into why certain planning units are more important than others. The disadvatange with this method is that it can only be applied to conservation problems with a minimum set objective and a single zone (i.e., similar to _Marxan_-type problems).
+```{r, fig.height = h, fig.width = w}
+# calculate Ferrier scores and extract total score
+fs41 <- eval_ferrier_importance(p40, s40)[["total"]]
+
+# plot Ferrier scores
+plot(fs41, main = "Ferrier scores")
+```
+* __Rarity weighted richness__: Evaluate importance by computing rarity weighted richness scores [@r33]. The only advantage with this method is that it can be computed very quickly for very large problems. The key disadvantage with this approach is that it merely describes the spatial patterns of biodiversity, and does not consider any of the goals that underpin conservation planning exercise. For instance, it does not account for planning costs, management zones, objective functions, or feature representation targets.
+```{r, fig.height = h, fig.width = w}
+# calculate rarity weighted richness scores
+rwr41 <- eval_rare_richness_importance(p40, s40)
+
+# plot rarity weighted richness scores
+plot(rwr41, main = "Rarity weighted richness")
+```
+
+In general, we recommend using replacement cost scores for small and moderate sized problems (e.g., less than 30,000 planning units) when it is feasible to do so. It can take a very long time to compute replacement cost scores, and so it is simply not feasible to compute these scores for particularly large problems. For moderate and large sized problems (e.g., more than 30,000 planning units), we recommend using the Ferrier method. This is because it explicitly accounts for representation targets, unlike the rarity weighted richness scores. We almost never recommend using the rarity weighted richness scores. This is because they do not consider criteria needed to inform conservation decision making [@r51].
+
+## _Marxan_ problems
+
+Although we encourage users to build and tailor conservation planning problems to suit their own needs, sometimes it just simply easier to use something you're already familiar with. The `marxan_problem()` function is provided as a convenient wrapper for building and solving _Marxan_-style conservation problems. If users already have their conservation planning data formatted for use with _Marxan_, this function can also read _Marxan_ data files and solve the _Marxan_-style problems using exact algorithm solvers. __Please note that problems built using the `marxan_problem()` function are still solved the same way as a problem initialized using the `problem()` function, and therefore still require the installation of one of the solver packages.__
+
+Here is a short example showing how the `marxan_problem()` function can be used to read _Marxan_ input files and the `solve` function can be used to solve the problem.
+
+```{r, results = "hide"}
+# set file path for Marxan input file
+minput <- system.file("extdata/input.dat", package = "prioritizr")
+
+# read Marxan input file
+mp <- marxan_problem(minput)
+
+# print problem
+print(mp)
+
+# solve the problem
+ms <- solve(mp)
+
+# since the Marxan data was in a tabular format, the solution is also returned
+# in a tabular format, so we will print the first six rows of the table
+# containing the solution
+head(ms)
+```
+
+Alternatively, rather then using a _Marxan_ input file to construct the problem, we can manually read in the _Marxan_ data files and input these to the `marxan_problem()` function.
+
+```{r}
+# load data
+pu <- system.file("extdata/input/pu.dat", package = "prioritizr") %>%
+      read.table(sep = ",", header = TRUE)
+features <- system.file("extdata/input/spec.dat", package = "prioritizr") %>%
+            read.table(sep = ",", header = TRUE)
+bound <- system.file("extdata/input/bound.dat", package = "prioritizr") %>%
+         read.table(sep = "\t", header = TRUE)
+rij <- system.file("extdata/input/puvspr.dat", package = "prioritizr") %>%
+       read.table(sep = ",", header = TRUE)
+
+# build Marxan problem using data.frame objects
+mp2 <- marxan_problem(x = pu, spec = features, puvspr = rij, bound = bound,
+                      blm = 0)
+
+# print problem
+print(mp2)
+```
+
+Conservation planning problems that are built using the `marxan_problem()` function can also be customized. For example, we could change the decision type for `mp2` to involve selecting a proportion of each planing unit (using the `add_proportion_decisions()` function).
+
+## Conclusion
+
+Hopefully, this vignette has provided an informative overview of the _prioritizr R_ package. For more examples using the package, please see the other vignettes. Perhaps, one of the best ways to learn a new piece of software is to just try it out. Test it, try breaking it, make mistakes, and learn from them. We would recommend trying to build conservation planning problems that resemble those you face in your own work---but using the built-in example data sets. This way you can quickly verify that the problems you build actually mean what you think they mean. For instance, you can try playing around with the targets and see what effect they have on the solutions, or try playing around with penalties and see what effect they have on the solutions. Finally, if you have any questions about using the package or suggestions for it, please [post an issue on the package's online coding repository](https://github.com/prioritizr/prioritizr/issues).
+
+## References
diff --git a/vignettes/prioritizr.Rmd b/vignettes/prioritizr.Rmd
index d6f896ebd..dc2883a47 100644
--- a/vignettes/prioritizr.Rmd
+++ b/vignettes/prioritizr.Rmd
@@ -1,5 +1,5 @@
 ---
-title: "prioritizr: Systematic Conservation Prioritization in R"
+title: "Getting started"
 output:
   rmarkdown::html_vignette:
     toc: true
@@ -10,900 +10,278 @@ documentclass: article
 bibliography: references.bib
 csl: reference-style.csl
 vignette: >
-  %\VignetteIndexEntry{prioritizr: Systematic Conservation Prioritization in R}
+  %\VignetteIndexEntry{Getting started}
   %\VignetteEngine{knitr::rmarkdown_notangle}
 ---
 
 ```{r, include = FALSE}
-h = 3.5
-w = 3.5
+# define dummy variables so that vignette passes package checks
+tas_features <- raster::raster(matrix(1))
+```
+
+```{r, include = FALSE}
+# define variables for vignette figures and code execution
+h <- 3.5
+w <- 3.5
 is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_",
              "_R_CHECK_LICENSE_") %in% names(Sys.getenv()))
-knitr::opts_chunk$set(fig.align = "center", eval = !is_check,
-                      root.dir = normalizePath("../.."))
+knitr::opts_chunk$set(fig.align = "center", eval = !is_check)
 ```
 
-## Summary
-
-The _prioritizr R_ package uses integer linear programming (ILP) techniques to provide a flexible interface for building and solving conservation planning problems [@r11; @r16]. It supports a broad range of objectives, constraints, and penalties that can be used to custom-tailor conservation planning problems to the specific needs of a conservation planning exercise. Once built, conservation planning problems can be solved using a variety of commercial and open-source exact algorithm solvers. In contrast to the algorithms conventionally used to solve conservation problems, such as heuristics or simulated annealing [@r3], the exact algorithms used here are guaranteed to find optimal solutions. Furthermore, conservation problems can be constructed to optimize the spatial allocation of different management zone (or actions), meaning that conservation practitioners can identify solutions that benefit multiple stakeholders. Finally, this package has the functionality to read input data formatted for the _Marxan_ conservation planning program [@r3], and find much cheaper solutions in a much shorter period of time than _Marxan_ [@r1].
-
 ## Introduction
 
-Systematic conservation planning is a rigorous, repeatable, and structured approach to designing new protected areas that efficiently meet conservation objectives [@r4]. Historically, conservation decision-making has often evaluated parcels opportunistically as they became available for purchase, donation, or under threat. Although purchasing such areas may improve the _status quo_, such decisions may not substantially enhance the long-term persistence of target species or communities. Faced with this realization, conservation planners began using decision support tools to help simulate alternative reserve designs over a range of different biodiversity and management goals and, ultimately, guide protected area acquisitions and management actions. Due to the systematic, evidence-based nature of these tools, conservation prioritization can help contribute to a transparent, inclusive, and more defensible decision making process.
-
-A conservation planning exercise typically starts by defining a study area. This study area should encompass all the areas relevant to the decision maker or the hypothesis being tested. The extent of a study area could encompass a few important localities [e.g. @r18], a single state [e.g. @r17], an entire country [@r19], or the entire planet [@r20]. Next, the study area is divided into a set of discrete areas termed _planning units_. Each planning unit represents a discrete locality in the study area that can be managed independently of other areas. The general idea is that some combination of the planning units can be selected for conservation actions (e.g. protected area establishment, habitat restoration). Planning units are often created as square or hexagon cells that are sized according to the scale of the conservation actions, and the resolution of the data that underpin the planning exercise [but see @r5].
-
-Cost data (or a surrogate thereof) are needed to inform the prioritization process. Specifically, these cost data describe the relative expenditure associated with managing each planning unit for conservation. For example, if the goal of the conservation planning exercise is to identify priority areas for expanding a local protected area system, then the cost data could represent the physical cost of purchasing the land. Alternatively, if such data are not available, then surrogate data could are often used instead (e.g. human population density, opportunity cost of foregone commercial activities, or planning unit size).
-
-Conservation planning exercises also require data on the biodiversity elements that are of conservation interest (termed _conservation features_). These features could be species (e.g. _Neofelis nebulosa_, the Clouded Leopard), populations, or habitats (e.g. mangroves or cloud forest). After identifying the set of relevant conservation features for a conservation planning exercise, spatially explicit data need to be obtained for each and every feature to describe their spatial distribution (e.g. habitat suitability data, probability of occurrence data, presence/absence data). This is important to ensure that conservation features are adequately covered (represented) by prioritizations. After assembling all the data, the next step is to define the conservation planning problem.
-
-The _prioritizr R_ package is designed to help you build and solve conservation planning problems. Specifically, prioritizations are generated by using formulating a mathematical optimization problem and then solving it to generate a solution. These mathematical optimization problems are formulated using the planning unit data, cost data, and feature data, and with information related to the overarching aim of the prioritization process. In general, the goal of an optimization problem is to minimize (or maximize) an _objective function_ that is calculated using a set of _decision variables_, subject to a series of constraints to ensure that solution exhibits specific properties. The objective function describes the quantity which we are trying to minimize (e.g. cost of the solution) or maximize (e.g. number of features conserved). The decision variables describe the entities that we can control, and indicate which planning units are selected for conservation management and which of those are not. The constraints can be thought of as rules that the need decision variables need to follow. For example, a commonly used constraint is specifying that the solution must not exceed a certain budget.
-
-A wide variety of approaches have been developed for solving optimization problems. Reserve design problems are frequently solved using simulated annealing [@r6] or heuristics [@r8; @r7]. These methods are conceptually simple and can be applied to a wide variety of optimization problems. However, they do not scale well for large or complex problems [@r1]. Additionally, these methods cannot tell you how close any given solution is to the optimal solution. The _prioritizr R_ package uses exact algorithms to efficiently solve conservation planning problems to within a pre-specified a optimality gap. In other words, you can specify that you need the optimal solution (i.e. a gap of 0%) and the algorithms will, given enough time, find a solution that meets this criteria. In the past, exact algorithms have been too slow for conservation planning exercises [@r9]. However, improvements over the last decade mean that they are now much faster [@r23; @r1].
-
-In this package, optimization problems are expressed using _integer linear programming_ (ILP) so that they can be solved using (linear) exact algorithm solvers. The general form of an integer programming problem can be expressed in matrix notation using the following equation.
-
-$$\text{Minimize} \space \boldsymbol{c}^\text{T} \boldsymbol{x} \space
-\space \text{subject to} \space A\boldsymbol{x}
-\space \Box \space \boldsymbol{b}$$
-
-Here, where $x$ is a vector of decision variables, $c$ and $b$ are vectors of known coefficients, and $A$ is the constraint matrix. The final term specifies a series of structural constants and the $\Box$ symbol is used to indicate that the relational operators for the constraints can be either $\geq$, $=$, or $\leq$. In the context of a conservation planning problem, $c$ could be used to represent the planning unit costs, $A$ could be used to store the data showing the presence / absence (or amount) of each feature in each planning unit, $b$ could be used to represent minimum amount of habitat required for each species in the solution, the $\Box$ could be set to $\geq$ symbols to indicate that the total amount of each feature in the solution must exceed the quantities in $b$. But there are many other ways of formulating the reserve selection problem [@r11].
-
-## Package overview
-
-The _prioritizr R_ package contains eight main types of functions. These
-functions are used to:
-
-* create a new conservation planning [problem](https://prioritizr.net/reference/problem.html) by specifying the planning units, features, and management zones of conservation interest (e.g. species, ecosystems).
-* add an [objective](https://prioritizr.net/reference/objectives.html) to a conservation planning problem.
-* add [targets](https://prioritizr.net/reference/targets.html) to a problem to specify how much of each feature is desired or required to be conserved in the solutions.
-* add [constraints](https://prioritizr.net/reference/constraints.html) to a conservation planning problem to ensure that solutions exhibit specific properties (e.g. select specific planning units for protection).
-* add [penalties](https://prioritizr.net/reference/penalties.html) to a problem to penalize solutions according to specific metric (e.g. connectivity).
-* add [decisions](https://prioritizr.net/reference/decisions.html) to a problem to specify the nature of the decisions in the problem.
-* add methods to generate a [portfolio](https://prioritizr.net/reference/portfolios.html) of solutions.
-* add a [solver](https://prioritizr.net/reference/solvers.html) to a conservation problem to specify which software should be used to generate solutions and customize the optimization process.
-* [solve](https://prioritizr.net/reference/solve.html) a conservation problem.
-* evaluate a solution by computing [summary](https://prioritizr.net/reference/summaries.html) statistics.
-* evaluate the relative [importance](https://prioritizr.net/reference/importance.html) (irreplaceability) of planning units selected in a solution.
+The aim of this tutorial is to provide a short introduction to the _prioritizr R_ package. It is also intended for helping conservation planners familiar the _Marxan_ decision support tool [@r3] to start using the package for their work.
 
-## Package workflow
+## Data
 
-The general workflow when using the _prioritizr R_ package starts with creating a new conservation planning `problem` object using data. Specifically, the `problem` object should be constructed using data that specify the planning units, biodiversity features, management zones (if applicable), and costs. After creating a new `problem` object, it can be customized---by adding objectives, penalties, constraints, and other information---to build a precise representation of the conservation planning problem required, and then solved to obtain a solutions.
+Let's load the packages and data used in this tutorial. Since this tutorial uses data from the _prioritizrdata R_ package, please ensure that it is installed. The data used in this tutorial were obtained from the _Introduction to Marxan_ course. Specifically, the data were originally a subset of a larger spatial prioritization project performed under contract to Australia's Department of Environment and Water Resources [@r30].
 
-All conservation planning problems require an objective. An objective specifies the property which is used to compare different feasible solutions. Simply put, the objective is the property of the solution which should be maximized or minimized during the optimization process. For instance, with the minimum set objective (specified using `add_min_set_objective`), we are seeking to minimize the cost of the solution (similar to _Marxan_). On the other hand, with the maximum coverage objective (specified using `add_max_cover_objective`), we are seeking to maximize the number of different features represented in the solution.
-
-Many objectives require `targets` (e.g. the minimum set objective). Targets are a specialized set of constraints that relate to the total quantity of each feature secured in the solution (e.g. amount of suitable habitat or number of individuals). In the case of the minimum set objective ( `add_min_set_objective`), they are used to ensure that solutions secure a sufficient quantity of each feature, and in other objectives, such as the maximum features objective ( `add_max_features_objective`) they are used to assess whether a feature has been adequately conserved by a candidate solution. Targets can be expressed numerically as the total amount required for a given feature (using `add_absolute_targets`), or as a proportion of the total amount found in the planning units (using `add_relative_targets`). Note that not all objectives require targets, and a warning will be thrown if an attempt is made to add targets to a problem with an objective that does not use them.
-
-Constraints and penalties can be added to a conservation planning problem to ensure that solutions exhibit a specific property or penalize solutions which don't exhibit a specific property (respectively). The difference between constraints and penalties, strictly speaking, is constraints are used to rule out potential solutions that don't exhibit a specific property. For instance, constraints can be used to ensure that specific planning units are selected in the solution for prioritization (using `add_locked_in_constraints`) or not selected in the solution for prioritization (using `add_locked_out_constraints`). On the other hand, penalties are combined with the objective of a problem, with a penalty factor, and the overall objective of the problem then becomes to minimize (or maximize) the primary objective function and the penalty function. For example, penalties can be added to a problem to penalize solutions that are excessively fragmented (using `add_boundary_penalties`). These penalties have a `penalty` argument that specifies the relative importance of having spatially clustered solutions. When the argument to `penalty` is high, then solutions which are less fragmented are valued more highly---even if they cost more---and when the argument to `penalty` is low, then the solutions which are more fragmented are valued less highly.
-
-After building a conservation problem, it can then be solved to obtain a solution (or portfolio of solutions if desired). The solution is returned in the same format as the planning unit data used to construct the problem. This means that if raster or shapefile / vector data was used when initializing the problem, then the solution will also be in raster or shapefile / vector data. This can be very helpful when it comes to interpreting and visualizing solutions because it means that the solution data does not first have to be merged with spatial data before they can be plotted on a map.
-
-## Usage
-
-Here we will provide an introduction to using the _prioritizr R_ package to build and solve a conservation planning problem. Please note that we will not discuss conservation planning with multiple zones in this vignette, for more information on working with multiple management zones please see the [zones vignette](zones.html).
-
-First, we will load the _prioritizr_ package.
-
-```{r, results = "hide", message = FALSE}
-# load package
+```{r, message = FALSE}
+# load packages
+library(prioritizrdata)
 library(prioritizr)
+library(vegan)
+library(cluster)
 
-# set default options for printing tabular data
-options(tibble.width = Inf)
-```
-
-### Data
-
-Now we will load some built-in data sets that are distributed with the _prioritizr R_ package. This package contains several different planning unit data sets. To provide a comprehensive overview of the different ways that we can initialize a conservation planning problem, we will load each of them.
-
-First, we will load the raster planning unit data (`sim_pu_raster`). Here, the planning units are represented as a raster (i.e. a `RasterLayer` object) and each pixel corresponds to the spatial extent of each panning unit. The pixel values correspond to the acquisition costs of each planning unit.
-
-```{r}
-# load raster planning unit data
-data(sim_pu_raster)
-
-# print description of the data
-print(sim_pu_raster)
-
-# plot the data
-plot(sim_pu_raster)
-```
-
-Secondly, we will load one of the spatial vector planning unit data sets (`sim_pu_polygons`). Here, each polygon (i.e. feature using ArcGIS terminology) corresponds to a different planning unit. This data set has an attribute table that contains additional information about each polygon. Namely, the `cost` field (column) in the attribute table contains the acquisition cost for each planning unit.
-
-```{r}
-# load polygon planning unit data
-data(sim_pu_polygons)
-
-# print first six rows of attribute table
-head(sim_pu_polygons@data)
-
-# plot the planning units
-spplot(sim_pu_polygons, zcol = "cost")
-```
-
-Thirdly, we will load some planning unit data stored in tabular format (i.e. `data.frame` format). For those familiar with _Marxan_ or dealing with very large conservation planning problems (> 10 million planning units), it may be useful to work with data in this format because it does not contain any spatial information which will reduce computational burden. When using tabular data to initialize conservation planning problems, the data must follow the conventions used by _Marxan_. Specifically, each row in the planning unit table must correspond to a different planning unit. The table must also have an "id" column to provide a unique integer identifier for each planning unit, and it must also have a column that indicates the cost of each planning unit. For more information, please see the [official _Marxan_ documentation](https://marxansolutions.org/).
-
-```{r}
-# specify file path for planning unit data
-pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr")
-
-# load in the tabular planning unit data
-# note that we use the data.table::fread function, as opposed to the read.csv
-# function, because it is much faster
-pu_dat <- data.table::fread(pu_path, data.table = FALSE)
-
-# preview first six rows of the tabular planning unit data
-# note that it has some extra columns other than id and cost as per the
-# Marxan format
-head(pu_dat)
-```
-
-Finally, we will load data showing the spatial distribution of the conservation features. Our conservation features (`sim_features`) are represented as a stack of raster objects (i.e. a `RasterStack` object) where each layer corresponds to a different feature (e.g. a multi-band GeoTIFF where each band corresponds to a different feature). The pixel values in each layer correspond to the amount of suitable habitat available in a given planning unit. Note that our planning unit raster layer and our conservation feature stack have exactly the same spatial properties (i.e. resolution, extent, coordinate reference system) so their pixels line up perfectly.
+# load planning unit data
+data(tas_pu)
 
-```{r, fig.width = 4, fig.height = 3}
 # load feature data
-data(sim_features)
-
-# plot the distribution of suitable habitat for each feature
-plot(sim_features, main = paste("Feature", seq_len(nlayers(sim_features))),
-     nr = 2, box = FALSE, axes = FALSE)
-```
-
-### Initialize a problem
-
-After having loaded our planning unit and feature data, we will now try initializing the some conservation planning problems. There are a lot of different ways to initialize a conservation planning problem, so here we will just showcase a few of the more commonly used methods. For an exhaustive description of all the ways you can initialize a conservation problem, see the help file for the `problem` function (which you can open using the code `?problem`). First off, we will initialize a conservation planning problem using the raster data.
-
-```{r}
-# create problem
-p1 <- problem(sim_pu_raster, sim_features)
-
-# print problem
-print(p1)
-
-# print number of planning units
-number_of_planning_units(p1)
-
-# print number of features
-number_of_features(p1)
-```
-
-Generally, we recommend initializing problems using raster data where possible. This is because the `problem` function needs to calculate the amount of each feature in each planning unit, and by providing both the planning unit and feature data in raster format with the same spatial resolution, extents, and coordinate systems, this means that the `problem` function does not need to do any geo-processing behind the scenes. But sometimes we can't use raster planning unit data because our planning units aren't equal-sized grid cells. So, below is an example showing how we can initialize a conservation planning problem using planning units that are formatted as spatial vector data. Note that if we had pre-computed the amount of each feature in each planning unit and stored the data in the attribute table, we could pass in the names of the columns as an argument to the `problem` function.
-
-```{r}
-# create problem with spatial vector data
-# note that we have to specify which column in the attribute table contains
-# the cost data
-p2 <- problem(sim_pu_polygons, sim_features, cost_column = "cost")
-
-# print problem
-print(p2)
-```
-
-We can also initialize a conservation planning problem using tabular planning unit data (i.e. a `data.frame`). Since the tabular planning unit data does not contain any spatial information, we also have to provide the feature data in tabular format (i.e. a `data.frame`) and data showing the amount of each feature in each planning unit in tabular format (i.e. a `data.frame`). The feature data must have an "id" column containing a unique integer identifier for each feature, and the planning unit by feature data must contain the following three columns: "pu" corresponding to the planning unit identifiers, "species" corresponding to the feature identifiers, and "amount" showing the amount of a given feature in a given planning unit.
-
-```{r}
-# set file path for feature data
-spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr")
-
-# load in feature data
-spec_dat <- data.table::fread(spec_path, data.table = FALSE)
-
-# print first six rows of the data
-# note that it contains extra columns
-head(spec_dat)
-
-# set file path for planning unit vs. feature data
-puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr")
-
-# load in planning unit vs feature data
-puvspr_dat <- data.table::fread(puvspr_path, data.table = FALSE)
-
-# print first six rows of the data
-head(puvspr_dat)
-
-# create problem
-p3 <- problem(pu_dat, spec_dat, cost_column = "cost", rij = puvspr_dat)
-
-# print problem
-print(p3)
+data(tas_features)
 ```
 
-For more information on initializing problems, please see the help page for the `problem` function (which you can open using the code `?problem`). Now that we have initialized a conservation planning problem, we will show you how you can customize it to suit the exact needs of your conservation planning scenario. Although we initialized the conservation planning problems using several different methods, moving forward, we will only use raster-based planning unit data to keep things simple.
+The `tas_pu` object contains planning units represented as spatial polygons (i.e., a `SpatialPolygonsDataFrame` object). This object has three columns that denote the following information for each planning unit: a unique identifier (`id`), unimproved land value (`cost`), and current conservation status (`locked_in`). Planning units that have at least half of their area overlapping with existing protected areas are denoted with a locked in value of 1, otherwise they are denoted with a value of 0. If you are familiar with the _Marxan_ decision support tool, then you will notice that some of these columns are formatted similar conventions.
 
-### Add an objective
+Now, let's have a look at the planning unit data. We can see that the planning units correspond to hexagonal land parcels. We can also see that is a clear spatial pattern in the cost and conservation status the planning units.
 
-The next step is to add an objective to the problem. A problem objective is used to specify the primary goal of the problem (i.e. the quantity that is to be maximized or minimized). All conservation planning problems involve minimizing or maximizing some kind of objective. For instance, we might require a solution that conserves enough habitat for each species while minimizing the overall cost of the reserve network. Alternatively, we might require a solution that maximizes the number of conserved species while ensuring that the cost of the reserve network does not exceed the budget. Please note that objectives are added in the same way regardless of the type of data used to initialize the problem.
+```{r, fig.width = w, fig.height = h}
+# print planning unit data
+print(tas_pu)
 
-The _prioritizr R_ package supports a variety of different objective functions.
+# plot map of planning unit costs
+plot(st_as_sf(tas_pu[, "cost"]), main = "Planning unit costs")
 
-* __Minimum set objective__: Minimize the cost of the solution whilst ensuring that all targets are met [@r11]. This objective is similar to that used in _Marxan_ [@r3]. For example, we can add a minimum set objective to a problem using the following code.
-```{r}
-# create a new problem that has the minimum set objective
-p3 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective()
-
-# print the problem
-print(p3)
+# plot map of planning unit coverage by protected areas
+plot(st_as_sf(tas_pu[, "locked_in"]), main = "Protected area coverage")
 ```
-* __Maximum cover objective__: Represent at least one instance of as many features as possible within a given budget [@r12].
-```{r}
-# create a new problem that has the maximum coverage objective and a budget
-# of 5000
-p4 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_cover_objective(5000)
 
-# print the problem
-print(p4)
-```
-* __Maximum features objective__: Fulfill as many targets as possible while ensuring that the cost of the solution does not exceed a budget [inspired by @r10]. This object is similar to the maximum cover objective except that we have the option of later specifying targets for each feature. In practice, this objective is more useful than the maximum cover objective because features often require a certain amount of area for them to persist and simply capturing a single instance of habitat for each feature is generally unlikely to enhance their long-term persistence.
-```{r}
-# create a new problem that has the maximum features objective and a budget
-# of 5000
-p5 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_features_objective(budget = 5000)
+The `tas_features` object describes the spatial distribution of the features. Specifically, the feature data are expressed as a stack of `r raster::nlayers(tas_features)` rasters (i.e., a `RasterStack` object). Each layer in the stack corresponds to one of `r raster::nlayers(tas_features)` different vegetation communities. To describe the spatial distribution of a given vegetation community, each layer contains a spatially referenced grid of rectangular cells and each of these grid cells is associated with information on the distribution of the a given vegetation community. Specifically, these grid cells are assigned values that indicate if a given vegetation community is present (using value of 1) or absent (using value of 0) within the spatial extent of each grid cell.
 
-# print the problem
-print(p5)
-```
-* __Minimum shortfall objective__: Minimize the overall (weighted sum) shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when there is a large amount of left-over budget when using the maximum feature representation objective and the remaining funds need to be allocated to places that will enhance the representation of features with unmet targets.
-```{r}
-# create a new problem that has the minimum shortfall objective and a budget
-# of 5000
-p6 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_shortfall_objective(budget = 5000)
+Next, let's examine the feature data. Here we will only plot the first four features as an example. The pixel values denote the presence (denoted by a value of 1) or absence (denoted by a value of zero) of each feature within the extent of the study area.
 
-# print the problem
-print(p6)
-```
-* __Minimum largest shortfall objective__: Minimize the largest (maximum) shortfall while ensuring that the cost of the solution does not exceed a budget. In practice, this objective useful when the minimum shortfall objective returns solutions that focus too much on representing a small number of features (e.g. because they occur in much cheaper planning units), and solutions are needed to spread conservation effort out more evenly amongst all features---even if it means that all features will have (relatively) poor representation.
-```{r}
-# create a new problem that has the minimum largest shortfall objective and a
-# budget of 5000
-p7 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_largest_shortfall_objective(budget = 5000)
+```{r, fig.width = 4.5, fig.height = 4.5}
+# print planning unit data
+print(tas_features)
 
-# print the problem
-print(p7)
+# plot map of the first four vegetation classes
+plot(tas_features[[1:4]], main = paste("Feature", 1:4))
 ```
-* __Maximum phylogenetic diversity objective__: Maximize the phylogenetic diversity of the features represented in the solution subject to a budget [inspired by @r13; @r14]. This objective is similar to the maximum features objective except that emphasis is placed on protecting features which are associated with a diverse range of evolutionary histories. The _prioritizr R_ package contains a simulated phylogeny that can be used with the simulated feature data (`sim_phylogny`).
-```{r}
-# load simulated phylogeny data
-data(sim_phylogeny)
 
-# create a new problem that has the maximum phylogenetic diversity
-# objective and a budget of 5000
-p8 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_phylo_div_objective(budget = 5000, tree = sim_phylogeny)
+The planning units in this tutorial are stored as spatial polygons. Although spatial polygons provide considerable flexibility in the shape and size of the planning units, such flexibility comes at a cost. This is because the spatial data processing routines needed to combine spatial polygon data and raster data for optimization can be very computationally expensive (e.g., calculating zonal statistics). As a consequence, we generally recommend using raster-based planning unit data where possible to reduce processing time. Another strategy is to complete spatial data processing routines manually using other software (e.g., _ESRI ArcGIS_) and use the pre-processed data directly with the _prioritizr R_ package.
 
-# print the problem
-print(p8)
-```
-* __Maximum phylogenetic endemism objective__: Maximize the phylogenetic endemism of the features represented in the solution subject to a budget [inspired by @r13; @r14; @r32]. This objective is similar to the maximum phylogenetic diversity except that emphasis is placed conserving features that are associated with geographically restricted periods of evolutionary history rather than a diverse range of evolutionary histories.
-```{r}
-# load simulated phylogeny data
-data(sim_phylogeny)
+## Problem formulation
 
-# create a new problem that has the maximum phylogenetic diversity
-# objective and a budget of 5000
-p9 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_phylo_end_objective(budget = 5000, tree = sim_phylogeny)
+Now we will formulate a conservation planing problem. To achieve this, we first specify which objects contain the planning unit and feature data (using the `problem()` function). Next, we specify that we want to use the minimum set objective function (using the `add_min_set_objective()` function). This objective function indicates that we wish to minimize the total cost of planning units selected by the prioritization. We then specify boundary penalties reduce spatial fragmentation in the resulting prioritization (using the `add_boundary_penalties()` function; see the [_Calibrating trade-offs_ vignette](calibrating_trade-offs.html) for details on calibrating the penalty value). We also specify representation targets to ensure the resulting prioritization provides adequate coverage of each vegetation community (using the `add_relative_targets()` function). Specifically, we specify targets to ensure at least 17% of the spatial extent of each vegetation community (based on the [Aichi Target 11](https://www.cbd.int/sp/targets/)). Additionally, we set constraints to ensure that planning units predominately covered by existing protected areas are selected by the prioritization (using the `add_locked_in_constraints()` function). Finally, we specify that the prioritization should either select -- or not select -- planning units for prioritization (using the `add_binary_decisions()` function).
 
-# print the problem
-print(p9)
-```
-* __Maximum utility objective__: Secure as much of the features as possible without exceeding a budget. This objective is functionally equivalent to selecting the planning units with the greatest amounts of each feature (e.g. species richness). Generally, we don't encourage the use of this objective because it will only rarely identify complementary solutions---solutions which adequately conserve a range of different features---except perhaps to explore trade-offs or provide a baseline solution with which to compare other solutions.
-```{r}
-# create a new problem that has the maximum utility objective and a budget
-# of 5000
-p10 <- problem(sim_pu_raster, sim_features) %>%
-      add_max_utility_objective(budget = 5000)
+```{r, fig.width = w, fig.height = h}
+# build problem
+p1 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_boundary_penalties(penalty = 0.005) %>%
+      add_relative_targets(0.17) %>%
+      add_locked_in_constraints("locked_in") %>%
+      add_binary_decisions()
 
 # print the problem
-print(p10)
-```
-
-### Add targets
-
-Most conservation planning problems require targets. Targets are used to specify the minimum amount or proportion of a feature's distribution that needs to be protected in the solution. For example, we may want to develop a reserve network that will secure 20% of the distribution for each feature for minimal cost.
-
-There are four ways for specifying targets in the _prioritizr R_ package:
-
-* __Absolute targets__: Targets are expressed as the total amount of each feature in the study area that need to be secured. For example, if we had binary feature data that showed the absence or presence of suitable habitat across the study area, we could set an absolute target as 5 to mean that we require 5 planning units with suitable habitat in the solution.
-```{r}
-# create a problem with targets which specify that the solution must conserve
-# a need a sum total of 3 units of suitable habitat for each feature
-p11 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_absolute_targets(3)
-
-# print problem
-print(p11)
-```
-* __Relative targets__: Targets are set as a proportion (between 0 and 1) of the total amount of each feature in the study area. For example, if we had binary feature data and the feature occupied a total of 20 planning units in the study area, we could set a relative target of 50 % to specify that the solution must secure 10 planning units for the feature. We could alternatively specify an absolute target of 10 to achieve the same result, but sometimes proportions are easier to work with.
-```{r}
-# create a problem with the minimum set objective and relative targets of 10 %
-# for each feature
-p12 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1)
-
-# print problem
-print(p12)
-
-# create a problem with targets which specify that we need 10 % of the habitat
-# for the first feature, 15 % for the second feature, 20 % for the third feature
-# 25 % for the fourth feature and 30 % of the habitat for the fifth feature
-targets <- c(0.1, 0.15, 0.2, 0.25, 0.3)
-p13 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(targets)
-
-# print problem
-print(p13)
-```
-* __Log-linear targets__: Targets are expressed using scaling factors and log-linear interpolation. This method for specifying targets is commonly used for global prioritization analyses [@r15].
-```{r}
-# create problem with added log-linear targets
-p14 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_loglinear_targets(10, 0.9, 100, 0.2)
-
-# print problem
-print(p14)
-```
-* __Manual targets__: Targets are manually specified. This is only really recommended for advanced users or problems that involve multiple management zones. See the [zones vignette](zones.html) for more information on these targets.
-
-As with the functions for specifying the objective of a problem, if we try adding multiple targets to a problem, only the most recently added set of targets are used.
-
-### Add constraints
-
-A constraint can be added to a conservation planning problem to ensure that all solutions exhibit a specific property. For example, they can be used to make sure that all solutions select a specific planning unit or that all selected planning units in the solution follow a certain configuration.
-
-The following constraints can be added to conservation planning problems in the _prioritizr R_ package.
-
-* __Locked in constraints__: Add constraints to ensure that certain planning units are prioritized in the solution. For example, it may be desirable to lock in planning units that are inside existing protected areas so that the solution fills in the gaps in the existing reserve network.
-```{r}
-# create problem with constraints which specify that the first planning unit
-# must be selected in the solution
-p15 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_in_constraints(1)
-
-# print problem
-print(p15)
-```
-* __Locked out constraints__: Add constraints to ensure that certain planning units are not prioritized in the solution. For example, it may be useful to lock out planning units that have been degraded and are not suitable for conserving species.
-```{r}
-# create problem with constraints which specify that the second planning unit
-# must not be selected in the solution
-p16 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_out_constraints(2)
-
-# print problem
-print(p16)
-```
-* __Neighbor constraints__: Add constraints to a conservation problem to ensure that all selected planning units have at least a certain number of neighbors.
-```{r}
-# create problem with constraints which specify that all selected planning units
-# in the solution must have at least 1 neighbor
-p17 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_neighbor_constraints(1)
-
-# print problem
-print(p17)
-```
-* __Contiguity constraints__: Add constraints to a conservation problem to ensure that all selected planning units are spatially connected to each other and form spatially contiguous unit.
-```{r}
-# create problem with constraints which specify that all selected planning units
-# in the solution must form a single contiguous unit
-p18 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_contiguity_constraints()
-
-# print problem
-print(p18)
-```
-* __Feature contiguity constraints__: Add constraints to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of those implemented in the `add_contiguity_constraints` function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit.
-```{r}
-# create problem with constraints which specify that the planning units used
-# to conserve each feature must form a contiguous unit
-p19 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_feature_contiguity_constraints()
-
-# print problem
-print(p19)
-```
-
-* __Linear constraints__: Add constraints to ensure that all selected planning units meet certain criteria. For example, they can be used to add multiple budgets, or limit the number of planning units selected in different administrative areas within a study region (e.g. different countries).
-
-```{r}
-# create problem with constraints which specify that the sum of
-# values in sim_features[[1]] among selected planning units must not exceed a
-#' threshold value of 190.
-p20 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_shortfall_objective(budget = 1800) %>%
-       add_relative_targets(0.1) %>%
-       add_linear_constraints(190, "<=", sim_features[[1]])
-
-# print problem
-print(p20)
+print(p1)
 ```
 
-* __Mandatory allocation constraints__: Add constraints to ensure that every planning unit is allocated to a management zone in the solution. Please note that this function can only be used with problems that contain multiple zones. For more information on problems with multiple zones and an example using this function, see the Management Zones vignette.
+## Prioritization
 
-In particular, The `add_locked_in_constraints` and `add_locked_out_constraints` functions are incredibly useful for real-world conservation planning exercises, so it's worth pointing out that there are several ways we can specify which planning units should be locked in or out of the solutions. If we use raster planning unit data, we can also use raster data to specify which planning units should be locked in our locked out.
+We can now solve the problem formulation (`p1`) to generate a prioritization (using the `solve()` function). The _prioritizr_ R package supports a range of different exact algorithm solvers, including _Gurobi_, _IBM CPLEX_, _CBC_, _Rsymphony_, and _lpsymphony_. Although there are benefits and limitations associated with each of these different solvers, they should return similar results. Note that you will need at least one solver installed on your system to generate prioritizations. Since we did not specify a solver when building the problem, the _prioritizr R_ package will automatically select the best available solver installed. We recommend using the _Gurobi_ solver if possible, and have used it for this tutorial (see the _Gurobi Installation Guide_ vignette for installation instructions). After solving the problem, the prioritization will be stored in the `solution_1` column of the `s1` object.
 
-```{r, fig.width = 6.5, fig.height = 2.5}
-# load data to lock in or lock out planning units
-data(sim_locked_in_raster)
-data(sim_locked_out_raster)
+```{r, fig.width = w, fig.height = h}
+# solve problem
+s1 <- solve(p1)
 
-# plot the locked data
-plot(stack(sim_locked_in_raster, sim_locked_out_raster),
-     main = c("Locked In", "Locked Out"))
-
-# create a problem using raster planning unit data and use the locked raster
-# data to lock in some planning units and lock out some other planning units
-p21 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_in_constraints(sim_locked_in_raster) %>%
-       add_locked_out_constraints(sim_locked_out_raster)
-
-# print problem
-print(p21)
+# plot map of prioritization
+plot(st_as_sf(s1[, "solution_1"]), main = "Prioritization",
+     pal = c("grey90", "darkgreen"))
 ```
 
-If our planning unit data are in a spatial vector format (similar to the `sim_pu_polygons` data) or a tabular format (similar to `pu_dat`), we can use the field names in the data to refer to which planning units should be locked in and / or out. For example, the `sim_pu_polygons` object has `TRUE` / `FALSE` values in the "locked_in" field which indicate which planning units should be selected in the solution. We could use the data in this field to specify that those planning units with `TRUE` values should be locked in using the following methods.
-
-```{r}
-# preview first six rows of the attribute table for sim_pu_polygons
-head(sim_pu_polygons@data)
+## Feature representation
 
-# specify locked in data using the field name
-p22 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_in_constraints("locked_in")
+Let's examine how well the vegetation communities are represented by existing protected areas and the prioritization.
 
-# print problem
-print(p22)
+```{r, fig.width = 7}
+# create column with existing protected areas
+tas_pu$pa <- round(tas_pu$locked_in)
 
-# specify locked in data using the values in the field
-p23 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_locked_in_constraints(which(sim_pu_polygons$locked_in))
+# calculate feature representation statistics based on existing protected areas
+tc_pa <- eval_target_coverage_summary(p1, tas_pu[, "pa"])
+print(tc_pa)
 
-# print problem
-print(p23)
-```
+# calculate  feature representation statistics based on the prioritization
+tc_s1 <- eval_target_coverage_summary(p1, s1[, "solution_1"])
+print(tc_s1)
 
-### Add penalties
+# explore representation by existing protected areas
+## calculate number of features adequately represented by existing protected
+## areas
+sum(tc_pa$met)
 
-We can also add penalties to a problem to favor or penalize solutions according to a secondary objective. Unlike the constraint functions, these functions will add extra information to the objective function of the optimization function to penalize solutions that do not exhibit specific characteristics. For example, penalties can be added to a problem to avoid highly fragmented solutions at the expense of accepting slightly more expensive solutions. All penalty functions have a `penalty` argument that controls the relative importance of the secondary penalty function compared to the primary objective function. It is worth noting that incredibly low or incredibly high `penalty` values---relative to the main objective function---can cause problems to take a very long time to solve, so when trying out a range of different penalty values it can be helpful to limit the solver to run for a set period of time.
+## summarize representation (values show percent coverage)
+summary(tc_pa$relative_held * 100)
 
-The _prioritizr R_ package currently offers only two methods for adding penalties to a conservation planning problem.
+## visualize representation  (values show percent coverage)
+hist(tc_pa$relative_held * 100,
+     main = "Feature representation by existing protected areas",
+     xlim = c(0, 100),
+     xlab = "Percent coverage of features (%)")
 
-* __Boundary penalties__:  Add penalties to penalize solutions that are excessively fragmented. These penalties are similar to those used in _Marxan_ [@r3; @r1].
-```{r}
-# create problem with penalties that penalize fragmented solutions with a
-# penalty factor of 0.01
-p24 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_boundary_penalties(penalty = 0.01)
 
-# print problem
-print(p24)
-```
-* __Connectivity penalties__: Add penalties to favor solutions that select combinations of planning units with high connectivity between them. These penalties are similar to those used in _Marxan with Zones_ [@r2; @r1]. This function supports both symmetric and asymmetric connectivities among planning units.
-```{r}
-# create problem with penalties that favor combinations of planning units with
-# high connectivity, here we will use only the first four layers in
-# sim_features for the features and we will use the fifth layer in sim_features
-# to represent the connectivity data, where the connectivity_matrix function
-# will create a matrix showing the average strength of connectivity between
-# adjacent planning units using the data in the fifth layer of sim_features
-p25 <- problem(sim_pu_raster, sim_features[[1:4]]) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_boundary_penalties(
-         penalty = 5,
-         data = connectivity_matrix(sim_pu_raster, sim_features[[5]]))
+# explore representation by prioritization
+## summarize representation (values show percent coverage)
+summary(tc_s1$relative_held * 100)
 
-# print problem
-print(p25)
-```
-* __Linear penalties__: Add penalties to penalize solutions that select planning units according to a certain variable (e.g. anthropogenic pressure).
-```{r}
-# create data for penalizing planning units
-# (note this requires the RandomFields package to be installed)
-pen_raster <- simulate_cost(sim_pu_raster)
-
-# create problem with penalties that penalize solutions that select
-# planning units with high values in the pen_raster object,
-# here we will use a penalty value of 5 to indicate the trade-off (scaling)
-# between the penalty values (in the sim_pu_raster) and the main objective
-# (i.e. the cost of the solution)
-p26 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_linear_penalties(penalty = 5, data = pen_raster)
+## calculate number of features adequately represented by the prioritization
+sum(tc_s1$met)
 
-# print problem
-print(p26)
+## visualize representation  (values show percent coverage)
+hist(tc_s1$relative_held * 100,
+     main = "Feature representation by prioritization",
+     xlim = c(0, 100),
+     xlab = "Percent coverage of features (%)")
 ```
 
-### Add the decision types
+We can see that representation of the vegetation communities by existing protected areas is remarkably poor. For example, many of the vegetation communities have nearly zero coverage by existing protected areas. In other words, are almost entirely absent from  existing protected areas. We can also see that all vegetation communities have at least 17% coverage by the prioritization -- meaning that it meets the representation targets for all of the features.
 
-Conservation planning problems involve making decisions on how planning units will be managed. These decisions are then associated with management actions (e.g. turning a planning unit into a protected area). The type of decision describes how the action is applied to planning units. For instance, the default decision-type is a binary decision type, meaning that we are either selecting or not selecting planning units for management.
+## Irreplaceability
 
-The _prioritizr R_ package currently offers the following types of decisions for customizing problems.
+After generating the prioritization, we can examine the relative importance of planning units selected by the prioritization. This can be useful to identify critically important planning units for conservation -- in other words, places that contain biodiversity features which cannot be represented anywhere else -- and schedule implementation of the prioritization. To achieve this, we will use the Ferrier metric [@r34].
 
-* __Binary decisions__: Add a binary decision to a conservation planning problem. This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem object, then this decision class will be used by default.
-```{r}
-# add binary decisions to a problem
-p27 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions()
-
-# print problem
-print(p27)
-```
-* __Proportion decisions__: Add a proportion decision to a problem. This is a relaxed decision where a part of a planning unit can be prioritized, as opposed to the default of the entire planning unit. Typically, this decision has the assumed action of buying a fraction of a planning unit to include in a protected area network. Generally, problems can be solved much faster with proportion-type decisions than binary-type decisions, so they can be very useful when commercial solvers are not available.
-```{r}
-# add proportion decisions to a problem
-p28 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_proportion_decisions()
+```{r, fig.width = w, fig.height = h}
+# calculate irreplaceability
+irrep_s1 <- eval_ferrier_importance(p1, s1["solution_1"])
+print(irrep_s1)
 
-# print problem
-print(p28)
-```
-* __Semi-continuous decisions__: Add a semi-continuous decision to a problem. This decision is similar to proportion decisions except that it has an upper bound parameter. By default, the decision can range from prioritizing none (0%) to all (100%) of a planning unit. However, a upper bound can be specified to ensure that at most only a fraction (e.g. 80%) of a planning unit can be purchased. This type of decision may be useful when it is not practical to conserve the entire area indicated by a planning unit.
-```{r}
-# add semi-continuous decisions to a problem, where we can only manage at most
-# 50 % of the area encompassed by a planning unit
-p29 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_semicontinuous_decisions(0.5)
+# manually coerce values for planning units not selected in prioritization
+# to NA, so that they are shown in white
+irrep_s1$plot_total <- irrep_s1$total
+irrep_s1$plot_total[s1$solution_1 < 0.5] <- NA_real_
 
-# print problem
-print(p29)
+# plot map of overall importance scores
+plot(st_as_sf(irrep_s1[, "plot_total"]), main = "Overall importance")
 ```
 
-### Add a solver
-
-Next, after specifying the mathematical formulation that underpins your conservation planning problem, you can specify how the problem should be solved. If you do not specify this information, the _prioritizr R_ package will automatically use the best solver currently installed on your system with some reasonable defaults. __We strongly recommend installing the [Gurobi software suite and the _gurobi_ _R_ package](https://www.gurobi.com/) to solve problems, and for more information on this topic please refer to the [Gurobi Installation Guide](gurobi_installation.html)__.
-
-Currently, the _prioritizr R_ package supports five different solvers.
-
-* __*Gurobi* solver__: [_Gurobi_](https://www.gurobi.com/) is a state of the art commercial optimization software. It is by far the fastest of the solvers that can be used to solve conservation problems. However, it is not freely available. That said, special licenses are available to academics at no cost.
-```{r}
-# create a problem and specify that Gurobi should be used to solve the problem
-# and specify an optimality gap of zero to obtain the optimal solution
-p30 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_gurobi_solver(gap = 0)
-
-# print problem
-print(p30)
-```
-* __*IBM CPLEX* solver__: [_IBM CPLEX_](https://www.ibm.com/analytics/cplex-optimizer) is a commercial optimization software. It is faster than the open source solvers available for generating prioritizations (see below), however, it is not freely available. Similar to the _Gurobi_ software, special licenses are available to academics at no cost.
-```{r}
-# create a problem and specify that IBM CPLEX should be used to solve the
-# problem and specify an optimality gap of zero to obtain the optimal solution
-p31 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_cplex_solver(gap = 0)
+## Portfolios
 
-# print problem
-print(p31)
-```
-* __*CBC* solver__: [*CBC*](https://projects.coin-or.org/Cbc) is an
-open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. Although formal benchmarks have yet to be completed, preliminary analyses suggest that it is
-the fastest open-source solver available for generating prioritizations. It requires the _rcbc R_ package, which is currently only available on [GitHub](https://github.com/dirkschumacher/rcbc).
-```{r}
-# create a problem and specify that CBC should be used to solve the
-# problem and specify an optimality gap of zero to obtain the optimal solution
-p32 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_cbc_solver(gap = 0)
+Conservation planning exercises often involve generating multiple different prioritizations. This can help decision makers consider different options, and provide starting points for building consensus among stakeholders. To generate a range of different prioritizations given the same problem formulation, we can use portfolio functions. Here we will use the gap portfolio to generate 1000 solutions that are within 30% of optimality. Please note that you will need to have the *Gurobi* solver installed to use this specific portfolio. If you don'thave access to *Gurobi*, you could try using the shuffle portfolio instead (using the `add_shuffle_portfolio()` function).
 
-# print problem
-print(p32)
-```
-* __*lpsymphony* solver__: [_SYMPHONY_](https://projects.coin-or.org/SYMPHONY) is an open-source integer programming solver that is also part of the COIN-OR project. This solver uses the _lpsymphony R_ package (available on [Bioconductor](http://bioconductor.org/packages/release/bioc/html/lpsymphony.html)) to interface with the _SYMPHONY_ software.
 ```{r}
-# create a problem and specify that lpsymphony should be used to solve the
-# problem and specify an optimality gap of zero to obtain the optimal solution
-p33 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_lpsymphony_solver(gap = 0)
+# create new problem with a portfolio added to it
+p2 <- p1 %>%
+      add_gap_portfolio(number_solutions = 1000, pool_gap = 0.2)
 
 # print problem
-print(p33)
-```
-* __*Rsymphony* solver__: This solver provides a different interface to the [_SYMPHONY_](https://projects.coin-or.org/SYMPHONY) software. It uses the _Rsymphony R_ package which is available on The Comprehensive R Archive Network (CRAN). This solver is generally slower than the other solvers, because it cannot use parallel processing.
-```{r}
-# create a problem and specify that Rsymphony should be used to solve the
-# problem and specify an optimality gap of zero to obtain the optimal solution
-p34 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_rsymphony_solver(gap = 0)
+print(p2)
 
-# print problem
-print(p34)
+# generate prioritizations
+prt <- solve(p2)
+print(prt)
 ```
 
-### Add a portfolio
-
-Many conservation planning exercises require a portfolio of solutions. For example, real-world exercises can involve presenting decision makers with a range of near-optimal decisions. Additionally, the number of times that different planning units are selected in different solutions can provide insight into their relative importance.
-
-The following methods are available for generating a portfolio of solutions.
-
-* __Extra portfolio__: Generate a portfolio of solutions by storing feasible solutions found during the optimization process. Note that this method requires that the _Gurobi_ optimization software is used to generate solutions.
-```{r}
-# create a problem and specify that a portfolio should be created using
-# extra solutions found while solving the problem
-p35 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_extra_portfolio()
-
-# print problem
-print(p35)
-```
-* __Top portfolio__: Generate a portfolio of solutions by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions). Note that this method requires that the _Gurobi_ optimization software is used to generate solutions.
-```{r}
-# create a problem and specify that a portfolio should be created using
-# the top five solutions
-p36 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_top_portfolio(number_solutions = 5)
+After generating all these prioritizations, we now want some way to visualize them. Because it would be onerous to look at each and every prioritization individually, we will use statistical analyses to help us. We can visualize the differences between these different prioritizations -- based on which planning units they selected -- using a hierarchical cluster analysis [@r35].
 
-# print problem
-print(p36)
-```
-* __Gap portfolio__: Generate a portfolio of solutions by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is especially useful for generating multiple solutions that can used be to calculate selection frequencies (similar to _Marxan_). Note that this method requires that the _Gurobi_ optimization software is used to generate solutions.
-```{r}
-# create a problem and specify that a portfolio should be created by
-# finding five solutions within 10% of optimality
-p37 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_gap_portfolio(number_solutions = 5, pool_gap = 0.2)
+```{r, fig.height = 4.5, fig.width = 7, fig.show = "hold"}
+# extract solutions
+prt_results <- prt@data[, startsWith(names(prt), "solution_"), ]
 
-# print problem
-print(p37)
-```
-* __Cuts portfolio__: Generate a portfolio of distinct solutions within a pre-specified optimality gap. This method is only recommended if the _Gurobi_ optimization solver is not available.
-```{r}
-# create a problem and specify that a portfolio containing 10 solutions
-# should be created using using Bender's cuts
-p38 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_cuts_portfolio(number_solutions = 10)
+# calculate pair-wise distances between different prioritizations for analysis
+prt_dists <- vegan::vegdist(t(prt_results), method = "jaccard", binary = TRUE)
 
-# print problem
-print(p38)
-```
-* __Shuffle portfolio__: Generate a portfolio of solutions by randomly reordering the data prior to attempting to solve the problem. If the _Gurobi_ optimization solver is not available, this method is the fastest method for generating a set number of solutions within a specified distance from optimality.
-```{r}
-# create a problem and specify a portfolio should be created that contains
-# 10 solutions and that any duplicate solutions should not be removed
-p39 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions() %>%
-       add_shuffle_portfolio(number_solutions = 10, remove_duplicates = FALSE)
+# run cluster analysis
+prt_clust <- hclust(as.dist(prt_dists), method = "average")
 
-# print problem
-print(p39)
+# visualize clusters
+opar <- par()
+par(oma = c(0, 0, 0, 0), mar= c(0, 4.1, 1.5, 2.1))
+plot(prt_clust, labels = FALSE, sub = NA, xlab = "",
+     main = "Different prioritizations in portfolio")
+suppressWarnings(par(opar))
 ```
 
-### Solve the problem
+We can see that there are approximately six main groups of prioritizations in the portfolio. To explore these different groups, let's conduct another cluster analysis (i.e., a _k_-medoids analysis) to extract the most representative prioritization from each of these groups. In other words, we will run another statistical analysis to find the most central prioritization within each group.
 
-Finally, after formulating our conservation planning problem and specifying how the problem should be solved, we can use the `solve` function to obtain a solution. Note that the solver will typically print out some information describing the size of the problem and report its progress when searching for a suitable solution.
+```{r, fig.width = 7, fig.height = 5}
+# run k-medoids analysis
+prt_med <- pam(prt_dists, k = 6)
 
-```{r, fig.height = h, fig.width = w}
-# formulate the problem
-p40 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_boundary_penalties(penalty = 500, edge_factor = 0.5) %>%
-       add_binary_decisions()
+# extract names of prioritizations that are most central for each group.
+prt_med_names <- prt_med$medoids
+print(prt_med_names)
 
-# solve the problem (using the default solver)
-s40 <- solve(p40)
+# create a copy of prt and set values for locked in planning units to -1
+# so we can easily visualize differences between prioritizations
+prt2 <- prt[, prt_med_names]
+prt2@data[which(tas_pu$locked_in > 0.5), prt_med_names] <- -1
 
-# plot solution
-plot(s40, col = c("grey90", "darkgreen"), main = "Solution",
-     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
+# plot a map showing main different prioritizations
+# dark grey: locked in planning units
+# grey: planning units not selected
+# green: selected planning units
+plot(st_as_sf(prt2), pal = c("grey60", "grey90", "darkgreen"))
 ```
 
-We can plot this solution because the planning unit input data are spatially referenced in a raster format. The output format will always match the planning unit data used to initialize the problem. For example, the solution to a problem with planning units in a spatial vector (shapefile) format would also be in a spatial vector format. Similarly, if the planning units were in a tabular format (i.e. `data.frame`), the solution would also be returned in a tabular format.
-
-We can also extract attributes from the solution that describe the quality of the solution and the optimization process.
-
-```{r}
-# extract the objective (numerical value being minimized or maximized)
-print(attr(s40, "objective"))
-
-# extract time spent solving solution
-print(attr(s40, "runtime"))
+## _Marxan_ compatibility
 
-# extract state message from the solver that describes why this specific
-# solution was returned
-print(attr(s40, "status"))
-```
-
-### Evaluate the performance of a solution
+The _prioritizr R_ package provides functionality to help _Marxan_ users generate prioritizations. Specifically, it can import conservation planning data prepared for _Marxan_, and can generate prioritizations using a similar problem formulation as _Marxan_ [based on @r1]. Indeed, the problem formulation presented earlier in this vignette is very similar to that used by _Marxan_. The key difference is that the problem formulation we specified earlier uses "hard constraints" for feature representation, and _Marxan_ uses "soft constraints" for feature representation. This means that prioritization we generated earlier was mathematically guaranteed to reach the targets for all features. However, if we used _Marxan_ to generate the prioritization, then we could have produced a prioritization that would fail to reach targets (depending the _Species Penalty Factors_ used to generate the prioritization). In addition to these differences in terms problem formulation, the _prioritizr R_ package uses exact algorithms -- instead of the simulated annealing algorithm -- which ensures that we obtain prioritizations that are near optimal.
 
-After obtaining a solution to a conservation planning problem, it can be useful to calculate various summary statistics to understand its performance. The following functions are available to summarize a solution:
+Here we will show the _prioritizr R_ package can import _Marxan_ data and generate a prioritization. To begin with, let's import a conservation planning data prepared for _Marxan_.
 
-* Calculate the number of planning units selected within a solution.
-```{r}
-# calculate statistic
-eval_n_summary(p40, s40)
-```
-* Calculate the total cost of a solution.
-```{r}
-# calculate statistic
-eval_cost_summary(p40, s40)
-```
-* Calculate how well features are represented by a solution. This function can be used for problems that are built using targets and those that are not built using targets.
-```{r}
-# calculate statistics
-eval_feature_representation_summary(p40, s40)
-```
-* Calculate how well feature representation targets are met by a solution. This function can only be used with problems contain targets.
 ```{r}
-# calculate statistics
-eval_target_coverage_summary(p40, s40)
-```
-* Calculate the exposed boundary length (perimeter) associated with a solution.
-```{r}
-# calculate statistic
-eval_boundary_summary(p40, s40)
-```
-* Calculate the connectivity held within a solution.
-```{r}
-# calculate statistic
-# here we use the raster data for the first feature as an example
-# to parametrize pair-wise connectivity between different planning units
-eval_connectivity_summary(
-  p40, s40, data = connectivity_matrix(sim_pu_raster, sim_features[[1]]))
-```
-
-### _Marxan_ problems
-
-Although users are encouraged to build and tailor conservation planning problems to suit their own needs using the `problem` function, sometimes it just simply easier to use a more familiar formulation.  The `marxan_problem` function is provided as a convenient wrapper for building and solving _Marxan_-style conservation problems. If users already have their conservation planning data formatted for use with _Marxan_, this function can also read _Marxan_ data files and solve the _Marxan_-style problems using exact algorithm solvers. __Please note that problems built using the `marxan_problem` function are still solved the same way as a problem initialized using the `problem` function, and therefore still require the installation of one of the solver packages.__
-
-Here is a short example showing how the `marxan_problem` function can be used to read _Marxan_ input files and the `solve` function can be used to solve the problem.
 
-```{r, results = "hide"}
-# set file path for Marxan input file
-minput <- system.file("extdata/input.dat", package = "prioritizr")
-
-# read Marxan input file
-mp <- marxan_problem(minput)
+# import data
+## planning unit data
+pu_path <- system.file("extdata/input/pu.dat", package = "prioritizr")
+pu_data <- read.csv(pu_path, header = TRUE, stringsAsFactors = FALSE)
+print(head(pu_data))
 
-# print problem
-print(mp)
+## feature data
+spec_path <- system.file("extdata/input/spec.dat", package = "prioritizr")
+spec_data <- read.csv(spec_path, header = TRUE, stringsAsFactors = FALSE)
+print(head(spec_data))
 
-# solve the problem
-ms <- solve(mp)
+## amount of each feature within each planning unit data
+puvspr_path <- system.file("extdata/input/puvspr.dat", package = "prioritizr")
+puvspr_data <- read.csv(puvspr_path, header = TRUE, stringsAsFactors = FALSE)
+print(head(puvspr_data))
 
-# since the Marxan data was in a tabular format, the solution is also returned
-# in a tabular format, so we will print the first six rows of the table
-# containing the solution
-head(ms)
+## boundary data
+bound_path <- system.file("extdata/input/bound.dat", package = "prioritizr")
+bound_data <- read.table(bound_path, header = TRUE, stringsAsFactors = FALSE)
+print(head(bound_data))
 ```
 
-Alternatively, rather then using a _Marxan_ input file to construct the problem, we can manually read in the _Marxan_ data files and input these to the `marxan_problem` function.
+After importing the data, we can now generate a prioritization based on the _Marxan_ problem formulation (using the `marxan_problem()` function). **Please note that this function does not generate prioritizations using _Marxan_.** Instead, it uses the data to create an optimization problem formulation similar to _Marxan_ -- using hard constraints instead of soft constraints -- and uses an exact algorithm solver to generate a prioritization.
 
 ```{r}
-# load data
-pu <- system.file("extdata/input/pu.dat", package = "prioritizr") %>%
-      read.table(sep = ",", header = TRUE)
-features <- system.file("extdata/input/spec.dat", package = "prioritizr") %>%
-            read.table(sep = ",", header = TRUE)
-bound <- system.file("extdata/input/bound.dat", package = "prioritizr") %>%
-         read.table(sep = "\t", header = TRUE)
-rij <- system.file("extdata/input/puvspr.dat", package = "prioritizr") %>%
-       read.table(sep = ",", header = TRUE)
-
-# build Marxan problem using data.frame objects
-mp2 <- marxan_problem(x = pu, spec = features, puvspr = rij, bound = bound,
-                      blm = 0)
+# create problem
+p2 <- marxan_problem(pu_data, spec_data, puvspr_data, bound_data,
+                     blm = 0.0005)
 
 # print problem
-print(mp2)
-```
-
-### Importance (irreplaceability)
-
-Conservation plans can take a long time to implement. Since funding availability and habitat quality can decline over time, it is critical that the most important places in a prioritization are scheduled for protection as early as possible. For instance, some planning units in a solution might contain many rare species which do not occur in any other planning units. Alternatively, some planning units might offer an especially high return on investment that reduces costs considerably. As a consequence, conservation planners often need information on which planning units selected in a prioritization are most important to the overall success of the prioritization. To achieve this, conservation planners can use importance (irreplaceability) scores for each planning unit selected in a solution.
-
-The _prioritizr R_ package offers multiple methods for assessing importance. These includes scores calculated based on replacement costs [`eval_replacement_importance()`; @r31], Ferrier _et al._ [-@r34] (`eval_ferrier_importance()`), and rarity weighted richness scores [`eval_rare_richness_importance()`; @r33]. The replacement cost scores quantify the change in the objective function (e.g. additional costs required to meet feature targets) of the optimal solution if a given planning unit in a solution cannot be acquired. They can (i) account for the cost of different planning units, (ii) account for multiple management zones, (iii) apply to any objective function, and (iv) identify truly irreplaceable planning units (denoted with infinite values). The Ferrier scores quantify the importance of planning units for meeting feature targets. They can only be applied to conservation problems with a minimum set objective and a single zone (i.e. the classic _Marxan_-type problem). Furthermore---unlike the replacement cost scores---the Ferrier scores provide a score for each feature within each planning unit, providing insight into why certain planning units are more important than other planning units. The rarity weighted richness scores are simply a measure of biological diversity. They do not account for planning costs, multiple management zones, objective functions, or feature targets (or weightings). They merely describe the spatial patterns of biodiversity, and do not account for many of the factors needed to quantify the importance of a planning unit for achieving conservation goals.
-
-We recommend using replacement cost scores for small and moderate sized problems (e.g. less than 30,000 planning units) when it is feasible to do so. It can take a very long time to compute replacement cost scores, and so it is simply not feasible to compute these scores for particularly large problems. For moderate and large sized problems (e.g. more than 30,000 planning units),  we recommend using the Ferrier method. This is because it explicitly accounts for representation targets, unlike the rarity weighted richness scores.
-
-Below we will generate a solution, and then calculate importance scores for the planning units selected in the solution using the three different methods.
-
-```{r, fig.height = h, fig.width = w}
-# formulate the problem
-p41 <- problem(sim_pu_raster, sim_features) %>%
-       add_min_set_objective() %>%
-       add_relative_targets(0.1) %>%
-       add_binary_decisions()
-
-# solve the problem
-s41 <- solve(p41)
-
-# plot solution
-plot(s41, col = c("grey90", "darkgreen"), main = "Solution",
-     xlim = c(-0.1, 1.1), ylim = c(-0.1, 1.1))
-
-# calculate replacement cost scores and make the solver quiet
-rc41 <- p41 %>%
-        add_default_solver(gap = 0, verbose = FALSE) %>%
-        eval_replacement_importance(s41)
-
-# plot replacement cost scores
-plot(rc41, main = "replacement cost")
-```
-
-```{r, fig.height = h, fig.width = w}
-# calculate Ferrier scores and extract total score
-fs41 <- eval_ferrier_importance(p40, s40)[["total"]]
-
-# plot Ferrier scores
-plot(fs41, main = "Ferrier scores")
-```
+print(p2)
 
-```{r, fig.height = h, fig.width = w}
-# calculate rarity weighted richness scores
-rwr41 <- eval_rare_richness_importance(p40, s40)
+# solve problem
+s2 <- solve(p2)
 
-# plot replacement cost scores
-plot(rwr41, main = "rarity weighted richness")
+# print first six rows of solution object
+print(head(s2))
 ```
 
-Although rarity weighted richness scores can approximate scores derived from the other two methods in certain conservation planning exercises, we can see that the rarity weighted richness scores provide completely different results in this case.
-
 ## Conclusion
 
-Hopefully, this vignette has provided an informative introduction to the _prioritizr R_ package. For more worked examples using the _prioritizr R_ package, check out the [Tasmania](tasmania.html) and [Salt Spring Island](saltspring.html) vignettes. Perhaps, one of the best ways to learn a new piece of software is to just try it out. Test it, try breaking it, make mistakes, and learn from them. We would recommend trying to build conservation planning problems that resemble those you face in your own work---but using the built-in example data sets. This way you can quickly verify that the problems you build actually mean what you think they mean. For instance, you can try playing around with the targets and see what effect they have on the solutions, or try playing around with penalties and see what effect they have on the solutions. Finally, if you have any questions about using the _prioritizr R_ package or suggestions for it, please file an issue on the package's online coding repository (https://github.com/prioritizr/prioritizr/issues).
+This tutorial shows how the _prioritizr R_ package can be used to build a conservation problem, generate a prioritization, and evaluate it. Although we explored just a few functions, the package provides many different functions so that you can build and custom-tailor conservation planning problems to suit your needs. To learn more about the package, please see the package vignettes for [an overview of the package](package_overview.html), [instructions for installing the _Gurobi_ optimization suite](gurobi_installation_guide.html), [benchmarks comparing the performance of different solvers](solver_benchmarks.html), and [a record of publications that have cited the package](publication_record.html). In addition to this tutorial, the package also provides tutorials on [incorporating connectivity into prioritizations](connectivity_tutorial.html), [calibrating trade-offs between different criteria](calibrating_trade-offs.html) (e.g., total cost and spatial fragmentation), and [creating prioritizations that have multiple management zones or management actions](management_zones_tutorial.html).
 
 ## References
diff --git a/vignettes/publication_record.Rmd b/vignettes/publication_record.Rmd
index 7768b00fc..f7ca8b88d 100644
--- a/vignettes/publication_record.Rmd
+++ b/vignettes/publication_record.Rmd
@@ -1,5 +1,5 @@
 ---
-title: "Publication Record"
+title: "Publication record"
 output:
   rmarkdown::html_vignette:
     toc: true
@@ -8,7 +8,7 @@ output:
 fontsize: 11pt
 documentclass: article
 vignette: >
-  %\VignetteIndexEntry{Publication Record}
+  %\VignetteIndexEntry{Publication record}
   %\VignetteEngine{knitr::rmarkdown_notangle}
 ---
 
diff --git a/vignettes/references.bib b/vignettes/references.bib
index cf3f73fd2..8c2a1a1d2 100644
--- a/vignettes/references.bib
+++ b/vignettes/references.bib
@@ -357,3 +357,316 @@ @article{r34
   pages={303--325},
   year={2000},
 }
+
+@article{r35,
+  year = {2014},
+  volume = {51},
+  number = {6},
+  pages = {1504--1514},
+  author = {Linda R. Harris and Matthew E. Watts and Ronel Nel and David S. Schoeman and Hugh P. Possingham},
+  editor = {Paul Armsworth},
+  title = {Using multivariate statistics to explore trade-offs among spatial planning scenarios},
+  journal = {Journal of Applied Ecology}
+}
+
+@article{r36,
+  year = {1991},
+  volume = {55},
+  number = {3},
+  pages = {235--254},
+  author = {R.I. Vane-Wright and C.J. Humphries and P.H. Williams},
+  title = {What to protect? --- {Systematics} and the agony of choice},
+  journal = {Biological Conservation}
+}
+
+@article{r37,
+  year = {2013},
+  pages = {324--332},
+  author = {Carissa J. Klein and Vivitskaia J. Tulloch and Benjamin S. Halpern and Kimberly A. Selkoe and Matthew E. Watts and Charles Steinback and Astrid Scholz and Hugh P. Possingham},
+  title = {Tradeoffs in marine reserve design: habitat condition,  representation, and socioeconomic costs},
+  journal = {Conservation Letters}
+}
+
+@article{r38,
+  title={Incorporating asymmetric connectivity into spatial decision making for conservation},
+  author={Beger, Maria and Linke, Simon and Watts, Matt and Game, Eddie and Treml, Eric and Ball, Ian and Possingham, Hugh P},
+  journal={Conservation Letters},
+  volume={3},
+  number={5},
+  pages={359--368},
+  year={2010},
+}
+
+@article{r39,
+  title={Catchment zoning to enhance co-benefits and minimize trade-offs between ecosystem services and freshwater biodiversity conservation},
+  author={Hermoso, Virgilio and Cattarino, Lorenzo and Linke, Simon and Kennard, Mark J},
+  journal={Aquatic Conservation: Marine and Freshwater Ecosystems},
+  volume={28},
+  number={4},
+  pages={1004--1014},
+  year={2018},
+  publisher={Wiley Online Library}
+}
+
+@article{r40,
+  title={Freshwater conservation planning in the context of nature needs half and protected area dynamism in Bhutan},
+  author={Dorji, Tshering and Linke, Simon and Sheldon, Fran},
+  journal={Biological Conservation},
+  volume={251},
+  pages={108785},
+  year={2020},
+  publisher={Elsevier}
+}
+
+@article{r41,
+  title={Addressing longitudinal connectivity in the systematic conservation planning of fresh waters},
+  author={Hermoso, V and Linke, S and Prenda, J and Possingham, H P},
+  journal={Freshwater Biology},
+  volume={56},
+  number={1},
+  pages={57--70},
+  year={2011},
+  publisher={Wiley Online Library}
+}
+
+@article{r42,
+  year = {2005},
+  volume = {10},
+  number = {3},
+  pages = {203--213},
+  author = {Romola R. Stewart and Hugh P. Possingham},
+  title = {Efficiency, costs and trade-offs in marine reserve system design},
+  journal = {Environmental Modeling and Assessment}
+}
+
+@article{r43,
+  year = {2012},
+  volume = {18},
+  number = {5},
+  pages = {448--458},
+  author = {Virgilio Hermoso and Mark J. Kennard and Simon Linke},
+  title = {Integrating multidirectional connectivity requirements in systematic conservation planning for freshwater systems},
+  journal = {Diversity and Distributions}
+}
+
+@article{r44,
+  title={{GIS}-based multiple-criteria decision analysis},
+  author={Greene, Randal and Devillers, Rodolphe and Luther, Joan E and Eddy, Brian G},
+  journal={Geography Compass},
+  volume={5},
+  number={6},
+  pages={412--432},
+  year={2011},
+  publisher={Wiley Online Library}
+}
+
+@book{r45,
+  title={{Marxan Good Practices Handbook}},
+  author={Ardron, Jeff A and Possingham, Hugh P and Klein, Carissa J},
+  publisher={Pacific Marine Analysis and Research Association, Vancouver},
+  pages={149},
+  notes={Version 2},
+  year={2010},
+  address={Victoria, BC}
+}
+
+@book{r46,
+  title={{Multiple Attribute Decision Making: Methods and Applications}},
+  author={Hwang, C L and Yoon, K G},
+  year={1981},
+  publisher={Springer-Verlag},
+  address={New York, NY}
+}
+
+@article{r47,
+  year = {2020},
+  volume = {3},
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+  pages = {371--382},
+  author = {Brooke A. Williams and Oscar Venter and James R. Allan and Scott C. Atkinson and Jose A. Rehbein and Michelle Ward and Moreno Di Marco and Hedley S. Grantham and Jamison Ervin and Scott J. Goetz and Andrew J. Hansen and Patrick Jantz and Rajeev Pillay and Susana Rodr{\'{\i}}guez-Buritic{\'{a}} and Christina Supples and Anne L.S. Virnig and James E.M. Watson},
+  title = {Change in Terrestrial Human Footprint Drives Continued Loss of Intact Ecosystems},
+  journal = {One Earth}
+}
+
+@article{r48,
+  year = {2019},
+  volume = {13},
+  number = {2},
+  author = {Hawthorne L. Beyer and Oscar Venter and Hedley S. Grantham and James E.M. Watson},
+  title = {Substantial losses in ecoregion intactness highlight urgency of globally coordinated action},
+  journal = {Conservation Letters}
+}
+
+@article{r49,
+  title={Generating multiobjective trade-offs: An algorithm for bicriterion problems},
+  author={Cohon, Jared L and Church, Richard L and Sheer, Daniel P},
+  journal={Water Resources Research},
+  volume={15},
+  number={5},
+  pages={1001--1010},
+  year={1979},
+  publisher={Wiley Online Library}
+}
+
+@article{r50,
+  year = {2005},
+  volume = {10},
+  number = {3},
+  pages = {215--228},
+  author = {Douglas T. Fischer and Richard L. Church},
+  title = {The {SITES} reserve selection system: A critical review},
+  journal = {Environmental Modeling and Assessment}
+}
+
+@article{r51,
+  title={Effective conservation requires clear objectives and prioritizing actions, not places or species},
+  author={Brown, Christopher J and Bode, Michael and Venter, Oscar and Barnes, Megan D and McGowan, Jennifer and Runge, Claire A and Watson, James E M and Possingham, Hugh P},
+  journal={Proceedings of the National Academy of Sciences},
+  volume={112},
+  number={32},
+  pages={E4342},
+  year={2015},
+}
+
+@article{r52,
+  title={Operationalizing ecological connectivity in spatial conservation planning with {Marxan Connect}},
+  author={Daigle, R{\'e}mi M and Metaxas, Anna and Balbar, Arieanna C and McGowan, Jennifer and Treml, Eric A and Kuempel, Caitlin D and Possingham, Hugh P and Beger, Maria},
+  journal={Methods in Ecology and Evolution},
+  volume={11},
+  number={4},
+  pages={570--579},
+  year={2020},
+  publisher={Wiley Online Library}
+}
+
+@article{r53,
+  doi = {10.1016/j.xpro.2021.100882},
+  url = {https://doi.org/10.1016/j.xpro.2021.100882},
+  year = {2021},
+  month = dec,
+  publisher = {Elsevier {BV}},
+  volume = {2},
+  number = {4},
+  pages = {100882},
+  author = {Kathleen Anne Carroll},
+  title = {Systematic prioritization protocol applied to wolverine habitat connectivity},
+  journal = {{STAR} Protocols}
+}
+
+@article{r54,
+  year = {2020},
+  volume = {57},
+  number = {11},
+  pages = {2159--2169},
+  author = {Jeffrey O. Hanson and Adam Marques and Ana Ver{\'{\i}}ssimo and Miguel Camacho-Sanchez and Guillermo Velo-Ant{\'{o}}n and {\'{I}}{\~{n}}igo Mart{\'{\i}}nez-Solano and Silvia B. Carvalho},
+  title = {Conservation planning for adaptive and neutral evolutionary processes},
+  journal = {Journal of Applied Ecology}
+}
+
+@article{r55,
+  title={Incorporating connectivity into reserve selection procedures},
+  author={Briers, Robert A},
+  journal={Biological Conservation},
+  volume={103},
+  number={1},
+  pages={77--83},
+  year={2002},
+  publisher={Elsevier}
+}
+
+@article{r56,
+  title={The current application of ecological connectivity in the design of marine protected areas},
+  author={Balbar, Arieanna C and Metaxas, Anna},
+  journal={Global Ecology and Conservation},
+  volume={17},
+  pages={e00569},
+  year={2019},
+  publisher={Elsevier}
+}
+
+@article{r57,
+ author = {Hayri {\"O}nal and Robert A. Briers},
+ journal = {Operations Research},
+ number = {2},
+ pages = {379-388},
+ title = {Optimal selection of a connected reserve network},
+ volume = {54},
+ year = {2006}
+}
+
+@article{r58,
+  title={Using individual-based movement information to identify spatial conservation priorities for mobile species},
+  author={Dwyer, Ross G and Campbell, Hamish A and Pillans, Richard D and Watts, Matthew E and Lyon, Barry J and Guru, Siddeswara M and Dinh, Minh N and Possingham, Hugh P and Franklin, Craig E},
+  journal={Conservation Biology},
+  volume={33},
+  number={6},
+  pages={1426--1437},
+  year={2019},
+  publisher={Wiley Online Library}
+}
+
+@article{r59,
+  title={Landscape-scale conservation design across biotic realms: sequential integration of aquatic and terrestrial landscapes},
+  author={Leonard, Paul B and Baldwin, Robert F and Hanks, R Daniel},
+  journal={Scientific Reports},
+  volume={7},
+  number={1},
+  pages={1--12},
+  year={2017},
+  publisher={Nature Publishing Group}
+}
+
+@article{r60,
+  title={Habitat fragmentation reduces genetic diversity and connectivity among toad populations in the Brazilian Atlantic Coastal Forest},
+  author={Dixo, Marianna and Metzger, Jean Paul and Morgante, Jo{\~a}o S and Zamudio, Kelly R},
+  journal={Biological Conservation},
+  volume={142},
+  number={8},
+  pages={1560--1569},
+  year={2009},
+  publisher={Elsevier}
+}
+
+@article{r61,
+  title={Habitat connectivity improves reserve performance},
+  author={Olds, Andrew D and Connolly, Rod M and Pitt, Kylie A and Maxwell, Paul S},
+  journal={Conservation Letters},
+  volume={5},
+  number={1},
+  pages={56--63},
+  year={2012},
+  publisher={Wiley Online Library}
+}
+
+@article{r62,
+  title={Climate change, connectivity and conservation decision making: back to basics},
+  author={Hodgson, Jenny A and Thomas, Chris D and Wintle, Brendan A and Moilanen, Atte},
+  journal={Journal of Applied Ecology},
+  volume={46},
+  number={5},
+  pages={964--969},
+  year={2009},
+  publisher={Wiley Online Library}
+}
+
+@article{r63,
+  title={Linking like with like: optimising connectivity between environmentally-similar habitats},
+  author={Alagador, Diogo and Trivino, Maria and Cerdeira, Jorge Orestes and Br{\'a}s, Raul and Cabeza, Mar and Ara{\'u}jo, Miguel Bastos},
+  journal={Landscape Ecology},
+  volume={27},
+  number={2},
+  pages={291--301},
+  year={2012},
+  publisher={Springer}
+}
+
+@article{r64,
+  title={Species specific connectivity in reserve-network design using graphs},
+  author={Cerdeira, J Orestes and Pinto, Leonor S and Cabeza, Mar and Gaston, Kevin J},
+  journal={Biological Conservation},
+  volume={143},
+  number={2},
+  pages={408--415},
+  year={2010},
+  publisher={Elsevier}
+}
diff --git a/vignettes/saltspring.Rmd b/vignettes/saltspring.Rmd
deleted file mode 100644
index 91284e3d2..000000000
--- a/vignettes/saltspring.Rmd
+++ /dev/null
@@ -1,212 +0,0 @@
----
-title: "Salt Spring Island Tutorial"
-output:
-  rmarkdown::html_vignette:
-    toc: true
-    fig_caption: true
-    self_contained: yes
-fontsize: 11pt
-documentclass: article
-bibliography: references.bib
-csl: reference-style.csl
-vignette: >
-  %\VignetteIndexEntry{Salt Spring Island Tutorial}
-  %\VignetteEngine{knitr::rmarkdown_notangle}
----
-
-```{r, include = FALSE}
-h <- 3.5
-w <- 3.5
-is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_",
-             "_R_CHECK_LICENSE_") %in% names(Sys.getenv()))
-knitr::opts_chunk$set(fig.align = "center", eval = !is_check)
-```
-
-## Introduction
-
-This aim of this tutorial is to show how raster data can used to build conservation problems with the _prioritizr R_ package. The data used here is a subset of a much larger dataset for the Georgia Basin obtained as part of an online _Marxan_-based planning tool created for the Coastal Douglas-fir Conservation Partnership [CDFCP; @r29]. For simplicity, we focus only on Salt Spring Island, British Columbia. Salt Spring Island is central to the region and supports a diverse and globally unique mix of dry forest and savanna habitats. Today, these habitats are critically threatened due to land conversion, invasive species, and altered disturbance regimes. Known broadly as the Georgia Depression-Puget Lowlands, this region includes threatened Coastal Douglas-fir forest and Oak-Savannah habitats, also referred to as Garry oak ecosystems. Please note that this tutorial uses data from the _prioritizrdata R_ package, so ensure that it is installed before trying out the code yourself. For more information on the dataset refer to the [Marxan tool portal](https://arcese.forestry.ubc.ca/marxan-tool/) and the [tool tutorial](https://peter-arcese-lab.sites.olt.ubc.ca/files/2016/09/CDFCP_tutorial_2017_05.pdf).
-
-
      
-
-![_Extent of Coastal Douglas-fir Conservation Partnership Tool area and location of Salt Spring Island_](figures/map.jpg)
-
-
      
-
-## Exploring the data
-
-This dataset contains two items. First, a single-band raster planning unit layer where each one hectare pixel represents a planning unit and contains its corresponding cost [@r28]. Second, a raster stack containing ecological community feature data. Field and remote sensed data were used to calculate the probability of occurrence of five key ecological communities found on Salt Spring island. Each layer in the stack represents a different community type. In order these are; Old Forest, Savannah, Wetland, Shrub, and a layer representing the inverse probability of occurrence of human commensal species. For a given layer, the cell value indicates the composite probability of encountering the suite of bird species most commonly associated with that community type.
-
-First, load the required packages and the data.
-
-```{r, message = FALSE}
-# load packages
-library(prioritizrdata)
-library(prioritizr)
-
-# load planning unit data
-data(salt_pu)
-
-# load conservation feature data
-data(salt_features)
-```
-
-Let's have a look at the planning unit data. Note that we log-transformed the raster to better visualize the variation in planning unit cost.
-
-```{r, fig.width = w, fig.height = h}
-# print planning unit data
-print(salt_pu)
-
-# plot histogram of the planning unit costs
-hist(values(salt_pu), main = "Distribution of costs",
-     xlab = "Planning unit costs")
-```
-
-```{r, fig.width = w, fig.height = h}
-# plot map showing the planning units costs on a log-scale
-plot(log(salt_pu), main = "Planning unit costs (log)")
-```
-
-Next, let's look at the feature data.
-
-```{r, fig.width = 4.5, fig.height = 4.5}
-# print features
-print(salt_features)
-
-# plot map showing the distribution of the features
-plot(salt_features, main = names(salt_features))
-```
-
-## Formulating the Problem
-
-In this tutorial, we will only cover a few of the different ways that conservation planning problems can be formulated. The examples used here are provided to highlight how different parameters can substantially---or only slightly---alter solutions. Here, we use the minimum set objective to fulfill all targets and constraints for the smallest cost. This objective is similar to that used in the _Marxan_ decision support tool. To keep this simple, we will set biodiversity targets at 17 % to reflect the [Aichi Biodiversity Target 11](https://www.cbd.int/sp/targets/). Because properties on Salt Spring Island can either be acquired in their entirety or not at all, we leave the decision framework as the default; binary decision making. This means that planning units are either selected in the solution or not selected in the solution---planning units cannot be partially acquired.
-
-Now we will formulate the conservation planning problem.
-
-```{r}
-# create problem
-p1 <- problem(salt_pu, salt_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_binary_decisions() %>%
-      add_default_solver()
-
-# print problem
-print(p1)
-```
-
-Note that the `%>%` notation is used to attach the objectives, targets, and decisions to the problem. Since binary-type decisions are the default decision-type, we don't have to explicitly specify the decision-type, but we specify it here for clarity.
-
-## Solving the problem
-
-The _prioritizr R_ package supports three different integer linear programming solvers: _gurobi_ (via the _gurobi_ package), _IBM CPLEX_ (via the _cplexAPI_ package), _SYMPHONY_ (via the _Rsymphony_ and _lpsymphony_ packages) and _CBC_ (via the _rcbc_ package). There are costs and benefits associated with each of these solvers, but the solver itself should have little impact on the actual solution returned (though certain solvers may take longer to return solutions than others).
-
-First, remember that the solvers must be installed. You can check if these packages are installed by running the code below. Some of these solvers are a bit complicated to install. For instance, the _gurobi_ package is distributed with the [_Gurobi_ commercial software suite](https://www.gurobi.com/) and is not available on the Comprehensive R Archive Network (CRAN). For more information on installing the _gurobi_ package, please refer to the [_Gurobi Installation Guide_](gurobi_installation.html) for more information on installing the _gurobi R_ package. Additionally, the _rcbc_ package is not available on CRAN, and must be installed from GitHub ([please refer to its documentation for installation instructions](https://dirkschumacher.github.io/rcbc/). Furthermore, although the _Rcplex_ package is available on CRAN, it cannot be successfully installed unless the [IBM CPLEX software](https://www.ibm.com/analytics/cplex-optimizer) has [already installed on your system](https://github.com/cran/cplexAPI/blob/master/inst/INSTALL).
-
-```{r, eval = FALSE}
-print(require(gurobi))
-print(require(cplexAPI))
-print(require(Rsymphony))
-print(require(lpsymphony))
-print(require(rcbc))
-```
-
-Now we will try solving the problem using the different solvers (see [`?solve`](https://prioritizr.net/reference/solve.html) for more information). We will also experiment with limiting the maximum amount of time that can be spent looking for each solution when solving the problem (using the `time_limit` parameter), and see how this alters the solutions.
-
-```{r, message = FALSE, results = "hide"}
-titles <- c() # create vector to store plot titles
-s1 <- stack()  # create empty stack to store solutions
-
-# create new problem object with added solver
-if (require("Rsymphony")) {
-  titles <- c(titles, "Rsymphony (5s)")
-  p2 <- p1 %>% add_rsymphony_solver(time_limit = 5)
-  s1 <- addLayer(s1, solve(p2))
-}
-
-if (require("Rsymphony")) {
-  titles <- c(titles, "Rsymphony (10s)")
-  p3 <- p1 %>% add_rsymphony_solver(time_limit = 10)
-  s1 <- addLayer(s1, solve(p3))
-}
-
-if (require("gurobi")) {
-  titles <- c(titles, "Gurobi (5s)")
-  p4 <- p1 %>% add_gurobi_solver(time_limit = 5)
-  s1 <- addLayer(s1, solve(p4))
-}
-
-if (require("cplexAPI")) {
-  titles <- c(titles, "IBM CPLEX (5s)")
-  p5 <- p1 %>% add_cplex_solver(time_limit = 5)
-  s1 <- addLayer(s1, solve(p5))
-}
-
-if (require("lpsymphony")) {
-  titles <- c(titles, "lpsymphony (10s)")
-  p6 <- p1 %>% add_lpsymphony_solver(time_limit = 10)
-  s1 <- addLayer(s1, solve(p6))
-}
-
-if (require("rcbc")) {
-  titles <- c(titles, "CBC (10s)")
-  p7 <- p1 %>% add_cbc_solver(time_limit = 10)
-  s1 <- addLayer(s1, solve(p7))
-}
-```
-
-Now let's visualize the solutions.
-
-```{r, fig.height = 5.5, fig.width = 5}
-plot(s1, main = titles, breaks = c(0, 0.5, 1),  col = c("grey70", "darkgreen"))
-```
-
-We can see that all of the solutions are very similar. Therefore it would appear that for this particular problem, the solution is not highly sensitive to solver choice. For larger and more complex problems, however, we would expect the solution from _Gurobi_ to be far superior when setting time limits. At a glance, it also appears that the time limit settings did not largely impact the solutions (5 seconds vs. 10 seconds), but a more rigorous analysis is needed to investigate this.
-
-## Adding connectivity
-
-Isolated and fragmented populations are often more vulnerable to extinction. As a consequence, landscape connectivity is a key focus of many conservation planning exercises. There are a number of methods that can be used to increase connectivity in prioritizations. These methods typically involve adding constraints to a problem to ensure that solutions exhibit a specific property (e.g. selected planning units that form a contiguous reserve), or adding penalties to a problem to penalize solutions that exhibit specific properties (e.g. high levels of fragmentation). Here we will explore a couple different strategies for increasing connectivity in solutions. For brevity, we will use default solver which is automatically added to a problem if a solver is not manually specified.
-
-```{r}
-# basic problem formulation
-p6 <- problem(salt_pu, salt_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_binary_decisions() %>%
-      add_default_solver()
-
-# print problem
-print(p6)
-```
-
-```{r, results = "hide"}
-titles2 <- c() # create vector to store plot titles
-s2 <- stack()  # create empty stack to store solutions
-
-# no connectivity requirement
-titles2 <- c(titles2, "No connectivity")
-s2 <- addLayer(s2, solve(p6))
-
-# require at least two for each selected planning unit
-titles2 <- c(titles2, "Neighbor constraints (two)")
-p7 <- p6 %>% add_neighbor_constraints(2)
-s2 <- addLayer(s2, solve(p7))
-
-# impose small penalty for fragmented solutions
-titles2 <- c(titles2, "Boundary penalty (low)")
-p8 <- p6 %>% add_boundary_penalties(0.0005, 0.5)
-s2 <- addLayer(s2, solve(p8))
-
-# impose high penalty for fragmented solutions
-titles2 <- c(titles2, "Boundary penalty (high)")
-p9 <- p6 %>% add_boundary_penalties(0.05, 0.5)
-s2 <- addLayer(s2, solve(p9))
-```
-
-```{r, fig.height = 5.5, fig.width = 5}
-# plot solutions
-plot(s2, main = titles2, breaks = c(0, 0.5, 1),  col = c("grey70", "darkgreen"))
-```
-
-Here we can see that adding the constraints and penalties to the problem has a small, but noticeable effect on the solutions. We would expect to see larger difference between the solutions for problems that contain more than five conservation features. You may also wish to explore the `add_connectivity_penalties` and `add_feature_contiguity_constraints` functions. These functions use additional data on landscape resistance to provide a more accurate parametrization of connectivity and, in turn, deliver more effective solutions.
-
-## References
diff --git a/vignettes/solver_benchmark.Rmd b/vignettes/solver_benchmarks.Rmd
similarity index 77%
rename from vignettes/solver_benchmark.Rmd
rename to vignettes/solver_benchmarks.Rmd
index a91dafadc..f0c6cd3e3 100644
--- a/vignettes/solver_benchmark.Rmd
+++ b/vignettes/solver_benchmarks.Rmd
@@ -1,5 +1,5 @@
 ---
-title: "Solver Benchmarks"
+title: "Solver benchmarks"
 output:
   rmarkdown::html_vignette:
     toc: true
@@ -10,7 +10,7 @@ documentclass: article
 bibliography: references.bib
 csl: reference-style.csl
 vignette: >
-  %\VignetteIndexEntry{Solver Benchmarks}
+  %\VignetteIndexEntry{Solver benchmarks}
   %\VignetteEngine{knitr::rmarkdown_notangle}
 ---
 
@@ -35,17 +35,17 @@ boundary_penalty_values <- list(
 devtools::load_all()
 ```
 
-# Introduction
+## Introduction
 
-The _prioritizr R_ package supports a variety of optimization solvers for generating prioritizations. Specifically, the following functions can be used: [`add_gurobi_solver()`](https://prioritizr.net/reference/add_gurobi_solver.html) (interfaces with the [_Gurobi_ software](https://www.gurobi.com/)), [`add_cplex_solver()`](https://prioritizr.net/reference/add_cplex_solver.html) (interfaces with the [_IBM CPLEX_ software](https://www.ibm.com/analytics/cplex-optimizer)), [`add_cbc_solver()`](https://prioritizr.net/reference/add_cbc_solver.html) (interfaces with the [_CBC_ software](https://projects.coin-or.org/Cbc) using the [_rcbc R_ package](https://dirkschumacher.github.io/rcbc/)), [`add_rsymphony_solver()`](https://prioritizr.net/reference/add_rsymphony_solver.html) (interfaces with the [_SYMPHONY_ software](https://projects.coin-or.org/SYMPHONY) using the [_Rsymphony R_ package](https://CRAN.R-project.org/package=Rsymphony)), and the [`add_lpsymphony_solver()`](https://prioritizr.net/reference/add_lsymphony_solver.html) function (interfaces with the [_SYMPHONY_ software](https://projects.coin-or.org/SYMPHONY) using the [_lpsymphony R_ package](https://www.bioconductor.org/packages/release/bioc/html/lpsymphony.html)). Broadly speaking, _IBM CPLEX_ and _Gurobi_ tend to be the fastest among the supported solvers. Although they are both commercial software, special academic licenses are available at no cost.
+The _prioritizr R_ package supports a variety of optimization solvers for generating prioritizations. Specifically, the following functions can be used: `add_gurobi_solver()` (interfaces with the [_Gurobi_ software](https://www.gurobi.com/)), `add_cplex_solver()` (interfaces with the [_IBM CPLEX_ software](https://www.ibm.com/analytics/cplex-optimizer)), `add_cbc_solver()` (interfaces with the [_CBC_ software](https://projects.coin-or.org/Cbc) using the [_rcbc R_ package](https://dirkschumacher.github.io/rcbc/)), `add_rsymphony_solver()` (interfaces with the [_SYMPHONY_ software](https://projects.coin-or.org/SYMPHONY) using the [_Rsymphony R_ package](https://CRAN.R-project.org/package=Rsymphony)), and the `add_lpsymphony_solver()` function (interfaces with the [_SYMPHONY_ software](https://projects.coin-or.org/SYMPHONY) using the [_lpsymphony R_ package](https://www.bioconductor.org/packages/release/bioc/html/lpsymphony.html)). Broadly speaking, _IBM CPLEX_ and _Gurobi_ tend to be the fastest among the supported solvers. Although they are both commercial software, special academic licenses are available at no cost.
 
-In this vignette, we will explore the performance of different solvers. Using a benchmark analysis, we will see how well they can tackle problems of varying size (e.g. number of planning units) and complexity (e.g. adding boundary length penalties to reduce spatial fragmentation). Since users working in governmental and non-governmental organizations may need to purchase licenses for _IBM CPLEX_ or _Gurobi_ to use them, this vignette also aims to provide insight into whether the potential benefits of purchasing such licenses is worthwhile. Indeed -- depending on the size and complexity of a given conservation planning problem -- solvers based on open source software may only take slightly longer than commercial solvers.
+In this vignette, we will explore the performance of different solvers. Using a benchmark analysis, we will see how well they can tackle problems of varying size (e.g., number of planning units) and complexity (e.g., adding boundary length penalties to reduce spatial fragmentation). Since users working in governmental and non-governmental organizations may need to purchase licenses for _IBM CPLEX_ or _Gurobi_ to use them, this vignette also aims to provide insight into whether the potential benefits of purchasing such licenses is worthwhile. Indeed -- depending on the size and complexity of a given conservation planning problem -- solvers based on open source software may only take slightly longer than commercial solvers.
 
-# Methods
+## Methods
 
-This vignette will report the results of a benchmark analysis. To reduce computational burden, we previously completed the benchmark analysis and [uploaded the results to an online repository](https://github.com/prioritizr/benchmark/releases) ([code available online](https://github.com/prioritizr/benchmark)). This analysis involved generating prioritizations using different solvers and recording how long it took for the solvers to finish. To help understand the factors that influence how long it takes for solvers to generate a prioritization, we examined a suite of conservation planning problems with varying size (i.e. number of planning units), complexity (i.e. varying penalties to reduce spatial fragmentation), and with different objective functions (i.e. [metric used to evaluate competing solutions](https://prioritizr.net/reference/objectives.html)). In this section, we will download the results for the previously completed benchmark analysis and examine the parameters used to conduct it.
+This vignette will report the results of a benchmark analysis. To reduce computational burden, we previously completed the benchmark analysis and [uploaded the results to an online repository](https://github.com/prioritizr/benchmark/releases) ([code available online](https://github.com/prioritizr/benchmark)). This analysis involved generating prioritizations using different solvers and recording how long it took for the solvers to finish. To help understand the factors that influence how long it takes for solvers to generate a prioritization, we examined a suite of conservation planning problems with varying size (i.e., number of planning units), complexity (i.e., varying penalties to reduce spatial fragmentation), and with different objective functions (i.e., [metric used to evaluate competing solutions](https://prioritizr.net/reference/objectives.html)). In this section, we will download the results for the previously completed benchmark analysis and examine the parameters used to conduct it.
 
-## Set up
+### Set up
 
 To start off, we will the load packages used in this vignette.
 
@@ -58,7 +58,7 @@ library(units)
 library(dplyr)
 ```
 
-## Download benchmark results
+### Download benchmark results
 
 Let's download the results of the benchmark analysis. This code will save the results to a temporary folder on your computer. Please note that downloading the results might take several minutes to complete depending on your Internet connection. If you are unable to download the results onto your computer, you can view the graphs shown in this vignette. You only need to run the code in this vignette if you wish to explore certain aspects of the results yourself.
 
@@ -73,7 +73,7 @@ pb_download(
 load(file.path(tempdir(), "results.rda"))
 ```
 
-## Benchmark parameters
+### Benchmark parameters
 
 After downloading the benchmark results, let's have a look at the parameters that were used to conduct it. Note that all benchmark scenarios have 72 features.
 
@@ -82,11 +82,11 @@ After downloading the benchmark results, let's have a look at the parameters tha
 n_planning_units <- unique(benchmark_results$number_of_planning_units)
 print(n_planning_units)
 
-# number of features (e.g. number of different species examined)
+# number of features (e.g., number of different species examined)
 unique(benchmark_results$number_features)
 
 # representation targets,
-# units are proportion of the total amount of each feature (e.g. 0.1 = 10%)
+# units are proportion of the total amount of each feature (e.g., 0.1 = 10%)
 unique(benchmark_results$relative_target)
 
 # number of planning units
@@ -107,7 +107,7 @@ boundary_penalty_values$add_min_set_objective
 ## boundary penalty values for min shortfall objective function
 boundary_penalty_values$add_min_shortfall_objective
 
-# budgets examined for budget-limited objectives (e.g. 0.1 = 10% of total cost)
+# budgets examined for budget-limited objectives (e.g., 0.1 = 10% of total cost)
 ## note that the min set objective function does not use a budget,
 ## and thus it has a NA value
 tibble(objective = unique(benchmark_results$objective),
@@ -115,7 +115,7 @@ tibble(objective = unique(benchmark_results$objective),
 
 ```
 
-## Helper function
+### Helper function
 
 Now we will define a helper function to quickly plot the results from the benchmark analysis. This will be helpful for interpreting the results of the benchmark analysis in the following section.
 
@@ -208,9 +208,9 @@ plot_benchmark <- function(
 }
 ```
 
-# Results
+## Results
 
-We will now inspect the results of the benchmark analysis. The `benchmark_results` object is a table (i.e. `tibble()`) containing information for each benchmark run (e.g. run time), and the `solution_raster_data` object (i.e. `RasterStack`) contains the prioritizations generated for each benchmark run.
+We will now inspect the results of the benchmark analysis. The `benchmark_results` object is a table (i.e., `tibble()`) containing information for each benchmark run (e.g., run time), and the `solution_raster_data` object (i.e., `RasterStack`) contains the prioritizations generated for each benchmark run.
 
 ```{r "preview_results"}
 # preview results
@@ -233,7 +233,7 @@ theme(axis.text.x = element_text(size = 7)) +
 labs(x = "Solver", y = "Run time (hours)")
 ```
 
-## Minimum set results (no boundary penalty)
+### Minimum set results (no boundary penalty)
 
 Now, let's investigate the solver behavior in more detail. Specifically, we will examine the benchmark results generated for the minimum set objective function. This is because the minimum set objective function is the most commonly used objective function in systematic conservation, due to the fact that it is used by the [_Marxan_ decision support software](https://marxansolutions.org/). To begin with, let's examine the results for the smallest and simplest conservation planning problems examined in the benchmark analysis. Here, all prioritizations were generated using problems that involved `r formatC(n_planning_units[1], big.mark = ",")` planning units and did not contain any boundary length penalties. Since all benchmark scenarios have 72 features -- as mentioned earlier -- all of these prioritizations were generated with 72 features. When looking at the results, we can see that all solvers solve the problem in a comparable amount of time across all targets investigated.
 
@@ -244,7 +244,7 @@ plot_benchmark(
   boundary_penalty = 0)
 ```
 
-Next, let's look at the results for a more realistic problem involving `r formatC(n_planning_units[2], big.mark = ",")` planning units and see how the timing of the different solvers used compares. Note that all other factors (e.g. absence of boundary length penalties) are the same as for the previous graph.
+Next, let's look at the results for a more realistic problem involving `r formatC(n_planning_units[2], big.mark = ",")` planning units and see how the timing of the different solvers used compares. Note that all other factors (e.g., absence of boundary length penalties) are the same as for the previous graph.
 
 ```{r "min_set_pu_n_2"}
 plot_benchmark(
@@ -271,7 +271,7 @@ plot_benchmark(
   boundary_penalty = 0)
 ```
 
-To get a better sense of how the faster solvers (i.e. based on _CBC_, _IBM CPLEX_, _Gurobi_) compare for such a large problem, let's take a closer look at these three solvers. Interestingly, we can see that the solver based on the open source _CBC_ software is slightly faster -- by a few minutes -- than the other solvers.
+To get a better sense of how the faster solvers (i.e., based on _CBC_, _IBM CPLEX_, _Gurobi_) compare for such a large problem, let's take a closer look at these three solvers. Interestingly, we can see that the solver based on the open source _CBC_ software is slightly faster -- by a few minutes -- than the other solvers.
 
 ```{r "min_set_pu_n_4_fast_only"}
 plot_benchmark(
@@ -282,9 +282,9 @@ plot_benchmark(
 ```
 
 
-## Minimum set results with low boundary penalty
+### Minimum set results with low boundary penalty
 
-Now let's at the same problem types, but this time with a low boundary length penalty value added to the problem formulation. To start with, we will look at scenarios with a low `boundary_penalty` value (i.e. $`r boundary_penalty_values$add_min_set_objective[2]`$). Let's start again with the smallest problem size we've benchmarked. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units.
+Now let's at the same problem types, but this time with a low boundary length penalty value added to the problem formulation. To start with, we will look at scenarios with a low `boundary_penalty` value (i.e., $`r boundary_penalty_values$add_min_set_objective[2]`$). Let's start again with the smallest problem size we've benchmarked. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units.
 
 ```{r "min_set_pu_n_1_with_low_boundary_penalty"}
 plot_benchmark(
@@ -330,9 +330,9 @@ plot_benchmark(
   solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver"))
 ```
 
-## Minimum set results with high boundary penalty
+### Minimum set results with high boundary penalty
 
-Now let's look at the same problem types, but this time with a high boundary length penalty parameter added to the problem formulation (i.e. $`r boundary_penalty_values$add_min_set_objective[3]`$). Let's start again with the smallest problem size we've benchmarked. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. Although there are some differences between the solvers, they all have very similar run times (i.e. all less than one second).
+Now let's look at the same problem types, but this time with a high boundary length penalty parameter added to the problem formulation (i.e., $`r boundary_penalty_values$add_min_set_objective[3]`$). Let's start again with the smallest problem size we've benchmarked. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. Although there are some differences between the solvers, they all have very similar run times (i.e., all less than one second).
 
 ```{r "min_set_pu_n_1_with_high_boundary_penalty"}
 plot_benchmark(
@@ -378,7 +378,7 @@ plot_benchmark(
   solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver"))
 ```
 
-## Minimize shortfall results (no boundary penalty)
+### Minimize shortfall results (no boundary penalty)
 
 Now, let's investigate the solver behavior for the minimum shortfall objective function. Let's start with the smallest problem size examined. All benchmark scenarios have 72 features. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units. We can see that all solvers solve the problem in a comparable amount of time across all targets investigated.
 
@@ -407,7 +407,7 @@ plot_benchmark(
   boundary_penalty = 0)
 ```
 
-Finally, let's look at timing comparisons for a large problem with `r formatC(n_planning_units[4], big.mark = ",")` planning units. We can see that all the open source solvers (i.e. _CBC_, _Rsymphony_ and _lpsymphony_) take a lot longer than the commercial solvers (i.e. _IBM CPLEX_ and _Guorbi_).
+Finally, let's look at timing comparisons for a large problem with `r formatC(n_planning_units[4], big.mark = ",")` planning units. We can see that all the open source solvers (i.e., _CBC_, _Rsymphony_ and _lpsymphony_) take a lot longer than the commercial solvers (i.e., _IBM CPLEX_ and _Guorbi_).
 
 ```{r "min_short_pu_n_4"}
 plot_benchmark(
@@ -416,9 +416,9 @@ plot_benchmark(
   boundary_penalty = 0)
 ```
 
-## Minimize shortfall results with low boundary penalty
+### Minimize shortfall results with low boundary penalty
 
-Now let's look at the same problem type, but this time with a low `boundary_penalty` parameter added to the problem formulation (i.e. $`r boundary_penalty_values$add_min_shortfall_objective[2]`$). Let's start again with the smallest problem size examined. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units.
+Now let's look at the same problem type, but this time with a low `boundary_penalty` parameter added to the problem formulation (i.e., $`r boundary_penalty_values$add_min_shortfall_objective[2]`$). Let's start again with the smallest problem size examined. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units.
 
 ```{r "min_short_pu_n_1_with_low_boundary_penalty"}
 plot_benchmark(
@@ -454,7 +454,7 @@ plot_benchmark(
   boundary_penalty = boundary_penalty_values$add_min_shortfall_objective[2])
 ```
 
-To get a better sense of how the faster solvers compare (i.e. _CBC_, _IBM CPLEX_, and _Gurobi_), let's take a closer look at these three solvers. We can see that the _CBC_ solver takes a lot longer to generate prioritizations than the _IBM CPLEX_ and _Gurobi_ solvers. This result suggests that _IBM CPLEX_ and _Gurobi_ could be really beneficial for large-scale conservation planning problems with boundary length penalties and the minimum shortfall objective function.
+To get a better sense of how the faster solvers compare (i.e., _CBC_, _IBM CPLEX_, and _Gurobi_), let's take a closer look at these three solvers. We can see that the _CBC_ solver takes a lot longer to generate prioritizations than the _IBM CPLEX_ and _Gurobi_ solvers. This result suggests that _IBM CPLEX_ and _Gurobi_ could be really beneficial for large-scale conservation planning problems with boundary length penalties and the minimum shortfall objective function.
 
 ```{r "min_short_pu_n_4_and_boundary_penalty_and_fast_solvers"}
 plot_benchmark(
@@ -464,7 +464,7 @@ plot_benchmark(
   solver = c("add_cbc_solver", "add_cplex_solver", "add_gurobi_solver"))
 ```
 
-## Minimize shortfall results with high boundary penalty
+### Minimize shortfall results with high boundary penalty
 
 Now let's look at the same problem types, but this time with a higher `boundary_penalty` parameter added to the problem formulation ($`r boundary_penalty_values$add_min_shortfall_objective[3]`$). Let's start again with the smallest problem size examined. This problem has only `r formatC(n_planning_units[1], big.mark = ",")` planning units.
 
@@ -475,7 +475,7 @@ plot_benchmark(
   boundary_penalty = boundary_penalty_values$add_min_shortfall_objective[3])
 ```
 
-Next, let's look at the results for a greater number of planning units (i.e. `r formatC(n_planning_units[2], big.mark = ",")` planning units) and see how the timings compare. All the solvers have a similar run time now. Interestingly, the _Gurobi_ solver is the slowest -- but only by a couple of minutes -- for these benchmark parameters.
+Next, let's look at the results for a greater number of planning units (i.e., `r formatC(n_planning_units[2], big.mark = ",")` planning units) and see how the timings compare. All the solvers have a similar run time now. Interestingly, the _Gurobi_ solver is the slowest -- but only by a couple of minutes -- for these benchmark parameters.
 
 ```{r "min_short_pu_n_2 with boundary penalty"}
 plot_benchmark(
@@ -502,6 +502,6 @@ plot_benchmark(
   boundary_penalty = boundary_penalty_values$add_min_shortfall_objective[3])
 ```
 
-# Conclusion
+## Conclusion
 
-The benchmark results demonstrate that the time required to solve a conservation planning problem can vary considerably depending on the size and complexity of the problem, and also the solver used to generate the prioritization. Indeed, some solvers (e.g. _Rsymphony_ solver) may require many hours to solve a problem that other solvers (e.g. _CBC_ or _Gurobi_ solvers) can solve within minutes. Broadly speaking, we recommend using the _Gurobi_ and _IBM CPLEX_ solvers where possible. This is because they often have the best performance. Although academics can obtain a special license to use these solvers at no cost, conservation planners working in governmental or non-governmental organizations may not have access to these solvers. In such cases, we recommend using the _CBC_ solver because it generally has better performance than the other open source solvers (i.e. the _Rsymphony_ and _lpsymphony_ solvers). Since the _CBC_ solver did not always have better performance than the other open source solvers, we recommend trying the _lpsymphony_ solver if the _CBC_ solver is taking a long time to solve a particular problem.
+The benchmark results demonstrate that the time required to solve a conservation planning problem can vary considerably depending on the size and complexity of the problem, and also the solver used to generate the prioritization. Indeed, some solvers (e.g., _Rsymphony_ solver) may require many hours to solve a problem that other solvers (e.g., _CBC_ or _Gurobi_ solvers) can solve within minutes. Broadly speaking, we recommend using the _Gurobi_ and _IBM CPLEX_ solvers where possible. This is because they often have the best performance. Although academics can obtain a special license to use these solvers at no cost, conservation planners working in governmental or non-governmental organizations may not have access to these solvers. In such cases, we recommend using the _CBC_ solver because it generally has better performance than the other open source solvers (i.e., the _Rsymphony_ and _lpsymphony_ solvers). Since the _CBC_ solver did not always have better performance than the other open source solvers, we recommend trying the _lpsymphony_ solver if the _CBC_ solver is taking a long time to solve a particular problem.
diff --git a/vignettes/tasmania.Rmd b/vignettes/tasmania.Rmd
deleted file mode 100644
index 62aaddab1..000000000
--- a/vignettes/tasmania.Rmd
+++ /dev/null
@@ -1,225 +0,0 @@
----
-title: "Tasmania Tutorial"
-output:
-  rmarkdown::html_vignette:
-    toc: true
-    fig_caption: true
-    self_contained: yes
-fontsize: 11pt
-documentclass: article
-bibliography: references.bib
-csl: reference-style.csl
-vignette: >
-  %\VignetteIndexEntry{Tasmania Tutorial}
-  %\VignetteEngine{knitr::rmarkdown_notangle}
----
-
-```{r, include = FALSE}
-h <- 3.5
-w <- 3.5
-is_check <- ("CheckExEnv" %in% search()) || any(c("_R_CHECK_TIMINGS_",
-             "_R_CHECK_LICENSE_") %in% names(Sys.getenv()))
-knitr::opts_chunk$set(fig.align = "center", eval = !is_check)
-```
-
-## Introduction
-
-The aim of this tutorial is to provide a worked example of how vector-based data can be used to develop conservation prioritizations using the _prioritizr R_ package. It is also written for conservation planners that have used the _Marxan_ decision support tool [@r3] and are interested in applying the _prioritizr R_ package to their own work. The dataset used in this tutorial was obtained from the _Introduction to Marxan_ course. This data was originally a subset of a larger spatial prioritization project performed under contract to Australia's Department of Environment and Water Resources [@r30].
-
-Please note that this tutorial uses data from the _prioritizrdata R_, so ensure that it is installed before trying out the code yourself.
-
-## Exploring the data
-
-This dataset contains two items. First, a spatial planning unit layer that has an attribute table which contains three columns: integer unique identifiers ("id"), unimproved land values ("cost"), and their existing level of protection ("status"). Units with 50 % or more of their area contained in protected areas are associated with a status of 2, otherwise they are associated with a value of 0. If you are familiar with the _Marxan_ decision support tool, then you will notice that these columns are formatted in a similar manner to the input data for _Marxan_. For _Marxan_ input data, planning units must be described in a table containing one row for each planning unit with a unique identifier and the corresponding cost.
-
-The second item in this dataset is the raster-based feature data. Specifically, the feature data is expressed as a stack of rasters (termed a `RasterStack` object). Here each layer in the stack represents the distribution of a different vegetation class in Tasmania, Australia. There are 62 vegetation classes in total. For a given layer, pixel values indicate the presence (value of 1) or absence (value of 0) of the vegetation class in an area.
-
-First, load the required packages and the data.
-
-```{r, message = FALSE}
-# load packages
-library(prioritizrdata)
-library(prioritizr)
-
-# load planning unit data
-data(tas_pu)
-
-# load conservation feature data
-data(tas_features)
-```
-
-Now, let's have a look at the planning unit data.
-
-```{r, fig.width = w, fig.height = h}
-# print planning unit data
-print(tas_pu)
-
-# plot map of planning unit costs
-plot(st_as_sf(tas_pu[, "cost"]), main = "Planning unit costs")
-```
-
-Next, let examine the feature data. Here we will only plot the first four features as an example. The pixel values denote the presence or absence of each feature within the extent of the study area.
-
-```{r, fig.width = 4.5, fig.height = 4.5}
-# print planning unit data
-print(tas_features)
-
-# plot map of the first four vegetation classes
-plot(tas_features[[1:4]], main = paste("Feature", 1:4))
-```
-
-The planning units in this example are a spatial polygon layer---not a raster---and so there can be considerable flexibility in the shape of the planning units. That said, there is a trade-off with the efficiency of data pre-processing in vector-based planning unit data compared to raster-based planning unit data. Vector-based planning unit data generally require more time to complete pre-processing computations (e.g. overlaying the planning unit data with the feature data, or generating boundary data). As a consequence, we generally recommend using raster-based planning unit data where possible to reduce processing time---but note that this is not possible when not all planning units are equal-sized squares. Another strategy is to complete the pre-processing in other software environments (e.g. _ArcGIS_) and use the pre-processed data directly with the _prioritizr_ package.
-
-## _Marxan_ problem formulation
-
-Here, we will provide an example of using the `marxan_problem` function to build and solve a typical _Marxan_ conservation planning problem. Then we will show how this same problem can be built and solved using the fully customizable `problem` function as a comparison.
-
-The dataset used in this example follows many of the conventions used by the _Marxan_ decision support tool. As a consequence, it is not too difficult to format the data for use with the `marxan_problem` function. The `marxan_problem` function is essentially a wrapper to the `problem` function. This means that when we solve problems created using the `marxan_problem` function, we will solve them using exact algorithms and not the simulated annealing algorithm used by _Marxan_.
-
-All problem objects formulated with `marxan_problem` use the minimum set objective. Targets can be either relative or absolute, and planning units can be specified for masking in or out using the `locked_in` and `locked_out` arguments. To favor clumped solutions, use the `penalty` argument to impose a penalty on solutions with high boundary lengths (equivalent to the Boundary Length Modifier (BLM) used in _Marxan_), and the `edge_factor` argument to scale the penalty for edges that do not have neighboring planning units, such as the coastline. For simplicity we set all of the targets at the same level, 17 %, to reflect the [Aichi](https://www.cbd.int/sp/targets/) biodiversity target to "safeguard" at least 17% of terrestrial ecosystems by 2020. For example, to prioritize planning units in Tasmania that meet the 17 % representation target at the least cost.
-
-First, we will convert the vector-based planning unit data and raster-based feature data into the tabular formats required by the `marxan_problem` function. These formats are very similar to the formats used by _Marxan_.
-
-```{r}
-# create table with planning unit data
-pu_data <- tas_pu@data
-
-# print first six rows
-head(pu_data)
-
-# create table with the feature identifiers, names, and targets
-spec_data <- data.frame(id = seq_len(nlayers(tas_features)),
-                        name = paste0("veg", seq_len(nlayers(tas_features))),
-                        prop = 0.17)
-
-# print first six rows
-head(spec_data)
-
-# create table with the planning unit vs. feature data
-puvspr_data <- rij_matrix(tas_pu, tas_features)
-puvspr_data <- as(puvspr_data, "dgTMatrix")
-puvspr_data <- data.frame(pu = puvspr_data@j + 1, species = puvspr_data@i + 1,
-                          amount = puvspr_data@x)
-
-# print first six rows
-head(puvspr_data)
-
-# create table with the boundary data
-bound_data <- boundary_matrix(tas_pu)
-bound_data <- as(bound_data, "dgTMatrix")
-bound_data <- data.frame(id1 = bound_data@i + 1, id2 = bound_data@j + 1,
-                         boundary = bound_data@x)
-# print first six rows
-head(bound_data)
-```
-
-Now that we have converted the data to tabular format, we can use the `marxan_problem` function to create a conservation planning problem.
-
-```{r}
-# create problem
-p1 <- marxan_problem(pu_data, spec_data, puvspr_data, bound_data,
-                     blm = 0.0005)
-
-# print problem
-print(p1)
-```
-
-Next, we can solve the problem (see [`?solve`](https://prioritizr.net/reference/solve.html) for more information). The _prioritizr_ R package supports three different exact algorithm software packages: _gurobi_, _Rsymphony_, and _lpsymphony_. There are costs and benefits associated with each of these different solvers, but each software should return similar results. Note that you will need at least one of these package installed on your system to solve problems. We recommend using the _gurobi_ solver if possible, and have used this solver when building this tutorial. After solving the problem, we will calculate some statistics to describe the solution. Note that the planning unit selections are stored in the "solution_1" column of the solution object.
-
-```{r, fig.width = w, fig.height = h}
-# solve problem
-s1 <- solve(p1)
-
-# print first six rows of solution object
-head(s1)
-
-# count number of planning units in solution
-sum(s1$solution_1)
-
-# proportion of planning units in solution
-mean(s1$solution_1)
-
-# calculate feature representation
-r1 <- eval_feature_representation_summary(p1, s1[, "solution_1", drop = FALSE])
-print(r1)
-
-# visualize the solution by converting the solution to a spatial object
-s1 <- SpatialPolygonsDataFrame(as(tas_pu, "SpatialPolygons"), data = s1)
-s1$solution_1 <- factor(s1$solution_1)
-plot(st_as_sf(s1[, "solution_1"]), pal = c("grey90", "darkgreen"),
-    main = "marxan_problem solution")
-```
-
-## General problem formulation
-
-Now we will formulate the exact same problem using the `problem` function and the spatially referenced data. We recommend using this approach instead of the `marxan_problem` because it is more verbose and you can specify exactly how the conservation planning problem should be formulated.
-
-```{r, fig.width = w, fig.height = h}
-# build problem
-p2 <- problem(tas_pu, tas_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.17) %>%
-      add_locked_in_constraints("locked_in") %>%
-      add_binary_decisions() %>%
-      add_boundary_penalties(penalty = 0.0005, edge_factor = 1)
-
-# print the problem
-print(p2)
-
-# solve problem
-s2 <- solve(p2)
-
-# calculate feature representation
-r2 <- eval_feature_representation_summary(p2, s2[, "solution_1"])
-print(r2)
-
-# visualize solution
-s2$solution_1 <- factor(s2$solution_1)
-plot(st_as_sf(s2[, "solution_1"]), pal = c("grey90", "darkgreen"),
-    main = "problem solution")
-```
-
-## Selection frequencies
-
-Similar to the _Marxan_ decision support tool, we can generate a portfolio of solutions and compute the planning unit selection frequencies to understand their relative importance. This can be useful when trying to understand which planning units in the solution are the most irreplaceable. To do this, we will create a portfolio containing 1000 solutions within 20% of optimality, and calculate the number of times that each planning unit was selected. Note that this requires the _Gurobi_ software to be installed.
-
-```{r}
-# create new problem with a portfolio added to it
-p3 <- p2 %>%
-      add_gap_portfolio(number_solutions = 1000, pool_gap = 0.2)
-
-# print problem
-print(p3)
-```
-
-```{r, message = FALSE, results = "hide"}
-# generate solutions
-s3 <- solve(p3)
-
-# find column numbers with the solutions
-solution_columns <- which(grepl("solution", names(s3)))
-
-# calculate selection frequencies
-s3$selection_frequencies <- rowSums(as.matrix(s3@data[, solution_columns]))
-```
-
-```{r, fig.width = 4.5, fig.height = 4.5}
-# plot first four solutions in the portfolio
-s3$solution_1 <- factor(s3$solution_1)
-s3$solution_2 <- factor(s3$solution_2)
-s3$solution_3 <- factor(s3$solution_3)
-s3$solution_4 <- factor(s3$solution_4)
-plot(st_as_sf(s3[, c("solution_1", "solution_2", "solution_3", "solution_4")]),
-  pal = c("grey90", "darkgreen"))
-```
-
-```{r, fig.width = w, fig.height = h}
-# plot histogram of selection frequencies
-hist(s3$selection_frequencies, main = "Selection frequencies",
-     xlab = "Number of times units were selected")
-
-# plot spatial distribution of the selection frequencies
-plot(st_as_sf(s3[, "selection_frequencies"]), main = "Selection frequencies")
-```
-
-## References
      -
      -

      Evaluate feature representation

      - Source: R/eval_feature_representation_summary.R + Source: R/eval_feature_representation_summary.R

      Calculate how well features are represented by a solution -to a conservation planning problem(). +to a conservation planning problem(). These summary statistics are reported for each and every feature, and each and every zone, within a conservation planning problem.

      - 
      eval_feature_representation_summary(x, solution)
+    
      Usage,
      eval_feature_representation_summary(x, solution)
 
-# S4 method for ConservationProblem,numeric
-eval_feature_representation_summary(x, solution)
+# S4 method for ConservationProblem,numeric
+eval_feature_representation_summary(x, solution)
 
-# S4 method for ConservationProblem,matrix
-eval_feature_representation_summary(x, solution)
+# S4 method for ConservationProblem,matrix
+eval_feature_representation_summary(x, solution)
 
-# S4 method for ConservationProblem,data.frame
-eval_feature_representation_summary(x, solution)
+# S4 method for ConservationProblem,data.frame
+eval_feature_representation_summary(x, solution)
 
-# S4 method for ConservationProblem,Spatial
-eval_feature_representation_summary(x, solution)
+# S4 method for ConservationProblem,Spatial
+eval_feature_representation_summary(x, solution)
 
-# S4 method for ConservationProblem,sf
-eval_feature_representation_summary(x, solution)
+# S4 method for ConservationProblem,sf
+eval_feature_representation_summary(x, solution)
 
-# S4 method for ConservationProblem,Raster
-eval_feature_representation_summary(x, solution)
      
+# S4 method for ConservationProblem,Raster
+eval_feature_representation_summary(x, solution)
      -

      Arguments

      - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      solution

      numeric, matrix, data.frame, -Raster, Spatial, -or sf::sf() object. +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      solution
      +

      numeric, matrix, data.frame, +Raster, Spatial, +or sf::sf() object. The argument should be in the same format as the planning unit cost data in the argument to x. -See the Solution format section for more information.

      - -

      Value

      - -

      tibble::tibble() object describing feature representation. +See the Solution format section for more information.

      +
      +
      +

      Value

      +

      tibble::tibble() object describing feature representation. Here, each row describes a specific summary statistic -(e.g. different management zone) for a specific feature. -It contains the following columns:

      -
      - -
      summary

      character description of the summary statistic. +(e.g., different management zone) for a specific feature. +It contains the following columns:

      summary
      +

      character description of the summary statistic. The statistic associated with the "overall" value in this column is calculated using the entire solution (including all management zones if there are multiple zones). @@ -244,47 +153,57 @@

      Value

      are also provided for each zone separately (indicated using zone names).

      -
      feature

      character name of the feature.

      -
      total_amount

      numeric total amount of each feature available +

      feature
      +

      character name of the feature.

      + + +
      total_amount
      +

      numeric total amount of each feature available in the entire conservation planning problem (not just planning units selected within the solution). It is calculated as the sum of the feature data, -supplied when creating a problem() object -(e.g. presence/absence values).

      +supplied when creating a problem() object +(e.g., presence/absence values).

      -
      absolute_held

      numeric total amount of each feature secured within + +

      absolute_held
      +

      numeric total amount of each feature secured within the solution. It is calculated as the sum of the feature data, -supplied when creating a problem() object -(e.g. presence/absence values), weighted by the status of each -planning unit in the solution (e.g. selected or not for prioritization).

      +supplied when creating a problem() object +(e.g., presence/absence values), weighted by the status of each +planning unit in the solution (e.g., selected or not for +prioritization).

      + -
      relative_held

      numeric proportion of +

      relative_held
      +

      numeric proportion of each feature secured within the solution. It is calculated by dividing values in the "absolute_held" column by those in the "total_amount" column.

      -
      - -

      Solution format

      +
      +
      +

      Solution format

      Broadly speaking, the argument to solution must be in the same format as the planning unit data in the argument to x. Further details on the correct format are listed separately for each of the different planning unit data formats:

      -
      - -
      x has numeric planning units

      The argument to solution must be a +

      x has numeric planning units
      +

      The argument to solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to solution.

      -
      x has matrix planning units

      The argument to solution must be a + +

      x has matrix planning units
      +

      The argument to solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones @@ -292,8 +211,10 @@

      Raster planning units +

      The argument to solution +be a Raster object where different grid cells (pixels) correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference @@ -301,35 +222,41 @@

      sf::sf() data). Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has Spatial planning units

      The argument to solution -must be a Spatial object with each column corresponding to a + +

      x has Spatial planning units
      +

      The argument to solution +must be a Spatial object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -Spatial object containing the solution also contains additional +Spatial object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this -function (see below for example with sf::sf() data). +function (see below for example with sf::sf() data). Additionally, the argument to solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to solution.

      -
      x has sf::sf() planning units

      The argument to solution must be -a sf::sf() object with each column corresponding to a different + +

      x has sf::sf() planning units
      +

      The argument to solution must be +a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the -sf::sf() object containing the solution also contains additional +sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, the argument to solution must also have the same @@ -338,342 +265,340 @@

      See also

      -

      See summaries for an overview of all functions for summarizing solutions.

      +

      +
      +

      See also

      +

      See summaries for an overview of all functions for summarizing solutions.

      Other summaries: -eval_boundary_summary(), -eval_connectivity_summary(), -eval_cost_summary(), -eval_n_summary(), -eval_target_coverage_summary()

      - -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_raster, sim_pu_polygons, sim_pu_zones_sf, sim_features,
-     sim_pu_zones_stack, sim_features_zones)
-
-# create a simple conservation planning dataset so we can see exactly
-# how feature representation is calculated
-pu <- data.frame(id = seq_len(10), cost = c(0.2, NA, runif(8)),
-                 spp1 = runif(10), spp2 = c(rpois(9, 4), NA))
-
-# create problem
-p1 <- problem(pu, c("spp1", "spp2"), cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create a solution
-# specifically, a data.frame with a single column that contains
-# binary values indicating if each planning units was selected or not
-s1 <- data.frame(s = c(1, NA, rep(c(1, 0), 4)))
-print(s1)
-#>     s
-#> 1   1
-#> 2  NA
-#> 3   1
-#> 4   0
-#> 5   1
-#> 6   0
-#> 7   1
-#> 8   0
-#> 9   1
-#> 10  0
-
-# calculate feature representation
-r1 <- eval_feature_representation_summary(p1, s1)
-print(r1)
-#> # A tibble: 2 × 5
-#>   summary feature total_amount absolute_held relative_held
-#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-#> 1 overall spp1            5.76          3.12         0.541
-#> 2 overall spp2           33            14            0.424
-
-# let's verify that feature representation calculations are correct
-# by manually performing the calculations and compare the results with r1
-## calculate total amount for each feature
-print(setNames(
-  c(sum(pu$spp1, na.rm = TRUE),
-    sum(pu$spp2, na.rm = TRUE)),
-  c("spp1", "spp2")))
-#>      spp1      spp2 
-#>  5.755739 33.000000 
-
-## calculate absolute amount held for each feature
-print(setNames(
-  c(sum(pu$spp1 * s1$s, na.rm = TRUE),
-    sum(pu$spp2 * s1$s, na.rm = TRUE)),
-  c("spp1", "spp2")))
-#>      spp1      spp2 
-#>  3.116052 14.000000 
-
-## calculate relative amount held for each feature
-print(setNames(
-  c(sum(pu$spp1 * s1$s, na.rm = TRUE) / sum(pu$spp1, na.rm = TRUE),
-    sum(pu$spp2 * s1$s, na.rm = TRUE) / sum(pu$spp2, na.rm = TRUE)),
-  c("spp1", "spp2")))
-#>      spp1      spp2 
-#> 0.5413818 0.4242424 
-
-# \dontrun{
-# solve the problem using an exact algorithm solver
-s1_2 <- solve(p1)
-print(s1_2)
-#>    id      cost      spp1 spp2 solution_1
-#> 1   1 0.2000000 0.8288314    4          1
-#> 2   2        NA 0.7115770    3         NA
-#> 3   3 0.8336000 0.2820609    1          0
-#> 4   4 0.7250118 0.8928427    6          0
-#> 5   5 0.9753142 0.7647062    1          0
-#> 6   6 0.4676038 0.1643470    4          0
-#> 7   7 0.8122781 0.7320744    3          0
-#> 8   8 0.2056958 0.2531062    6          0
-#> 9   9 0.5121819 0.5083795    5          0
-#> 10 10 0.9254660 0.6178138   NA          0
-
-# calculate feature representation in this solution
-r1_2 <- eval_feature_representation_summary(
-  p1, s1_2[, "solution_1", drop = FALSE])
-print(r1_2)
-#> # A tibble: 2 × 5
-#>   summary feature total_amount absolute_held relative_held
-#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-#> 1 overall spp1            5.76         0.829         0.144
-#> 2 overall spp2           33            4             0.121
-
-# build minimal conservation problem with raster data
-p2 <- problem(sim_pu_raster, sim_features) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# solve the problem
-s2 <- solve(p2)
-
-# print solution
-print(s2)
-#> class      : RasterLayer 
-#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> source     : memory
-#> names      : layer 
-#> values     : 0, 1  (min, max)
-#> 
-
-# calculate feature representation in the solution
-r2 <- eval_feature_representation_summary(p2, s2)
-print(r2)
-#> # A tibble: 5 × 5
-#>   summary feature total_amount absolute_held relative_held
-#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-#> 1 overall layer.1         83.3          8.91         0.107
-#> 2 overall layer.2         31.2          3.13         0.100
-#> 3 overall layer.3         72.0          7.34         0.102
-#> 4 overall layer.4         42.7          4.35         0.102
-#> 5 overall layer.5         56.7          6.01         0.106
-
-# plot solution
-plot(s2, main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# build minimal conservation problem with polygon (Spatial) data
-p3 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s3 <- solve(p3)
-
-# print first six rows of the attribute table
-print(head(s3))
-#>       cost locked_in locked_out solution_1
-#> 1 215.8638     FALSE      FALSE          0
-#> 2 212.7823     FALSE      FALSE          0
-#> 3 207.4962     FALSE      FALSE          0
-#> 4 208.9322     FALSE       TRUE          0
-#> 5 214.0419     FALSE      FALSE          0
-#> 6 213.7636     FALSE      FALSE          0
-
-# calculate feature representation in the solution
-r3 <- eval_feature_representation_summary(p3, s3[, "solution_1"])
-print(r3)
-#> # A tibble: 5 × 5
-#>   summary feature total_amount absolute_held relative_held
-#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
-#> 1 overall layer.1         74.5          8.05         0.108
-#> 2 overall layer.2         28.1          2.83         0.101
-#> 3 overall layer.3         64.9          6.65         0.103
-#> 4 overall layer.4         38.2          3.87         0.101
-#> 5 overall layer.5         50.7          5.41         0.107
-
-# plot solution
-spplot(s3, zcol = "solution_1", main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# build multi-zone conservation problem with raster data
-p4 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s4 <- solve(p4)
-
-# print solution
-print(s4)
-#> class      : RasterStack 
-#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
-#> resolution : 0.1, 0.1  (x, y)
-#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
-#> crs        : NA 
-#> names      : zone_1, zone_2, zone_3 
-#> min values :      0,      0,      0 
-#> max values :      1,      1,      1 
-#> 
-
-# calculate feature representation in the solution
-r4 <- eval_feature_representation_summary(p4, s4)
-print(r4)
-#> # A tibble: 20 × 5
-#>    summary feature   total_amount absolute_held relative_held
-#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
-#>  1 overall feature_1        250.          45.8          0.183
-#>  2 overall feature_2         93.6         17.7          0.189
-#>  3 overall feature_3        216.          40.2          0.186
-#>  4 overall feature_4        128.          23.7          0.186
-#>  5 overall feature_5        170.          31.2          0.183
-#>  6 zone_1  feature_1         83.3         16.0          0.192
-#>  7 zone_1  feature_2         31.2          5.07         0.162
-#>  8 zone_1  feature_3         72.0         13.2          0.183
-#>  9 zone_1  feature_4         42.7          7.04         0.165
-#> 10 zone_1  feature_5         56.7         11.2          0.197
-#> 11 zone_2  feature_1         83.3         16.0          0.192
-#> 12 zone_2  feature_2         31.2          6.45         0.207
-#> 13 zone_2  feature_3         72.0         15.1          0.210
-#> 14 zone_2  feature_4         42.7          8.22         0.193
-#> 15 zone_2  feature_5         56.7         10.4          0.184
-#> 16 zone_3  feature_1         83.3         13.8          0.166
-#> 17 zone_3  feature_2         31.2          6.16         0.197
-#> 18 zone_3  feature_3         72.0         11.9          0.165
-#> 19 zone_3  feature_4         42.7          8.49         0.199
-#> 20 zone_3  feature_5         56.7          9.58         0.169
-
-# plot solution
-plot(category_layer(s4), main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
-# build multi-zone conservation problem with polygon (sf) data
-p5 <- problem(sim_pu_zones_sf, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-# \dontrun{
-# solve the problem
-s5 <- solve(p5)
-
-# print first six rows of the attribute table
-print(head(s5))
-#> Simple feature collection with 6 features and 9 fields
-#> Geometry type: POLYGON
-#> Dimension:     XY
-#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
-#> CRS:           NA
-#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
-#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
-#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
-#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
-#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
-#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
-#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
-#>   solution_1_zone_2 solution_1_zone_3                       geometry
-#> 1                 1                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
-#> 2                 0                 0 POLYGON ((0.1 1, 0.2 1, 0.2...
-#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
-#> 4                 0                 0 POLYGON ((0.3 1, 0.4 1, 0.4...
-#> 5                 0                 0 POLYGON ((0.4 1, 0.5 1, 0.5...
-#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
-
-# calculate feature representation in the solution
-r5 <- eval_feature_representation_summary(
-  p5, s5[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-print(r5)
-#> # A tibble: 20 × 5
-#>    summary feature   total_amount absolute_held relative_held
-#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
-#>  1 overall feature_1        225.          40.9          0.182
-#>  2 overall feature_2         83.9         13.8          0.164
-#>  3 overall feature_3        195.          34.3          0.176
-#>  4 overall feature_4        114.          18.7          0.164
-#>  5 overall feature_5        154.          28.3          0.184
-#>  6 zone_1  feature_1         75.1         14.9          0.198
-#>  7 zone_1  feature_2         28.0          4.77         0.170
-#>  8 zone_1  feature_3         65.0         12.7          0.195
-#>  9 zone_1  feature_4         38.0          6.39         0.168
-#> 10 zone_1  feature_5         51.2         10.2          0.200
-#> 11 zone_2  feature_1         75.1         15.0          0.199
-#> 12 zone_2  feature_2         28.0          5.02         0.179
-#> 13 zone_2  feature_3         65.0         12.9          0.199
-#> 14 zone_2  feature_4         38.0          6.03         0.158
-#> 15 zone_2  feature_5         51.2         10.2          0.199
-#> 16 zone_3  feature_1         75.1         11.1          0.148
-#> 17 zone_3  feature_2         28.0          3.98         0.142
-#> 18 zone_3  feature_3         65.0          8.71         0.134
-#> 19 zone_3  feature_4         38.0          6.33         0.166
-#> 20 zone_3  feature_5         51.2          7.84         0.153
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s5$solution <- category_vector(
-  s5[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
-s5$solution <- factor(s5$solution)
-
-# plot solution
-plot(s5[, "solution"])
-
-# }
+eval_boundary_summary(),
+eval_connectivity_summary(),
+eval_cost_summary(),
+eval_n_summary(),
+eval_target_coverage_summary()
      +
      + +
      +

      Examples

      + 
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_raster, sim_pu_polygons, sim_pu_zones_sf, sim_features,
+     sim_pu_zones_stack, sim_features_zones)
+
+# create a simple conservation planning dataset so we can see exactly
+# how feature representation is calculated
+pu <- data.frame(id = seq_len(10), cost = c(0.2, NA, runif(8)),
+                 spp1 = runif(10), spp2 = c(rpois(9, 4), NA))
+
+# create problem
+p1 <- problem(pu, c("spp1", "spp2"), cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create a solution
+# specifically, a data.frame with a single column that contains
+# binary values indicating if each planning units was selected or not
+s1 <- data.frame(s = c(1, NA, rep(c(1, 0), 4)))
+print(s1)
+#>     s
+#> 1   1
+#> 2  NA
+#> 3   1
+#> 4   0
+#> 5   1
+#> 6   0
+#> 7   1
+#> 8   0
+#> 9   1
+#> 10  0
+
+# calculate feature representation
+r1 <- eval_feature_representation_summary(p1, s1)
+print(r1)
+#> # A tibble: 2 × 5
+#>   summary feature total_amount absolute_held relative_held
+#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+#> 1 overall spp1            5.76          3.12         0.541
+#> 2 overall spp2           33            14            0.424
+
+# let's verify that feature representation calculations are correct
+# by manually performing the calculations and compare the results with r1
+## calculate total amount for each feature
+print(setNames(
+  c(sum(pu$spp1, na.rm = TRUE),
+    sum(pu$spp2, na.rm = TRUE)),
+  c("spp1", "spp2")))
+#>      spp1      spp2 
+#>  5.755739 33.000000 
+
+## calculate absolute amount held for each feature
+print(setNames(
+  c(sum(pu$spp1 * s1$s, na.rm = TRUE),
+    sum(pu$spp2 * s1$s, na.rm = TRUE)),
+  c("spp1", "spp2")))
+#>      spp1      spp2 
+#>  3.116052 14.000000 
+
+## calculate relative amount held for each feature
+print(setNames(
+  c(sum(pu$spp1 * s1$s, na.rm = TRUE) / sum(pu$spp1, na.rm = TRUE),
+    sum(pu$spp2 * s1$s, na.rm = TRUE) / sum(pu$spp2, na.rm = TRUE)),
+  c("spp1", "spp2")))
+#>      spp1      spp2 
+#> 0.5413818 0.4242424 
+
+# \dontrun{
+# solve the problem using an exact algorithm solver
+s1_2 <- solve(p1)
+print(s1_2)
+#>    id      cost      spp1 spp2 solution_1
+#> 1   1 0.2000000 0.8288314    4          1
+#> 2   2        NA 0.7115770    3         NA
+#> 3   3 0.8336000 0.2820609    1          0
+#> 4   4 0.7250118 0.8928427    6          0
+#> 5   5 0.9753142 0.7647062    1          0
+#> 6   6 0.4676038 0.1643470    4          0
+#> 7   7 0.8122781 0.7320744    3          0
+#> 8   8 0.2056958 0.2531062    6          0
+#> 9   9 0.5121819 0.5083795    5          0
+#> 10 10 0.9254660 0.6178138   NA          0
+
+# calculate feature representation in this solution
+r1_2 <- eval_feature_representation_summary(
+  p1, s1_2[, "solution_1", drop = FALSE])
+print(r1_2)
+#> # A tibble: 2 × 5
+#>   summary feature total_amount absolute_held relative_held
+#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+#> 1 overall spp1            5.76         0.829         0.144
+#> 2 overall spp2           33            4             0.121
+
+# build minimal conservation problem with raster data
+p2 <- problem(sim_pu_raster, sim_features) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# solve the problem
+s2 <- solve(p2)
+
+# print solution
+print(s2)
+#> class      : RasterLayer 
+#> dimensions : 10, 10, 100  (nrow, ncol, ncell)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> source     : memory
+#> names      : layer 
+#> values     : 0, 1  (min, max)
+#> 
+
+# calculate feature representation in the solution
+r2 <- eval_feature_representation_summary(p2, s2)
+print(r2)
+#> # A tibble: 5 × 5
+#>   summary feature total_amount absolute_held relative_held
+#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+#> 1 overall layer.1         83.3          8.91         0.107
+#> 2 overall layer.2         31.2          3.13         0.100
+#> 3 overall layer.3         72.0          7.34         0.102
+#> 4 overall layer.4         42.7          4.35         0.102
+#> 5 overall layer.5         56.7          6.01         0.106
+
+# plot solution
+plot(s2, main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# build minimal conservation problem with polygon (Spatial) data
+p3 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s3 <- solve(p3)
+
+# print first six rows of the attribute table
+print(head(s3))
+#>       cost locked_in locked_out solution_1
+#> 1 215.8638     FALSE      FALSE          0
+#> 2 212.7823     FALSE      FALSE          0
+#> 3 207.4962     FALSE      FALSE          0
+#> 4 208.9322     FALSE       TRUE          0
+#> 5 214.0419     FALSE      FALSE          0
+#> 6 213.7636     FALSE      FALSE          0
+
+# calculate feature representation in the solution
+r3 <- eval_feature_representation_summary(p3, s3[, "solution_1"])
+print(r3)
+#> # A tibble: 5 × 5
+#>   summary feature total_amount absolute_held relative_held
+#>   <chr>   <chr>          <dbl>         <dbl>         <dbl>
+#> 1 overall layer.1         74.5          8.05         0.108
+#> 2 overall layer.2         28.1          2.83         0.101
+#> 3 overall layer.3         64.9          6.65         0.103
+#> 4 overall layer.4         38.2          3.87         0.101
+#> 5 overall layer.5         50.7          5.41         0.107
+
+# plot solution
+spplot(s3, zcol = "solution_1", main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# build multi-zone conservation problem with raster data
+p4 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s4 <- solve(p4)
+
+# print solution
+print(s4)
+#> class      : RasterStack 
+#> dimensions : 10, 10, 100, 3  (nrow, ncol, ncell, nlayers)
+#> resolution : 0.1, 0.1  (x, y)
+#> extent     : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
+#> crs        : NA 
+#> names      : zone_1, zone_2, zone_3 
+#> min values :      0,      0,      0 
+#> max values :      1,      1,      1 
+#> 
+
+# calculate feature representation in the solution
+r4 <- eval_feature_representation_summary(p4, s4)
+print(r4)
+#> # A tibble: 20 × 5
+#>    summary feature   total_amount absolute_held relative_held
+#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
+#>  1 overall feature_1        250.          45.8          0.183
+#>  2 overall feature_2         93.6         17.7          0.189
+#>  3 overall feature_3        216.          40.2          0.186
+#>  4 overall feature_4        128.          23.7          0.186
+#>  5 overall feature_5        170.          31.2          0.183
+#>  6 zone_1  feature_1         83.3         16.0          0.192
+#>  7 zone_1  feature_2         31.2          5.07         0.162
+#>  8 zone_1  feature_3         72.0         13.2          0.183
+#>  9 zone_1  feature_4         42.7          7.04         0.165
+#> 10 zone_1  feature_5         56.7         11.2          0.197
+#> 11 zone_2  feature_1         83.3         16.0          0.192
+#> 12 zone_2  feature_2         31.2          6.45         0.207
+#> 13 zone_2  feature_3         72.0         15.1          0.210
+#> 14 zone_2  feature_4         42.7          8.22         0.193
+#> 15 zone_2  feature_5         56.7         10.4          0.184
+#> 16 zone_3  feature_1         83.3         13.8          0.166
+#> 17 zone_3  feature_2         31.2          6.16         0.197
+#> 18 zone_3  feature_3         72.0         11.9          0.165
+#> 19 zone_3  feature_4         42.7          8.49         0.199
+#> 20 zone_3  feature_5         56.7          9.58         0.169
+
+# plot solution
+plot(category_layer(s4), main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
+# build multi-zone conservation problem with polygon (sf) data
+p5 <- problem(sim_pu_zones_sf, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+# \dontrun{
+# solve the problem
+s5 <- solve(p5)
+
+# print first six rows of the attribute table
+print(head(s5))
+#> Simple feature collection with 6 features and 9 fields
+#> Geometry type: POLYGON
+#> Dimension:     XY
+#> Bounding box:  xmin: 0 ymin: 0.9 xmax: 0.6 ymax: 1
+#> CRS:           NA
+#>     cost_1   cost_2   cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
+#> 1 215.8638 183.3344 205.4113    FALSE    FALSE    FALSE                 0
+#> 2 212.7823 189.4978 209.6404    FALSE    FALSE    FALSE                 0
+#> 3 207.4962 193.6007 215.4212     TRUE    FALSE    FALSE                 0
+#> 4 208.9322 197.5897 218.5241    FALSE    FALSE    FALSE                 0
+#> 5 214.0419 199.8033 220.7100    FALSE    FALSE    FALSE                 0
+#> 6 213.7636 203.1867 224.6809    FALSE    FALSE    FALSE                 0
+#>   solution_1_zone_2 solution_1_zone_3                       geometry
+#> 1                 1                 0 POLYGON ((0 1, 0.1 1, 0.1 0...
+#> 2                 0                 0 POLYGON ((0.1 1, 0.2 1, 0.2...
+#> 3                 0                 0 POLYGON ((0.2 1, 0.3 1, 0.3...
+#> 4                 0                 0 POLYGON ((0.3 1, 0.4 1, 0.4...
+#> 5                 0                 0 POLYGON ((0.4 1, 0.5 1, 0.5...
+#> 6                 0                 0 POLYGON ((0.5 1, 0.6 1, 0.6...
+
+# calculate feature representation in the solution
+r5 <- eval_feature_representation_summary(
+  p5, s5[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+print(r5)
+#> # A tibble: 20 × 5
+#>    summary feature   total_amount absolute_held relative_held
+#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
+#>  1 overall feature_1        225.          40.9          0.182
+#>  2 overall feature_2         83.9         13.8          0.164
+#>  3 overall feature_3        195.          34.3          0.176
+#>  4 overall feature_4        114.          18.7          0.164
+#>  5 overall feature_5        154.          28.3          0.184
+#>  6 zone_1  feature_1         75.1         14.9          0.198
+#>  7 zone_1  feature_2         28.0          4.77         0.170
+#>  8 zone_1  feature_3         65.0         12.7          0.195
+#>  9 zone_1  feature_4         38.0          6.39         0.168
+#> 10 zone_1  feature_5         51.2         10.2          0.200
+#> 11 zone_2  feature_1         75.1         15.0          0.199
+#> 12 zone_2  feature_2         28.0          5.02         0.179
+#> 13 zone_2  feature_3         65.0         12.9          0.199
+#> 14 zone_2  feature_4         38.0          6.03         0.158
+#> 15 zone_2  feature_5         51.2         10.2          0.199
+#> 16 zone_3  feature_1         75.1         11.1          0.148
+#> 17 zone_3  feature_2         28.0          3.98         0.142
+#> 18 zone_3  feature_3         65.0          8.71         0.134
+#> 19 zone_3  feature_4         38.0          6.33         0.166
+#> 20 zone_3  feature_5         51.2          7.84         0.153
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s5$solution <- category_vector(
+  s5[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")])
+s5$solution <- factor(s5$solution)
+
+# plot solution
+plot(s5[, "solution"])
+
+# }
      +
      -
      -

      Add locked out constraints

      - Source: R/add_locked_out_constraints.R + Source: R/add_locked_out_constraints.R
      -

      Add constraints to a conservation planning problem() to ensure +

      Add constraints to a conservation planning problem() to ensure that specific planning units are not selected (or allocated to a specific zone) in the solution. For example, it may be useful to lock out planning units that have been degraded and are not suitable for conserving species. If specific planning units should be locked in to the solution, use add_locked_out_constraints(). For -problems with non-binary planning unit allocations (e.g. proportions), the -add_manual_locked_constraints() function can be used to lock +problems with non-binary planning unit allocations (e.g., proportions), the +add_manual_locked_constraints() function can be used to lock planning unit allocations to a specific value.

      - 
      add_locked_out_constraints(x, locked_out)
-
-# S4 method for ConservationProblem,numeric
-add_locked_out_constraints(x, locked_out)
-
-# S4 method for ConservationProblem,logical
-add_locked_out_constraints(x, locked_out)
+    
      Usage,
      add_locked_out_constraints(x, locked_out)
 
-# S4 method for ConservationProblem,matrix
-add_locked_out_constraints(x, locked_out)
+# S4 method for ConservationProblem,numeric
+add_locked_out_constraints(x, locked_out)
 
-# S4 method for ConservationProblem,character
-add_locked_out_constraints(x, locked_out)
+# S4 method for ConservationProblem,logical
+add_locked_out_constraints(x, locked_out)
 
-# S4 method for ConservationProblem,Spatial
-add_locked_out_constraints(x, locked_out)
+# S4 method for ConservationProblem,matrix
+add_locked_out_constraints(x, locked_out)
 
-# S4 method for ConservationProblem,sf
-add_locked_out_constraints(x, locked_out)
+# S4 method for ConservationProblem,character
+add_locked_out_constraints(x, locked_out)
 
-# S4 method for ConservationProblem,Raster
-add_locked_out_constraints(x, locked_out)
      
+# S4 method for ConservationProblem,Spatial
+add_locked_out_constraints(x, locked_out)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
      x
      problem() (i.e. ConservationProblem) object.
      locked_out
      Object that determines which planning units that should be
-locked out. See the Data format section for more information.
      
+# S4 method for ConservationProblem,sf
+add_locked_out_constraints(x, locked_out)
 
-    
      Value
      
+# S4 method for ConservationProblem,Raster
+add_locked_out_constraints(x, locked_out)
      -

      Object (i.e. ConservationProblem) with the constraints +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      locked_out
      +

      Object that determines which planning units that should be +locked out. See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the constraints added to it.

      -

      Data format

      - +
      +
      +

      Data format

      The locked planning units can be specified using the following formats. Generally, the locked data should correspond to the planning units in the argument to x. To help make working with -Raster planning unit data easier, +Raster planning unit data easier, the locked data should correspond to cell indices in the -Raster data. For example, integer arguments +Raster data. For example, integer arguments should correspond to cell indices and logical arguments should have a value for each cell---regardless of which planning unit cells contain NA values.

      -
      - -
      data as an integer vector

      containing indices that indicate which +

      data as an integer vector
      +

      containing indices that indicate which planning units should be locked for the solution. This argument is only compatible with problems that contain a single zone.

      -
      data as a logical vector

      containing TRUE and/or + +

      data as a logical vector
      +

      containing TRUE and/or FALSE values that indicate which planning units should be locked in the solution. This argument is only compatible with problems that contain a single zone.

      -
      data as a matrix object

      containing logical TRUE and/or + +

      data as a matrix object
      +

      containing logical TRUE and/or FALSE values which indicate if certain planning units are should be locked to a specific zone in the solution. Each row corresponds to a planning unit, each column corresponds to a zone, and @@ -274,212 +189,216 @@

      TRUE value.

      -
      data as a character vector

      containing field (column) name(s) + +

      data as a character vector
      +

      containing field (column) name(s) that indicate if planning units should be locked for the solution. This format is only compatible if the planning units in the argument to x are a -Spatial, sf::sf(), or +Spatial, sf::sf(), or data.frame object. The fields -(columns) must have logical (i.e. TRUE or FALSE) +(columns) must have logical (i.e., TRUE or FALSE) values indicating if the planning unit is to be locked for the solution. For problems that contain a single zone, the argument to data must contain a single field name. Otherwise, for problems that contain multiple zones, the argument to data must contain a field name for each zone.

      -
      data as a Spatial or sf::sf() object

      containing geometries that will be used to lock planning units for + +

      data as a Spatial or sf::sf() object
      +

      containing geometries that will be used to lock planning units for the solution. Specifically, planning units in x that spatially -intersect with y will be locked (per intersecting_units()). +intersect with y will be locked (per intersecting_units()). Note that this option is only available for problems that contain a single management zone.

      -
      data as a Raster object

      containing cells used to lock + +

      data as a Raster object
      +

      containing cells used to lock planning units for the solution. Specifically, planning units in x that intersect with cells that have non-zero and non-NA values are locked. For problems that contain multiple zones, the -Raster object must contain a layer +Raster object must contain a layer for each zone. Note that for multi-band arguments, each pixel must only contain a non-zero value in a single band. Additionally, if the -cost data in x is a Raster object, we +cost data in x is a Raster object, we recommend standardizing NA values in this dataset with the cost data. In other words, the pixels in x that have NA values should also have NA values in the locked data.

      -
      -

      See also

      - -

      See constraints for an overview of all functions for adding constraints.

      +
      +
      +

      See also

      +

      See constraints for an overview of all functions for adding constraints.

      Other constraints: -add_contiguity_constraints(), -add_feature_contiguity_constraints(), -add_linear_constraints(), -add_locked_in_constraints(), -add_mandatory_allocation_constraints,ConservationProblem-method, -add_manual_bounded_constraints(), -add_manual_locked_constraints()

      - -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_polygons, sim_features, sim_locked_out_raster)
-
-# create minimal problem
-p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with added locked out constraints using integers
-p2 <- p1 %>% add_locked_out_constraints(which(sim_pu_polygons$locked_out))
-
-# create problem with added locked out constraints using a field name
-p3 <- p1 %>% add_locked_out_constraints("locked_out")
-
-# create problem with added locked out constraints using raster data
-p4 <- p1 %>% add_locked_out_constraints(sim_locked_out_raster)
-
-# create problem with added locked out constraints using spatial polygon data
-locked_out <- sim_pu_polygons[sim_pu_polygons$locked_out == 1, ]
-p5 <- p1 %>% add_locked_out_constraints(locked_out)
-# \dontrun{
-# solve problems
-s1 <- solve(p1)
-s2 <- solve(p2)
-s3 <- solve(p3)
-s4 <- solve(p4)
-s5 <- solve(p5)
-
-# plot solutions
-par(mfrow = c(3,2), mar = c(0, 0, 4.1, 0))
-plot(s1, main = "none locked out")
-plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s2, main = "locked out (integer input)")
-plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s3, main = "locked out (character input)")
-plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s4, main = "locked out (raster input)")
-plot(s4[s4$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s5, main = "locked out (polygon input)")
-plot(s5[s5$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-# reset plot
-par(mfrow = c(1, 1))
-
-# }
-
-# create minimal multi-zone problem with spatial data
-p6 <- problem(sim_pu_zones_polygons, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create multi-zone problem with locked out constraints using matrix data
-locked_matrix <- sim_pu_zones_polygons@data[, c("locked_1", "locked_2",
-                                                "locked_3")]
-locked_matrix <- as.matrix(locked_matrix)
-
-p7 <- p6 %>% add_locked_out_constraints(locked_matrix)
-# \dontrun{
-# solve problem
-s6 <- solve(p6)
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s6$solution <- category_vector(s6@data[, c("solution_1_zone_1",
-                                           "solution_1_zone_2",
-                                           "solution_1_zone_3")])
-s6$solution <- factor(s6$solution)
-
-# plot solution
-spplot(s6, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create multi-zone problem with locked out constraints using field names
-p8 <- p6 %>% add_locked_out_constraints(c("locked_1", "locked_2",
-                                          "locked_3"))
-# \dontrun{
-# solve problem
-s8 <- solve(p8)
-
-# create new column in s8 representing the zone id that each planning unit
-# was allocated to in the solution
-s8$solution <- category_vector(s8@data[, c("solution_1_zone_1",
-                                           "solution_1_zone_2",
-                                           "solution_1_zone_3")])
-s8$solution[s8$solution == 1 & s8$solution_1_zone_1 == 0] <- 0
-s8$solution <- factor(s8$solution)
-
-# plot solution
-spplot(s8, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create multi-zone problem with raster planning units
-p9 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create raster stack with locked out units
-locked_out_stack <- sim_pu_zones_stack[[1]]
-locked_out_stack[!is.na(locked_out_stack)] <- 0
-locked_out_stack <- locked_out_stack[[c(1, 1, 1)]]
-locked_out_stack[[1]][1] <- 1
-locked_out_stack[[2]][2] <- 1
-locked_out_stack[[3]][3] <- 1
-
-# plot locked out stack
-# \dontrun{
-plot(locked_out_stack)
-
-# }
-# add locked out raster units to problem
-p9 <- p9 %>% add_locked_out_constraints(locked_out_stack)
-
-# \dontrun{
-# solve problem
-s9 <- solve(p9)
-
-# plot solution
-plot(category_layer(s9), main = "solution", axes = FALSE, box = FALSE)
-
-# }
+add_contiguity_constraints(),
+add_feature_contiguity_constraints(),
+add_linear_constraints(),
+add_locked_in_constraints(),
+add_mandatory_allocation_constraints,ConservationProblem-method,
+add_manual_bounded_constraints(),
+add_manual_locked_constraints()
      +
      + +
      +

      Examples

      + 
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_polygons, sim_features, sim_locked_out_raster)
+
+# create minimal problem
+p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with added locked out constraints using integers
+p2 <- p1 %>% add_locked_out_constraints(which(sim_pu_polygons$locked_out))
+
+# create problem with added locked out constraints using a field name
+p3 <- p1 %>% add_locked_out_constraints("locked_out")
+
+# create problem with added locked out constraints using raster data
+p4 <- p1 %>% add_locked_out_constraints(sim_locked_out_raster)
+
+# create problem with added locked out constraints using spatial polygon data
+locked_out <- sim_pu_polygons[sim_pu_polygons$locked_out == 1, ]
+p5 <- p1 %>% add_locked_out_constraints(locked_out)
+# \dontrun{
+# solve problems
+s1 <- solve(p1)
+s2 <- solve(p2)
+s3 <- solve(p3)
+s4 <- solve(p4)
+s5 <- solve(p5)
+
+# plot solutions
+par(mfrow = c(3,2), mar = c(0, 0, 4.1, 0))
+plot(s1, main = "none locked out")
+plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s2, main = "locked out (integer input)")
+plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s3, main = "locked out (character input)")
+plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s4, main = "locked out (raster input)")
+plot(s4[s4$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s5, main = "locked out (polygon input)")
+plot(s5[s5$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+# reset plot
+par(mfrow = c(1, 1))
+
+# }
+
+# create minimal multi-zone problem with spatial data
+p6 <- problem(sim_pu_zones_polygons, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create multi-zone problem with locked out constraints using matrix data
+locked_matrix <- sim_pu_zones_polygons@data[, c("locked_1", "locked_2",
+                                                "locked_3")]
+locked_matrix <- as.matrix(locked_matrix)
+
+p7 <- p6 %>% add_locked_out_constraints(locked_matrix)
+# \dontrun{
+# solve problem
+s6 <- solve(p6)
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s6$solution <- category_vector(s6@data[, c("solution_1_zone_1",
+                                           "solution_1_zone_2",
+                                           "solution_1_zone_3")])
+s6$solution <- factor(s6$solution)
+
+# plot solution
+spplot(s6, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create multi-zone problem with locked out constraints using field names
+p8 <- p6 %>% add_locked_out_constraints(c("locked_1", "locked_2",
+                                          "locked_3"))
+# \dontrun{
+# solve problem
+s8 <- solve(p8)
+
+# create new column in s8 representing the zone id that each planning unit
+# was allocated to in the solution
+s8$solution <- category_vector(s8@data[, c("solution_1_zone_1",
+                                           "solution_1_zone_2",
+                                           "solution_1_zone_3")])
+s8$solution[s8$solution == 1 & s8$solution_1_zone_1 == 0] <- 0
+s8$solution <- factor(s8$solution)
+
+# plot solution
+spplot(s8, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create multi-zone problem with raster planning units
+p9 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create raster stack with locked out units
+locked_out_stack <- sim_pu_zones_stack[[1]]
+locked_out_stack[!is.na(locked_out_stack)] <- 0
+locked_out_stack <- locked_out_stack[[c(1, 1, 1)]]
+locked_out_stack[[1]][1] <- 1
+locked_out_stack[[2]][2] <- 1
+locked_out_stack[[3]][3] <- 1
+
+# plot locked out stack
+# \dontrun{
+plot(locked_out_stack)
+
+# }
+# add locked out raster units to problem
+p9 <- p9 %>% add_locked_out_constraints(locked_out_stack)
+
+# \dontrun{
+# solve problem
+s9 <- solve(p9)
+
+# plot solution
+plot(category_layer(s9), main = "solution", axes = FALSE, box = FALSE)
+
+# }
      +
      +
      -
      -

      Add locked in constraints

      - Source: R/add_locked_in_constraints.R + Source: R/add_locked_in_constraints.R
      -

      Add constraints to a conservation planning problem() to ensure +

      Add constraints to a conservation planning problem() to ensure that specific planning units are selected (or allocated to a specific zone) in the solution. For example, it may be desirable to lock in planning units that are inside existing protected areas so that the solution fills in the gaps in the existing reserve network. If specific planning units should be locked out of a solution, use -add_locked_out_constraints(). For problems with non-binary -planning unit allocations (e.g. proportions), the -add_manual_locked_constraints() function can be used to lock +add_locked_out_constraints(). For problems with non-binary +planning unit allocations (e.g., proportions), the +add_manual_locked_constraints() function can be used to lock planning unit allocations to a specific value.

      - 
      add_locked_in_constraints(x, locked_in)
-
-# S4 method for ConservationProblem,numeric
-add_locked_in_constraints(x, locked_in)
-
-# S4 method for ConservationProblem,logical
-add_locked_in_constraints(x, locked_in)
+    
      Usage,
      add_locked_in_constraints(x, locked_in)
 
-# S4 method for ConservationProblem,matrix
-add_locked_in_constraints(x, locked_in)
+# S4 method for ConservationProblem,numeric
+add_locked_in_constraints(x, locked_in)
 
-# S4 method for ConservationProblem,character
-add_locked_in_constraints(x, locked_in)
+# S4 method for ConservationProblem,logical
+add_locked_in_constraints(x, locked_in)
 
-# S4 method for ConservationProblem,Spatial
-add_locked_in_constraints(x, locked_in)
+# S4 method for ConservationProblem,matrix
+add_locked_in_constraints(x, locked_in)
 
-# S4 method for ConservationProblem,sf
-add_locked_in_constraints(x, locked_in)
+# S4 method for ConservationProblem,character
+add_locked_in_constraints(x, locked_in)
 
-# S4 method for ConservationProblem,Raster
-add_locked_in_constraints(x, locked_in)
      
+# S4 method for ConservationProblem,Spatial
+add_locked_in_constraints(x, locked_in)
 
-    
      Arguments
      
-    
-    
-    
-      
-      
-    
-    
-      
-      
-    
-    
      x
      problem() (i.e. ConservationProblem) object.
      locked_in
      Object that determines which planning units that should be
-locked in. See the Data format section for more information.
      
+# S4 method for ConservationProblem,sf
+add_locked_in_constraints(x, locked_in)
 
-    
      Value
      
+# S4 method for ConservationProblem,Raster
+add_locked_in_constraints(x, locked_in)
      -

      Object (i.e. ConservationProblem) with the constraints +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      locked_in
      +

      Object that determines which planning units that should be +locked in. See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the constraints added to it.

      -

      Data format

      - +
      +
      +

      Data format

      The locked planning units can be specified using the following formats. Generally, the locked data should correspond to the planning units in the argument to x. To help make working with -Raster planning unit data easier, +Raster planning unit data easier, the locked data should correspond to cell indices in the -Raster data. For example, integer arguments +Raster data. For example, integer arguments should correspond to cell indices and logical arguments should have a value for each cell---regardless of which planning unit cells contain NA values.

      -
      - -
      data as an integer vector

      containing indices that indicate which +

      data as an integer vector
      +

      containing indices that indicate which planning units should be locked for the solution. This argument is only compatible with problems that contain a single zone.

      -
      data as a logical vector

      containing TRUE and/or + +

      data as a logical vector
      +

      containing TRUE and/or FALSE values that indicate which planning units should be locked in the solution. This argument is only compatible with problems that contain a single zone.

      -
      data as a matrix object

      containing logical TRUE and/or + +

      data as a matrix object
      +

      containing logical TRUE and/or FALSE values which indicate if certain planning units are should be locked to a specific zone in the solution. Each row corresponds to a planning unit, each column corresponds to a zone, and @@ -276,213 +191,217 @@

      TRUE value.

      -
      data as a character vector

      containing field (column) name(s) + +

      data as a character vector
      +

      containing field (column) name(s) that indicate if planning units should be locked for the solution. This format is only compatible if the planning units in the argument to x are a -Spatial, sf::sf(), or +Spatial, sf::sf(), or data.frame object. The fields -(columns) must have logical (i.e. TRUE or FALSE) +(columns) must have logical (i.e., TRUE or FALSE) values indicating if the planning unit is to be locked for the solution. For problems that contain a single zone, the argument to data must contain a single field name. Otherwise, for problems that contain multiple zones, the argument to data must contain a field name for each zone.

      -
      data as a Spatial or sf::sf() object

      containing geometries that will be used to lock planning units for + +

      data as a Spatial or sf::sf() object
      +

      containing geometries that will be used to lock planning units for the solution. Specifically, planning units in x that spatially -intersect with y will be locked (per intersecting_units()). +intersect with y will be locked (per intersecting_units()). Note that this option is only available for problems that contain a single management zone.

      -
      data as a Raster object

      containing cells used to lock + +

      data as a Raster object
      +

      containing cells used to lock planning units for the solution. Specifically, planning units in x that intersect with cells that have non-zero and non-NA values are locked. For problems that contain multiple zones, the -Raster object must contain a layer +Raster object must contain a layer for each zone. Note that for multi-band arguments, each pixel must only contain a non-zero value in a single band. Additionally, if the -cost data in x is a Raster object, we +cost data in x is a Raster object, we recommend standardizing NA values in this dataset with the cost data. In other words, the pixels in x that have NA values should also have NA values in the locked data.

      -
      -

      See also

      - -

      See constraints for an overview of all functions for adding constraints.

      +
      +
      +

      See also

      +

      See constraints for an overview of all functions for adding constraints.

      Other constraints: -add_contiguity_constraints(), -add_feature_contiguity_constraints(), -add_linear_constraints(), -add_locked_out_constraints(), -add_mandatory_allocation_constraints,ConservationProblem-method, -add_manual_bounded_constraints(), -add_manual_locked_constraints()

      - -

      Examples

      - 
      # set seed for reproducibility
-set.seed(500)
-
-# load data
-data(sim_pu_polygons, sim_features, sim_locked_in_raster)
-
-# create minimal problem
-p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.2) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create problem with added locked in constraints using integers
-p2 <- p1 %>% add_locked_in_constraints(which(sim_pu_polygons$locked_in))
-
-# create problem with added locked in constraints using a field name
-p3 <- p1 %>% add_locked_in_constraints("locked_in")
-
-# create problem with added locked in constraints using raster data
-p4 <- p1 %>% add_locked_in_constraints(sim_locked_in_raster)
-
-# create problem with added locked in constraints using spatial polygon data
-locked_in <- sim_pu_polygons[sim_pu_polygons$locked_in == 1, ]
-p5 <- p1 %>% add_locked_in_constraints(locked_in)
-# \dontrun{
-# solve problems
-s1 <- solve(p1)
-s2 <- solve(p2)
-s3 <- solve(p3)
-s4 <- solve(p4)
-s5 <- solve(p5)
-
-# plot solutions
-par(mfrow = c(3, 2), mar = c(0, 0, 4.1, 0))
-plot(s1, main = "none locked in")
-plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s2, main = "locked in (integer input)")
-plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s3, main = "locked in (character input)")
-plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s4, main = "locked in (raster input)")
-plot(s4[s4$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-plot(s5, main = "locked in (polygon input)")
-plot(s5[s5$solution_1 == 1, ], col = "darkgreen", add = TRUE)
-
-# reset plot
-par(mfrow = c(1, 1))
-
-# }
-
-# create minimal multi-zone problem with spatial data
-p6 <- problem(sim_pu_zones_polygons, sim_features_zones,
-              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
-      add_min_set_objective() %>%
-      add_absolute_targets(matrix(rpois(15, 1), nrow = 5,
-                                  ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create multi-zone problem with locked in constraints using matrix data
-locked_matrix <- sim_pu_zones_polygons@data[, c("locked_1", "locked_2",
-                                                "locked_3")]
-locked_matrix <- as.matrix(locked_matrix)
-
-p7 <- p6 %>% add_locked_in_constraints(locked_matrix)
-# \dontrun{
-# solve problem
-s6 <- solve(p6)
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s6$solution <- category_vector(s6@data[, c("solution_1_zone_1",
-                                           "solution_1_zone_2",
-                                           "solution_1_zone_3")])
-s6$solution <- factor(s6$solution)
-
-# plot solution
-spplot(s6, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create multi-zone problem with locked in constraints using field names
-p8 <- p6 %>% add_locked_in_constraints(c("locked_1", "locked_2", "locked_3"))
-# \dontrun{
-# solve problem
-s8 <- solve(p8)
-
-# create new column representing the zone id that each planning unit
-# was allocated to in the solution
-s8$solution <- category_vector(s8@data[, c("solution_1_zone_1",
-                                           "solution_1_zone_2",
-                                           "solution_1_zone_3")])
-s8$solution[s8$solution == 1 & s8$solution_1_zone_1 == 0] <- 0
-s8$solution <- factor(s8$solution)
-
-# plot solution
-spplot(s8, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
-
-# }
-# create multi-zone problem with raster planning units
-p9 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# create raster stack with locked in units
-locked_in_stack <- sim_pu_zones_stack[[1]]
-locked_in_stack[!is.na(locked_in_stack)] <- 0
-locked_in_stack <- locked_in_stack[[c(1, 1, 1)]]
-locked_in_stack[[1]][1] <- 1
-locked_in_stack[[2]][2] <- 1
-locked_in_stack[[3]][3] <- 1
-
-# plot locked in stack
-# \dontrun{
-plot(locked_in_stack)
-
-# }
-# add locked in raster units to problem
-p9 <- p9 %>% add_locked_in_constraints(locked_in_stack)
-
-# \dontrun{
-# solve problem
-s9 <- solve(p9)
-
-# plot solution
-plot(category_layer(s9), main = "solution", axes = FALSE, box = FALSE)
-
-# }
-
+add_contiguity_constraints(),
+add_feature_contiguity_constraints(),
+add_linear_constraints(),
+add_locked_out_constraints(),
+add_mandatory_allocation_constraints,ConservationProblem-method,
+add_manual_bounded_constraints(),
+add_manual_locked_constraints()
      +
      + +
      +

      Examples

      + 
      # set seed for reproducibility
+set.seed(500)
+
+# load data
+data(sim_pu_polygons, sim_features, sim_locked_in_raster)
+
+# create minimal problem
+p1 <- problem(sim_pu_polygons, sim_features, "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.2) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create problem with added locked in constraints using integers
+p2 <- p1 %>% add_locked_in_constraints(which(sim_pu_polygons$locked_in))
+
+# create problem with added locked in constraints using a field name
+p3 <- p1 %>% add_locked_in_constraints("locked_in")
+
+# create problem with added locked in constraints using raster data
+p4 <- p1 %>% add_locked_in_constraints(sim_locked_in_raster)
+
+# create problem with added locked in constraints using spatial polygon data
+locked_in <- sim_pu_polygons[sim_pu_polygons$locked_in == 1, ]
+p5 <- p1 %>% add_locked_in_constraints(locked_in)
+# \dontrun{
+# solve problems
+s1 <- solve(p1)
+s2 <- solve(p2)
+s3 <- solve(p3)
+s4 <- solve(p4)
+s5 <- solve(p5)
+
+# plot solutions
+par(mfrow = c(3, 2), mar = c(0, 0, 4.1, 0))
+plot(s1, main = "none locked in")
+plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s2, main = "locked in (integer input)")
+plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s3, main = "locked in (character input)")
+plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s4, main = "locked in (raster input)")
+plot(s4[s4$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+plot(s5, main = "locked in (polygon input)")
+plot(s5[s5$solution_1 == 1, ], col = "darkgreen", add = TRUE)
+
+# reset plot
+par(mfrow = c(1, 1))
+
+# }
+
+# create minimal multi-zone problem with spatial data
+p6 <- problem(sim_pu_zones_polygons, sim_features_zones,
+              cost_column = c("cost_1", "cost_2", "cost_3")) %>%
+      add_min_set_objective() %>%
+      add_absolute_targets(matrix(rpois(15, 1), nrow = 5,
+                                  ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create multi-zone problem with locked in constraints using matrix data
+locked_matrix <- sim_pu_zones_polygons@data[, c("locked_1", "locked_2",
+                                                "locked_3")]
+locked_matrix <- as.matrix(locked_matrix)
+
+p7 <- p6 %>% add_locked_in_constraints(locked_matrix)
+# \dontrun{
+# solve problem
+s6 <- solve(p6)
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s6$solution <- category_vector(s6@data[, c("solution_1_zone_1",
+                                           "solution_1_zone_2",
+                                           "solution_1_zone_3")])
+s6$solution <- factor(s6$solution)
+
+# plot solution
+spplot(s6, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create multi-zone problem with locked in constraints using field names
+p8 <- p6 %>% add_locked_in_constraints(c("locked_1", "locked_2", "locked_3"))
+# \dontrun{
+# solve problem
+s8 <- solve(p8)
+
+# create new column representing the zone id that each planning unit
+# was allocated to in the solution
+s8$solution <- category_vector(s8@data[, c("solution_1_zone_1",
+                                           "solution_1_zone_2",
+                                           "solution_1_zone_3")])
+s8$solution[s8$solution == 1 & s8$solution_1_zone_1 == 0] <- 0
+s8$solution <- factor(s8$solution)
+
+# plot solution
+spplot(s8, zcol = "solution", main = "solution", axes = FALSE, box = FALSE)
+
+# }
+# create multi-zone problem with raster planning units
+p9 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# create raster stack with locked in units
+locked_in_stack <- sim_pu_zones_stack[[1]]
+locked_in_stack[!is.na(locked_in_stack)] <- 0
+locked_in_stack <- locked_in_stack[[c(1, 1, 1)]]
+locked_in_stack[[1]][1] <- 1
+locked_in_stack[[2]][2] <- 1
+locked_in_stack[[3]][3] <- 1
+
+# plot locked in stack
+# \dontrun{
+plot(locked_in_stack)
+
+# }
+# add locked in raster units to problem
+p9 <- p9 %>% add_locked_in_constraints(locked_in_stack)
+
+# \dontrun{
+# solve problem
+s9 <- solve(p9)
+
+# plot solution
+plot(category_layer(s9), main = "solution", axes = FALSE, box = FALSE)
+
+# }
+
      +
      +
      -
      -

      Add linear penalties

      - Source: R/add_linear_penalties.R + Source: R/add_linear_penalties.R
      -

      Add penalties to a conservation planning problem() to penalize +

      Add penalties to a conservation planning problem() to penalize solutions that select planning units with higher values from a specific -data source (e.g. anthropogenic impact). These penalties assume +data source (e.g., anthropogenic impact). These penalties assume a linear trade-off between the penalty values and the primary -objective of the conservation planning problem() (e.g. -solution cost for minimum set problems; add_min_set_objective().

      +objective of the conservation planning problem() (e.g., +solution cost for minimum set problems; add_min_set_objective().

      - 
      # S4 method for ConservationProblem,ANY,character
-add_linear_penalties(x, penalty, data)
+    
      Usage,
      # S4 method for ConservationProblem,ANY,character
+add_linear_penalties(x, penalty, data)
 
-# S4 method for ConservationProblem,ANY,numeric
-add_linear_penalties(x, penalty, data)
+# S4 method for ConservationProblem,ANY,numeric
+add_linear_penalties(x, penalty, data)
 
-# S4 method for ConservationProblem,ANY,matrix
-add_linear_penalties(x, penalty, data)
+# S4 method for ConservationProblem,ANY,matrix
+add_linear_penalties(x, penalty, data)
 
-# S4 method for ConservationProblem,ANY,Matrix
-add_linear_penalties(x, penalty, data)
+# S4 method for ConservationProblem,ANY,Matrix
+add_linear_penalties(x, penalty, data)
 
-# S4 method for ConservationProblem,ANY,Raster
-add_linear_penalties(x, penalty, data)
+# S4 method for ConservationProblem,ANY,Raster
+add_linear_penalties(x, penalty, data)
 
-# S4 method for ConservationProblem,ANY,dgCMatrix
-add_linear_penalties(x, penalty, data)
      
+# S4 method for ConservationProblem,ANY,dgCMatrix
+add_linear_penalties(x, penalty, data)
      -

      Arguments

      - - - - - - - - - - - - - - -
      x

      problem() (i.e. ConservationProblem) object.

      penalty

      numeric penalty value that is used to scale the +

      +

      Arguments

      +
      x
      +

      problem() (i.e., ConservationProblem) object.

      +
      penalty
      +

      numeric penalty value that is used to scale the importance not selecting planning units with high data values. Higher penalty values can be used to obtain solutions that are strongly averse to selecting places with high data @@ -231,39 +144,36 @@

      Arg penalty values can be used to obtain solutions that prefer places with high data values. Additionally, when adding these penalties to problems with multiple zones, the argument to penalty -must have a value for each zone.

      data

      character, numeric, -Raster, matrix, or Matrix object +must have a value for each zone.

      +
      data
      +

      character, numeric, +Raster, matrix, or Matrix object containing the values used to penalize solutions. Planning units that are associated with higher data values are penalized more strongly -in the solution. See the Data format section for more information.

      - -

      Value

      - -

      Object (i.e. ConservationProblem) with the penalties +in the solution. See the Data format section for more information.

      +
      +
      +

      Value

      +

      Object (i.e., ConservationProblem) with the penalties added to it.

      -

      Details

      - +
      +
      +

      Details

      This function penalizes solutions that have higher values according to the sum of the penalty values associated with each planning unit, weighted by status of each planning unit in the solution.

      -

      Data format

      - +
      +
      +

      Data format

      The argument to data can be specified using the following formats.

      -
      - -
      data as character vector

      containing field (column) name(s) that +

      data as character vector
      +

      containing field (column) name(s) that contain penalty values for planning units. This format is only compatible if the planning units in the argument to x are a -Spatial, sf::sf(), or +Spatial, sf::sf(), or data.frame object. The fields (columns) must have numeric values, and must not contain any missing (NA) values. For problems that contain a single zone, the argument to data must @@ -271,28 +181,34 @@

      data must contain a field name for each zone.

      -
      data as a numeric vector

      containing values for + +

      data as a numeric vector
      +

      containing values for planning units. These values must not contain any missing (NA) values. Note that this format is only available for planning units that contain a single zone.

      -
      data as a matrix/Matrix object

      containing numeric values + +

      data as a matrix/Matrix object
      +

      containing numeric values that specify data for each planning unit. Each row corresponds to a planning unit, each column corresponds to a zone, and each cell indicates the data for penalizing a planning unit when it is allocated to a given zone.

      -
      data as a Raster object

      containing values for planning + +

      data as a Raster object
      +

      containing values for planning units. This format is only compatible if the planning units in the argument to x are -Spatial, sf::sf(), or -Raster objects. -If the planning unit data are a Spatial or -sf::sf() object, then the values are calculated by overlaying the +Spatial, sf::sf(), or +Raster objects. +If the planning unit data are a Spatial or +sf::sf() object, then the values are calculated by overlaying the planning units with the argument to data and calculating the sum of the values associated with each planning unit. If the planning unit data are a -Raster object then the values are calculated by extracting the +Raster object then the values are calculated by extracting the cell values (note that the planning unit data and the argument to data must have exactly the same dimensionality, extent, and missingness). @@ -300,10 +216,10 @@

      -
      - -

      Mathematical formulation

      +
      +
      +

      Mathematical formulation

      The linear penalties are implemented using the following @@ -311,7 +227,7 @@

      See also

      - -

      See penalties for an overview of all functions for adding penalties.

      +
      +
      +

      See also

      +

      See penalties for an overview of all functions for adding penalties.

      Other penalties: -add_boundary_penalties(), -add_connectivity_penalties(), -add_feature_weights()

      - -

      Examples

      - 
      # set seed for reproducibility
-set.seed(600)
-
-# load data
-data(sim_pu_polygons, sim_pu_zones_stack, sim_features, sim_features_zones)
-
-# add a column to contain the penalty data for each planning unit
-# e.g. these values could indicate the level of habitat
-sim_pu_polygons$penalty_data <- runif(nrow(sim_pu_polygons))
-
-# plot the penalty data to visualise its spatial distribution
-spplot(sim_pu_polygons, zcol = "penalty_data", main = "penalty data",
-       axes = FALSE, box = FALSE)
-
-
-# create minimal problem with minimum set objective,
-# this does not use the penalty data
-p1 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
-      add_min_set_objective() %>%
-      add_relative_targets(0.1) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# print problem
-print(p1)
-#> Conservation Problem
-#>   planning units: SpatialPolygonsDataFrame (90 units)
-#>   cost:           min: 190.13276, max: 215.86384
-#>   features:       layer.1, layer.2, layer.3, ... (5 features)
-#>   objective:      Minimum set objective 
-#>   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-#>   decisions:      Binary decision 
-#>   constraints:    <none>
-#>   penalties:      <none>
-#>   portfolio:      default
-#>   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (0)]
-
-# create an updated version of the previous problem,
-# with the penalties added to it
-p2 <- p1 %>% add_linear_penalties(100, data = "penalty_data")
-
-# print problem
-print(p2)
-#> Conservation Problem
-#>   planning units: SpatialPolygonsDataFrame (90 units)
-#>   cost:           min: 190.13276, max: 215.86384
-#>   features:       layer.1, layer.2, layer.3, ... (5 features)
-#>   objective:      Minimum set objective 
-#>   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-#>   decisions:      Binary decision 
-#>   constraints:    <none>
-#>   penalties:      <Linear penalties [penalty (100)]>
-#>   portfolio:      default
-#>   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (0)]
-
-# \dontrun{
-# solve the two problems
-s1 <- solve(p1)
-s2 <- solve(p2)
-
-# plot the solutions and compare them,
-# since we supplied a very high penalty value (i.e. 100), relative
-# to the range of values in the penalty data and the objective function,
-# the solution in s2 is very sensitive to values in the penalty data
-spplot(s1, zcol = "solution_1", main = "solution without penalties",
-       axes = FALSE, box = FALSE)
-
-spplot(s2, zcol = "solution_1", main = "solution with penalties",
-       axes = FALSE, box = FALSE)
-
-
-# for real conservation planning exercises,
-# it would be worth exploring a range of penalty values (e.g. ranging
-# from 1 to 100 increments of 5) to explore the trade-offs
-# }
-
-# now, let's examine a conservation planning exercise involving multiple
-# management zones
-
-# \dontrun{
-# create targets for each feature within each zone,
-# these targets indicate that each zone needs to represent 10% of the
-# spatial distribution of each feature
-targ <- matrix(0.1, ncol = number_of_zones(sim_features_zones),
-               nrow = number_of_features(sim_features_zones))
-
-# create penalty data for allocating each planning unit to each zone,
-# these data will be generated by simulating values
-# (note this requires the RandomFields package to be installed)
-penalty_stack <- simulate_cost(sim_pu_zones_stack[[1]],
-                               n = number_of_zones(sim_features_zones))
-#> ...
-
-# plot the penalty data, each layer corresponds to a different zone
-plot(penalty_stack, main = "penalty data", axes = FALSE, box = FALSE)
-
-
-# create a multi-zone problem with the minimum set objective
-# and penalties for allocating planning units to each zone,
-# with a penalty scaling factor of 1 for each zone
-p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
-      add_min_set_objective() %>%
-      add_relative_targets(targ) %>%
-      add_linear_penalties(c(1, 1, 1), penalty_stack) %>%
-      add_binary_decisions() %>%
-      add_default_solver(verbose = FALSE)
-
-# print problem
-print(p3)
-#> Conservation Problem
-#>   zones:          zone_1, zone_2, zone_3 (3 zones)
-#>   planning units: RasterStack (90 units)
-#>   cost:           min: 182.60173, max: 224.84924
-#>   features:       feature_1, feature_2, feature_3, ... (5 features)
-#>   objective:      Minimum set objective 
-#>   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
-#>   decisions:      Binary decision 
-#>   constraints:    <none>
-#>   penalties:      <Linear penalties [penalty (min: 1, max: 1)]>
-#>   portfolio:      default
-#>   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (0)]
-
-# solve problem
-s3 <- solve(p3)
-
-# plot solution
-plot(category_layer(s3), main = "multi-zone solution",
-     axes = FALSE, box = FALSE)
-
-# }
+add_boundary_penalties(),
+add_connectivity_penalties(),
+add_feature_weights()
      +
      + +
      +

      Examples

      + 
      # set seed for reproducibility
+set.seed(600)
+
+# load data
+data(sim_pu_polygons, sim_pu_zones_stack, sim_features, sim_features_zones)
+
+# add a column to contain the penalty data for each planning unit
+# e.g., these values could indicate the level of habitat
+sim_pu_polygons$penalty_data <- runif(nrow(sim_pu_polygons))
+
+# plot the penalty data to visualise its spatial distribution
+spplot(sim_pu_polygons, zcol = "penalty_data", main = "penalty data",
+       axes = FALSE, box = FALSE)
+
+
+# create minimal problem with minimum set objective,
+# this does not use the penalty data
+p1 <- problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
+      add_min_set_objective() %>%
+      add_relative_targets(0.1) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# print problem
+print(p1)
+#> Conservation Problem
+#>   planning units: SpatialPolygonsDataFrame (90 units)
+#>   cost:           min: 190.13276, max: 215.86384
+#>   features:       layer.1, layer.2, layer.3, ... (5 features)
+#>   objective:      Minimum set objective 
+#>   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+#>   decisions:      Binary decision 
+#>   constraints:    <none>
+#>   penalties:      <none>
+#>   portfolio:      default
+#>   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (0)]
+
+# create an updated version of the previous problem,
+# with the penalties added to it
+p2 <- p1 %>% add_linear_penalties(100, data = "penalty_data")
+
+# print problem
+print(p2)
+#> Conservation Problem
+#>   planning units: SpatialPolygonsDataFrame (90 units)
+#>   cost:           min: 190.13276, max: 215.86384
+#>   features:       layer.1, layer.2, layer.3, ... (5 features)
+#>   objective:      Minimum set objective 
+#>   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+#>   decisions:      Binary decision 
+#>   constraints:    <none>
+#>   penalties:      <Linear penalties [penalty (100)]>
+#>   portfolio:      default
+#>   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (0)]
+
+# \dontrun{
+# solve the two problems
+s1 <- solve(p1)
+s2 <- solve(p2)
+
+# plot the solutions and compare them,
+# since we supplied a very high penalty value (i.e., 100), relative
+# to the range of values in the penalty data and the objective function,
+# the solution in s2 is very sensitive to values in the penalty data
+spplot(s1, zcol = "solution_1", main = "solution without penalties",
+       axes = FALSE, box = FALSE)
+
+spplot(s2, zcol = "solution_1", main = "solution with penalties",
+       axes = FALSE, box = FALSE)
+
+
+# for real conservation planning exercises,
+# it would be worth exploring a range of penalty values (e.g., ranging
+# from 1 to 100 increments of 5) to explore the trade-offs
+# }
+
+# now, let's examine a conservation planning exercise involving multiple
+# management zones
+
+# \dontrun{
+# create targets for each feature within each zone,
+# these targets indicate that each zone needs to represent 10% of the
+# spatial distribution of each feature
+targ <- matrix(0.1, ncol = number_of_zones(sim_features_zones),
+               nrow = number_of_features(sim_features_zones))
+
+# create penalty data for allocating each planning unit to each zone,
+# these data will be generated by simulating values
+# (note this requires the RandomFields package to be installed)
+penalty_stack <- simulate_cost(sim_pu_zones_stack[[1]],
+                               n = number_of_zones(sim_features_zones))
+#> ...
+
+# plot the penalty data, each layer corresponds to a different zone
+plot(penalty_stack, main = "penalty data", axes = FALSE, box = FALSE)
+
+
+# create a multi-zone problem with the minimum set objective
+# and penalties for allocating planning units to each zone,
+# with a penalty scaling factor of 1 for each zone
+p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
+      add_min_set_objective() %>%
+      add_relative_targets(targ) %>%
+      add_linear_penalties(c(1, 1, 1), penalty_stack) %>%
+      add_binary_decisions() %>%
+      add_default_solver(verbose = FALSE)
+
+# print problem
+print(p3)
+#> Conservation Problem
+#>   zones:          zone_1, zone_2, zone_3 (3 zones)
+#>   planning units: RasterStack (90 units)
+#>   cost:           min: 182.60173, max: 224.84924
+#>   features:       feature_1, feature_2, feature_3, ... (5 features)
+#>   objective:      Minimum set objective 
+#>   targets:        Relative targets [targets (min: 0.1, max: 0.1)]
+#>   decisions:      Binary decision 
+#>   constraints:    <none>
+#>   penalties:      <Linear penalties [penalty (min: 1, max: 1)]>
+#>   portfolio:      default
+#>   solver:         Gurobi [first_feasible (0), gap (0.1), node_file_start (-1), numeric_focus (0), presolve (2), threads (1), time_limit (2147483647), verbose (0)]
+
+# solve problem
+s3 <- solve(p3)
+
+# plot solution
+plot(category_layer(s3), main = "multi-zone solution",
+     axes = FALSE, box = FALSE)
+
+# }
      +
      +