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<!DOCTYPE html>
<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Add a penalty — penalties • prioritizr</title><!-- favicons --><link rel="icon" type="image/png" sizes="16x16" href="../favicon-16x16.png"><link rel="icon" type="image/png" sizes="32x32" href="../favicon-32x32.png"><link rel="apple-touch-icon" type="image/png" sizes="180x180" href="../apple-touch-icon.png"><link rel="apple-touch-icon" type="image/png" sizes="120x120" href="../apple-touch-icon-120x120.png"><link rel="apple-touch-icon" type="image/png" sizes="76x76" href="../apple-touch-icon-76x76.png"><link rel="apple-touch-icon" type="image/png" sizes="60x60" href="../apple-touch-icon-60x60.png"><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/flatly/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><!-- docsearch --><script src="../docsearch.js"></script><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/docsearch.js/2.6.3/docsearch.min.css" integrity="sha256-QOSRU/ra9ActyXkIBbiIB144aDBdtvXBcNc3OTNuX/Q=" crossorigin="anonymous"><link href="../docsearch.css" rel="stylesheet"><script src="https://cdnjs.cloudflare.com/ajax/libs/mark.js/8.11.1/jquery.mark.min.js" integrity="sha256-4HLtjeVgH0eIB3aZ9mLYF6E8oU5chNdjU6p6rrXpl9U=" crossorigin="anonymous"></script><link href="../extra.css" rel="stylesheet"><meta property="og:title" content="Add a penalty — penalties"><meta property="og:description" content="A penalty can be applied to a conservation planning problem() to
penalize solutions according to a specific metric. They
directly trade-off with the primary objective of a problem
(e.g., the primary objective when using add_min_set_objective() is
to minimize solution cost)."><meta property="og:image" content="https://prioritizr.net/logo.png"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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<h1>Add a penalty</h1>
<small class="dont-index">Source: <a href="https://github.com/prioritizr/prioritizr/blob/HEAD/R/penalties.R" class="external-link"><code>R/penalties.R</code></a></small>
<div class="hidden name"><code>penalties.Rd</code></div>
</div>
<div class="ref-description">
<p>A penalty can be applied to a conservation planning <code><a href="problem.html">problem()</a></code> to
penalize solutions according to a specific metric. They
directly trade-off with the primary objective of a problem
(e.g., the primary objective when using <code><a href="add_min_set_objective.html">add_min_set_objective()</a></code> is
to minimize solution cost).</p>
</div>
<div id="details">
<h2>Details</h2>
<p>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
primary problem objective and are mediated by a penalty factor.</p>
<p>The following penalties can be added to a conservation planning
<code><a href="problem.html">problem()</a></code>:</p>
<dl><dt><code><a href="add_boundary_penalties.html">add_boundary_penalties()</a></code></dt>
<dd><p>Add penalties to a
conservation problem to favor solutions that have
planning units clumped together into contiguous areas.</p></dd>
<dt><code><a href="add_asym_connectivity_penalties.html">add_asym_connectivity_penalties()</a></code></dt>
<dd><p>Add penalties to a
conservation problem to account for asymmetric connectivity.</p></dd>
<dt><code><a href="add_connectivity_penalties.html">add_connectivity_penalties()</a></code></dt>
<dd><p>Add penalties to a
conservation problem to account for
symmetric connectivity.</p></dd>
<dt><code><a href="add_linear_penalties.html">add_linear_penalties()</a></code></dt>
<dd><p>Add penalties to a
conservation problem to favor solutions that avoid selecting
planning units based on a certain variable
(e.g., anthropogenic pressure).</p></dd>
</dl></div>
<div id="see-also">
<h2>See also</h2>
<div class="dont-index"><p>Other overviews:
<code><a href="constraints.html">constraints</a></code>,
<code><a href="decisions.html">decisions</a></code>,
<code><a href="importance.html">importance</a></code>,
<code><a href="objectives.html">objectives</a></code>,
<code><a href="portfolios.html">portfolios</a></code>,
<code><a href="solvers.html">solvers</a></code>,
<code><a href="summaries.html">summaries</a></code>,
<code><a href="targets.html">targets</a></code></p></div>
</div>
<div id="ref-examples">
<h2>Examples</h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># load data</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/utils/data.html" class="external-link">data</a></span><span class="op">(</span><span class="va">sim_pu_raster</span>, <span class="va">sim_features</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># create basic problem</span></span></span>
<span class="r-in"><span><span class="va">p1</span> <span class="op"><-</span> <span class="fu"><a href="problem.html">problem</a></span><span class="op">(</span><span class="va">sim_pu_raster</span>, <span class="va">sim_features</span><span class="op">)</span> <span class="op"><a href="pipe.html">%>%</a></span></span></span>
<span class="r-in"><span> <span class="fu"><a href="add_min_set_objective.html">add_min_set_objective</a></span><span class="op">(</span><span class="op">)</span> <span class="op"><a href="pipe.html">%>%</a></span></span></span>
<span class="r-in"><span> <span class="fu"><a href="add_relative_targets.html">add_relative_targets</a></span><span class="op">(</span><span class="fl">0.2</span><span class="op">)</span> <span class="op"><a href="pipe.html">%>%</a></span></span></span>
<span class="r-in"><span> <span class="fu"><a href="add_default_solver.html">add_default_solver</a></span><span class="op">(</span>verbose <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># create problem with boundary penalties</span></span></span>
<span class="r-in"><span><span class="va">p2</span> <span class="op"><-</span> <span class="va">p1</span> <span class="op"><a href="pipe.html">%>%</a></span> <span class="fu"><a href="add_boundary_penalties.html">add_boundary_penalties</a></span><span class="op">(</span><span class="fl">5</span>, <span class="fl">1</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># create connectivity matrix based on spatial proximity</span></span></span>
<span class="r-in"><span> <span class="va">scm</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/as.data.frame.html" class="external-link">as.data.frame</a></span><span class="op">(</span><span class="va">sim_pu_raster</span>, xy <span class="op">=</span> <span class="cn">TRUE</span>, na.rm <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></span>
<span class="r-in"><span> <span class="va">scm</span> <span class="op"><-</span> <span class="fl">1</span> <span class="op">/</span> <span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">as.matrix</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/dist.html" class="external-link">dist</a></span><span class="op">(</span><span class="va">scm</span><span class="op">)</span><span class="op">)</span> <span class="op">+</span> <span class="fl">1</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># remove weak and moderate connections between planning units to reduce</span></span></span>
<span class="r-in"><span><span class="co"># run time</span></span></span>
<span class="r-in"><span><span class="va">scm</span><span class="op">[</span><span class="va">scm</span> <span class="op"><</span> <span class="fl">0.85</span><span class="op">]</span> <span class="op"><-</span> <span class="fl">0</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># create problem with connectivity penalties</span></span></span>
<span class="r-in"><span><span class="va">p3</span> <span class="op"><-</span> <span class="va">p1</span> <span class="op"><a href="pipe.html">%>%</a></span> <span class="fu"><a href="add_connectivity_penalties.html">add_connectivity_penalties</a></span><span class="op">(</span><span class="fl">25</span>, data <span class="op">=</span> <span class="va">scm</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># create asymmetric connectivity data by randomly simulating values</span></span></span>
<span class="r-in"><span><span class="va">acm</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Uniform.html" class="external-link">runif</a></span><span class="op">(</span><span class="fu"><a href="OptimizationProblem-methods.html">ncell</a></span><span class="op">(</span><span class="va">sim_pu_raster</span><span class="op">)</span> <span class="op">^</span> <span class="fl">2</span><span class="op">)</span>, ncol <span class="op">=</span> <span class="fu"><a href="OptimizationProblem-methods.html">ncell</a></span><span class="op">(</span><span class="va">sim_pu_raster</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="va">acm</span><span class="op">[</span><span class="va">acm</span> <span class="op"><</span> <span class="fl">0.85</span><span class="op">]</span> <span class="op"><-</span> <span class="fl">0</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># create problem with asymmetric connectivity penalties</span></span></span>
<span class="r-in"><span><span class="va">p4</span> <span class="op"><-</span> <span class="va">p1</span> <span class="op"><a href="pipe.html">%>%</a></span> <span class="fu"><a href="add_asym_connectivity_penalties.html">add_asym_connectivity_penalties</a></span><span class="op">(</span><span class="fl">1</span>, data <span class="op">=</span> <span class="va">acm</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># create problem with linear penalties,</span></span></span>
<span class="r-in"><span><span class="co"># here the penalties will be based on random numbers to keep it simple</span></span></span>
<span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
<span class="r-in"><span><span class="co"># simulate penalty data</span></span></span>
<span class="r-in"><span><span class="va">sim_penalty_raster</span> <span class="op"><-</span> <span class="fu"><a href="simulate_cost.html">simulate_cost</a></span><span class="op">(</span><span class="va">sim_pu_raster</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># plot penalty data</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">sim_penalty_raster</span>, main <span class="op">=</span> <span class="st">"penalty data"</span>, axes <span class="op">=</span> <span class="cn">FALSE</span>, box <span class="op">=</span> <span class="cn">FALSE</span><span class="op">)</span></span></span>
<span class="r-plt img"><img src="penalties-1.png" alt="" width="700" height="433"></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># create problem with linear penalties, with a penalty scaling factor of 100</span></span></span>
<span class="r-in"><span><span class="va">p5</span> <span class="op"><-</span> <span class="va">p1</span> <span class="op"><a href="pipe.html">%>%</a></span> <span class="fu"><a href="add_linear_penalties.html">add_linear_penalties</a></span><span class="op">(</span><span class="fl">100</span>, data <span class="op">=</span> <span class="va">sim_penalty_raster</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># solve problems</span></span></span>
<span class="r-in"><span><span class="va">s</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/pkg/raster/man/stack.html" class="external-link">stack</a></span><span class="op">(</span><span class="fu"><a href="solve.html">solve</a></span><span class="op">(</span><span class="va">p1</span><span class="op">)</span>, <span class="fu"><a href="solve.html">solve</a></span><span class="op">(</span><span class="va">p2</span><span class="op">)</span>, <span class="fu"><a href="solve.html">solve</a></span><span class="op">(</span><span class="va">p3</span><span class="op">)</span>, <span class="fu"><a href="solve.html">solve</a></span><span class="op">(</span><span class="va">p4</span><span class="op">)</span>, <span class="fu"><a href="solve.html">solve</a></span><span class="op">(</span><span class="va">p5</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># plot solutions</span></span></span>
<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/plot.html" class="external-link">plot</a></span><span class="op">(</span><span class="va">s</span>, axes <span class="op">=</span> <span class="cn">FALSE</span>, box <span class="op">=</span> <span class="cn">FALSE</span>,</span></span>
<span class="r-in"><span> main <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"basic solution"</span>, <span class="st">"boundary penalties"</span>,</span></span>
<span class="r-in"><span> <span class="st">"connectivity penalties"</span>, <span class="st">"asymmetric penalties"</span>,</span></span>
<span class="r-in"><span> <span class="st">"linear penalties"</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-plt img"><img src="penalties-2.png" alt="" width="700" height="433"></span>
<span class="r-in"><span> <span class="co"># }</span></span></span>
</code></pre></div>
</div>
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