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<meta property="og:description" content="Set the objective of a conservation planning problem() to
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This objective is similar to that used in
Marxan and is detailed in Rodrigues et al. (2000)." />
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<h1>Add minimum set objective</h1>
<small class="dont-index">Source: <a href='https://github.com/prioritizr/prioritizr/blob/master/R/add_min_set_objective.R'><code>R/add_min_set_objective.R</code></a></small>
<div class="hidden name"><code>add_min_set_objective.Rd</code></div>
</div>
<div class="ref-description">
<p>Set the objective of a conservation planning <code><a href='problem.html'>problem()</a></code> to
minimize the cost of the solution whilst ensuring that all <a href='targets.html'>targets</a> are met.
This objective is similar to that used in
<em>Marxan</em> and is detailed in Rodrigues <em>et al.</em> (2000).</p>
</div>
<div class="ref-usage sourceCode"><pre class='sourceCode r'><code><span class='fu'>add_min_set_objective</span><span class='op'>(</span><span class='va'>x</span><span class='op'>)</span></code></pre></div>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>x</th>
<td><p><code><a href='problem.html'>problem()</a></code> (i.e. <code><a href='ConservationProblem-class.html'>ConservationProblem</a></code>) object.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
<p>Object (i.e. <code><a href='ConservationProblem-class.html'>ConservationProblem</a></code>) with the objective
added to it.</p>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>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
targets for the conservation features. This objective is equivalent to a
simplified <em>Marxan</em> reserve design problem with the Boundary Length Modifier
(BLM) set to zero. The difference between this objective and the
<em>Marxan</em> software is that the targets for the features will always be met
(and as such it does not use Species Penalty Factors).</p>
<h2 class="hasAnchor" id="mathematical-formulation"><a class="anchor" href="#mathematical-formulation"></a>Mathematical formulation</h2>
<p>This objective can be expressed
mathematically for a set of planning units (\(I\) indexed by
\(i\)) and a set of features (\(J\) indexed by \(j\)) as:</p>
<p>$$\mathit{Minimize} \space \sum_{i = 1}^{I} x_i c_i \\
\mathit{subject \space to} \\
\sum_{i = 1}^{I} x_i r_{ij} \geq T_j \space \forall \space j \in J$$</p>
<p>Here, \(x_i\) is the <a href='decisions.html'>decisions</a> 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
\(i\), and \(T_j\) is the target for feature \(j\). The
first term is the objective function and the second is the set of
constraints. In words this says find the set of planning units that meets
all the representation targets while minimizing the overall cost.</p>
<h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
<p>Rodrigues AS, Cerdeira OJ, and Gaston KJ (2000) Flexibility,
efficiency, and accountability: adapting reserve selection algorithms to
more complex conservation problems. <em>Ecography</em>, 23: 565--574.</p>
<h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
<div class='dont-index'><p>See <a href='objectives.html'>objectives</a> for an overview of all functions for adding objectives.
Also see <a href='targets.html'>targets</a> for an overview of all functions for adding targets.</p>
<p>Other objectives:
<code><a href='add_max_cover_objective.html'>add_max_cover_objective</a>()</code>,
<code><a href='add_max_features_objective.html'>add_max_features_objective</a>()</code>,
<code><a href='add_max_phylo_div_objective.html'>add_max_phylo_div_objective</a>()</code>,
<code><a href='add_max_phylo_end_objective.html'>add_max_phylo_end_objective</a>()</code>,
<code><a href='add_max_utility_objective.html'>add_max_utility_objective</a>()</code>,
<code><a href='add_min_largest_shortfall_objective.html'>add_min_largest_shortfall_objective</a>()</code>,
<code><a href='add_min_shortfall_objective.html'>add_min_shortfall_objective</a>()</code></p></div>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<div class="ref-examples sourceCode"><pre class='sourceCode r'><code><span class='r-in'><span class='co'># set seed for reproducibility</span></span>
<span class='r-in'><span class='fu'><a href='https://rdrr.io/r/base/Random.html'>set.seed</a></span><span class='op'>(</span><span class='fl'>500</span><span class='op'>)</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># load data</span></span>
<span class='r-in'><span class='fu'><a href='https://rdrr.io/r/utils/data.html'>data</a></span><span class='op'>(</span><span class='va'>sim_pu_raster</span>, <span class='va'>sim_features</span>, <span class='va'>sim_pu_zones_stack</span>, <span class='va'>sim_features_zones</span><span class='op'>)</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># create minimal problem with minimum set objective</span></span>
<span class='r-in'><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 class='r-in'> <span class='fu'>add_min_set_objective</span><span class='op'>(</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_relative_targets.html'>add_relative_targets</a></span><span class='op'>(</span><span class='fl'>0.1</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_binary_decisions.html'>add_binary_decisions</a></span><span class='op'>(</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <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 class='r-in'><span class='co'># \dontrun{</span></span>
<span class='r-in'><span class='co'># solve problem</span></span>
<span class='r-in'><span class='va'>s1</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>
<span class='r-in'></span>
<span class='r-in'><span class='co'># plot solution</span></span>
<span class='r-in'><span class='fu'><a href='https://rdrr.io/pkg/raster/man/plot.html'>plot</a></span><span class='op'>(</span><span class='va'>s1</span>, main <span class='op'>=</span> <span class='st'>"solution"</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 class='r-plt'><img src='add_min_set_objective-1.png' alt='' width='700' height='433' /></span>
<span class='r-in'><span class='co'># }</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='co'># create multi-zone problem with minimum set objective</span></span>
<span class='r-in'><span class='va'>targets_matrix</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/matrix.html'>matrix</a></span><span class='op'>(</span><span class='fu'><a href='https://rdrr.io/r/stats/Poisson.html'>rpois</a></span><span class='op'>(</span><span class='fl'>15</span>, <span class='fl'>1</span><span class='op'>)</span>, nrow <span class='op'>=</span> <span class='fl'>5</span>, ncol <span class='op'>=</span> <span class='fl'>3</span><span class='op'>)</span></span>
<span class='r-in'></span>
<span class='r-in'><span class='va'>p2</span> <span class='op'><-</span> <span class='fu'><a href='problem.html'>problem</a></span><span class='op'>(</span><span class='va'>sim_pu_zones_stack</span>, <span class='va'>sim_features_zones</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'>add_min_set_objective</span><span class='op'>(</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_absolute_targets.html'>add_absolute_targets</a></span><span class='op'>(</span><span class='va'>targets_matrix</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <span class='fu'><a href='add_binary_decisions.html'>add_binary_decisions</a></span><span class='op'>(</span><span class='op'>)</span> <span class='op'><a href='pipe.html'>%>%</a></span></span>
<span class='r-in'> <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 class='r-in'><span class='co'># \dontrun{</span></span>
<span class='r-in'><span class='co'># solve problem</span></span>
<span class='r-in'><span class='va'>s2</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>
<span class='r-in'></span>
<span class='r-in'><span class='co'># plot solution</span></span>
<span class='r-in'><span class='fu'><a href='https://rdrr.io/pkg/raster/man/plot.html'>plot</a></span><span class='op'>(</span><span class='fu'><a href='category_layer.html'>category_layer</a></span><span class='op'>(</span><span class='va'>s2</span><span class='op'>)</span>, main <span class='op'>=</span> <span class='st'>"solution"</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 class='r-plt'><img src='add_min_set_objective-2.png' alt='' width='700' height='433' /></span>
<span class='r-in'><span class='co'># }</span></span>
</code></pre></div>
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