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340 lines
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<div class="headertitle"><div class="title">linear_relaxation.h</div></div>
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<a href="linear__relaxation_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#ifndef OR_TOOLS_SAT_LINEAR_RELAXATION_H_</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#define OR_TOOLS_SAT_LINEAR_RELAXATION_H_</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include "<a class="code" href="cp__model__mapping_8h.html">ortools/sat/cp_model_mapping.h</a>"</span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include "<a class="code" href="integer_8h.html">ortools/sat/integer.h</a>"</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include "<a class="code" href="sat_2linear__constraint_8h.html">ortools/sat/linear_constraint.h</a>"</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include "<a class="code" href="linear__programming__constraint_8h.html">ortools/sat/linear_programming_constraint.h</a>"</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "<a class="code" href="sat_2model_8h.html">ortools/sat/model.h</a>"</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">namespace </span>sat {</div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_linear_relaxation.html"> 28</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a> {</div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_linear_relaxation.html#a787dea05b34122764c7fb5fd13e9a1c9"> 29</a></span> std::vector<LinearConstraint> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_linear_relaxation.html#a787dea05b34122764c7fb5fd13e9a1c9">linear_constraints</a>;</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_linear_relaxation.html#a0bffb74eb458b339aa75f20b6c982a60"> 30</a></span> std::vector<std::vector<Literal>> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_linear_relaxation.html#a0bffb74eb458b339aa75f20b6c982a60">at_most_ones</a>;</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_linear_relaxation.html#ae6fdc05264dc58e553116fe3d9dbe236"> 31</a></span> std::vector<CutGenerator> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_linear_relaxation.html#ae6fdc05264dc58e553116fe3d9dbe236">cut_generators</a>;</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span>};</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// Looks at all the encoding literal (li <=> var == value_i) that have a</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// view and add a linear relaxation of their relationship with var.</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">//</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// If the encoding is full, we can just add:</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// - Sum li == 1</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// - var == min_value + Sum li * (value_i - min_value)</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">//</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// When the set of such encoding literals do not cover the full domain of var,</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// we do something a bit more involved. Let min_not_encoded/max_not_encoded the</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// min and max value of the domain of var that is NOT part of the encoding.</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// We add:</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// - Sum li <= 1</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// - var >= (Sum li * value_i) + (1 - Sum li) * min_not_encoded</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// - var <= (Sum li * value_i) + (1 - Sum li) * max_not_encoded</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">//</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// Note of the special case where min_not_encoded == max_not_encoded that kind</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// of reduce to the full encoding, except with a different "rhs" value.</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">//</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// We also increment the corresponding counter if we added something. We</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// consider the relaxation "tight" if the encoding was full or if</span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// min_not_encoded == max_not_encoded.</span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ad8ea8c0f170334873faaa68785e3c636">AppendRelaxationForEqualityEncoding</a>(IntegerVariable <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>,</div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>& <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation,</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keywordtype">int</span>* num_tight, <span class="keywordtype">int</span>* num_loose);</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">// This is a different relaxation that use a partial set of literal li such that</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// (li <=> var >= xi). In which case we use the following encoding:</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment">// - li >= l_{i+1} for all possible i. Note that the xi need to be sorted.</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment">// - var >= min + l0 * (x0 - min) + Sum_{i>0} li * (xi - x_{i-1})</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment">// - and same as above for NegationOf(var) for the upper bound.</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment">//</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">// Like for AppendRelaxationForEqualityEncoding() we skip any li that do not</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment">// have an integer view.</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#aff14a4092356fceea657393b7b234b7f">AppendPartialGreaterThanEncodingRelaxation</a>(IntegerVariable <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>,</div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>& <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="comment">// Returns a vector of new literals in exactly one relationship.</span></div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="comment">// In addition, this create an IntegerView for all these literals and also add</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="comment">// the exactly one to the LinearRelaxation.</span></div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span>std::vector<Literal> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a938790a385e658a61d53843b6bb5dfd6">CreateAlternativeLiteralsWithView</a>(</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordtype">int</span> num_literals, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>, <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a14b7bbca8fef62918577fe4618090e66">AppendBoolOrRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a53d4cc6dea5adf2353b4af43bc1bb2f0">AppendBoolAndRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> </div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a305feb6370d1048b959ea498bb2f391b">AppendAtMostOneRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a8b2517dbe721a55849b77267941df8d1">AppendExactlyOneRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="comment">// Adds linearization of int max constraints. Returns a vector of z vars such</span></div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span><span class="comment">// that: z_vars[l] == 1 <=> target = exprs[l].</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="comment">//</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="comment">// Consider the Lin Max constraint with d expressions and n variables in the</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="comment">// form: target = max {exprs[l] = Sum (wli * xi + bl)}. l in {1,..,d}.</span></div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="comment">// Li = lower bound of xi</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="comment">// Ui = upper bound of xi.</span></div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span><span class="comment">// Let zl be in {0,1} for all l in {1,..,d}.</span></div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">// The target = exprs[l] when zl = 1.</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment">//</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment">// The following is a valid linearization for Lin Max.</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment">// target >= exprs[l], for all l in {1,..,d}</span></div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="comment">// target <= Sum_i(wki * xi) + Sum_l((Nkl + bl) * zl), for all k in {1,..,d}</span></div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span><span class="comment">// Where Nkl is a large number defined as:</span></div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span><span class="comment">// Nkl = Sum_i(max((wli - wki)*Li, (wli - wki)*Ui))</span></div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span><span class="comment">// = Sum (max corner difference for variable i, target expr k, max expr l)</span></div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span><span class="comment">// Reference: "Strong mixed-integer programming formulations for trained neural</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment">// networks" by Ross Anderson et. (https://arxiv.org/pdf/1811.01988.pdf).</span></div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment">// TODO(user): Support linear expression as target.</span></div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a12d2d24c73fef12818b04df8d5cc368f">AppendLinMaxRelaxationPart1</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> </div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#afceeea6ad3cc4cb2a78315be297824f3">AppendLinMaxRelaxationPart2</a>(</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> IntegerVariable target, <span class="keyword">const</span> std::vector<Literal>& alternative_literals,</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keyword">const</span> std::vector<LinearExpression>& exprs, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span><span class="comment">// Note: This only works if all affine expressions share the same variable.</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a87f6694cfc0f549668a974462118f99e">AppendMaxAffineRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> </div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment">// Appends linear constraints to the relaxation. This also handles the</span></div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="comment">// relaxation of linear constraints with enforcement literals.</span></div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span><span class="comment">// A linear constraint lb <= ax <= ub with enforcement literals {ei} is relaxed</span></div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span><span class="comment">// as following.</span></div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span><span class="comment">// lb <= (Sum Negated(ei) * (lb - implied_lb)) + ax <= inf</span></div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span><span class="comment">// -inf <= (Sum Negated(ei) * (ub - implied_ub)) + ax <= ub</span></div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span><span class="comment">// Where implied_lb and implied_ub are trivial lower and upper bounds of the</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span><span class="comment">// constraint.</span></div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a5df2c2953d660d96c11967cd903a55fe">AppendLinearConstraintRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>,</div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordtype">bool</span> linearize_enforced_constraints,</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> </div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#aa4529cf0e90f927c1d7005c3cc4b70c5">AppendCircuitRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> </div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ac2091b9e5e6e887337a566d5ca547234">AppendRoutesRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> </div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span><span class="comment">// Adds linearization of no overlap constraints.</span></div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span><span class="comment">// It adds an energetic equation linking the duration of all potential tasks to</span></div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span><span class="comment">// the actual span of the no overlap constraint.</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a2c9b8bc7ebfcbcfea8022b92afe3f2aa">AppendNoOverlapRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_cp_model_proto.html">CpModelProto</a>& <a class="code hl_variable" href="cp__model__solver_8cc.html#a6ac76d8a372013f67c4973012948ec84">model_proto</a>,</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> </div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span><span class="comment">// Adds linearization of cumulative constraints.The second part adds an</span></div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="comment">// energetic equation linking the duration of all potential tasks to the actual</span></div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="comment">// max span * capacity of the cumulative constraint.</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a3396948941651349892572b564bc29e6">AppendCumulativeRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_cp_model_proto.html">CpModelProto</a>& <a class="code hl_variable" href="cp__model__solver_8cc.html#a6ac76d8a372013f67c4973012948ec84">model_proto</a>,</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> </div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="comment">// Cut generators.</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a750b06e478ba967ec89e70fb3fa7394a">AddIntProdCutGenerator</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <span class="keywordtype">int</span> linearization_level,</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* m, <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> </div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ab4a9f371c11b989199cb8e867d05d813">AddAllDiffCutGenerator</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* m,</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> </div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ac17bc38e4e32fb15f01b0346eb6d0d70">AddLinMaxCutGenerator</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* m,</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> </div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a7545a11562b86718d401f1aeb5781c2a">AddCircuitCutGenerator</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* m,</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> </div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ae9204d7e95002b030bdc1cff7bb9bc83">AddRoutesCutGenerator</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* m,</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> </div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a018f1d29220c1b0d75024dcb5a82b883">AddCumulativeCutGenerator</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* m,</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> </div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a3bb33b0ea560d1818c283bacd4b3838e">AddNoOverlapCutGenerator</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* m,</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> </div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a6acf605cd9a3d72b8e33e8d145c07da5">AddNoOverlap2dCutGenerator</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* m,</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> </div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span><span class="comment">// Adds linearization of different types of constraints.</span></div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a1ccfd912c87b8ca68a7fe0d62d7f49bc">TryToLinearizeConstraint</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_cp_model_proto.html">CpModelProto</a>& <a class="code hl_variable" href="cp__model__solver_8cc.html#a6ac76d8a372013f67c4973012948ec84">model_proto</a>,</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_constraint_proto.html">ConstraintProto</a>& <a class="code hl_variable" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>,</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordtype">int</span> linearization_level, <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a>* relaxation);</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> </div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span><span class="comment">// Builds the linear relaxation of a CpModelProto.</span></div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span><a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_relaxation.html">LinearRelaxation</a> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#af68ee38b3d32ecb81072b0cc4d28226b">ComputeLinearRelaxation</a>(<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_cp_model_proto.html">CpModelProto</a>& <a class="code hl_variable" href="cp__model__solver_8cc.html#a6ac76d8a372013f67c4973012948ec84">model_proto</a>,</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_model.html">Model</a>* m);</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> </div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span>} <span class="comment">// namespace sat</span></div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span>} <span class="comment">// namespace operations_research</span></div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> </div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_SAT_LINEAR_RELAXATION_H_</span></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_constraint_proto_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_constraint_proto.html">operations_research::sat::ConstraintProto</a></div><div class="ttdef"><b>Definition:</b> <a href="cp__model_8pb_8h_source.html#l03772">cp_model.pb.h:3773</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cp_model_proto_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cp_model_proto.html">operations_research::sat::CpModelProto</a></div><div class="ttdef"><b>Definition:</b> <a href="cp__model_8pb_8h_source.html#l06111">cp_model.pb.h:6112</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_model_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_model.html">operations_research::sat::Model</a></div><div class="ttdoc">Class that owns everything related to a particular optimization model.</div><div class="ttdef"><b>Definition:</b> <a href="sat_2model_8h_source.html#l00038">sat/model.h:38</a></div></div>
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<div class="ttc" id="acp__model__mapping_8h_html"><div class="ttname"><a href="cp__model__mapping_8h.html">cp_model_mapping.h</a></div></div>
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<div class="ttc" id="acp__model__solver_8cc_html_a6ac76d8a372013f67c4973012948ec84"><div class="ttname"><a href="cp__model__solver_8cc.html#a6ac76d8a372013f67c4973012948ec84">model_proto</a></div><div class="ttdeci">CpModelProto const * model_proto</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__solver_8cc_source.html#l01949">cp_model_solver.cc:1949</a></div></div>
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<div class="ttc" id="ademon__profiler_8cc_html_a05da18ca9c7b657a4a6ea24e07c9b695"><div class="ttname"><a href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a></div><div class="ttdeci">const Constraint * ct</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00043">demon_profiler.cc:43</a></div></div>
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<div class="ttc" id="aexpr__array_8cc_html_a472a99923cbe11ae7b5a5d157d9ad465"><div class="ttname"><a href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a></div><div class="ttdeci">IntVar * var</div><div class="ttdef"><b>Definition:</b> <a href="expr__array_8cc_source.html#l01874">expr_array.cc:1874</a></div></div>
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<div class="ttc" id="agurobi__interface_8cc_html_a0728f23c9a47655d38e0bf1a2f200bcf"><div class="ttname"><a href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a></div><div class="ttdeci">GRBmodel * model</div><div class="ttdef"><b>Definition:</b> <a href="gurobi__interface_8cc_source.html#l00274">gurobi_interface.cc:274</a></div></div>
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<div class="ttc" id="ainteger_8h_html"><div class="ttname"><a href="integer_8h.html">integer.h</a></div></div>
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<div class="ttc" id="alinear__programming__constraint_8h_html"><div class="ttname"><a href="linear__programming__constraint_8h.html">linear_programming_constraint.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a018f1d29220c1b0d75024dcb5a82b883"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a018f1d29220c1b0d75024dcb5a82b883">operations_research::sat::AddCumulativeCutGenerator</a></div><div class="ttdeci">void AddCumulativeCutGenerator(const ConstraintProto &ct, Model *m, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01248">linear_relaxation.cc:1248</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a12d2d24c73fef12818b04df8d5cc368f"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a12d2d24c73fef12818b04df8d5cc368f">operations_research::sat::AppendLinMaxRelaxationPart1</a></div><div class="ttdeci">void AppendLinMaxRelaxationPart1(const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00809">linear_relaxation.cc:809</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a14b7bbca8fef62918577fe4618090e66"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a14b7bbca8fef62918577fe4618090e66">operations_research::sat::AppendBoolOrRelaxation</a></div><div class="ttdeci">void AppendBoolOrRelaxation(const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00396">linear_relaxation.cc:396</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a1ccfd912c87b8ca68a7fe0d62d7f49bc"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a1ccfd912c87b8ca68a7fe0d62d7f49bc">operations_research::sat::TryToLinearizeConstraint</a></div><div class="ttdeci">void TryToLinearizeConstraint(const CpModelProto &model_proto, const ConstraintProto &ct, int linearization_level, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01014">linear_relaxation.cc:1014</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a2c9b8bc7ebfcbcfea8022b92afe3f2aa"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a2c9b8bc7ebfcbcfea8022b92afe3f2aa">operations_research::sat::AppendNoOverlapRelaxation</a></div><div class="ttdeci">void AppendNoOverlapRelaxation(const CpModelProto &model_proto, const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00724">linear_relaxation.cc:724</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a305feb6370d1048b959ea498bb2f391b"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a305feb6370d1048b959ea498bb2f391b">operations_research::sat::AppendAtMostOneRelaxation</a></div><div class="ttdeci">void AppendAtMostOneRelaxation(const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00442">linear_relaxation.cc:442</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a3396948941651349892572b564bc29e6"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a3396948941651349892572b564bc29e6">operations_research::sat::AppendCumulativeRelaxation</a></div><div class="ttdeci">void AppendCumulativeRelaxation(const CpModelProto &model_proto, const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00695">linear_relaxation.cc:695</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a3bb33b0ea560d1818c283bacd4b3838e"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a3bb33b0ea560d1818c283bacd4b3838e">operations_research::sat::AddNoOverlapCutGenerator</a></div><div class="ttdeci">void AddNoOverlapCutGenerator(const ConstraintProto &ct, Model *m, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01299">linear_relaxation.cc:1299</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a53d4cc6dea5adf2353b4af43bc1bb2f0"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a53d4cc6dea5adf2353b4af43bc1bb2f0">operations_research::sat::AppendBoolAndRelaxation</a></div><div class="ttdeci">void AppendBoolAndRelaxation(const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00410">linear_relaxation.cc:410</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a5df2c2953d660d96c11967cd903a55fe"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a5df2c2953d660d96c11967cd903a55fe">operations_research::sat::AppendLinearConstraintRelaxation</a></div><div class="ttdeci">void AppendLinearConstraintRelaxation(const ConstraintProto &ct, bool linearize_enforced_constraints, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00940">linear_relaxation.cc:940</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a6acf605cd9a3d72b8e33e8d145c07da5"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a6acf605cd9a3d72b8e33e8d145c07da5">operations_research::sat::AddNoOverlap2dCutGenerator</a></div><div class="ttdeci">void AddNoOverlap2dCutGenerator(const ConstraintProto &ct, Model *m, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01327">linear_relaxation.cc:1327</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a750b06e478ba967ec89e70fb3fa7394a"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a750b06e478ba967ec89e70fb3fa7394a">operations_research::sat::AddIntProdCutGenerator</a></div><div class="ttdeci">void AddIntProdCutGenerator(const ConstraintProto &ct, int linearization_level, Model *m, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01160">linear_relaxation.cc:1160</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a7545a11562b86718d401f1aeb5781c2a"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a7545a11562b86718d401f1aeb5781c2a">operations_research::sat::AddCircuitCutGenerator</a></div><div class="ttdeci">void AddCircuitCutGenerator(const ConstraintProto &ct, Model *m, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01120">linear_relaxation.cc:1120</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a87f6694cfc0f549668a974462118f99e"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a87f6694cfc0f549668a974462118f99e">operations_research::sat::AppendMaxAffineRelaxation</a></div><div class="ttdeci">void AppendMaxAffineRelaxation(const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00831">linear_relaxation.cc:831</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a8b2517dbe721a55849b77267941df8d1"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a8b2517dbe721a55849b77267941df8d1">operations_research::sat::AppendExactlyOneRelaxation</a></div><div class="ttdeci">void AppendExactlyOneRelaxation(const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00451">linear_relaxation.cc:451</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a938790a385e658a61d53843b6bb5dfd6"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a938790a385e658a61d53843b6bb5dfd6">operations_research::sat::CreateAlternativeLiteralsWithView</a></div><div class="ttdeci">std::vector< Literal > CreateAlternativeLiteralsWithView(int num_literals, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00472">linear_relaxation.cc:472</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_aa4529cf0e90f927c1d7005c3cc4b70c5"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#aa4529cf0e90f927c1d7005c3cc4b70c5">operations_research::sat::AppendCircuitRelaxation</a></div><div class="ttdeci">void AppendCircuitRelaxation(const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00513">linear_relaxation.cc:513</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ab4a9f371c11b989199cb8e867d05d813"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ab4a9f371c11b989199cb8e867d05d813">operations_research::sat::AddAllDiffCutGenerator</a></div><div class="ttdeci">void AddAllDiffCutGenerator(const ConstraintProto &ct, Model *m, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01211">linear_relaxation.cc:1211</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ac17bc38e4e32fb15f01b0346eb6d0d70"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ac17bc38e4e32fb15f01b0346eb6d0d70">operations_research::sat::AddLinMaxCutGenerator</a></div><div class="ttdeci">void AddLinMaxCutGenerator(const ConstraintProto &ct, Model *m, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01372">linear_relaxation.cc:1372</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ac2091b9e5e6e887337a566d5ca547234"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ac2091b9e5e6e887337a566d5ca547234">operations_research::sat::AppendRoutesRelaxation</a></div><div class="ttdeci">void AppendRoutesRelaxation(const ConstraintProto &ct, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00554">linear_relaxation.cc:554</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ad8ea8c0f170334873faaa68785e3c636"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ad8ea8c0f170334873faaa68785e3c636">operations_research::sat::AppendRelaxationForEqualityEncoding</a></div><div class="ttdeci">void AppendRelaxationForEqualityEncoding(IntegerVariable var, const Model &model, LinearRelaxation *relaxation, int *num_tight, int *num_loose)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00160">linear_relaxation.cc:160</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ae9204d7e95002b030bdc1cff7bb9bc83"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ae9204d7e95002b030bdc1cff7bb9bc83">operations_research::sat::AddRoutesCutGenerator</a></div><div class="ttdeci">void AddRoutesCutGenerator(const ConstraintProto &ct, Model *m, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01134">linear_relaxation.cc:1134</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_af68ee38b3d32ecb81072b0cc4d28226b"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#af68ee38b3d32ecb81072b0cc4d28226b">operations_research::sat::ComputeLinearRelaxation</a></div><div class="ttdeci">LinearRelaxation ComputeLinearRelaxation(const CpModelProto &model_proto, Model *m)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l01470">linear_relaxation.cc:1470</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_afceeea6ad3cc4cb2a78315be297824f3"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#afceeea6ad3cc4cb2a78315be297824f3">operations_research::sat::AppendLinMaxRelaxationPart2</a></div><div class="ttdeci">void AppendLinMaxRelaxationPart2(IntegerVariable target, const std::vector< Literal > &alternative_literals, const std::vector< LinearExpression > &exprs, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00873">linear_relaxation.cc:873</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_aff14a4092356fceea657393b7b234b7f"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#aff14a4092356fceea657393b7b234b7f">operations_research::sat::AppendPartialGreaterThanEncodingRelaxation</a></div><div class="ttdeci">void AppendPartialGreaterThanEncodingRelaxation(IntegerVariable var, const Model &model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00266">linear_relaxation.cc:266</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
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<div class="ttc" id="asat_2linear__constraint_8h_html"><div class="ttname"><a href="sat_2linear__constraint_8h.html">linear_constraint.h</a></div></div>
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<div class="ttc" id="asat_2model_8h_html"><div class="ttname"><a href="sat_2model_8h.html">model.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_linear_relaxation_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_linear_relaxation.html">operations_research::sat::LinearRelaxation</a></div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8h_source.html#l00028">linear_relaxation.h:28</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_linear_relaxation_html_a0bffb74eb458b339aa75f20b6c982a60"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_linear_relaxation.html#a0bffb74eb458b339aa75f20b6c982a60">operations_research::sat::LinearRelaxation::at_most_ones</a></div><div class="ttdeci">std::vector< std::vector< Literal > > at_most_ones</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8h_source.html#l00030">linear_relaxation.h:30</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_linear_relaxation_html_a787dea05b34122764c7fb5fd13e9a1c9"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_linear_relaxation.html#a787dea05b34122764c7fb5fd13e9a1c9">operations_research::sat::LinearRelaxation::linear_constraints</a></div><div class="ttdeci">std::vector< LinearConstraint > linear_constraints</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8h_source.html#l00029">linear_relaxation.h:29</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_linear_relaxation_html_ae6fdc05264dc58e553116fe3d9dbe236"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_linear_relaxation.html#ae6fdc05264dc58e553116fe3d9dbe236">operations_research::sat::LinearRelaxation::cut_generators</a></div><div class="ttdeci">std::vector< CutGenerator > cut_generators</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8h_source.html#l00031">linear_relaxation.h:31</a></div></div>
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