gMOIP - Tools for 2D and 3D plots of single and multi-objective linear/integer programming models

With this package you can make 2D and 3D plots of linear programming (LP), integer linear programming (ILP), or mixed integer linear programming (MILP) models with up to three objectives. Plots of both the solution and criterion space are possible. For instance the non-dominated (Pareto) set for bi-objective LP/ILP/MILP programming models.

The convex hull of a set of points in 2D or 3D can also be plotted. A general function for checking if a point is inside the convex hull is also provided.

Usage

We define the model (\max{cx | Ax \leq b}) (could also be minimized) with 2 variables:

A <- matrix(c(-3,2,2,4,9,10), ncol = 2, byrow = TRUE)
b <- c(3,27,90)
obj <- c(7.75, 10)  # coefficients c

The polytope of the LP model with non-negative continuous variables ((x \geq 0)):

plotPolytope(
   A,
   b,
   obj,
   type = rep("c", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)

The polytope of the ILP model with LP faces ((x\in \mathbb{Z}_0)):

plotPolytope(
   A,
   b,
   obj,
   type = rep("i", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)

The polytope of the MILP model (first variable integer) with LP faces:

plotPolytope(
   A,
   b,
   obj,
   type = c("i", "c"),
   crit = "max",
   faces = c("c", "c"),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)

You can do the same with three variables:

A <- matrix( c(
   3, 2, 5,
   2, 1, 1,
   1, 1, 3,
   5, 2, 4
), nc = 3, byrow = TRUE)
b <- c(55, 26, 30, 57)
obj <- c(20, 10, 15)

# LP model
view <- matrix( c(-0.412063330411911, -0.228006735444069, 0.882166087627411, 0, 0.910147845745087,
                  -0.0574885793030262, 0.410274744033813, 0, -0.042830865830183, 0.97196090221405,
                  0.231208890676498, 0, 0, 0, 0, 1), nc = 4)   
loadView(v = view)  # set view angle
plotPolytope(A, b, plotOptimum = TRUE, obj = obj, labels = "n")
snapshot3d("README-3d-1.png")

The 3D plot is here a static image (so it can be seen in markdown). However, it may be an interactive plot as seen in this example.

For more examples see example("gMOIP-package") or browseVignettes('gMOIP').

LaTeX support

You may create a TikZ file of the plot for LaTeX using

library(tikzDevice)
tikz(file = "plot_polytope.tex", standAlone=F, width = 7, height = 6)
plotPolytope(
   A,
   b,
   obj,
   type = rep("i", ncol(A)),
   crit = "max",
   faces = rep("c", ncol(A)),
   plotFaces = TRUE,
   plotFeasible = TRUE,
   plotOptimum = TRUE,
   labels = "coord"
)
dev.off()

Installation

Install the latest stable release from CRAN:

install.packages("gMOIP")

Alternatively, install the latest development version from GitHub:

install.packages("remotes")
remotes::install_github("relund/gMOIP")

library(gMOIP)
browseVignettes('gMOIP')
example("gMOIP-package")