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<title>9. Benchmark Problems &#8212; MIPLearn 0.3</title>
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<a class="reference internal nav-link" href="#module-miplearn.problems.binpack">
9.1. miplearn.problems.binpack
</a>
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<a class="reference internal nav-link" href="#module-miplearn.problems.multiknapsack">
9.2. miplearn.problems.multiknapsack
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9.3. miplearn.problems.pmedian
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9.4. miplearn.problems.setcover
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9.5. miplearn.problems.setpack
</a>
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<a class="reference internal nav-link" href="#module-miplearn.problems.stab">
9.6. miplearn.problems.stab
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9.7. miplearn.problems.tsp
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9.8. miplearn.problems.uc
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<a class="reference internal nav-link" href="#module-miplearn.problems.vertexcover">
9.9. miplearn.problems.vertexcover
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<div class="section" id="benchmark-problems">
<h1><span class="section-number">9. </span>Benchmark Problems<a class="headerlink" href="#benchmark-problems" title="Permalink to this headline"></a></h1>
<div class="section" id="module-miplearn.problems.binpack">
<span id="miplearn-problems-binpack"></span><h2><span class="section-number">9.1. </span>miplearn.problems.binpack<a class="headerlink" href="#module-miplearn.problems.binpack" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt id="miplearn.problems.binpack.BinPackData">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.binpack.</span></code><code class="sig-name descname"><span class="pre">BinPackData</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sizes</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">capacity</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">int</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.binpack.BinPackData" title="Permalink to this definition"></a></dt>
<dd><p>Data for the bin packing problem.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>sizes</strong> (<em>numpy.ndarray</em>) – Sizes of the items</p></li>
<li><p><strong>capacity</strong> (<em>int</em>) – Capacity of the bin</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py class">
<dt id="miplearn.problems.binpack.BinPackGenerator">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.binpack.</span></code><code class="sig-name descname"><span class="pre">BinPackGenerator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sizes</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">capacity</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sizes_jitter</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">capacity_jitter</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fix_items</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">bool</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.binpack.BinPackGenerator" title="Permalink to this definition"></a></dt>
<dd><p>Random instance generator for the bin packing problem.</p>
<p>If <cite>fix_items=False</cite>, the class samples the user-provided probability distributions
n, sizes and capacity to decide, respectively, the number of items, the sizes of
the items and capacity of the bin. All values are sampled independently.</p>
<p>If <cite>fix_items=True</cite>, the class creates a reference instance, using the method
previously described, then generates additional instances by perturbing its item
sizes and bin capacity. More specifically, the sizes of the items are set to <cite>s_i
* gamma_i</cite> where <cite>s_i</cite> is the size of the i-th item in the reference instance and
<cite>gamma_i</cite> is sampled from <cite>sizes_jitter</cite>. Similarly, the bin capacity is set to <cite>B *
beta</cite>, where <cite>B</cite> is the reference bin capacity and <cite>beta</cite> is sampled from
<cite>capacity_jitter</cite>. The number of items remains the same across all generated
instances.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>n</strong> – Probability distribution for the number of items.</p></li>
<li><p><strong>sizes</strong> – Probability distribution for the item sizes.</p></li>
<li><p><strong>capacity</strong> – Probability distribution for the bin capacity.</p></li>
<li><p><strong>sizes_jitter</strong> – Probability distribution for the item size randomization.</p></li>
<li><p><strong>capacity_jitter</strong> – Probability distribution for the bin capacity.</p></li>
<li><p><strong>fix_items</strong> – If <cite>True</cite>, generates a reference instance, then applies some perturbation to it.
If <cite>False</cite>, generates completely different instances.</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt id="miplearn.problems.binpack.BinPackGenerator.generate">
<code class="sig-name descname"><span class="pre">generate</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_samples</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">int</span></span></em><span class="sig-paren">)</span> &#x2192; <span class="pre">List</span><span class="p"><span class="pre">[</span></span><a class="reference internal" href="#miplearn.problems.binpack.BinPackData" title="miplearn.problems.binpack.BinPackData"><span class="pre">miplearn.problems.binpack.BinPackData</span></a><span class="p"><span class="pre">]</span></span><a class="headerlink" href="#miplearn.problems.binpack.BinPackGenerator.generate" title="Permalink to this definition"></a></dt>
<dd><p>Generates random instances.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>n_samples</strong> – Number of samples to generate.</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="py function">
<dt id="miplearn.problems.binpack.build_binpack_model">
<code class="sig-prename descclassname"><span class="pre">miplearn.problems.binpack.</span></code><code class="sig-name descname"><span class="pre">build_binpack_model</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">,</span> </span><a class="reference internal" href="#miplearn.problems.binpack.BinPackData" title="miplearn.problems.binpack.BinPackData"><span class="pre">miplearn.problems.binpack.BinPackData</span></a><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="../solvers/#miplearn.solvers.gurobi.GurobiModel" title="miplearn.solvers.gurobi.GurobiModel"><span class="pre">miplearn.solvers.gurobi.GurobiModel</span></a><a class="headerlink" href="#miplearn.problems.binpack.build_binpack_model" title="Permalink to this definition"></a></dt>
<dd><p>Converts bin packing problem data into a concrete Gurobipy model.</p>
</dd></dl>
</div>
<div class="section" id="module-miplearn.problems.multiknapsack">
<span id="miplearn-problems-multiknapsack"></span><h2><span class="section-number">9.2. </span>miplearn.problems.multiknapsack<a class="headerlink" href="#module-miplearn.problems.multiknapsack" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt id="miplearn.problems.multiknapsack.MultiKnapsackData">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.multiknapsack.</span></code><code class="sig-name descname"><span class="pre">MultiKnapsackData</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prices</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">capacities</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.multiknapsack.MultiKnapsackData" title="Permalink to this definition"></a></dt>
<dd><p>Data for the multi-dimensional knapsack problem</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>prices</strong> (<em>numpy.ndarray</em>) – Item prices.</p></li>
<li><p><strong>capacities</strong> (<em>numpy.ndarray</em>) – Knapsack capacities.</p></li>
<li><p><strong>weights</strong> (<em>numpy.ndarray</em>) – Matrix of item weights.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py class">
<dt id="miplearn.problems.multiknapsack.MultiKnapsackGenerator">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.multiknapsack.</span></code><code class="sig-name descname"><span class="pre">MultiKnapsackGenerator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="pre">n:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">m:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">w:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">K:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">u:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">alpha:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">fix_w:</span> <span class="pre">bool</span> <span class="pre">=</span> <span class="pre">False</span></em>, <em class="sig-param"><span class="pre">w_jitter:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">p_jitter:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">round:</span> <span class="pre">bool</span> <span class="pre">=</span> <span class="pre">True</span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.multiknapsack.MultiKnapsackGenerator" title="Permalink to this definition"></a></dt>
<dd><p>Random instance generator for the multi-dimensional knapsack problem.</p>
<p>Instances have a random number of items (or variables) and a random number of
knapsacks (or constraints), as specified by the provided probability
distributions <cite>n</cite> and <cite>m</cite>, respectively. The weight of each item <cite>i</cite> on knapsack
<cite>j</cite> is sampled independently from the provided distribution <cite>w</cite>. The capacity of
knapsack <cite>j</cite> is set to <code class="docutils literal notranslate"><span class="pre">alpha_j</span> <span class="pre">*</span> <span class="pre">sum(w[i,j]</span> <span class="pre">for</span> <span class="pre">i</span> <span class="pre">in</span> <span class="pre">range(n))</span></code>,
where <cite>alpha_j</cite>, the tightness ratio, is sampled from the provided probability
distribution <cite>alpha</cite>.</p>
<p>To make the instances more challenging, the costs of the items are linearly
correlated to their average weights. More specifically, the weight of each item
<cite>i</cite> is set to <code class="docutils literal notranslate"><span class="pre">sum(w[i,j]/m</span> <span class="pre">for</span> <span class="pre">j</span> <span class="pre">in</span> <span class="pre">range(m))</span> <span class="pre">+</span> <span class="pre">K</span> <span class="pre">*</span> <span class="pre">u_i</span></code>, where <cite>K</cite>,
the correlation coefficient, and <cite>u_i</cite>, the correlation multiplier, are sampled
from the provided probability distributions. Note that <cite>K</cite> is only sample once
for the entire instance.</p>
<p>If <cite>fix_w=True</cite>, then <cite>weights[i,j]</cite> are kept the same in all generated
instances. This also implies that n and m are kept fixed. Although the prices and
capacities are derived from <cite>weights[i,j]</cite>, as long as <cite>u</cite> and <cite>K</cite> are not
constants, the generated instances will still not be completely identical.</p>
<p>If a probability distribution <cite>w_jitter</cite> is provided, then item weights will be
set to <code class="docutils literal notranslate"><span class="pre">w[i,j]</span> <span class="pre">*</span> <span class="pre">gamma[i,j]</span></code> where <cite>gamma[i,j]</cite> is sampled from <cite>w_jitter</cite>.
When combined with <cite>fix_w=True</cite>, this argument may be used to generate instances
where the weight of each item is roughly the same, but not exactly identical,
across all instances. The prices of the items and the capacities of the knapsacks
will be calculated as above, but using these perturbed weights instead.</p>
<p>By default, all generated prices, weights and capacities are rounded to the
nearest integer number. If <cite>round=False</cite> is provided, this rounding will be
disabled.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>n</strong> (<em>rv_discrete</em>) – Probability distribution for the number of items (or variables).</p></li>
<li><p><strong>m</strong> (<em>rv_discrete</em>) – Probability distribution for the number of knapsacks (or constraints).</p></li>
<li><p><strong>w</strong> (<em>rv_continuous</em>) – Probability distribution for the item weights.</p></li>
<li><p><strong>K</strong> (<em>rv_continuous</em>) – Probability distribution for the profit correlation coefficient.</p></li>
<li><p><strong>u</strong> (<em>rv_continuous</em>) – Probability distribution for the profit multiplier.</p></li>
<li><p><strong>alpha</strong> (<em>rv_continuous</em>) – Probability distribution for the tightness ratio.</p></li>
<li><p><strong>fix_w</strong> (<em>boolean</em>) – If true, weights are kept the same (minus the noise from w_jitter) in all
instances.</p></li>
<li><p><strong>w_jitter</strong> (<em>rv_continuous</em>) – Probability distribution for random noise added to the weights.</p></li>
<li><p><strong>round</strong> (<em>boolean</em>) – If true, all prices, weights and capacities are rounded to the nearest
integer.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="miplearn.problems.multiknapsack.build_multiknapsack_model">
<code class="sig-prename descclassname"><span class="pre">miplearn.problems.multiknapsack.</span></code><code class="sig-name descname"><span class="pre">build_multiknapsack_model</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">,</span> </span><a class="reference internal" href="#miplearn.problems.multiknapsack.MultiKnapsackData" title="miplearn.problems.multiknapsack.MultiKnapsackData"><span class="pre">miplearn.problems.multiknapsack.MultiKnapsackData</span></a><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="../solvers/#miplearn.solvers.gurobi.GurobiModel" title="miplearn.solvers.gurobi.GurobiModel"><span class="pre">miplearn.solvers.gurobi.GurobiModel</span></a><a class="headerlink" href="#miplearn.problems.multiknapsack.build_multiknapsack_model" title="Permalink to this definition"></a></dt>
<dd><p>Converts multi-knapsack problem data into a concrete Gurobipy model.</p>
</dd></dl>
</div>
<div class="section" id="module-miplearn.problems.pmedian">
<span id="miplearn-problems-pmedian"></span><h2><span class="section-number">9.3. </span>miplearn.problems.pmedian<a class="headerlink" href="#module-miplearn.problems.pmedian" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt id="miplearn.problems.pmedian.PMedianData">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.pmedian.</span></code><code class="sig-name descname"><span class="pre">PMedianData</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">distances</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">demands</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">capacities</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.pmedian.PMedianData" title="Permalink to this definition"></a></dt>
<dd><p>Data for the capacitated p-median problem</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>distances</strong> (<em>numpy.ndarray</em>) – Matrix of distances between customer i and facility j.</p></li>
<li><p><strong>demands</strong> (<em>numpy.ndarray</em>) – Customer demands.</p></li>
<li><p><strong>p</strong> (<em>int</em>) – Number of medians that need to be chosen.</p></li>
<li><p><strong>capacities</strong> (<em>numpy.ndarray</em>) – Facility capacities.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py class">
<dt id="miplearn.problems.pmedian.PMedianGenerator">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.pmedian.</span></code><code class="sig-name descname"><span class="pre">PMedianGenerator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="pre">x:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">y:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">n:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">p:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">demands:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">capacities:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">distances_jitter:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">demands_jitter:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">capacities_jitter:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">fixed:</span> <span class="pre">bool</span> <span class="pre">=</span> <span class="pre">True</span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.pmedian.PMedianGenerator" title="Permalink to this definition"></a></dt>
<dd><p>Random generator for the capacitated p-median problem.</p>
<p>This class first decides the number of customers and the parameter <cite>p</cite> by
sampling the provided <cite>n</cite> and <cite>p</cite> distributions, respectively. Then, for each
customer <cite>i</cite>, the class builds its geographical location <cite>(xi, yi)</cite> by sampling
the provided <cite>x</cite> and <cite>y</cite> distributions. For each <cite>i</cite>, the demand for customer <cite>i</cite>
and the capacity of facility <cite>i</cite> are decided by sampling the distributions
<cite>demands</cite> and <cite>capacities</cite>, respectively. Finally, the costs <cite>w[i,j]</cite> are set to
the Euclidean distance between the locations of customers <cite>i</cite> and <cite>j</cite>.</p>
<p>If <cite>fixed=True</cite>, then the number of customers, their locations, the parameter
<cite>p</cite>, the demands and the capacities are only sampled from their respective
distributions exactly once, to build a reference instance which is then
perturbed. Specifically, for each perturbation, the distances, demands and
capacities are multiplied by factors sampled from the distributions
<cite>distances_jitter</cite>, <cite>demands_jitter</cite> and <cite>capacities_jitter</cite>, respectively. The
result is a list of instances that have the same set of customers, but slightly
different demands, capacities and distances.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – Probability distribution for the x-coordinate of the points.</p></li>
<li><p><strong>y</strong> – Probability distribution for the y-coordinate of the points.</p></li>
<li><p><strong>n</strong> – Probability distribution for the number of customer.</p></li>
<li><p><strong>p</strong> – Probability distribution for the number of medians.</p></li>
<li><p><strong>demands</strong> – Probability distribution for the customer demands.</p></li>
<li><p><strong>capacities</strong> – Probability distribution for the facility capacities.</p></li>
<li><p><strong>distances_jitter</strong> – Probability distribution for the random scaling factor applied to distances.</p></li>
<li><p><strong>demands_jitter</strong> – Probability distribution for the random scaling factor applied to demands.</p></li>
<li><p><strong>capacities_jitter</strong> – Probability distribution for the random scaling factor applied to capacities.</p></li>
<li><p><strong>fixed</strong> – If <cite>True</cite>, then customer are kept the same across instances.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt id="miplearn.problems.pmedian.build_pmedian_model">
<code class="sig-prename descclassname"><span class="pre">miplearn.problems.pmedian.</span></code><code class="sig-name descname"><span class="pre">build_pmedian_model</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">,</span> </span><a class="reference internal" href="#miplearn.problems.pmedian.PMedianData" title="miplearn.problems.pmedian.PMedianData"><span class="pre">miplearn.problems.pmedian.PMedianData</span></a><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="../solvers/#miplearn.solvers.gurobi.GurobiModel" title="miplearn.solvers.gurobi.GurobiModel"><span class="pre">miplearn.solvers.gurobi.GurobiModel</span></a><a class="headerlink" href="#miplearn.problems.pmedian.build_pmedian_model" title="Permalink to this definition"></a></dt>
<dd><p>Converts capacitated p-median data into a concrete Gurobipy model.</p>
</dd></dl>
</div>
<div class="section" id="module-miplearn.problems.setcover">
<span id="miplearn-problems-setcover"></span><h2><span class="section-number">9.4. </span>miplearn.problems.setcover<a class="headerlink" href="#module-miplearn.problems.setcover" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt id="miplearn.problems.setcover.SetCoverData">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.setcover.</span></code><code class="sig-name descname"><span class="pre">SetCoverData</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">costs</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">incidence_matrix</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.setcover.SetCoverData" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
</div>
<div class="section" id="module-miplearn.problems.setpack">
<span id="miplearn-problems-setpack"></span><h2><span class="section-number">9.5. </span>miplearn.problems.setpack<a class="headerlink" href="#module-miplearn.problems.setpack" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt id="miplearn.problems.setpack.SetPackData">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.setpack.</span></code><code class="sig-name descname"><span class="pre">SetPackData</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">costs</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">incidence_matrix</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.setpack.SetPackData" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
</div>
<div class="section" id="module-miplearn.problems.stab">
<span id="miplearn-problems-stab"></span><h2><span class="section-number">9.6. </span>miplearn.problems.stab<a class="headerlink" href="#module-miplearn.problems.stab" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt id="miplearn.problems.stab.MaxWeightStableSetData">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.stab.</span></code><code class="sig-name descname"><span class="pre">MaxWeightStableSetData</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">graph</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">networkx.classes.graph.Graph</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.stab.MaxWeightStableSetData" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py class">
<dt id="miplearn.problems.stab.MaxWeightStableSetGenerator">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.stab.</span></code><code class="sig-name descname"><span class="pre">MaxWeightStableSetGenerator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="pre">w:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">n:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">p:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">fix_graph:</span> <span class="pre">bool</span> <span class="pre">=</span> <span class="pre">True</span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.stab.MaxWeightStableSetGenerator" title="Permalink to this definition"></a></dt>
<dd><p>Random instance generator for the Maximum-Weight Stable Set Problem.</p>
<p>The generator has two modes of operation. When <cite>fix_graph=True</cite> is provided,
one random Erdős-Rényi graph $G_{n,p}$ is generated in the constructor, where $n$
and $p$ are sampled from user-provided probability distributions <cite>n</cite> and <cite>p</cite>. To
generate each instance, the generator independently samples each $w_v$ from the
user-provided probability distribution <cite>w</cite>.</p>
<p>When <cite>fix_graph=False</cite>, a new random graph is generated for each instance; the
remaining parameters are sampled in the same way.</p>
</dd></dl>
</div>
<div class="section" id="module-miplearn.problems.tsp">
<span id="miplearn-problems-tsp"></span><h2><span class="section-number">9.7. </span>miplearn.problems.tsp<a class="headerlink" href="#module-miplearn.problems.tsp" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt id="miplearn.problems.tsp.TravelingSalesmanData">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.tsp.</span></code><code class="sig-name descname"><span class="pre">TravelingSalesmanData</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_cities</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">distances</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.tsp.TravelingSalesmanData" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py class">
<dt id="miplearn.problems.tsp.TravelingSalesmanGenerator">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.tsp.</span></code><code class="sig-name descname"><span class="pre">TravelingSalesmanGenerator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="pre">x:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">y:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">n:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">gamma:</span> <span class="pre">scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">=</span> <span class="pre">&lt;scipy.stats._distn_infrastructure.rv_frozen</span> <span class="pre">object&gt;</span></em>, <em class="sig-param"><span class="pre">fix_cities:</span> <span class="pre">bool</span> <span class="pre">=</span> <span class="pre">True</span></em>, <em class="sig-param"><span class="pre">round:</span> <span class="pre">bool</span> <span class="pre">=</span> <span class="pre">True</span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.tsp.TravelingSalesmanGenerator" title="Permalink to this definition"></a></dt>
<dd><p>Random generator for the Traveling Salesman Problem.</p>
</dd></dl>
</div>
<div class="section" id="module-miplearn.problems.uc">
<span id="miplearn-problems-uc"></span><h2><span class="section-number">9.8. </span>miplearn.problems.uc<a class="headerlink" href="#module-miplearn.problems.uc" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt id="miplearn.problems.uc.UnitCommitmentData">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.uc.</span></code><code class="sig-name descname"><span class="pre">UnitCommitmentData</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">demand</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_power</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_power</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_uptime</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_downtime</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cost_startup</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cost_prod</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cost_fixed</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.uc.UnitCommitmentData" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py function">
<dt id="miplearn.problems.uc.build_uc_model">
<code class="sig-prename descclassname"><span class="pre">miplearn.problems.uc.</span></code><code class="sig-name descname"><span class="pre">build_uc_model</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">data</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">Union</span><span class="p"><span class="pre">[</span></span><span class="pre">str</span><span class="p"><span class="pre">,</span> </span><a class="reference internal" href="#miplearn.problems.uc.UnitCommitmentData" title="miplearn.problems.uc.UnitCommitmentData"><span class="pre">miplearn.problems.uc.UnitCommitmentData</span></a><span class="p"><span class="pre">]</span></span></span></em><span class="sig-paren">)</span> &#x2192; <a class="reference internal" href="../solvers/#miplearn.solvers.gurobi.GurobiModel" title="miplearn.solvers.gurobi.GurobiModel"><span class="pre">miplearn.solvers.gurobi.GurobiModel</span></a><a class="headerlink" href="#miplearn.problems.uc.build_uc_model" title="Permalink to this definition"></a></dt>
<dd><p>Models the unit commitment problem according to equations (1)-(5) of:</p>
<blockquote>
<div><p>Bendotti, P., Fouilhoux, P. &amp; Rottner, C. The min-up/min-down unit
commitment polytope. J Comb Optim 36, 1024-1058 (2018).
<a class="reference external" href="https://doi.org/10.1007/s10878-018-0273-y">https://doi.org/10.1007/s10878-018-0273-y</a></p>
</div></blockquote>
</dd></dl>
</div>
<div class="section" id="module-miplearn.problems.vertexcover">
<span id="miplearn-problems-vertexcover"></span><h2><span class="section-number">9.9. </span>miplearn.problems.vertexcover<a class="headerlink" href="#module-miplearn.problems.vertexcover" title="Permalink to this headline"></a></h2>
<dl class="py class">
<dt id="miplearn.problems.vertexcover.MinWeightVertexCoverData">
<em class="property"><span class="pre">class</span> </em><code class="sig-prename descclassname"><span class="pre">miplearn.problems.vertexcover.</span></code><code class="sig-name descname"><span class="pre">MinWeightVertexCoverData</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">graph</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">networkx.classes.graph.Graph</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span><span class="p"><span class="pre">:</span></span> <span class="n"><span class="pre">numpy.ndarray</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#miplearn.problems.vertexcover.MinWeightVertexCoverData" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
</div>
</div>
</div>
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