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<h1>Learning Solver</h1>
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<h2> Contents </h2>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Configuring-the-solver">9.1. Configuring the solver</a></li>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Training-and-solving-new-instances">9.2. Training and solving new instances</a></li>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Complete-example">9.3. Complete example</a></li>
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<article class="bd-article">
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<section id="Learning-Solver">
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<h1><span class="section-number">9. </span>Learning Solver<a class="headerlink" href="#Learning-Solver" title="Link to this heading">#</a></h1>
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<p>On previous pages, we discussed various components of the MIPLearn framework, including training data collectors, feature extractors, and individual machine learning components. In this page, we introduce <strong>LearningSolver</strong>, the main class of the framework which integrates all the aforementioned components into a cohesive whole. Using <strong>LearningSolver</strong> involves three steps: (i) configuring the solver; (ii) training the ML components; and (iii) solving new MIP instances. In the following, we
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describe each of these steps, then conclude with a complete runnable example.</p>
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<section id="Configuring-the-solver">
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<h2><span class="section-number">9.1. </span>Configuring the solver<a class="headerlink" href="#Configuring-the-solver" title="Link to this heading">#</a></h2>
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<p><strong>LearningSolver</strong> is composed by multiple individual machine learning components, each targeting a different part of the solution process, or implementing a different machine learning strategy. This architecture allows strategies to be easily enabled, disabled or customized, making the framework flexible. By default, no components are provided and <strong>LearningSolver</strong> is equivalent to a traditional MIP solver. To specify additional components, the <code class="docutils literal notranslate"><span class="pre">components</span></code> constructor argument may be used:</p>
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<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">solver</span> <span class="o">=</span> <span class="n">LearningSolver</span><span class="p">(</span>
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<span class="n">components</span><span class="o">=</span><span class="p">[</span>
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<span class="n">comp1</span><span class="p">,</span>
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<span class="n">comp2</span><span class="p">,</span>
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<span class="n">comp3</span><span class="p">,</span>
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<span class="p">]</span>
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<span class="p">)</span>
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</pre></div>
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</div>
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<p>In this example, three components <code class="docutils literal notranslate"><span class="pre">comp1</span></code>, <code class="docutils literal notranslate"><span class="pre">comp2</span></code> and <code class="docutils literal notranslate"><span class="pre">comp3</span></code> are provided. The strategies implemented by these components are applied sequentially when solving the problem. For example, <code class="docutils literal notranslate"><span class="pre">comp1</span></code> and <code class="docutils literal notranslate"><span class="pre">comp2</span></code> could fix a subset of decision variables, while <code class="docutils literal notranslate"><span class="pre">comp3</span></code> constructs a warm start for the remaining problem.</p>
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</section>
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<section id="Training-and-solving-new-instances">
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<h2><span class="section-number">9.2. </span>Training and solving new instances<a class="headerlink" href="#Training-and-solving-new-instances" title="Link to this heading">#</a></h2>
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<p>Once a solver is configured, its ML components need to be trained. This can be achieved by the <code class="docutils literal notranslate"><span class="pre">solver.fit</span></code> method, as illustrated below. The method accepts a list of HDF5 files and trains each individual component sequentially. Once the solver is trained, new instances can be solved using <code class="docutils literal notranslate"><span class="pre">solver.optimize</span></code>. The method returns a dictionary of statistics collected by each component, such as the number of variables fixed.</p>
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<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># Build instances</span>
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<span class="n">train_data</span> <span class="o">=</span> <span class="o">...</span>
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<span class="n">test_data</span> <span class="o">=</span> <span class="o">...</span>
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<span class="c1"># Collect training data</span>
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<span class="n">bc</span> <span class="o">=</span> <span class="n">BasicCollector</span><span class="p">()</span>
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<span class="n">bc</span><span class="o">.</span><span class="n">collect</span><span class="p">(</span><span class="n">train_data</span><span class="p">,</span> <span class="n">build_model</span><span class="p">)</span>
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<span class="c1"># Build solver</span>
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<span class="n">solver</span> <span class="o">=</span> <span class="n">LearningSolver</span><span class="p">(</span><span class="o">...</span><span class="p">)</span>
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<span class="c1"># Train components</span>
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<span class="n">solver</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">train_data</span><span class="p">)</span>
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<span class="c1"># Solve a new test instance</span>
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<span class="n">stats</span> <span class="o">=</span> <span class="n">solver</span><span class="o">.</span><span class="n">optimize</span><span class="p">(</span><span class="n">test_data</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">build_model</span><span class="p">)</span>
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</pre></div>
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</div>
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</section>
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<section id="Complete-example">
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<h2><span class="section-number">9.3. </span>Complete example<a class="headerlink" href="#Complete-example" title="Link to this heading">#</a></h2>
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<p>In the example below, we illustrate the usage of <strong>LearningSolver</strong> by building instances of the Traveling Salesman Problem, collecting training data, training the ML components, then solving a new instance.</p>
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<div class="nbinput docutils container">
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<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[1]:
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</pre></div>
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</div>
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<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">random</span>
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<span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">scipy.stats</span><span class="w"> </span><span class="kn">import</span> <span class="n">uniform</span><span class="p">,</span> <span class="n">randint</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.linear_model</span><span class="w"> </span><span class="kn">import</span> <span class="n">LogisticRegression</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">miplearn.classifiers.minprob</span><span class="w"> </span><span class="kn">import</span> <span class="n">MinProbabilityClassifier</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">miplearn.classifiers.singleclass</span><span class="w"> </span><span class="kn">import</span> <span class="n">SingleClassFix</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">miplearn.collectors.basic</span><span class="w"> </span><span class="kn">import</span> <span class="n">BasicCollector</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">miplearn.components.primal.actions</span><span class="w"> </span><span class="kn">import</span> <span class="n">SetWarmStart</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">miplearn.components.primal.indep</span><span class="w"> </span><span class="kn">import</span> <span class="n">IndependentVarsPrimalComponent</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">miplearn.extractors.AlvLouWeh2017</span><span class="w"> </span><span class="kn">import</span> <span class="n">AlvLouWeh2017Extractor</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">miplearn.io</span><span class="w"> </span><span class="kn">import</span> <span class="n">write_pkl_gz</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">miplearn.problems.tsp</span><span class="w"> </span><span class="kn">import</span> <span class="p">(</span>
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<span class="n">TravelingSalesmanGenerator</span><span class="p">,</span>
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<span class="n">build_tsp_model_gurobipy</span><span class="p">,</span>
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<span class="p">)</span>
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<span class="kn">from</span><span class="w"> </span><span class="nn">miplearn.solvers.learning</span><span class="w"> </span><span class="kn">import</span> <span class="n">LearningSolver</span>
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<span class="c1"># Set random seed to make example reproducible.</span>
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<span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
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<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span>
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<span class="c1"># Generate a few instances of the traveling salesman problem.</span>
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<span class="n">data</span> <span class="o">=</span> <span class="n">TravelingSalesmanGenerator</span><span class="p">(</span>
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<span class="n">n</span><span class="o">=</span><span class="n">randint</span><span class="p">(</span><span class="n">low</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">high</span><span class="o">=</span><span class="mi">11</span><span class="p">),</span>
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<span class="n">x</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">1000.0</span><span class="p">),</span>
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<span class="n">y</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">1000.0</span><span class="p">),</span>
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<span class="n">gamma</span><span class="o">=</span><span class="n">uniform</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="mf">0.90</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="mf">0.20</span><span class="p">),</span>
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<span class="n">fix_cities</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
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<span class="nb">round</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
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<span class="p">)</span><span class="o">.</span><span class="n">generate</span><span class="p">(</span><span class="mi">50</span><span class="p">)</span>
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<span class="c1"># Save instance data to data/tsp/00000.pkl.gz, data/tsp/00001.pkl.gz, ...</span>
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<span class="n">all_data</span> <span class="o">=</span> <span class="n">write_pkl_gz</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="s2">"data/tsp"</span><span class="p">)</span>
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<span class="c1"># Split train/test data</span>
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<span class="n">train_data</span> <span class="o">=</span> <span class="n">all_data</span><span class="p">[:</span><span class="mi">40</span><span class="p">]</span>
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<span class="n">test_data</span> <span class="o">=</span> <span class="n">all_data</span><span class="p">[</span><span class="mi">40</span><span class="p">:]</span>
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<span class="c1"># Collect training data</span>
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<span class="n">bc</span> <span class="o">=</span> <span class="n">BasicCollector</span><span class="p">()</span>
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<span class="n">bc</span><span class="o">.</span><span class="n">collect</span><span class="p">(</span><span class="n">train_data</span><span class="p">,</span> <span class="n">build_tsp_model_gurobipy</span><span class="p">,</span> <span class="n">n_jobs</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
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<span class="c1"># Build learning solver</span>
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<span class="n">solver</span> <span class="o">=</span> <span class="n">LearningSolver</span><span class="p">(</span>
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<span class="n">components</span><span class="o">=</span><span class="p">[</span>
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<span class="n">IndependentVarsPrimalComponent</span><span class="p">(</span>
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<span class="n">base_clf</span><span class="o">=</span><span class="n">SingleClassFix</span><span class="p">(</span>
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<span class="n">MinProbabilityClassifier</span><span class="p">(</span>
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<span class="n">base_clf</span><span class="o">=</span><span class="n">LogisticRegression</span><span class="p">(),</span>
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<span class="n">thresholds</span><span class="o">=</span><span class="p">[</span><span class="mf">0.95</span><span class="p">,</span> <span class="mf">0.95</span><span class="p">],</span>
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<span class="p">),</span>
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<span class="p">),</span>
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<span class="n">extractor</span><span class="o">=</span><span class="n">AlvLouWeh2017Extractor</span><span class="p">(),</span>
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<span class="n">action</span><span class="o">=</span><span class="n">SetWarmStart</span><span class="p">(),</span>
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<span class="p">)</span>
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<span class="p">]</span>
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<span class="p">)</span>
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<span class="c1"># Train ML models</span>
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<span class="n">solver</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">train_data</span><span class="p">)</span>
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<span class="c1"># Solve a test instance</span>
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<span class="n">solver</span><span class="o">.</span><span class="n">optimize</span><span class="p">(</span><span class="n">test_data</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">build_tsp_model_gurobipy</span><span class="p">);</span>
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</pre></div>
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</div>
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</div>
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<div class="nboutput nblast docutils container">
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<div class="prompt empty docutils container">
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</div>
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<div class="output_area docutils container">
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<div class="highlight"><pre>
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Restricted license - for non-production use only - expires 2026-11-23
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Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - "Ubuntu 22.04.4 LTS")
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CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]
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Thread count: 10 physical cores, 20 logical processors, using up to 20 threads
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Optimize a model with 10 rows, 45 columns and 90 nonzeros
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Model fingerprint: 0x6ddcd141
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Coefficient statistics:
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Matrix range [1e+00, 1e+00]
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Objective range [4e+01, 1e+03]
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Bounds range [1e+00, 1e+00]
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RHS range [2e+00, 2e+00]
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Presolve time: 0.00s
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Presolved: 10 rows, 45 columns, 90 nonzeros
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Iteration Objective Primal Inf. Dual Inf. Time
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0 6.3600000e+02 1.700000e+01 0.000000e+00 0s
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15 2.7610000e+03 0.000000e+00 0.000000e+00 0s
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Solved in 15 iterations and 0.01 seconds (0.00 work units)
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Optimal objective 2.761000000e+03
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User-callback calls 56, time in user-callback 0.00 sec
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Set parameter PreCrush to value 1
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Set parameter LazyConstraints to value 1
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Gurobi Optimizer version 12.0.2 build v12.0.2rc0 (linux64 - "Ubuntu 22.04.4 LTS")
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CPU model: 13th Gen Intel(R) Core(TM) i7-13800H, instruction set [SSE2|AVX|AVX2]
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Thread count: 10 physical cores, 20 logical processors, using up to 20 threads
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Non-default parameters:
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PreCrush 1
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LazyConstraints 1
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Optimize a model with 10 rows, 45 columns and 90 nonzeros
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Model fingerprint: 0x74ca3d0a
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Variable types: 0 continuous, 45 integer (45 binary)
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Coefficient statistics:
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Matrix range [1e+00, 1e+00]
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Objective range [4e+01, 1e+03]
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Bounds range [1e+00, 1e+00]
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RHS range [2e+00, 2e+00]
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User MIP start produced solution with objective 2796 (0.00s)
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Loaded user MIP start with objective 2796
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Presolve time: 0.00s
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Presolved: 10 rows, 45 columns, 90 nonzeros
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Variable types: 0 continuous, 45 integer (45 binary)
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Root relaxation: objective 2.761000e+03, 14 iterations, 0.00 seconds (0.00 work units)
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Nodes | Current Node | Objective Bounds | Work
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Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
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0 0 2761.00000 0 - 2796.00000 2761.00000 1.25% - 0s
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Cutting planes:
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Lazy constraints: 3
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Explored 1 nodes (14 simplex iterations) in 0.01 seconds (0.00 work units)
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Thread count was 20 (of 20 available processors)
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Solution count 1: 2796
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Optimal solution found (tolerance 1.00e-04)
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Best objective 2.796000000000e+03, best bound 2.796000000000e+03, gap 0.0000%
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User-callback calls 114, time in user-callback 0.00 sec
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</pre></div></div>
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</div>
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<div class="nbinput nblast docutils container">
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<div class="prompt highlight-none notranslate"><div class="highlight"><pre><span></span>[ ]:
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</pre></div>
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</div>
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<div class="input_area highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>
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</pre></div>
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</div>
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</section>
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</section>
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<i class="fa-solid fa-list"></i> Contents
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<ul class="visible nav section-nav flex-column">
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Configuring-the-solver">9.1. Configuring the solver</a></li>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Training-and-solving-new-instances">9.2. Training and solving new instances</a></li>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#Complete-example">9.3. Complete example</a></li>
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