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731 lines
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<div class="title">cuts.h</div> </div>
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<a href="cuts_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a 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 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 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 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 name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a 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 name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a 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 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 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 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 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 name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#ifndef OR_TOOLS_SAT_CUTS_H_</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#define OR_TOOLS_SAT_CUTS_H_</span></div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  </div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <utility></span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="preprocessor">#include <vector></span></div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  </div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "<a class="code" href="int__type_8h.html">ortools/base/int_type.h</a>"</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "<a class="code" href="strong__vector_8h.html">ortools/base/strong_vector.h</a>"</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "<a class="code" href="implied__bounds_8h.html">ortools/sat/implied_bounds.h</a>"</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</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 name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include "<a class="code" href="intervals_8h.html">ortools/sat/intervals.h</a>"</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</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 name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include "<a class="code" href="linear__constraint__manager_8h.html">ortools/sat/linear_constraint_manager.h</a>"</span></div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</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 name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include "<a class="code" href="time__limit_8h.html">ortools/util/time_limit.h</a>"</span></div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  </div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">namespace </span>sat {</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  </div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">// A "cut" generator on a set of IntegerVariable.</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// The generate_cuts() function will usually be called with the current LP</span></div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// optimal solution (but should work for any lp_values). Note that a</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// CutGenerator should:</span></div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// - Only look at the lp_values positions that corresponds to its 'vars' or</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// their negation.</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// - Only add cuts in term of the same variables or their negation.</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_cut_generator.html"> 41</a></span> <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1_cut_generator.html">CutGenerator</a> {</div>
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<div class="line"><a name="l00042"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_cut_generator.html#a73e4094f2d4e2adbe5e8d79a5b61fcd1"> 42</a></span>  std::vector<IntegerVariable> <a class="code" href="structoperations__research_1_1sat_1_1_cut_generator.html#a73e4094f2d4e2adbe5e8d79a5b61fcd1">vars</a>;</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  std::function<void(</div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <a class="code" href="classoperations__research_1_1sat_1_1_linear_constraint_manager.html">LinearConstraintManager</a>* manager)></div>
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<div class="line"><a name="l00046"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_cut_generator.html#af7117deb3f57ff3ecceddc6e9bb2c561"> 46</a></span>  <a class="code" href="structoperations__research_1_1sat_1_1_cut_generator.html#af7117deb3f57ff3ecceddc6e9bb2c561">generate_cuts</a>;</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> };</div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  </div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// Given an upper-bounded linear relation (sum terms <= ub), this algorithm</span></div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// inspects the integer variable appearing in the sum and try to replace each of</span></div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// them by a tight lower bound (>= coeff * binary + lb) using the implied bound</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">// repository. By tight, we mean that it will take the same value under the</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// current LP solution.</span></div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// We use a class to reuse memory of the tmp terms.</span></div>
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<div class="line"><a name="l00056"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html"> 56</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html">ImpliedBoundsProcessor</a> {</div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">// We will only replace IntegerVariable appearing in lp_vars_.</span></div>
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<div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#acc1b04e5f7e2423d189a70388e177e97"> 59</a></span>  <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#acc1b04e5f7e2423d189a70388e177e97">ImpliedBoundsProcessor</a>(absl::Span<const IntegerVariable> lp_vars_,</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <a class="code" href="classoperations__research_1_1sat_1_1_integer_trail.html">IntegerTrail</a>* integer_trail,</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds.html">ImpliedBounds</a>* implied_bounds)</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  : lp_vars_(lp_vars_.begin(), lp_vars_.end()),</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  integer_trail_(integer_trail),</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  implied_bounds_(implied_bounds) {}</div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">// Processes and updates the given cut.</span></div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a7fb8d0b24091252e79aea6e5666f29e8">ProcessUpperBoundedConstraint</a>(</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <a class="code" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>* cut);</div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  </div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// Same as ProcessUpperBoundedConstraint() but instead of just using</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">// var >= coeff * binary + lb we use var == slack + coeff * binary + lb where</span></div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="comment">// slack is a new temporary variable that we create.</span></div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// The new slack will be such that slack_infos[(slack - first_slack) / 2]</span></div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">// contains its definition so that we can properly handle it in the cut</span></div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="comment">// generation and substitute it back later.</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html"> 78</a></span>  <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html">SlackInfo</a> {</div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// This slack is equal to sum of terms + offset.</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a250583d63e8184c6f9f4deba1125e6bb"> 80</a></span>  std::vector<std::pair<IntegerVariable, IntegerValue>> <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a250583d63e8184c6f9f4deba1125e6bb">terms</a>;</div>
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<div class="line"><a name="l00081"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#acd07f8397a2e61932c8ee17a4e300e23"> 81</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#acd07f8397a2e61932c8ee17a4e300e23">offset</a>;</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  </div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">// The slack bounds and current lp_value.</span></div>
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<div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a0ee34e5c6fbf075def1a6c2f0c42d040"> 84</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a0ee34e5c6fbf075def1a6c2f0c42d040">lb</a> = IntegerValue(0);</div>
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<div class="line"><a name="l00085"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a6e2915dc7e5345d6959390b53f026c5f"> 85</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a6e2915dc7e5345d6959390b53f026c5f">ub</a> = IntegerValue(0);</div>
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<div class="line"><a name="l00086"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#adb47ac0cff7c9dc4dc5f101d38a91185"> 86</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#adb47ac0cff7c9dc4dc5f101d38a91185">lp_value</a> = 0.0;</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  };</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a135d2e8757ef674942be0b1d6f46f75b">ProcessUpperBoundedConstraintWithSlackCreation</a>(</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordtype">bool</span> substitute_only_inner_variables, IntegerVariable first_slack,</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <a class="code" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>* cut, std::vector<SlackInfo>* slack_infos);</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  </div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">// See if some of the implied bounds equation are violated and add them to</span></div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="comment">// the IB cut pool if it is the case.</span></div>
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<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#aecf53d8ca125b38267c341d76cebf6a9">SeparateSomeImpliedBoundCuts</a>(</div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values);</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  </div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="comment">// Only used for debugging.</span></div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="comment">// Substituting back the slack created by the function above should give</span></div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">// exactly the same cut as the original one.</span></div>
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#ab1b4642341faf5ff972b02f034d88f21">DebugSlack</a>(IntegerVariable first_slack,</div>
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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keyword">const</span> <a class="code" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>& initial_cut,</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keyword">const</span> <a class="code" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>& cut,</div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keyword">const</span> std::vector<SlackInfo>& info);</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  </div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="comment">// Add a new variable that could be used in the new cuts.</span></div>
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<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a07e1de12d9a4b00c96911544e72b86d4"> 108</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a07e1de12d9a4b00c96911544e72b86d4">AddLpVariable</a>(IntegerVariable <a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>) { lp_vars_.insert(<a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>); }</div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  </div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="comment">// Must be called before we process any constraints with a different</span></div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="comment">// lp_values or level zero bounds.</span></div>
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<div class="line"><a name="l00112"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a011f5f336c989d356c5f06a5793473c1"> 112</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a011f5f336c989d356c5f06a5793473c1">ClearCache</a>()<span class="keyword"> const </span>{ cache_.clear(); }</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  </div>
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<div class="line"><a name="l00114"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html"> 114</a></span>  <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html">BestImpliedBoundInfo</a> {</div>
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<div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a9231f58e9d0f2dafc65c9eb41c979028"> 115</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a9231f58e9d0f2dafc65c9eb41c979028">bool_lp_value</a> = 0.0;</div>
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<div class="line"><a name="l00116"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#ac11e010c276514d6402c772d0651f82f"> 116</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#ac11e010c276514d6402c772d0651f82f">slack_lp_value</a> = std::numeric_limits<double>::infinity();</div>
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<div class="line"><a name="l00117"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a6d2822d5e07c3716efcdf73a4ae5eafc"> 117</a></span>  <span class="keywordtype">bool</span> <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a6d2822d5e07c3716efcdf73a4ae5eafc">is_positive</a>;</div>
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<div class="line"><a name="l00118"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a2c25b894240115eebb2e75e2d8491a79"> 118</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a2c25b894240115eebb2e75e2d8491a79">bound_diff</a>;</div>
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<div class="line"><a name="l00119"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a871eaa421116e3c7cd440b6299d0b74d"> 119</a></span>  IntegerVariable <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a871eaa421116e3c7cd440b6299d0b74d">bool_var</a> = <a class="code" href="namespaceoperations__research_1_1sat.html#a5bd8c44473618b7eafd33ba978db2f06">kNoIntegerVariable</a>;</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  };</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  <a class="code" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html">BestImpliedBoundInfo</a> <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#abb0b7cc2e259fc8ebe8fd3dd55816b75">GetCachedImpliedBoundInfo</a>(IntegerVariable <a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>);</div>
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<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  </div>
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<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// As we compute the best implied bounds for each variable, we add violated</span></div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">// cuts here.</span></div>
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<div class="line"><a name="l00125"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a6a4d553c8850c30428f1750d37d33d26"> 125</a></span>  <a class="code" href="classoperations__research_1_1sat_1_1_top_n_cuts.html">TopNCuts</a>& <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a6a4d553c8850c30428f1750d37d33d26">IbCutPool</a>() { <span class="keywordflow">return</span> ib_cut_pool_; }</div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  </div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  BestImpliedBoundInfo ComputeBestImpliedBound(</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  IntegerVariable <a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>,</div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values);</div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  </div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  absl::flat_hash_set<IntegerVariable> lp_vars_;</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">mutable</span> absl::flat_hash_map<IntegerVariable, BestImpliedBoundInfo> cache_;</div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  </div>
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<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <a class="code" href="classoperations__research_1_1sat_1_1_top_n_cuts.html">TopNCuts</a> ib_cut_pool_ = <a class="code" href="classoperations__research_1_1sat_1_1_top_n_cuts.html">TopNCuts</a>(50);</div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  </div>
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<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="comment">// Data from the constructor.</span></div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <a class="code" href="classoperations__research_1_1sat_1_1_integer_trail.html">IntegerTrail</a>* integer_trail_;</div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds.html">ImpliedBounds</a>* implied_bounds_;</div>
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<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  </div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="comment">// Temporary memory used by ProcessUpperBoundedConstraint().</span></div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keyword">mutable</span> std::vector<std::pair<IntegerVariable, IntegerValue>> tmp_terms_;</div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> };</div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  </div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment">// Visible for testing. Returns a function f on integers such that:</span></div>
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<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="comment">// - f is non-decreasing.</span></div>
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<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment">// - f is super-additive: f(a) + f(b) <= f(a + b)</span></div>
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<div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment">// - 1 <= f(divisor) <= max_scaling</span></div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment">// - For all x, f(x * divisor) = x * f(divisor)</span></div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment">// - For all x, f(x * divisor + remainder) = x * f(divisor)</span></div>
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<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment">// Preconditions:</span></div>
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<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// - 0 <= remainder < divisor.</span></div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment">// - 1 <= max_scaling.</span></div>
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<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment">// This is used in IntegerRoundingCut() and is responsible for "strengthening"</span></div>
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<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="comment">// the cut. Just taking f(x) = x / divisor result in the non-strengthened cut</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment">// and using any function that stricly dominate this one is better.</span></div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// Algorithm:</span></div>
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<div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment">// - We first scale by a factor t so that rhs_remainder >= divisor / 2.</span></div>
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<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment">// - Then, if max_scaling == 2, we use the function described</span></div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment">// in "Strenghtening Chvatal-Gomory cuts and Gomory fractional cuts", Adam N.</span></div>
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<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment">// Letchfrod, Andrea Lodi.</span></div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> <span class="comment">// - Otherwise, we use a generalization of this which is a discretized version</span></div>
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<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment">// of the classical MIR rounding function that only take the value of the</span></div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment">// form "an_integer / max_scaling". As max_scaling goes to infinity, this</span></div>
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<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment">// converge to the real-valued MIR function.</span></div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment">// Note that for each value of max_scaling we will get a different function.</span></div>
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<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment">// And that there is no dominance relation between any of these functions. So</span></div>
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<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="comment">// it could be nice to try to generate a cut using different values of</span></div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment">// max_scaling.</span></div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> IntegerValue <a class="code" href="namespaceoperations__research_1_1sat.html#a44bd0a015c444c2e2d58a002a09a1ea5">GetFactorT</a>(IntegerValue rhs_remainder, IntegerValue divisor,</div>
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<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  IntegerValue max_t);</div>
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<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> std::function<IntegerValue(IntegerValue)> <a class="code" href="namespaceoperations__research_1_1sat.html#a8e30df8580d6914abba28f43b6e4e667">GetSuperAdditiveRoundingFunction</a>(</div>
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<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  IntegerValue rhs_remainder, IntegerValue divisor, IntegerValue t,</div>
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<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  IntegerValue max_scaling);</div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  </div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// Given an upper bounded linear constraint, this function tries to transform it</span></div>
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<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment">// to a valid cut that violate the given LP solution using integer rounding.</span></div>
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<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// Note that the returned cut might not always violate the LP solution, in which</span></div>
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<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment">// case it can be discarded.</span></div>
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<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment">// What this does is basically take the integer division of the constraint by an</span></div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment">// integer. If the coefficients where doubles, this would be the same as scaling</span></div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment">// the constraint and then rounding. We choose the coefficient of the most</span></div>
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<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment">// fractional variable (rescaled by its coefficient) as the divisor, but there</span></div>
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<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment">// are other possible alternatives.</span></div>
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<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// Note that if the constraint is tight under the given lp solution, and if</span></div>
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<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment">// there is a unique variable not at one of its bounds and fractional, then we</span></div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment">// are guaranteed to generate a cut that violate the current LP solution. This</span></div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="comment">// should be the case for Chvatal-Gomory base constraints modulo our loss of</span></div>
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<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> <span class="comment">// precision while doing exact integer computations.</span></div>
|
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<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> <span class="comment">// Precondition:</span></div>
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<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// - We assumes that the given initial constraint is tight using the given lp</span></div>
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<div class="line"><a name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// values. This could be relaxed, but for now it should always be the case, so</span></div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// we log a message and abort if not, to ease debugging.</span></div>
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<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> <span class="comment">// - The IntegerVariable of the cuts are not used here. We assumes that the</span></div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="comment">// first three vectors are in one to one correspondence with the initial order</span></div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> <span class="comment">// of the variable in the cut.</span></div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment">// TODO(user): There is a bunch of heuristic involved here, and we could spend</span></div>
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<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment">// more effort tunning them. In particular, one can try many heuristics and keep</span></div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment">// the best looking cut (or more than one). This is not on the critical code</span></div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment">// path, so we can spend more effort in finding good cuts.</span></div>
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<div class="line"><a name="l00209"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_rounding_options.html"> 209</a></span> <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1_rounding_options.html">RoundingOptions</a> {</div>
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<div class="line"><a name="l00210"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_rounding_options.html#a01db407e90fac1c31c6705758a057908"> 210</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1_rounding_options.html#a01db407e90fac1c31c6705758a057908">max_scaling</a> = IntegerValue(60);</div>
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<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> };</div>
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<div class="line"><a name="l00212"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html"> 212</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html">IntegerRoundingCutHelper</a> {</div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a66c8e6dc26260b69dcdf7668925dc3aa">ComputeCut</a>(<a class="code" href="structoperations__research_1_1sat_1_1_rounding_options.html">RoundingOptions</a> options, <span class="keyword">const</span> std::vector<double>& lp_values,</div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keyword">const</span> std::vector<IntegerValue>& <a class="code" href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a>,</div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="keyword">const</span> std::vector<IntegerValue>& <a class="code" href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a>,</div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <a class="code" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html">ImpliedBoundsProcessor</a>* ib_processor, <a class="code" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>* cut);</div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  </div>
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="comment">// Returns the number of implied bound lifted Booleans in the last</span></div>
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="comment">// ComputeCut() call. Useful for investigation.</span></div>
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<div class="line"><a name="l00221"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a4f879f884fd170f77c9024aee023feb2"> 221</a></span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a4f879f884fd170f77c9024aee023feb2">NumLiftedBooleans</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_lifted_booleans_; }</div>
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<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  </div>
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<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="comment">// The helper is just here to reuse the memory for these vectors.</span></div>
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<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  std::vector<int> relevant_indices_;</div>
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<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  std::vector<double> relevant_lp_values_;</div>
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<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  std::vector<IntegerValue> relevant_coeffs_;</div>
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<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  std::vector<IntegerValue> relevant_bound_diffs_;</div>
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<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  std::vector<IntegerValue> divisors_;</div>
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<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  std::vector<std::pair<int, IntegerValue>> adjusted_coeffs_;</div>
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<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  std::vector<IntegerValue> remainders_;</div>
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<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  std::vector<bool> change_sign_at_postprocessing_;</div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  std::vector<IntegerValue> rs_;</div>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  std::vector<IntegerValue> best_rs_;</div>
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<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  </div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordtype">int</span> num_lifted_booleans_ = 0;</div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  std::vector<std::pair<IntegerVariable, IntegerValue>> tmp_terms_;</div>
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</span> };</div>
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<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  </div>
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<div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="comment">// Helper to find knapsack or flow cover cuts (not yet implemented).</span></div>
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<div class="line"><a name="l00241"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html"> 241</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html">CoverCutHelper</a> {</div>
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<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="comment">// Try to find a cut with a knapsack heuristic.</span></div>
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<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="comment">// If this returns true, you can get the cut via cut().</span></div>
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<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ad86e161bb994fe49fa9c4298ebb5ae2d">TrySimpleKnapsack</a>(<span class="keyword">const</span> <a class="code" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a> base_ct,</div>
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<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keyword">const</span> std::vector<double>& lp_values,</div>
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<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keyword">const</span> std::vector<IntegerValue>& <a class="code" href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a>,</div>
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<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keyword">const</span> std::vector<IntegerValue>& <a class="code" href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a>);</div>
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<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  </div>
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<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="comment">// If successful, info about the last generated cut.</span></div>
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<div class="line"><a name="l00251"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#a542e0108682bbed13c1ccaa078845520"> 251</a></span>  <a class="code" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>* <a class="code" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#a542e0108682bbed13c1ccaa078845520">mutable_cut</a>() { <span class="keywordflow">return</span> &cut_; }</div>
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<div class="line"><a name="l00252"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#a28706d15758f23844d625462fa39edbc"> 252</a></span>  <span class="keyword">const</span> <a class="code" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>& <a class="code" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#a28706d15758f23844d625462fa39edbc">cut</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> cut_; }</div>
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<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  </div>
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<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  <span class="comment">// Single line of text that we append to the cut log line.</span></div>
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<div class="line"><a name="l00255"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ac3816c1571dfd130851ed09c79224360"> 255</a></span>  <span class="keyword">const</span> std::string <a class="code" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ac3816c1571dfd130851ed09c79224360">Info</a>() { <span class="keywordflow">return</span> absl::StrCat(<span class="stringliteral">"lift="</span>, num_lifting_); }</div>
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<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  </div>
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<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keyword">struct </span>Term {</div>
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<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keywordtype">int</span> <a class="code" href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>;</div>
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<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keywordtype">double</span> dist_to_max_value;</div>
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<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  IntegerValue positive_coeff; <span class="comment">// abs(coeff in original constraint).</span></div>
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<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  IntegerValue diff;</div>
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<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  };</div>
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<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  std::vector<Term> terms_;</div>
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<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  std::vector<bool> in_cut_;</div>
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<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  </div>
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<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  LinearConstraint cut_;</div>
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<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordtype">int</span> num_lifting_;</div>
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<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> };</div>
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<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  </div>
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<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="comment">// If a variable is away from its upper bound by more than value 1.0, then it</span></div>
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<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment">// cannot be part of a cover that will violate the lp solution. This method</span></div>
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<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment">// returns a reduced constraint by removing such variables from the given</span></div>
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<div class="line"><a name="l00274"></a><span class="lineno"> 274</span> <span class="comment">// constraint.</span></div>
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<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> LinearConstraint <a class="code" href="namespaceoperations__research_1_1sat.html#a1de556a1559f25bd0819655d375f6c8e">GetPreprocessedLinearConstraint</a>(</div>
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<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keyword">const</span> LinearConstraint& constraint,</div>
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<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
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<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  </div>
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<div class="line"><a name="l00280"></a><span class="lineno"> 280</span> <span class="comment">// Returns true if sum of all the variables in the given constraint is less than</span></div>
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<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="comment">// or equal to constraint upper bound. This method assumes that all the</span></div>
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<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="comment">// coefficients are non negative.</span></div>
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<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#ac8b530afe36cf1521c919ca43429926d">ConstraintIsTriviallyTrue</a>(<span class="keyword">const</span> LinearConstraint& constraint,</div>
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<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
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<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  </div>
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<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="comment">// If the left variables in lp solution satisfies following inequality, we prove</span></div>
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<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> <span class="comment">// that there does not exist any knapsack cut which is violated by the solution.</span></div>
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<div class="line"><a name="l00288"></a><span class="lineno"> 288</span> <span class="comment">// Let |Cmin| = smallest possible cover size.</span></div>
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<div class="line"><a name="l00289"></a><span class="lineno"> 289</span> <span class="comment">// Let S = smallest (var_ub - lp_values[var]) first |Cmin| variables.</span></div>
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<div class="line"><a name="l00290"></a><span class="lineno"> 290</span> <span class="comment">// Let cut lower bound = sum_(var in S)(var_ub - lp_values[var])</span></div>
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<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="comment">// For any cover,</span></div>
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<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="comment">// If cut lower bound >= 1</span></div>
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<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="comment">// ==> sum_(var in S)(var_ub - lp_values[var]) >= 1</span></div>
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<div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="comment">// ==> sum_(var in cover)(var_ub - lp_values[var]) >= 1</span></div>
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<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="comment">// ==> The solution already satisfies cover. Since this is true for all covers,</span></div>
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<div class="line"><a name="l00296"></a><span class="lineno"> 296</span> <span class="comment">// this method returns false in such cases.</span></div>
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<div class="line"><a name="l00297"></a><span class="lineno"> 297</span> <span class="comment">// This method assumes that the constraint is preprocessed and has only non</span></div>
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<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="comment">// negative coefficients.</span></div>
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<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a588b516182cd6d5d8c048dfd76bc5523">CanBeFilteredUsingCutLowerBound</a>(</div>
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<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <span class="keyword">const</span> LinearConstraint& preprocessed_constraint,</div>
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<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
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<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  </div>
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<div class="line"><a name="l00304"></a><span class="lineno"> 304</span> <span class="comment">// Struct to help compute upper bound for knapsack instance.</span></div>
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<div class="line"><a name="l00305"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_knapsack_item.html"> 305</a></span> <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1_knapsack_item.html">KnapsackItem</a> {</div>
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<div class="line"><a name="l00306"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c"> 306</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c">profit</a>;</div>
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<div class="line"><a name="l00307"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513"> 307</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513">weight</a>;</div>
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<div class="line"><a name="l00308"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_knapsack_item.html#aa51ab05fd43c2d0962967f9d889c7bb7"> 308</a></span>  <span class="keywordtype">bool</span> <a class="code" href="structoperations__research_1_1sat_1_1_knapsack_item.html#aa51ab05fd43c2d0962967f9d889c7bb7">operator></a>(<span class="keyword">const</span> <a class="code" href="structoperations__research_1_1sat_1_1_knapsack_item.html">KnapsackItem</a>& other)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">return</span> <a class="code" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c">profit</a> * other.<a class="code" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513">weight</a> > other.<a class="code" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c">profit</a> * <a class="code" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513">weight</a>;</div>
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<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  }</div>
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<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> };</div>
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<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  </div>
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<div class="line"><a name="l00313"></a><span class="lineno"> 313</span> <span class="comment">// Gets upper bound on profit for knapsack instance by solving the linear</span></div>
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<div class="line"><a name="l00314"></a><span class="lineno"> 314</span> <span class="comment">// relaxation.</span></div>
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<div class="line"><a name="l00315"></a><span class="lineno"> 315</span> <span class="keywordtype">double</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a457076abfb3071fca80b8175363e3dfa">GetKnapsackUpperBound</a>(std::vector<KnapsackItem> items, <span class="keywordtype">double</span> <a class="code" href="routing__flow_8cc.html#a2acb49f4df5288066c43610bede123ec">capacity</a>);</div>
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<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  </div>
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<div class="line"><a name="l00317"></a><span class="lineno"> 317</span> <span class="comment">// Returns true if the linear relaxation upper bound for the knapsack instance</span></div>
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<div class="line"><a name="l00318"></a><span class="lineno"> 318</span> <span class="comment">// shows that this constraint cannot be used to form a cut. This method assumes</span></div>
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<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="comment">// that all the coefficients are non negative.</span></div>
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<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a8c8db245a613f2fb46d917cd78100f83">CanBeFilteredUsingKnapsackUpperBound</a>(</div>
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|
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keyword">const</span> LinearConstraint& constraint,</div>
|
|
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
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|
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  </div>
|
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<div class="line"><a name="l00325"></a><span class="lineno"> 325</span> <span class="comment">// Returns true if the given constraint passes all the filters described above.</span></div>
|
|
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span> <span class="comment">// This method assumes that the constraint is preprocessed and has only non</span></div>
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<div class="line"><a name="l00327"></a><span class="lineno"> 327</span> <span class="comment">// negative coefficients.</span></div>
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<div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a32f0016572d69bfcd1f3af811b2043ad">CanFormValidKnapsackCover</a>(</div>
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<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keyword">const</span> LinearConstraint& preprocessed_constraint,</div>
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<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
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|
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  </div>
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<div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="comment">// Converts the given constraint into canonical knapsack form (described</span></div>
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|
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span> <span class="comment">// below) and adds it to 'knapsack_constraints'.</span></div>
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<div class="line"><a name="l00335"></a><span class="lineno"> 335</span> <span class="comment">// Canonical knapsack form:</span></div>
|
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<div class="line"><a name="l00336"></a><span class="lineno"> 336</span> <span class="comment">// - Constraint has finite upper bound.</span></div>
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|
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="comment">// - All coefficients are positive.</span></div>
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<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="comment">// For constraint with finite lower bound, this method also adds the negation of</span></div>
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<div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="comment">// the given constraint after converting it to canonical knapsack form.</span></div>
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<div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a06e2118f6735d033f7f43a939abe558d">ConvertToKnapsackForm</a>(<span class="keyword">const</span> LinearConstraint& constraint,</div>
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|
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  std::vector<LinearConstraint>* knapsack_constraints,</div>
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<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  IntegerTrail* integer_trail);</div>
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<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  </div>
|
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<div class="line"><a name="l00344"></a><span class="lineno"> 344</span> <span class="comment">// Returns true if the cut is lifted. Lifting procedure is described below.</span></div>
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|
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="comment">//</span></div>
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|
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="comment">// First we decide a lifting sequence for the binary variables which are not</span></div>
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<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="comment">// already in cut. We lift the cut for each lifting candidate one by one.</span></div>
|
|
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="comment">// Given the original constraint where the lifting candidate is fixed to one, we</span></div>
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<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="comment">// compute the maximum value the cut can take and still be feasible using a</span></div>
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<div class="line"><a name="l00351"></a><span class="lineno"> 351</span> <span class="comment">// knapsack problem. We can then lift the variable in the cut using the</span></div>
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<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="comment">// difference between the cut upper bound and this maximum value.</span></div>
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<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#accb737ae1fad15d6798a4b8bc27cea51">LiftKnapsackCut</a>(</div>
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<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <span class="keyword">const</span> LinearConstraint& constraint,</div>
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<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  <span class="keyword">const</span> <a class="code" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keyword">const</span> std::vector<IntegerValue>& cut_vars_original_coefficients,</div>
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<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <span class="keyword">const</span> IntegerTrail& integer_trail, <a class="code" href="classoperations__research_1_1_time_limit.html">TimeLimit</a>* <a class="code" href="cp__model__solver_8cc.html#ac3cf9db02b23ea1455b5ae6955d03e47">time_limit</a>,</div>
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<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  LinearConstraint* cut);</div>
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<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  </div>
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<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> <span class="comment">// A cut generator that creates knpasack cover cuts.</span></div>
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|
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="comment">// For a constraint of type</span></div>
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<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="comment">// \sum_{i=1..n}(a_i * x_i) <= b</span></div>
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<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="comment">// where x_i are integer variables with upper bound u_i, a cover of size k is a</span></div>
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|
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="comment">// subset C of {1 , .. , n} such that \sum_{c \in C}(a_c * u_c) > b.</span></div>
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<div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="comment">//</span></div>
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|
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="comment">// A knapsack cover cut is a constraint of the form</span></div>
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|
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="comment">// \sum_{c \in C}(u_c - x_c) >= 1</span></div>
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|
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span> <span class="comment">// which is equivalent to \sum_{c \in C}(x_c) <= \sum_{c \in C}(u_c) - 1.</span></div>
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|
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span> <span class="comment">// In other words, in a feasible solution, at least some of the variables do</span></div>
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<div class="line"><a name="l00371"></a><span class="lineno"> 371</span> <span class="comment">// not take their maximum value.</span></div>
|
|
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> <span class="comment">// If all x_i are binary variables then the cover cut becomes</span></div>
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|
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> <span class="comment">// \sum_{c \in C}(x_c) <= |C| - 1.</span></div>
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|
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span> <span class="comment">//</span></div>
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|
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span> <span class="comment">// The major difficulty for generating Knapsack cover cuts is finding a minimal</span></div>
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|
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span> <span class="comment">// cover set C that cut a given floating point solution. There are many ways to</span></div>
|
|
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> <span class="comment">// heuristically generate the cover but the following method that uses a</span></div>
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|
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span> <span class="comment">// solution of the LP relaxation of the constraint works the best.</span></div>
|
|
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span> <span class="comment">// Look at a given linear relaxation solution for the integer problem x'</span></div>
|
|
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span> <span class="comment">// and try to solve the following knapsack problem:</span></div>
|
|
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span> <span class="comment">// Minimize \sum_{i=1..n}(z_i * (u_i - x_i')),</span></div>
|
|
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span> <span class="comment">// such that \sum_{i=1..n}(a_i * u_i * z_i) > b,</span></div>
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|
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="comment">// where z_i is a binary decision variable and x_i' are values of the variables</span></div>
|
|
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="comment">// in the given relaxation solution x'. If the objective of the optimal solution</span></div>
|
|
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span> <span class="comment">// of this problem is less than 1, this algorithm does not generate any cuts.</span></div>
|
|
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> <span class="comment">// Otherwise, it adds a knapsack cover cut in the form</span></div>
|
|
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span> <span class="comment">// \sum_{i=1..n}(z_i' * x_i) <= cb,</span></div>
|
|
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="comment">// where z_i' is the value of z_i in the optimal solution of the above</span></div>
|
|
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span> <span class="comment">// problem and cb is the upper bound for the cut constraint. Note that the above</span></div>
|
|
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span> <span class="comment">// problem can be converted into a standard kanpsack form by replacing z_i by 1</span></div>
|
|
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span> <span class="comment">// - y_i. In that case the problem becomes</span></div>
|
|
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="comment">// Maximize \sum_{i=1..n}((u_i - x_i') * (y_i - 1)),</span></div>
|
|
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span> <span class="comment">// such that</span></div>
|
|
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span> <span class="comment">// \sum_{i=1..n}(a_i * u_i * y_i) <= \sum_{i=1..n}(a_i * u_i) - b - 1.</span></div>
|
|
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="comment">// Solving this knapsack instance would help us find the smallest cover with</span></div>
|
|
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="comment">// maximum LP violation.</span></div>
|
|
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment">// Cut strengthning:</span></div>
|
|
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="comment">// Let lambda = \sum_{c \in C}(a_c * u_c) - b and max_coeff = \max_{c</span></div>
|
|
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="comment">// \in C}(a_c), then cut can be strengthened as</span></div>
|
|
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="comment">// \sum_{c \in C}(u_c - x_c) >= ceil(lambda / max_coeff)</span></div>
|
|
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="comment">// For further information about knapsack cover cuts see</span></div>
|
|
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment">// A. Atamtürk, Cover and Pack Inequalities for (Mixed) Integer Programming</span></div>
|
|
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="comment">// Annals of Operations Research Volume 139, Issue 1 , pp 21-38, 2005.</span></div>
|
|
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="comment">// TODO(user): Implement cut lifting.</span></div>
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|
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#ac158f737c8653b1fc1bd294ea2d3412d">CreateKnapsackCoverCutGenerator</a>(</div>
|
|
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="keyword">const</span> std::vector<LinearConstraint>& base_constraints,</div>
|
|
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  <span class="keyword">const</span> std::vector<IntegerVariable>& vars, Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  </div>
|
|
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="comment">// A cut generator for z = x * y (x and y >= 0).</span></div>
|
|
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#acd00c99b5770a8f86418ce2c60c716b8">CreatePositiveMultiplicationCutGenerator</a>(IntegerVariable z,</div>
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<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  IntegerVariable x,</div>
|
|
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  IntegerVariable y,</div>
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|
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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|
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  </div>
|
|
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="comment">// A cut generator for y = x ^ 2 (x >= 0).</span></div>
|
|
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="comment">// It will dynamically add a linear inequality to push y closer to the parabola.</span></div>
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|
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a562723a1a137cee8f869c1d7eb9641b0">CreateSquareCutGenerator</a>(IntegerVariable y, IntegerVariable x,</div>
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<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  </div>
|
|
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment">// A cut generator for all_diff(xi). Let the united domain of all xi be D. Sum</span></div>
|
|
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="comment">// of any k-sized subset of xi need to be greater or equal to the sum of</span></div>
|
|
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> <span class="comment">// smallest k values in D and lesser or equal to the sum of largest k values in</span></div>
|
|
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="comment">// D. The cut generator first sorts the variables based on LP values and adds</span></div>
|
|
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span> <span class="comment">// cuts of the form described above if they are violated by lp solution. Note</span></div>
|
|
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span> <span class="comment">// that all the fixed variables are ignored while generating cuts.</span></div>
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|
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a7feb76be212dca01ffe7ba3a0391e118">CreateAllDifferentCutGenerator</a>(</div>
|
|
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  <span class="keyword">const</span> std::vector<IntegerVariable>& vars, Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  </div>
|
|
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="comment">// Consider the Lin Max constraint with d expressions and n variables in the</span></div>
|
|
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="comment">// form: target = max {exprs[k] = Sum (wki * xi + bk)}. k in {1,..,d}.</span></div>
|
|
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="comment">// Li = lower bound of xi</span></div>
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|
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="comment">// Ui = upper bound of xi.</span></div>
|
|
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span> <span class="comment">// Let zk be in {0,1} for all k in {1,..,d}.</span></div>
|
|
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span> <span class="comment">// The target = exprs[k] when zk = 1.</span></div>
|
|
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span> <span class="comment">// The following is a valid linearization for Lin Max.</span></div>
|
|
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span> <span class="comment">// target >= exprs[k], for all k in {1,..,d}</span></div>
|
|
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="comment">// target <= Sum (wli * xi) + Sum((Nlk + bk) * zk), for all l in {1,..,d}</span></div>
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|
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span> <span class="comment">// Where Nlk is a large number defined as:</span></div>
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|
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span> <span class="comment">// Nlk = Sum (max((wki - wli)*Li, (wki - wli)*Ui))</span></div>
|
|
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="comment">// = Sum (max corner difference for variable i, target expr l, max expr k)</span></div>
|
|
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span> <span class="comment">//</span></div>
|
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<div class="line"><a name="l00448"></a><span class="lineno"> 448</span> <span class="comment">// Consider a partition of variables xi into set {1,..,d} as I.</span></div>
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<div class="line"><a name="l00449"></a><span class="lineno"> 449</span> <span class="comment">// i.e. I(i) = j means xi is mapped to jth index.</span></div>
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<div class="line"><a name="l00450"></a><span class="lineno"> 450</span> <span class="comment">// The following inequality is valid and sharp cut for the lin max constraint</span></div>
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<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="comment">// described above.</span></div>
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<div class="line"><a name="l00452"></a><span class="lineno"> 452</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00453"></a><span class="lineno"> 453</span> <span class="comment">// target <= Sum(i=1..n)(wI(i)i * xi + Sum(k=1..d)(MPlusCoefficient_ki * zk))</span></div>
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<div class="line"><a name="l00454"></a><span class="lineno"> 454</span> <span class="comment">// + Sum(k=1..d)(bk * zk) ,</span></div>
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<div class="line"><a name="l00455"></a><span class="lineno"> 455</span> <span class="comment">// Where MPlusCoefficient_ki = max((wki - wI(i)i) * Li,</span></div>
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<div class="line"><a name="l00456"></a><span class="lineno"> 456</span> <span class="comment">// (wki - wI(i)i) * Ui)</span></div>
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<div class="line"><a name="l00457"></a><span class="lineno"> 457</span> <span class="comment">// = max corner difference for variable i,</span></div>
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<div class="line"><a name="l00458"></a><span class="lineno"> 458</span> <span class="comment">// target expr I(i), max expr k.</span></div>
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<div class="line"><a name="l00459"></a><span class="lineno"> 459</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00460"></a><span class="lineno"> 460</span> <span class="comment">// For detailed proof of validity, refer</span></div>
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<div class="line"><a name="l00461"></a><span class="lineno"> 461</span> <span class="comment">// Reference: "Strong mixed-integer programming formulations for trained neural</span></div>
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<div class="line"><a name="l00462"></a><span class="lineno"> 462</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 name="l00463"></a><span class="lineno"> 463</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00464"></a><span class="lineno"> 464</span> <span class="comment">// In the cut generator, we compute the most violated partition I by computing</span></div>
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<div class="line"><a name="l00465"></a><span class="lineno"> 465</span> <span class="comment">// the rhs value (wI(i)i * lp_value(xi) + Sum(k=1..d)(MPlusCoefficient_ki * zk))</span></div>
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<div class="line"><a name="l00466"></a><span class="lineno"> 466</span> <span class="comment">// for each variable for each partition index. We choose the partition index</span></div>
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<div class="line"><a name="l00467"></a><span class="lineno"> 467</span> <span class="comment">// that gives lowest rhs value for a given variable.</span></div>
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<div class="line"><a name="l00468"></a><span class="lineno"> 468</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00469"></a><span class="lineno"> 469</span> <span class="comment">// Note: This cut generator requires all expressions to contain only positive</span></div>
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<div class="line"><a name="l00470"></a><span class="lineno"> 470</span> <span class="comment">// vars.</span></div>
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<div class="line"><a name="l00471"></a><span class="lineno"> 471</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a7fea62548e11ae728e506874f767bdd3">CreateLinMaxCutGenerator</a>(</div>
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<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="keyword">const</span> IntegerVariable target, <span class="keyword">const</span> std::vector<LinearExpression>& exprs,</div>
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<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="keyword">const</span> std::vector<IntegerVariable>& z_vars, Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  </div>
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<div class="line"><a name="l00475"></a><span class="lineno"> 475</span> <span class="comment">// For a given set of intervals and demands, we compute the maximum energy of</span></div>
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<div class="line"><a name="l00476"></a><span class="lineno"> 476</span> <span class="comment">// each task and make sure it is less than the span of the intervals * its</span></div>
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<div class="line"><a name="l00477"></a><span class="lineno"> 477</span> <span class="comment">// capacity.</span></div>
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<div class="line"><a name="l00478"></a><span class="lineno"> 478</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00479"></a><span class="lineno"> 479</span> <span class="comment">// If an interval is optional, it contributes</span></div>
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<div class="line"><a name="l00480"></a><span class="lineno"> 480</span> <span class="comment">// min_demand * min_size * presence_literal</span></div>
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<div class="line"><a name="l00481"></a><span class="lineno"> 481</span> <span class="comment">// amount of total energy.</span></div>
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<div class="line"><a name="l00482"></a><span class="lineno"> 482</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00483"></a><span class="lineno"> 483</span> <span class="comment">// If an interval is performed, it contributes either min_demand * size or</span></div>
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<div class="line"><a name="l00484"></a><span class="lineno"> 484</span> <span class="comment">// demand * min_size. We choose the most violated formulation.</span></div>
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<div class="line"><a name="l00485"></a><span class="lineno"> 485</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00486"></a><span class="lineno"> 486</span> <span class="comment">// The maximum energy is capacity * span of intervals at level 0.</span></div>
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<div class="line"><a name="l00487"></a><span class="lineno"> 487</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a34b1d34844b9b1695dd45dfd9c33f663">CreateCumulativeCutGenerator</a>(</div>
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<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="keyword">const</span> std::vector<IntervalVariable>& intervals,</div>
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<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="keyword">const</span> IntegerVariable <a class="code" href="routing__flow_8cc.html#a2acb49f4df5288066c43610bede123ec">capacity</a>, <span class="keyword">const</span> std::vector<IntegerVariable>& demands,</div>
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<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  </div>
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<div class="line"><a name="l00492"></a><span class="lineno"> 492</span> <span class="comment">// For a given set of intervals and demands, we first compute the mandatory part</span></div>
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<div class="line"><a name="l00493"></a><span class="lineno"> 493</span> <span class="comment">// of the interval as [start_max , end_min]. We use this to calculate mandatory</span></div>
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<div class="line"><a name="l00494"></a><span class="lineno"> 494</span> <span class="comment">// demands for each start_max time points for eligible intervals.</span></div>
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<div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="comment">// Since the sum of these mandatory demands must be smaller or equal to the</span></div>
|
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<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="comment">// capacity, we create a cut representing that.</span></div>
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|
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00498"></a><span class="lineno"> 498</span> <span class="comment">// If an interval is optional, it contributes min_demand * presence_literal</span></div>
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<div class="line"><a name="l00499"></a><span class="lineno"> 499</span> <span class="comment">// amount of demand to the mandatory demands sum. So the final cut is generated</span></div>
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|
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span> <span class="comment">// as follows:</span></div>
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<div class="line"><a name="l00501"></a><span class="lineno"> 501</span> <span class="comment">// sum(demands of always present intervals)</span></div>
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<div class="line"><a name="l00502"></a><span class="lineno"> 502</span> <span class="comment">// + sum(presence_literal * min_of_demand) <= capacity.</span></div>
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<div class="line"><a name="l00503"></a><span class="lineno"> 503</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a50b686357c19f67aa58931db58e801e6">CreateOverlappingCumulativeCutGenerator</a>(</div>
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<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  <span class="keyword">const</span> std::vector<IntervalVariable>& intervals,</div>
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<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  <span class="keyword">const</span> IntegerVariable <a class="code" href="routing__flow_8cc.html#a2acb49f4df5288066c43610bede123ec">capacity</a>, <span class="keyword">const</span> std::vector<IntegerVariable>& demands,</div>
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<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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|
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  </div>
|
|
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span> <span class="comment">// For a given set of intervals, we first compute the min and max of all</span></div>
|
|
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span> <span class="comment">// intervals. Then we create a cut that indicates that all intervals must fit</span></div>
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<div class="line"><a name="l00510"></a><span class="lineno"> 510</span> <span class="comment">// in that span.</span></div>
|
|
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span> <span class="comment">// If an interval is optional, it contributes min_size * presence_literal</span></div>
|
|
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span> <span class="comment">// amount of demand to the mandatory demands sum. So the final cut is generated</span></div>
|
|
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span> <span class="comment">// as follows:</span></div>
|
|
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span> <span class="comment">// sum(sizes of always present intervals)</span></div>
|
|
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span> <span class="comment">// + sum(presence_literal * min_of_size) <= span of all intervals.</span></div>
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|
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#ab62fb8f885a68c653b586424aa5863c8">CreateNoOverlapEnergyCutGenerator</a>(</div>
|
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<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <span class="keyword">const</span> std::vector<IntervalVariable>& intervals, Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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|
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  </div>
|
|
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span> <span class="comment">// For a given set of intervals in a no_overlap constraint, we detect violated</span></div>
|
|
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span> <span class="comment">// mandatory precedences and create a cut for these.</span></div>
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|
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a23849eabdcf8e9f6f90e7aa05b298dc9">CreateNoOverlapPrecedenceCutGenerator</a>(</div>
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<div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  <span class="keyword">const</span> std::vector<IntervalVariable>& intervals, Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  </div>
|
|
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span> <span class="comment">// For a given set of intervals in a no_overlap constraint, we detect violated</span></div>
|
|
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span> <span class="comment">// area based cuts from Balas 85 [see note in the code] and create a cut for</span></div>
|
|
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span> <span class="comment">// these.</span></div>
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|
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a90cb4e9fd1941ba3f7c011f086920d7a">CreateNoOverlapBalasCutGenerator</a>(</div>
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<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="keyword">const</span> std::vector<IntervalVariable>& intervals, Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  </div>
|
|
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span> <span class="comment">// Extracts the variables that have a Literal view from base variables and</span></div>
|
|
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span> <span class="comment">// create a generator that will returns constraint of the form "at_most_one"</span></div>
|
|
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span> <span class="comment">// between such literals.</span></div>
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|
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#adf176ac81e34e8fd124d823ee0033f1a">CreateCliqueCutGenerator</a>(</div>
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|
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  <span class="keyword">const</span> std::vector<IntegerVariable>& base_variables, Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  </div>
|
|
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span> } <span class="comment">// namespace sat</span></div>
|
|
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span> } <span class="comment">// namespace operations_research</span></div>
|
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<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  </div>
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<div class="line"><a name="l00540"></a><span class="lineno"> 540</span> <span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_SAT_CUTS_H_</span></div>
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<div class="ttc" id="aclassabsl_1_1_strong_vector_html"><div class="ttname"><a href="classabsl_1_1_strong_vector.html">absl::StrongVector< IntegerVariable, double ></a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1_time_limit_html"><div class="ttname"><a href="classoperations__research_1_1_time_limit.html">operations_research::TimeLimit</a></div><div class="ttdoc">A simple class to enforce both an elapsed time limit and a deterministic time limit in the same threa...</div><div class="ttdef"><b>Definition:</b> <a href="time__limit_8h_source.html#l00105">time_limit.h:105</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html">operations_research::sat::CoverCutHelper</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00241">cuts.h:241</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html_a28706d15758f23844d625462fa39edbc"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#a28706d15758f23844d625462fa39edbc">operations_research::sat::CoverCutHelper::cut</a></div><div class="ttdeci">const LinearConstraint & cut() const</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00252">cuts.h:252</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html_a542e0108682bbed13c1ccaa078845520"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#a542e0108682bbed13c1ccaa078845520">operations_research::sat::CoverCutHelper::mutable_cut</a></div><div class="ttdeci">LinearConstraint * mutable_cut()</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00251">cuts.h:251</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html_ac3816c1571dfd130851ed09c79224360"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ac3816c1571dfd130851ed09c79224360">operations_research::sat::CoverCutHelper::Info</a></div><div class="ttdeci">const std::string Info()</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00255">cuts.h:255</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html_ad86e161bb994fe49fa9c4298ebb5ae2d"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ad86e161bb994fe49fa9c4298ebb5ae2d">operations_research::sat::CoverCutHelper::TrySimpleKnapsack</a></div><div class="ttdeci">bool TrySimpleKnapsack(const LinearConstraint base_ct, const std::vector< double > &lp_values, const std::vector< IntegerValue > &lower_bounds, const std::vector< IntegerValue > &upper_bounds)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01159">cuts.cc:1159</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds.html">operations_research::sat::ImpliedBounds</a></div><div class="ttdef"><b>Definition:</b> <a href="implied__bounds_8h_source.html#l00078">implied_bounds.h:78</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html">operations_research::sat::ImpliedBoundsProcessor</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00056">cuts.h:56</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_a011f5f336c989d356c5f06a5793473c1"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a011f5f336c989d356c5f06a5793473c1">operations_research::sat::ImpliedBoundsProcessor::ClearCache</a></div><div class="ttdeci">void ClearCache() const</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00112">cuts.h:112</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_a07e1de12d9a4b00c96911544e72b86d4"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a07e1de12d9a4b00c96911544e72b86d4">operations_research::sat::ImpliedBoundsProcessor::AddLpVariable</a></div><div class="ttdeci">void AddLpVariable(IntegerVariable var)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00108">cuts.h:108</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_a135d2e8757ef674942be0b1d6f46f75b"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a135d2e8757ef674942be0b1d6f46f75b">operations_research::sat::ImpliedBoundsProcessor::ProcessUpperBoundedConstraintWithSlackCreation</a></div><div class="ttdeci">void ProcessUpperBoundedConstraintWithSlackCreation(bool substitute_only_inner_variables, IntegerVariable first_slack, const absl::StrongVector< IntegerVariable, double > &lp_values, LinearConstraint *cut, std::vector< SlackInfo > *slack_infos)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01588">cuts.cc:1588</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_a6a4d553c8850c30428f1750d37d33d26"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a6a4d553c8850c30428f1750d37d33d26">operations_research::sat::ImpliedBoundsProcessor::IbCutPool</a></div><div class="ttdeci">TopNCuts & IbCutPool()</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00125">cuts.h:125</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_a7fb8d0b24091252e79aea6e5666f29e8"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a7fb8d0b24091252e79aea6e5666f29e8">operations_research::sat::ImpliedBoundsProcessor::ProcessUpperBoundedConstraint</a></div><div class="ttdeci">void ProcessUpperBoundedConstraint(const absl::StrongVector< IntegerVariable, double > &lp_values, LinearConstraint *cut)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01495">cuts.cc:1495</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_ab1b4642341faf5ff972b02f034d88f21"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#ab1b4642341faf5ff972b02f034d88f21">operations_research::sat::ImpliedBoundsProcessor::DebugSlack</a></div><div class="ttdeci">bool DebugSlack(IntegerVariable first_slack, const LinearConstraint &initial_cut, const LinearConstraint &cut, const std::vector< SlackInfo > &info)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01729">cuts.cc:1729</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_abb0b7cc2e259fc8ebe8fd3dd55816b75"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#abb0b7cc2e259fc8ebe8fd3dd55816b75">operations_research::sat::ImpliedBoundsProcessor::GetCachedImpliedBoundInfo</a></div><div class="ttdeci">BestImpliedBoundInfo GetCachedImpliedBoundInfo(IntegerVariable var)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01504">cuts.cc:1504</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_acc1b04e5f7e2423d189a70388e177e97"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#acc1b04e5f7e2423d189a70388e177e97">operations_research::sat::ImpliedBoundsProcessor::ImpliedBoundsProcessor</a></div><div class="ttdeci">ImpliedBoundsProcessor(absl::Span< const IntegerVariable > lp_vars_, IntegerTrail *integer_trail, ImpliedBounds *implied_bounds)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00059">cuts.h:59</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_aecf53d8ca125b38267c341d76cebf6a9"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#aecf53d8ca125b38267c341d76cebf6a9">operations_research::sat::ImpliedBoundsProcessor::SeparateSomeImpliedBoundCuts</a></div><div class="ttdeci">void SeparateSomeImpliedBoundCuts(const absl::StrongVector< IntegerVariable, double > &lp_values)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01579">cuts.cc:1579</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_rounding_cut_helper_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html">operations_research::sat::IntegerRoundingCutHelper</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00212">cuts.h:212</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_rounding_cut_helper_html_a4f879f884fd170f77c9024aee023feb2"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a4f879f884fd170f77c9024aee023feb2">operations_research::sat::IntegerRoundingCutHelper::NumLiftedBooleans</a></div><div class="ttdeci">int NumLiftedBooleans() const</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00221">cuts.h:221</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_rounding_cut_helper_html_a66c8e6dc26260b69dcdf7668925dc3aa"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a66c8e6dc26260b69dcdf7668925dc3aa">operations_research::sat::IntegerRoundingCutHelper::ComputeCut</a></div><div class="ttdeci">void ComputeCut(RoundingOptions options, const std::vector< double > &lp_values, const std::vector< IntegerValue > &lower_bounds, const std::vector< IntegerValue > &upper_bounds, ImpliedBoundsProcessor *ib_processor, LinearConstraint *cut)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00710">cuts.cc:710</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_trail_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_trail.html">operations_research::sat::IntegerTrail</a></div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00545">integer.h:545</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_linear_constraint_manager_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_linear_constraint_manager.html">operations_research::sat::LinearConstraintManager</a></div><div class="ttdef"><b>Definition:</b> <a href="linear__constraint__manager_8h_source.html#l00043">linear_constraint_manager.h:43</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1_top_n_cuts_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_top_n_cuts.html">operations_research::sat::TopNCuts</a></div><div class="ttdef"><b>Definition:</b> <a href="linear__constraint__manager_8h_source.html#l00292">linear_constraint_manager.h:292</a></div></div>
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<div class="ttc" id="acp__model__solver_8cc_html_ac3cf9db02b23ea1455b5ae6955d03e47"><div class="ttname"><a href="cp__model__solver_8cc.html#ac3cf9db02b23ea1455b5ae6955d03e47">time_limit</a></div><div class="ttdeci">SharedTimeLimit * time_limit</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__solver_8cc_source.html#l02152">cp_model_solver.cc:2152</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#l00273">gurobi_interface.cc:273</a></div></div>
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<div class="ttc" id="aimplied__bounds_8h_html"><div class="ttname"><a href="implied__bounds_8h.html">implied_bounds.h</a></div></div>
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<div class="ttc" id="aint__type_8h_html"><div class="ttname"><a href="int__type_8h.html">int_type.h</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="aintervals_8h_html"><div class="ttname"><a href="intervals_8h.html">intervals.h</a></div></div>
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<div class="ttc" id="alinear__constraint__manager_8h_html"><div class="ttname"><a href="linear__constraint__manager_8h.html">linear_constraint_manager.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a06e2118f6735d033f7f43a939abe558d"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a06e2118f6735d033f7f43a939abe558d">operations_research::sat::ConvertToKnapsackForm</a></div><div class="ttdeci">void ConvertToKnapsackForm(const LinearConstraint &constraint, std::vector< LinearConstraint > *knapsack_constraints, IntegerTrail *integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00390">cuts.cc:390</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a1de556a1559f25bd0819655d375f6c8e"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a1de556a1559f25bd0819655d375f6c8e">operations_research::sat::GetPreprocessedLinearConstraint</a></div><div class="ttdeci">LinearConstraint GetPreprocessedLinearConstraint(const LinearConstraint &constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00252">cuts.cc:252</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a23849eabdcf8e9f6f90e7aa05b298dc9"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a23849eabdcf8e9f6f90e7aa05b298dc9">operations_research::sat::CreateNoOverlapPrecedenceCutGenerator</a></div><div class="ttdeci">CutGenerator CreateNoOverlapPrecedenceCutGenerator(const std::vector< IntervalVariable > &intervals, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l02352">cuts.cc:2352</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a32f0016572d69bfcd1f3af811b2043ad"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a32f0016572d69bfcd1f3af811b2043ad">operations_research::sat::CanFormValidKnapsackCover</a></div><div class="ttdeci">bool CanFormValidKnapsackCover(const LinearConstraint &preprocessed_constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00372">cuts.cc:372</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a34b1d34844b9b1695dd45dfd9c33f663"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a34b1d34844b9b1695dd45dfd9c33f663">operations_research::sat::CreateCumulativeCutGenerator</a></div><div class="ttdeci">CutGenerator CreateCumulativeCutGenerator(const std::vector< IntervalVariable > &intervals, const IntegerVariable capacity, const std::vector< IntegerVariable > &demands, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l02202">cuts.cc:2202</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a44bd0a015c444c2e2d58a002a09a1ea5"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a44bd0a015c444c2e2d58a002a09a1ea5">operations_research::sat::GetFactorT</a></div><div class="ttdeci">IntegerValue GetFactorT(IntegerValue rhs_remainder, IntegerValue divisor, IntegerValue max_t)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00618">cuts.cc:618</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a457076abfb3071fca80b8175363e3dfa"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a457076abfb3071fca80b8175363e3dfa">operations_research::sat::GetKnapsackUpperBound</a></div><div class="ttdeci">double GetKnapsackUpperBound(std::vector< KnapsackItem > items, const double capacity)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00320">cuts.cc:320</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a50b686357c19f67aa58931db58e801e6"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a50b686357c19f67aa58931db58e801e6">operations_research::sat::CreateOverlappingCumulativeCutGenerator</a></div><div class="ttdeci">CutGenerator CreateOverlappingCumulativeCutGenerator(const std::vector< IntervalVariable > &intervals, const IntegerVariable capacity, const std::vector< IntegerVariable > &demands, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l02221">cuts.cc:2221</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a562723a1a137cee8f869c1d7eb9641b0"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a562723a1a137cee8f869c1d7eb9641b0">operations_research::sat::CreateSquareCutGenerator</a></div><div class="ttdeci">CutGenerator CreateSquareCutGenerator(IntegerVariable y, IntegerVariable x, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01428">cuts.cc:1428</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a588b516182cd6d5d8c048dfd76bc5523"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a588b516182cd6d5d8c048dfd76bc5523">operations_research::sat::CanBeFilteredUsingCutLowerBound</a></div><div class="ttdeci">bool CanBeFilteredUsingCutLowerBound(const LinearConstraint &preprocessed_constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00292">cuts.cc:292</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a5bd8c44473618b7eafd33ba978db2f06"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a5bd8c44473618b7eafd33ba978db2f06">operations_research::sat::kNoIntegerVariable</a></div><div class="ttdeci">const IntegerVariable kNoIntegerVariable(-1)</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a7fea62548e11ae728e506874f767bdd3"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a7fea62548e11ae728e506874f767bdd3">operations_research::sat::CreateLinMaxCutGenerator</a></div><div class="ttdeci">CutGenerator CreateLinMaxCutGenerator(const IntegerVariable target, const std::vector< LinearExpression > &exprs, const std::vector< IntegerVariable > &z_vars, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01919">cuts.cc:1919</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a7feb76be212dca01ffe7ba3a0391e118"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a7feb76be212dca01ffe7ba3a0391e118">operations_research::sat::CreateAllDifferentCutGenerator</a></div><div class="ttdeci">CutGenerator CreateAllDifferentCutGenerator(const std::vector< IntegerVariable > &vars, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01822">cuts.cc:1822</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a8c8db245a613f2fb46d917cd78100f83"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a8c8db245a613f2fb46d917cd78100f83">operations_research::sat::CanBeFilteredUsingKnapsackUpperBound</a></div><div class="ttdeci">bool CanBeFilteredUsingKnapsackUpperBound(const LinearConstraint &constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00338">cuts.cc:338</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a8e30df8580d6914abba28f43b6e4e667"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a8e30df8580d6914abba28f43b6e4e667">operations_research::sat::GetSuperAdditiveRoundingFunction</a></div><div class="ttdeci">std::function< IntegerValue(IntegerValue)> GetSuperAdditiveRoundingFunction(IntegerValue rhs_remainder, IntegerValue divisor, IntegerValue t, IntegerValue max_scaling)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00626">cuts.cc:626</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a90cb4e9fd1941ba3f7c011f086920d7a"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a90cb4e9fd1941ba3f7c011f086920d7a">operations_research::sat::CreateNoOverlapBalasCutGenerator</a></div><div class="ttdeci">CutGenerator CreateNoOverlapBalasCutGenerator(const std::vector< IntervalVariable > &intervals, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l02416">cuts.cc:2416</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ab62fb8f885a68c653b586424aa5863c8"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ab62fb8f885a68c653b586424aa5863c8">operations_research::sat::CreateNoOverlapEnergyCutGenerator</a></div><div class="ttdeci">CutGenerator CreateNoOverlapEnergyCutGenerator(const std::vector< IntervalVariable > &intervals, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l02335">cuts.cc:2335</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ac158f737c8653b1fc1bd294ea2d3412d"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ac158f737c8653b1fc1bd294ea2d3412d">operations_research::sat::CreateKnapsackCoverCutGenerator</a></div><div class="ttdeci">CutGenerator CreateKnapsackCoverCutGenerator(const std::vector< LinearConstraint > &base_constraints, const std::vector< IntegerVariable > &vars, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00439">cuts.cc:439</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ac8b530afe36cf1521c919ca43429926d"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ac8b530afe36cf1521c919ca43429926d">operations_research::sat::ConstraintIsTriviallyTrue</a></div><div class="ttdeci">bool ConstraintIsTriviallyTrue(const LinearConstraint &constraint, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00276">cuts.cc:276</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_accb737ae1fad15d6798a4b8bc27cea51"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#accb737ae1fad15d6798a4b8bc27cea51">operations_research::sat::LiftKnapsackCut</a></div><div class="ttdeci">bool LiftKnapsackCut(const LinearConstraint &constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const std::vector< IntegerValue > &cut_vars_original_coefficients, const IntegerTrail &integer_trail, TimeLimit *time_limit, LinearConstraint *cut)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00174">cuts.cc:174</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_acd00c99b5770a8f86418ce2c60c716b8"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#acd00c99b5770a8f86418ce2c60c716b8">operations_research::sat::CreatePositiveMultiplicationCutGenerator</a></div><div class="ttdeci">CutGenerator CreatePositiveMultiplicationCutGenerator(IntegerVariable z, IntegerVariable x, IntegerVariable y, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01332">cuts.cc:1332</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_adf176ac81e34e8fd124d823ee0033f1a"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#adf176ac81e34e8fd124d823ee0033f1a">operations_research::sat::CreateCliqueCutGenerator</a></div><div class="ttdeci">CutGenerator CreateCliqueCutGenerator(const std::vector< IntegerVariable > &base_variables, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l02531">cuts.cc:2531</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="apack_8cc_html_a750b5d744c39a06bfb13e6eb010e35d0"><div class="ttname"><a href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a></div><div class="ttdeci">int index</div><div class="ttdef"><b>Definition:</b> <a href="pack_8cc_source.html#l00509">pack.cc:509</a></div></div>
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<div class="ttc" id="arouting__flow_8cc_html_a2acb49f4df5288066c43610bede123ec"><div class="ttname"><a href="routing__flow_8cc.html#a2acb49f4df5288066c43610bede123ec">capacity</a></div><div class="ttdeci">int64_t capacity</div><div class="ttdef"><b>Definition:</b> <a href="routing__flow_8cc_source.html#l00151">routing_flow.cc:151</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_2lp__utils_8cc_html_a561d7bf12fc7674b3fe0ad2ba2e175a0"><div class="ttname"><a href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a></div><div class="ttdeci">std::vector< double > lower_bounds</div><div class="ttdef"><b>Definition:</b> <a href="sat_2lp__utils_8cc_source.html#l00497">sat/lp_utils.cc:497</a></div></div>
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<div class="ttc" id="asat_2lp__utils_8cc_html_a88215c8581662c40eec0fb8621c44af3"><div class="ttname"><a href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a></div><div class="ttdeci">std::vector< double > upper_bounds</div><div class="ttdef"><b>Definition:</b> <a href="sat_2lp__utils_8cc_source.html#l00498">sat/lp_utils.cc:498</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="astrong__vector_8h_html"><div class="ttname"><a href="strong__vector_8h.html">strong_vector.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_cut_generator_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_cut_generator.html">operations_research::sat::CutGenerator</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00041">cuts.h:41</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_cut_generator_html_a73e4094f2d4e2adbe5e8d79a5b61fcd1"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_cut_generator.html#a73e4094f2d4e2adbe5e8d79a5b61fcd1">operations_research::sat::CutGenerator::vars</a></div><div class="ttdeci">std::vector< IntegerVariable > vars</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00042">cuts.h:42</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_cut_generator_html_af7117deb3f57ff3ecceddc6e9bb2c561"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_cut_generator.html#af7117deb3f57ff3ecceddc6e9bb2c561">operations_research::sat::CutGenerator::generate_cuts</a></div><div class="ttdeci">std::function< void(const absl::StrongVector< IntegerVariable, double > &lp_values, LinearConstraintManager *manager)> generate_cuts</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00046">cuts.h:46</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00114">cuts.h:114</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_a2c25b894240115eebb2e75e2d8491a79"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a2c25b894240115eebb2e75e2d8491a79">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::bound_diff</a></div><div class="ttdeci">IntegerValue bound_diff</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00118">cuts.h:118</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_a6d2822d5e07c3716efcdf73a4ae5eafc"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a6d2822d5e07c3716efcdf73a4ae5eafc">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::is_positive</a></div><div class="ttdeci">bool is_positive</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00117">cuts.h:117</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_a871eaa421116e3c7cd440b6299d0b74d"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a871eaa421116e3c7cd440b6299d0b74d">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::bool_var</a></div><div class="ttdeci">IntegerVariable bool_var</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00119">cuts.h:119</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_a9231f58e9d0f2dafc65c9eb41c979028"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a9231f58e9d0f2dafc65c9eb41c979028">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::bool_lp_value</a></div><div class="ttdeci">double bool_lp_value</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00115">cuts.h:115</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_ac11e010c276514d6402c772d0651f82f"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#ac11e010c276514d6402c772d0651f82f">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::slack_lp_value</a></div><div class="ttdeci">double slack_lp_value</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00116">cuts.h:116</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html">operations_research::sat::ImpliedBoundsProcessor::SlackInfo</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00078">cuts.h:78</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_a0ee34e5c6fbf075def1a6c2f0c42d040"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a0ee34e5c6fbf075def1a6c2f0c42d040">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::lb</a></div><div class="ttdeci">IntegerValue lb</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00084">cuts.h:84</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_a250583d63e8184c6f9f4deba1125e6bb"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a250583d63e8184c6f9f4deba1125e6bb">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::terms</a></div><div class="ttdeci">std::vector< std::pair< IntegerVariable, IntegerValue > > terms</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00080">cuts.h:80</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_a6e2915dc7e5345d6959390b53f026c5f"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a6e2915dc7e5345d6959390b53f026c5f">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::ub</a></div><div class="ttdeci">IntegerValue ub</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00085">cuts.h:85</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_acd07f8397a2e61932c8ee17a4e300e23"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#acd07f8397a2e61932c8ee17a4e300e23">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::offset</a></div><div class="ttdeci">IntegerValue offset</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00081">cuts.h:81</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_adb47ac0cff7c9dc4dc5f101d38a91185"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#adb47ac0cff7c9dc4dc5f101d38a91185">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::lp_value</a></div><div class="ttdeci">double lp_value</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00086">cuts.h:86</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_knapsack_item_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_knapsack_item.html">operations_research::sat::KnapsackItem</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00305">cuts.h:305</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_knapsack_item_html_a3ff84545f00a56ba7584b2a7f2cef69c"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c">operations_research::sat::KnapsackItem::profit</a></div><div class="ttdeci">double profit</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00306">cuts.h:306</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_knapsack_item_html_a99108733d00274978a4979dc072bd513"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513">operations_research::sat::KnapsackItem::weight</a></div><div class="ttdeci">double weight</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00307">cuts.h:307</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_knapsack_item_html_aa51ab05fd43c2d0962967f9d889c7bb7"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_knapsack_item.html#aa51ab05fd43c2d0962967f9d889c7bb7">operations_research::sat::KnapsackItem::operator></a></div><div class="ttdeci">bool operator>(const KnapsackItem &other) const</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00308">cuts.h:308</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_linear_constraint_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_linear_constraint.html">operations_research::sat::LinearConstraint</a></div><div class="ttdef"><b>Definition:</b> <a href="sat_2linear__constraint_8h_source.html#l00040">sat/linear_constraint.h:40</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_rounding_options_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_rounding_options.html">operations_research::sat::RoundingOptions</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00209">cuts.h:209</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1_rounding_options_html_a01db407e90fac1c31c6705758a057908"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_rounding_options.html#a01db407e90fac1c31c6705758a057908">operations_research::sat::RoundingOptions::max_scaling</a></div><div class="ttdeci">IntegerValue max_scaling</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00210">cuts.h:210</a></div></div>
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<div class="ttc" id="atime__limit_8h_html"><div class="ttname"><a href="time__limit_8h.html">time_limit.h</a></div></div>
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