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635 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 2010-2018 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="implied__bounds_8h.html">ortools/sat/implied_bounds.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="integer_8h.html">ortools/sat/integer.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="intervals_8h.html">ortools/sat/intervals.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="linear__constraint_8h.html">ortools/sat/linear_constraint.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="linear__constraint__manager_8h.html">ortools/sat/linear_constraint_manager.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="sat_2model_8h.html">ortools/sat/model.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="time__limit_8h.html">ortools/util/time_limit.h</a>"</span></div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  </div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</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="l00030"></a><span class="lineno"> 30</span> <span class="keyword">namespace </span>sat {</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  </div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">// A "cut" generator on a set of IntegerVariable.</span></div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</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="l00035"></a><span class="lineno"> 35</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="l00036"></a><span class="lineno"> 36</span> <span class="comment">// CutGenerator should:</span></div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</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="l00038"></a><span class="lineno"> 38</span> <span class="comment">// their negation.</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</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="l00040"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1CutGenerator.html"> 40</a></span> <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1CutGenerator.html">CutGenerator</a> {</div>
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<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1CutGenerator.html#a73e4094f2d4e2adbe5e8d79a5b61fcd1"> 41</a></span>  std::vector<IntegerVariable> <a class="code" href="structoperations__research_1_1sat_1_1CutGenerator.html#a73e4094f2d4e2adbe5e8d79a5b61fcd1">vars</a>;</div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  std::function<void(<span class="keyword">const</span> <a class="code" href="classgtl_1_1ITIVector.html">gtl::ITIVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <a class="code" href="classoperations__research_1_1sat_1_1LinearConstraintManager.html">LinearConstraintManager</a>* manager)></div>
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<div class="line"><a name="l00044"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1CutGenerator.html#ac64771783f46031abe2052d745e8b0a7"> 44</a></span>  <a class="code" href="structoperations__research_1_1sat_1_1CutGenerator.html#ac64771783f46031abe2052d745e8b0a7">generate_cuts</a>;</div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> };</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</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="l00048"></a><span class="lineno"> 48</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="l00049"></a><span class="lineno"> 49</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="l00050"></a><span class="lineno"> 50</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="l00051"></a><span class="lineno"> 51</span> <span class="comment">// current LP solution.</span></div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</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="l00054"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html"> 54</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html">ImpliedBoundsProcessor</a> {</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// We will only replace IntegerVariable appearing in lp_vars_.</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#acc1b04e5f7e2423d189a70388e177e97"> 57</a></span>  <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#acc1b04e5f7e2423d189a70388e177e97">ImpliedBoundsProcessor</a>(absl::Span<const IntegerVariable> lp_vars_,</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <a class="code" href="classoperations__research_1_1sat_1_1IntegerTrail.html">IntegerTrail</a>* integer_trail,</div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBounds.html">ImpliedBounds</a>* implied_bounds)</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  : lp_vars_(lp_vars_.begin(), lp_vars_.end()),</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  integer_trail_(integer_trail),</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  implied_bounds_(implied_bounds) {}</div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  </div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">// Processes and updates the given cut.</span></div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#a19e26dd5481c4a596ad8e6458d13a25c">ProcessUpperBoundedConstraint</a>(</div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">const</span> <a class="code" href="classgtl_1_1ITIVector.html">gtl::ITIVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <a class="code" href="structoperations__research_1_1sat_1_1LinearConstraint.html">LinearConstraint</a>* cut) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  </div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// Same as ProcessUpperBoundedConstraint() but instead of just using</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</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="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// slack is a new temporary variable that we create.</span></div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</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="l00074"></a><span class="lineno"> 74</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="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// generation and substitute it back later.</span></div>
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<div class="line"><a name="l00076"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html"> 76</a></span>  <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html">SlackInfo</a> {</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="comment">// This slack is equal to sum of terms + offset.</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_1ImpliedBoundsProcessor_1_1SlackInfo.html#a250583d63e8184c6f9f4deba1125e6bb"> 78</a></span>  std::vector<std::pair<IntegerVariable, IntegerValue>> <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html#a250583d63e8184c6f9f4deba1125e6bb">terms</a>;</div>
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<div class="line"><a name="l00079"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html#acd07f8397a2e61932c8ee17a4e300e23"> 79</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html#acd07f8397a2e61932c8ee17a4e300e23">offset</a>;</div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  </div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="comment">// The slack bounds and current lp_value.</span></div>
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<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html#a0ee34e5c6fbf075def1a6c2f0c42d040"> 82</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html#a0ee34e5c6fbf075def1a6c2f0c42d040">lb</a> = IntegerValue(0);</div>
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<div class="line"><a name="l00083"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html#a6e2915dc7e5345d6959390b53f026c5f"> 83</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html#a6e2915dc7e5345d6959390b53f026c5f">ub</a> = IntegerValue(0);</div>
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<div class="line"><a name="l00084"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html#adb47ac0cff7c9dc4dc5f101d38a91185"> 84</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html#adb47ac0cff7c9dc4dc5f101d38a91185">lp_value</a> = 0.0;</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  };</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#a01eca8210872034b3bca100ad24ecb23">ProcessUpperBoundedConstraintWithSlackCreation</a>(</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordtype">bool</span> substitute_only_inner_variables, IntegerVariable first_slack,</div>
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<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keyword">const</span> <a class="code" href="classgtl_1_1ITIVector.html">gtl::ITIVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <a class="code" href="structoperations__research_1_1sat_1_1LinearConstraint.html">LinearConstraint</a>* cut, std::vector<SlackInfo>* slack_infos,</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  std::vector<LinearConstraint>* implied_bound_cuts) <span class="keyword">const</span>;</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  </div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">// Only used for debugging.</span></div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="comment">//</span></div>
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<div class="line"><a name="l00094"></a><span class="lineno"> 94</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="l00095"></a><span class="lineno"> 95</span>  <span class="comment">// exactly the same cut as the original one.</span></div>
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<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordtype">bool</span> <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#ab1b4642341faf5ff972b02f034d88f21">DebugSlack</a>(IntegerVariable first_slack,</div>
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<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keyword">const</span> <a class="code" href="structoperations__research_1_1sat_1_1LinearConstraint.html">LinearConstraint</a>& initial_cut,</div>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keyword">const</span> <a class="code" href="structoperations__research_1_1sat_1_1LinearConstraint.html">LinearConstraint</a>& cut,</div>
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<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keyword">const</span> std::vector<SlackInfo>& info);</div>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  </div>
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<div class="line"><a name="l00101"></a><span class="lineno"> 101</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="l00102"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#a07e1de12d9a4b00c96911544e72b86d4"> 102</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.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="l00103"></a><span class="lineno"> 103</span>  </div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</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="l00105"></a><span class="lineno"> 105</span>  <span class="comment">// lp_values or level zero bounds.</span></div>
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<div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#a011f5f336c989d356c5f06a5793473c1"> 106</a></span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#a011f5f336c989d356c5f06a5793473c1">ClearCache</a>()<span class="keyword"> const </span>{ cache_.clear(); }</div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  </div>
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<div class="line"><a name="l00108"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html"> 108</a></span>  <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html">BestImpliedBoundInfo</a> {</div>
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<div class="line"><a name="l00109"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html#a9231f58e9d0f2dafc65c9eb41c979028"> 109</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html#a9231f58e9d0f2dafc65c9eb41c979028">bool_lp_value</a> = 0.0;</div>
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<div class="line"><a name="l00110"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html#ac11e010c276514d6402c772d0651f82f"> 110</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html#ac11e010c276514d6402c772d0651f82f">slack_lp_value</a> = std::numeric_limits<double>::infinity();</div>
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<div class="line"><a name="l00111"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html#a6d2822d5e07c3716efcdf73a4ae5eafc"> 111</a></span>  <span class="keywordtype">bool</span> <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html#a6d2822d5e07c3716efcdf73a4ae5eafc">is_positive</a>;</div>
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<div class="line"><a name="l00112"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html#a2c25b894240115eebb2e75e2d8491a79"> 112</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html#a2c25b894240115eebb2e75e2d8491a79">bound_diff</a>;</div>
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<div class="line"><a name="l00113"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html#a871eaa421116e3c7cd440b6299d0b74d"> 113</a></span>  IntegerVariable <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.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="l00114"></a><span class="lineno"> 114</span>  };</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html">BestImpliedBoundInfo</a> <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.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="l00116"></a><span class="lineno"> 116</span>  </div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <a class="code" href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html">BestImpliedBoundInfo</a> ComputeBestImpliedBound(</div>
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<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  IntegerVariable <a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>,</div>
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<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keyword">const</span> <a class="code" href="classgtl_1_1ITIVector.html">gtl::ITIVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  std::vector<LinearConstraint>* implied_bound_cuts) <span class="keyword">const</span>;</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>  absl::flat_hash_set<IntegerVariable> lp_vars_;</div>
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<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keyword">mutable</span> absl::flat_hash_map<IntegerVariable, BestImpliedBoundInfo> cache_;</div>
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<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  </div>
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<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="comment">// Data from the constructor.</span></div>
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<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <a class="code" href="classoperations__research_1_1sat_1_1IntegerTrail.html">IntegerTrail</a>* integer_trail_;</div>
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<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBounds.html">ImpliedBounds</a>* implied_bounds_;</div>
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<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  </div>
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<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="comment">// Temporary memory used by ProcessUpperBoundedConstraint().</span></div>
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<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keyword">mutable</span> std::vector<std::pair<IntegerVariable, IntegerValue>> tmp_terms_;</div>
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<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> };</div>
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<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  </div>
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<div class="line"><a name="l00134"></a><span class="lineno"> 134</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="l00135"></a><span class="lineno"> 135</span> <span class="comment">// - f is non-decreasing.</span></div>
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<div class="line"><a name="l00136"></a><span class="lineno"> 136</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="l00137"></a><span class="lineno"> 137</span> <span class="comment">// - 1 <= f(divisor) <= max_scaling</span></div>
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<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// - For all x, f(x * divisor) = x * f(divisor)</span></div>
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<div class="line"><a name="l00139"></a><span class="lineno"> 139</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="l00140"></a><span class="lineno"> 140</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment">// Preconditions:</span></div>
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<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// - 0 <= remainder < divisor.</span></div>
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<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment">// - 1 <= max_scaling.</span></div>
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<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00145"></a><span class="lineno"> 145</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="l00146"></a><span class="lineno"> 146</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="l00147"></a><span class="lineno"> 147</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="l00148"></a><span class="lineno"> 148</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment">// Algorithm:</span></div>
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<div class="line"><a name="l00150"></a><span class="lineno"> 150</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="l00151"></a><span class="lineno"> 151</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="l00152"></a><span class="lineno"> 152</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="l00153"></a><span class="lineno"> 153</span> <span class="comment">// Letchfrod, Andrea Lodi.</span></div>
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<div class="line"><a name="l00154"></a><span class="lineno"> 154</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="l00155"></a><span class="lineno"> 155</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="l00156"></a><span class="lineno"> 156</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="l00157"></a><span class="lineno"> 157</span> <span class="comment">// converge to the real-valued MIR function.</span></div>
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<div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00159"></a><span class="lineno"> 159</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="l00160"></a><span class="lineno"> 160</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="l00161"></a><span class="lineno"> 161</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="l00162"></a><span class="lineno"> 162</span> <span class="comment">// max_scaling.</span></div>
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<div class="line"><a name="l00163"></a><span class="lineno"> 163</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="l00164"></a><span class="lineno"> 164</span>  IntegerValue max_t);</div>
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<div class="line"><a name="l00165"></a><span class="lineno"> 165</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="l00166"></a><span class="lineno"> 166</span>  IntegerValue rhs_remainder, IntegerValue divisor, IntegerValue t,</div>
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<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  IntegerValue max_scaling);</div>
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<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  </div>
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<div class="line"><a name="l00169"></a><span class="lineno"> 169</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="l00170"></a><span class="lineno"> 170</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="l00171"></a><span class="lineno"> 171</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="l00172"></a><span class="lineno"> 172</span> <span class="comment">// case it can be discarded.</span></div>
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<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00174"></a><span class="lineno"> 174</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="l00175"></a><span class="lineno"> 175</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="l00176"></a><span class="lineno"> 176</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="l00177"></a><span class="lineno"> 177</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="l00178"></a><span class="lineno"> 178</span> <span class="comment">// are other possible alternatives.</span></div>
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<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00180"></a><span class="lineno"> 180</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="l00181"></a><span class="lineno"> 181</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="l00182"></a><span class="lineno"> 182</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="l00183"></a><span class="lineno"> 183</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="l00184"></a><span class="lineno"> 184</span> <span class="comment">// precision while doing exact integer computations.</span></div>
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<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment">// Precondition:</span></div>
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<div class="line"><a name="l00187"></a><span class="lineno"> 187</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="l00188"></a><span class="lineno"> 188</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="l00189"></a><span class="lineno"> 189</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="l00190"></a><span class="lineno"> 190</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="l00191"></a><span class="lineno"> 191</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="l00192"></a><span class="lineno"> 192</span> <span class="comment">// of the variable in the cut.</span></div>
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<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00194"></a><span class="lineno"> 194</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="l00195"></a><span class="lineno"> 195</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="l00196"></a><span class="lineno"> 196</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="l00197"></a><span class="lineno"> 197</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="l00198"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1RoundingOptions.html"> 198</a></span> <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1RoundingOptions.html">RoundingOptions</a> {</div>
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<div class="line"><a name="l00199"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1RoundingOptions.html#a01db407e90fac1c31c6705758a057908"> 199</a></span>  IntegerValue <a class="code" href="structoperations__research_1_1sat_1_1RoundingOptions.html#a01db407e90fac1c31c6705758a057908">max_scaling</a> = IntegerValue(60);</div>
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<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> };</div>
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<div class="line"><a name="l00201"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1IntegerRoundingCutHelper.html"> 201</a></span> <span class="keyword">class </span><a class="code" href="classoperations__research_1_1sat_1_1IntegerRoundingCutHelper.html">IntegerRoundingCutHelper</a> {</div>
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<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">public</span>:</div>
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<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordtype">void</span> <a class="code" href="classoperations__research_1_1sat_1_1IntegerRoundingCutHelper.html#a66c8e6dc26260b69dcdf7668925dc3aa">ComputeCut</a>(<a class="code" href="structoperations__research_1_1sat_1_1RoundingOptions.html">RoundingOptions</a> options, <span class="keyword">const</span> std::vector<double>& lp_values,</div>
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<div class="line"><a name="l00204"></a><span class="lineno"> 204</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="l00205"></a><span class="lineno"> 205</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="l00206"></a><span class="lineno"> 206</span>  <a class="code" href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html">ImpliedBoundsProcessor</a>* ib_processor, <a class="code" href="structoperations__research_1_1sat_1_1LinearConstraint.html">LinearConstraint</a>* cut);</div>
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<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  </div>
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<div class="line"><a name="l00208"></a><span class="lineno"> 208</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="l00209"></a><span class="lineno"> 209</span>  <span class="comment">// ComputeCut() call. Useful for investigation.</span></div>
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<div class="line"><a name="l00210"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1IntegerRoundingCutHelper.html#a4f879f884fd170f77c9024aee023feb2"> 210</a></span>  <span class="keywordtype">int</span> <a class="code" href="classoperations__research_1_1sat_1_1IntegerRoundingCutHelper.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="l00211"></a><span class="lineno"> 211</span>  </div>
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<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">private</span>:</div>
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<div class="line"><a name="l00213"></a><span class="lineno"> 213</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="l00214"></a><span class="lineno"> 214</span>  std::vector<int> relevant_indices_;</div>
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<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  std::vector<double> relevant_lp_values_;</div>
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<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  std::vector<IntegerValue> relevant_coeffs_;</div>
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<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  std::vector<IntegerValue> relevant_bound_diffs_;</div>
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<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  std::vector<IntegerValue> divisors_;</div>
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<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  std::vector<std::pair<int, IntegerValue>> adjusted_coeffs_;</div>
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<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  std::vector<IntegerValue> remainders_;</div>
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<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  std::vector<bool> change_sign_at_postprocessing_;</div>
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<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  std::vector<IntegerValue> rs_;</div>
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<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  std::vector<IntegerValue> best_rs_;</div>
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<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  </div>
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<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="keywordtype">int</span> num_lifted_booleans_ = 0;</div>
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<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  std::vector<std::pair<IntegerVariable, IntegerValue>> tmp_terms_;</div>
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<div class="line"><a name="l00227"></a><span class="lineno"> 227</span> };</div>
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<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  </div>
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<div class="line"><a name="l00229"></a><span class="lineno"> 229</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="l00230"></a><span class="lineno"> 230</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="l00231"></a><span class="lineno"> 231</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="l00232"></a><span class="lineno"> 232</span> <span class="comment">// constraint.</span></div>
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<div class="line"><a name="l00233"></a><span class="lineno"> 233</span> LinearConstraint <a class="code" href="namespaceoperations__research_1_1sat.html#aa07b0782b25220bea452557728abe747">GetPreprocessedLinearConstraint</a>(</div>
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<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keyword">const</span> LinearConstraint& constraint,</div>
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<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keyword">const</span> <a class="code" href="classgtl_1_1ITIVector.html">gtl::ITIVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
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<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  </div>
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<div class="line"><a name="l00238"></a><span class="lineno"> 238</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="l00239"></a><span class="lineno"> 239</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="l00240"></a><span class="lineno"> 240</span> <span class="comment">// coefficients are non negative.</span></div>
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<div class="line"><a name="l00241"></a><span class="lineno"> 241</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="l00242"></a><span class="lineno"> 242</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
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<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  </div>
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<div class="line"><a name="l00244"></a><span class="lineno"> 244</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="l00245"></a><span class="lineno"> 245</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="l00246"></a><span class="lineno"> 246</span> <span class="comment">// Let |Cmin| = smallest possible cover size.</span></div>
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<div class="line"><a name="l00247"></a><span class="lineno"> 247</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="l00248"></a><span class="lineno"> 248</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="l00249"></a><span class="lineno"> 249</span> <span class="comment">// For any cover,</span></div>
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<div class="line"><a name="l00250"></a><span class="lineno"> 250</span> <span class="comment">// If cut lower bound >= 1</span></div>
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<div class="line"><a name="l00251"></a><span class="lineno"> 251</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="l00252"></a><span class="lineno"> 252</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="l00253"></a><span class="lineno"> 253</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="l00254"></a><span class="lineno"> 254</span> <span class="comment">// this method returns false in such cases.</span></div>
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<div class="line"><a name="l00255"></a><span class="lineno"> 255</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="l00256"></a><span class="lineno"> 256</span> <span class="comment">// negative coefficients.</span></div>
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<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a5bdfb90b712b6e31c1078323edb2e0d5">CanBeFilteredUsingCutLowerBound</a>(</div>
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<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keyword">const</span> LinearConstraint& preprocessed_constraint,</div>
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<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="keyword">const</span> <a class="code" href="classgtl_1_1ITIVector.html">gtl::ITIVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
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<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  </div>
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<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="comment">// Struct to help compute upper bound for knapsack instance.</span></div>
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<div class="line"><a name="l00263"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1KnapsackItem.html"> 263</a></span> <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1KnapsackItem.html">KnapsackItem</a> {</div>
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<div class="line"><a name="l00264"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1KnapsackItem.html#a3ff84545f00a56ba7584b2a7f2cef69c"> 264</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1KnapsackItem.html#a3ff84545f00a56ba7584b2a7f2cef69c">profit</a>;</div>
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<div class="line"><a name="l00265"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1KnapsackItem.html#a99108733d00274978a4979dc072bd513"> 265</a></span>  <span class="keywordtype">double</span> <a class="code" href="structoperations__research_1_1sat_1_1KnapsackItem.html#a99108733d00274978a4979dc072bd513">weight</a>;</div>
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<div class="line"><a name="l00266"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1KnapsackItem.html#aa51ab05fd43c2d0962967f9d889c7bb7"> 266</a></span>  <span class="keywordtype">bool</span> <a class="code" href="structoperations__research_1_1sat_1_1KnapsackItem.html#aa51ab05fd43c2d0962967f9d889c7bb7">operator></a>(<span class="keyword">const</span> <a class="code" href="structoperations__research_1_1sat_1_1KnapsackItem.html">KnapsackItem</a>& other)<span class="keyword"> const </span>{</div>
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<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">return</span> <a class="code" href="structoperations__research_1_1sat_1_1KnapsackItem.html#a3ff84545f00a56ba7584b2a7f2cef69c">profit</a> * other.<a class="code" href="structoperations__research_1_1sat_1_1KnapsackItem.html#a99108733d00274978a4979dc072bd513">weight</a> > other.<a class="code" href="structoperations__research_1_1sat_1_1KnapsackItem.html#a3ff84545f00a56ba7584b2a7f2cef69c">profit</a> * <a class="code" href="structoperations__research_1_1sat_1_1KnapsackItem.html#a99108733d00274978a4979dc072bd513">weight</a>;</div>
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<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  }</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">// Gets upper bound on profit for knapsack instance by solving the linear</span></div>
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<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="comment">// relaxation.</span></div>
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<div class="line"><a name="l00273"></a><span class="lineno"> 273</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#adf3be22c64f10c0783c0cf277e857adf">capacity</a>);</div>
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<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  </div>
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<div class="line"><a name="l00275"></a><span class="lineno"> 275</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="l00276"></a><span class="lineno"> 276</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="l00277"></a><span class="lineno"> 277</span> <span class="comment">// that all the coefficients are non negative.</span></div>
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|
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a89c3facce82a049661167dd92f7f21f7">CanBeFilteredUsingKnapsackUpperBound</a>(</div>
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<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keyword">const</span> LinearConstraint& constraint,</div>
|
|
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keyword">const</span> <a class="code" href="classgtl_1_1ITIVector.html">gtl::ITIVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
|
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<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  </div>
|
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<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="comment">// Returns true if the given constraint passes all the filters described above.</span></div>
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|
<div class="line"><a name="l00284"></a><span class="lineno"> 284</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="l00285"></a><span class="lineno"> 285</span> <span class="comment">// negative coefficients.</span></div>
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<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a1f091a18daeedeeaff4aa22591757a0f">CanFormValidKnapsackCover</a>(</div>
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<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keyword">const</span> LinearConstraint& preprocessed_constraint,</div>
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|
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keyword">const</span> <a class="code" href="classgtl_1_1ITIVector.html">gtl::ITIVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
|
|
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  </div>
|
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<div class="line"><a name="l00291"></a><span class="lineno"> 291</span> <span class="comment">// Converts the given constraint into canonical knapsack form (described</span></div>
|
|
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="comment">// below) and adds it to 'knapsack_constraints'.</span></div>
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<div class="line"><a name="l00293"></a><span class="lineno"> 293</span> <span class="comment">// Canonical knapsack form:</span></div>
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<div class="line"><a name="l00294"></a><span class="lineno"> 294</span> <span class="comment">// - Constraint has finite upper bound.</span></div>
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<div class="line"><a name="l00295"></a><span class="lineno"> 295</span> <span class="comment">// - All coefficients are positive.</span></div>
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<div class="line"><a name="l00296"></a><span class="lineno"> 296</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="l00297"></a><span class="lineno"> 297</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="l00298"></a><span class="lineno"> 298</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="l00299"></a><span class="lineno"> 299</span>  std::vector<LinearConstraint>* knapsack_constraints,</div>
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<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  IntegerTrail* integer_trail);</div>
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<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  </div>
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<div class="line"><a name="l00302"></a><span class="lineno"> 302</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="l00303"></a><span class="lineno"> 303</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00304"></a><span class="lineno"> 304</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="l00305"></a><span class="lineno"> 305</span> <span class="comment">// already in cut. We lift the cut for each lifting candidate one by one.</span></div>
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<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00307"></a><span class="lineno"> 307</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="l00308"></a><span class="lineno"> 308</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="l00309"></a><span class="lineno"> 309</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="l00310"></a><span class="lineno"> 310</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="l00311"></a><span class="lineno"> 311</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a56f2839b344852506cb601bbf898c9b5">LiftKnapsackCut</a>(</div>
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<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keyword">const</span> LinearConstraint& constraint,</div>
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<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keyword">const</span> <a class="code" href="classgtl_1_1ITIVector.html">gtl::ITIVector<IntegerVariable, double></a>& lp_values,</div>
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<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keyword">const</span> std::vector<IntegerValue>& cut_vars_original_coefficients,</div>
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<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keyword">const</span> IntegerTrail& integer_trail, <a class="code" href="classoperations__research_1_1TimeLimit.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="l00316"></a><span class="lineno"> 316</span>  LinearConstraint* cut);</div>
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<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  </div>
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<div class="line"><a name="l00318"></a><span class="lineno"> 318</span> <span class="comment">// A cut generator that creates knpasack cover cuts.</span></div>
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<div class="line"><a name="l00319"></a><span class="lineno"> 319</span> <span class="comment">//</span></div>
|
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<div class="line"><a name="l00320"></a><span class="lineno"> 320</span> <span class="comment">// For a constraint of type</span></div>
|
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<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> <span class="comment">// \sum_{i=1..n}(a_i * x_i) <= b</span></div>
|
|
<div class="line"><a name="l00322"></a><span class="lineno"> 322</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="l00323"></a><span class="lineno"> 323</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="l00324"></a><span class="lineno"> 324</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00325"></a><span class="lineno"> 325</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="l00326"></a><span class="lineno"> 326</span> <span class="comment">// \sum_{c \in C}(u_c - x_c) >= 1</span></div>
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|
<div class="line"><a name="l00327"></a><span class="lineno"> 327</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="l00328"></a><span class="lineno"> 328</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="l00329"></a><span class="lineno"> 329</span> <span class="comment">// not take their maximum value.</span></div>
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<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00331"></a><span class="lineno"> 331</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="l00332"></a><span class="lineno"> 332</span> <span class="comment">// \sum_{c \in C}(x_c) <= |C| - 1.</span></div>
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|
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span> <span class="comment">//</span></div>
|
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<div class="line"><a name="l00334"></a><span class="lineno"> 334</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="l00335"></a><span class="lineno"> 335</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="l00336"></a><span class="lineno"> 336</span> <span class="comment">// heuristically generate the cover but the following method that uses a</span></div>
|
|
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span> <span class="comment">// solution of the LP relaxation of the constraint works the best.</span></div>
|
|
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="comment">// Look at a given linear relaxation solution for the integer problem x'</span></div>
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<div class="line"><a name="l00340"></a><span class="lineno"> 340</span> <span class="comment">// and try to solve the following knapsack problem:</span></div>
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|
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span> <span class="comment">// Minimize \sum_{i=1..n}(z_i * (u_i - x_i')),</span></div>
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|
<div class="line"><a name="l00342"></a><span class="lineno"> 342</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="l00343"></a><span class="lineno"> 343</span> <span class="comment">// where z_i is a binary decision variable and x_i' are values of the variables</span></div>
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|
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span> <span class="comment">// in the given relaxation solution x'. If the objective of the optimal solution</span></div>
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<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> <span class="comment">// of this problem is less than 1, this algorithm does not generate any cuts.</span></div>
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<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="comment">// Otherwise, it adds a knapsack cover cut in the form</span></div>
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|
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="comment">// \sum_{i=1..n}(z_i' * x_i) <= cb,</span></div>
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<div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="comment">// where z_i' is the value of z_i in the optimal solution of the above</span></div>
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<div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="comment">// problem and cb is the upper bound for the cut constraint. Note that the above</span></div>
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<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="comment">// problem can be converted into a standard kanpsack form by replacing z_i by 1</span></div>
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<div class="line"><a name="l00351"></a><span class="lineno"> 351</span> <span class="comment">// - y_i. In that case the problem becomes</span></div>
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|
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="comment">// Maximize \sum_{i=1..n}((u_i - x_i') * (y_i - 1)),</span></div>
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|
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="comment">// such that</span></div>
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<div class="line"><a name="l00354"></a><span class="lineno"> 354</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>
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<div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00356"></a><span class="lineno"> 356</span> <span class="comment">// Solving this knapsack instance would help us find the smallest cover with</span></div>
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<div class="line"><a name="l00357"></a><span class="lineno"> 357</span> <span class="comment">// maximum LP violation.</span></div>
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<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00359"></a><span class="lineno"> 359</span> <span class="comment">// Cut strengthning:</span></div>
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<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> <span class="comment">// Let lambda = \sum_{c \in C}(a_c * u_c) - b and max_coeff = \max_{c</span></div>
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<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> <span class="comment">// \in C}(a_c), then cut can be strengthened as</span></div>
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|
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span> <span class="comment">// \sum_{c \in C}(u_c - x_c) >= ceil(lambda / max_coeff)</span></div>
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|
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="comment">// For further information about knapsack cover cuts see</span></div>
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|
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="comment">// A. Atamtürk, Cover and Pack Inequalities for (Mixed) Integer Programming</span></div>
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<div class="line"><a name="l00366"></a><span class="lineno"> 366</span> <span class="comment">// Annals of Operations Research Volume 139, Issue 1 , pp 21-38, 2005.</span></div>
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<div class="line"><a name="l00367"></a><span class="lineno"> 367</span> <span class="comment">// TODO(user): Implement cut lifting.</span></div>
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<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#ac158f737c8653b1fc1bd294ea2d3412d">CreateKnapsackCoverCutGenerator</a>(</div>
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<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keyword">const</span> std::vector<LinearConstraint>& base_constraints,</div>
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<div class="line"><a name="l00370"></a><span class="lineno"> 370</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="l00371"></a><span class="lineno"> 371</span>  </div>
|
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<div class="line"><a name="l00372"></a><span class="lineno"> 372</span> <span class="comment">// A cut generator for z = x * y (x and y >= 0).</span></div>
|
|
<div class="line"><a name="l00373"></a><span class="lineno"> 373</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="l00374"></a><span class="lineno"> 374</span>  IntegerVariable x,</div>
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<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  IntegerVariable y,</div>
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<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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|
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  </div>
|
|
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> <span class="comment">// A cut generator for y = x ^ 2 (x >= 0).</span></div>
|
|
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span> <span class="comment">// It will dynamically add a linear inequality to push y closer to the parabola.</span></div>
|
|
<div class="line"><a name="l00380"></a><span class="lineno"> 380</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="l00381"></a><span class="lineno"> 381</span>  Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
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|
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  </div>
|
|
<div class="line"><a name="l00383"></a><span class="lineno"> 383</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="l00384"></a><span class="lineno"> 384</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="l00385"></a><span class="lineno"> 385</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="l00386"></a><span class="lineno"> 386</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="l00387"></a><span class="lineno"> 387</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="l00388"></a><span class="lineno"> 388</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="l00389"></a><span class="lineno"> 389</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a7feb76be212dca01ffe7ba3a0391e118">CreateAllDifferentCutGenerator</a>(</div>
|
|
<div class="line"><a name="l00390"></a><span class="lineno"> 390</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="l00391"></a><span class="lineno"> 391</span>  </div>
|
|
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span> <span class="comment">// Consider the Lin Max constraint with d expressions and n variables in the</span></div>
|
|
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span> <span class="comment">// form: target = max {exprs[k] = Sum (wki * xi + bk)}. k in {1,..,d}.</span></div>
|
|
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="comment">// Li = lower bound of xi</span></div>
|
|
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span> <span class="comment">// Ui = upper bound of xi.</span></div>
|
|
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span> <span class="comment">// Let zk be in {0,1} for all k in {1,..,d}.</span></div>
|
|
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span> <span class="comment">// The target = exprs[k] when zk = 1.</span></div>
|
|
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="comment">// The following is a valid linearization for Lin Max.</span></div>
|
|
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="comment">// target >= exprs[k], for all k in {1,..,d}</span></div>
|
|
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment">// target <= Sum (wli * xi) + Sum((Nlk + bk) * zk), for all l in {1,..,d}</span></div>
|
|
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="comment">// Where Nlk is a large number defined as:</span></div>
|
|
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="comment">// Nlk = Sum (max((wki - wli)*Li, (wki - wli)*Ui))</span></div>
|
|
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span> <span class="comment">// = Sum (max corner difference for variable i, target expr l, max expr k)</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">// Consider a partition of variables xi into set {1,..,d} as I.</span></div>
|
|
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment">// i.e. I(i) = j means xi is mapped to jth index.</span></div>
|
|
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="comment">// The following inequality is valid and sharp cut for the lin max constraint</span></div>
|
|
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="comment">// described above.</span></div>
|
|
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> <span class="comment">// target <= Sum(i=1..n)(wI(i)i * xi + Sum(k=1..d)(MPlusCoefficient_ki * zk))</span></div>
|
|
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span> <span class="comment">// + Sum(k=1..d)(bk * zk) ,</span></div>
|
|
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span> <span class="comment">// Where MPlusCoefficient_ki = max((wki - wI(i)i) * Li,</span></div>
|
|
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="comment">// (wki - wI(i)i) * Ui)</span></div>
|
|
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> <span class="comment">// = max corner difference for variable i,</span></div>
|
|
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="comment">// target expr I(i), max expr k.</span></div>
|
|
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span> <span class="comment">// For detailed proof of validity, refer</span></div>
|
|
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="comment">// Reference: "Strong mixed-integer programming formulations for trained neural</span></div>
|
|
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span> <span class="comment">// networks" by Ross Anderson et. (https://arxiv.org/pdf/1811.01988.pdf).</span></div>
|
|
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span> <span class="comment">// In the cut generator, we compute the most violated partition I by computing</span></div>
|
|
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span> <span class="comment">// the rhs value (wI(i)i * lp_value(xi) + Sum(k=1..d)(MPlusCoefficient_ki * zk))</span></div>
|
|
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="comment">// for each variable for each partition index. We choose the partition index</span></div>
|
|
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment">// that gives lowest rhs value for a given variable.</span></div>
|
|
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> <span class="comment">// Note: This cut generator requires all expressions to contain only positive</span></div>
|
|
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="comment">// vars.</span></div>
|
|
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a7fea62548e11ae728e506874f767bdd3">CreateLinMaxCutGenerator</a>(</div>
|
|
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keyword">const</span> IntegerVariable target, <span class="keyword">const</span> std::vector<LinearExpression>& exprs,</div>
|
|
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  <span class="keyword">const</span> std::vector<IntegerVariable>& z_vars, Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  </div>
|
|
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> <span class="comment">// Creates a cut generator for an optional interval.</span></div>
|
|
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#ac8ff64f6d85dd6e1708bf638df698b98">CreateOptionalIntervalCutGenerator</a>(IntegerVariable start,</div>
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|
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  IntegerVariable size,</div>
|
|
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  IntegerVariable end,</div>
|
|
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  Literal presence, Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  </div>
|
|
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span> <span class="comment">// For a given set of intervals and demands, we first compute the mandatory part</span></div>
|
|
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span> <span class="comment">// of the interval as [start_max , end_min]. We use this to calculate mandatory</span></div>
|
|
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span> <span class="comment">// demands for each start_max time points for eligible intervals.</span></div>
|
|
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span> <span class="comment">// Since the sum of these mandatory demands must be smaller or equal to the</span></div>
|
|
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="comment">// capacity, we create a cut representing that.</span></div>
|
|
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span> <span class="comment">// If an interval is optional, it contributes min_demand * presence_literal</span></div>
|
|
<div class="line"><a name="l00446"></a><span class="lineno"> 446</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="l00447"></a><span class="lineno"> 447</span> <span class="comment">// as follows:</span></div>
|
|
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span> <span class="comment">// sum(demands of always present intervals)</span></div>
|
|
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span> <span class="comment">// + sum(presence_literal * min_of_demand) <= capacity.</span></div>
|
|
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span> CutGenerator <a class="code" href="namespaceoperations__research_1_1sat.html#a34b1d34844b9b1695dd45dfd9c33f663">CreateCumulativeCutGenerator</a>(</div>
|
|
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="keyword">const</span> std::vector<IntervalVariable>& intervals,</div>
|
|
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  <span class="keyword">const</span> IntegerVariable <a class="code" href="routing__flow_8cc.html#adf3be22c64f10c0783c0cf277e857adf">capacity</a>, <span class="keyword">const</span> std::vector<IntegerVariable>& demands,</div>
|
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<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  Model* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  </div>
|
|
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span> } <span class="comment">// namespace sat</span></div>
|
|
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span> } <span class="comment">// namespace operations_research</span></div>
|
|
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  </div>
|
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<div class="line"><a name="l00458"></a><span class="lineno"> 458</span> <span class="preprocessor">#endif // OR_TOOLS_SAT_CUTS_H_</span></div>
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</div><!-- fragment --></div><!-- contents -->
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</div><!-- doc-content -->
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1ImpliedBoundsProcessor_html_a011f5f336c989d356c5f06a5793473c1"><div class="ttname"><a href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.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#l00106">cuts.h:106</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#l01858">expr_array.cc:1858</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1CutGenerator_html_a73e4094f2d4e2adbe5e8d79a5b61fcd1"><div class="ttname"><a href="structoperations__research_1_1sat_1_1CutGenerator.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#l00041">cuts.h:41</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1KnapsackItem_html_a3ff84545f00a56ba7584b2a7f2cef69c"><div class="ttname"><a href="structoperations__research_1_1sat_1_1KnapsackItem.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#l00264">cuts.h:264</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_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#l01627">cuts.cc:1627</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1IntegerRoundingCutHelper_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1IntegerRoundingCutHelper.html">operations_research::sat::IntegerRoundingCutHelper</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00201">cuts.h:201</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a5bdfb90b712b6e31c1078323edb2e0d5"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a5bdfb90b712b6e31c1078323edb2e0d5">operations_research::sat::CanBeFilteredUsingCutLowerBound</a></div><div class="ttdeci">bool CanBeFilteredUsingCutLowerBound(const LinearConstraint &preprocessed_constraint, const gtl::ITIVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00275">cuts.cc:275</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.html">operations_research::sat::ImpliedBoundsProcessor::SlackInfo</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00076">cuts.h:76</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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<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#l00601">cuts.cc:601</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1RoundingOptions_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1RoundingOptions.html">operations_research::sat::RoundingOptions</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00198">cuts.h:198</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1ImpliedBounds_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1ImpliedBounds.html">operations_research::sat::ImpliedBounds</a></div><div class="ttdef"><b>Definition:</b> <a href="implied__bounds_8h_source.html#l00077">implied_bounds.h:77</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo_html_ac11e010c276514d6402c772d0651f82f"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.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#l00110">cuts.h:110</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1ImpliedBoundsProcessor_html_a07e1de12d9a4b00c96911544e72b86d4"><div class="ttname"><a href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.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#l00102">cuts.h:102</a></div></div>
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<div class="ttc" id="alinear__constraint_8h_html"><div class="ttname"><a href="linear__constraint_8h.html">linear_constraint.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1KnapsackItem_html_aa51ab05fd43c2d0962967f9d889c7bb7"><div class="ttname"><a href="structoperations__research_1_1sat_1_1KnapsackItem.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#l00266">cuts.h:266</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1KnapsackItem_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1KnapsackItem.html">operations_research::sat::KnapsackItem</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00263">cuts.h:263</a></div></div>
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<div class="ttc" id="asat_2model_8h_html"><div class="ttname"><a href="sat_2model_8h.html">model.h</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo_html_a9231f58e9d0f2dafc65c9eb41c979028"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.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#l00109">cuts.h:109</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">The vehicle routing library lets one model and solve generic vehicle routing problems ranging from th...</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="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo_html_a871eaa421116e3c7cd440b6299d0b74d"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.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#l00113">cuts.h:113</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1ImpliedBoundsProcessor_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html">operations_research::sat::ImpliedBoundsProcessor</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00054">cuts.h:54</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1IntegerTrail_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1IntegerTrail.html">operations_research::sat::IntegerTrail</a></div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00534">integer.h:534</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo_html_a0ee34e5c6fbf075def1a6c2f0c42d040"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.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#l00082">cuts.h:82</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#l00373">cuts.cc:373</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a56f2839b344852506cb601bbf898c9b5"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a56f2839b344852506cb601bbf898c9b5">operations_research::sat::LiftKnapsackCut</a></div><div class="ttdeci">bool LiftKnapsackCut(const LinearConstraint &constraint, const gtl::ITIVector< 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#l00157">cuts.cc:157</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1ImpliedBoundsProcessor_html_acc1b04e5f7e2423d189a70388e177e97"><div class="ttname"><a href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.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#l00057">cuts.h:57</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#l01236">cuts.cc:1236</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1KnapsackItem_html_a99108733d00274978a4979dc072bd513"><div class="ttname"><a href="structoperations__research_1_1sat_1_1KnapsackItem.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#l00265">cuts.h:265</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo_html_a250583d63e8184c6f9f4deba1125e6bb"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.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#l00078">cuts.h:78</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1LinearConstraint_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1LinearConstraint.html">operations_research::sat::LinearConstraint</a></div><div class="ttdef"><b>Definition:</b> <a href="linear__constraint_8h_source.html#l00039">linear_constraint.h:39</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1ImpliedBoundsProcessor_html_ab1b4642341faf5ff972b02f034d88f21"><div class="ttname"><a href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.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#l01534">cuts.cc:1534</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_aa07b0782b25220bea452557728abe747"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#aa07b0782b25220bea452557728abe747">operations_research::sat::GetPreprocessedLinearConstraint</a></div><div class="ttdeci">LinearConstraint GetPreprocessedLinearConstraint(const LinearConstraint &constraint, const gtl::ITIVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00235">cuts.cc:235</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#l02025">cp_model_solver.cc:2025</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo_html_a6e2915dc7e5345d6959390b53f026c5f"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.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#l00083">cuts.h:83</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="aintervals_8h_html"><div class="ttname"><a href="intervals_8h.html">intervals.h</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1TimeLimit_html"><div class="ttname"><a href="classoperations__research_1_1TimeLimit.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="astructoperations__research_1_1sat_1_1RoundingOptions_html_a01db407e90fac1c31c6705758a057908"><div class="ttname"><a href="structoperations__research_1_1sat_1_1RoundingOptions.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#l00199">cuts.h:199</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo_html_acd07f8397a2e61932c8ee17a4e300e23"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.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#l00079">cuts.h:79</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1IntegerRoundingCutHelper_html_a4f879f884fd170f77c9024aee023feb2"><div class="ttname"><a href="classoperations__research_1_1sat_1_1IntegerRoundingCutHelper.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#l00210">cuts.h:210</a></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#l01724">cuts.cc:1724</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1LinearConstraintManager_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1LinearConstraintManager.html">operations_research::sat::LinearConstraintManager</a></div><div class="ttdef"><b>Definition:</b> <a href="linear__constraint__manager_8h_source.html#l00040">linear_constraint_manager.h:40</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a89c3facce82a049661167dd92f7f21f7"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a89c3facce82a049661167dd92f7f21f7">operations_research::sat::CanBeFilteredUsingKnapsackUpperBound</a></div><div class="ttdeci">bool CanBeFilteredUsingKnapsackUpperBound(const LinearConstraint &constraint, const gtl::ITIVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00321">cuts.cc:321</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#l01140">cuts.cc:1140</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="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo_html_a6d2822d5e07c3716efcdf73a4ae5eafc"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.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#l00111">cuts.h:111</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#l00195">gurobi_interface.cc:195</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a1f091a18daeedeeaff4aa22591757a0f"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a1f091a18daeedeeaff4aa22591757a0f">operations_research::sat::CanFormValidKnapsackCover</a></div><div class="ttdeci">bool CanFormValidKnapsackCover(const LinearConstraint &preprocessed_constraint, const gtl::ITIVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00355">cuts.cc:355</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ac8ff64f6d85dd6e1708bf638df698b98"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ac8ff64f6d85dd6e1708bf638df698b98">operations_research::sat::CreateOptionalIntervalCutGenerator</a></div><div class="ttdeci">CutGenerator CreateOptionalIntervalCutGenerator(IntegerVariable start, IntegerVariable size, IntegerVariable end, Literal presence, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01793">cuts.cc:1793</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.html">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo</a></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="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#l00609">cuts.cc:609</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo_html_a2c25b894240115eebb2e75e2d8491a79"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1BestImpliedBoundInfo.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#l00112">cuts.h:112</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="aclassoperations__research_1_1sat_1_1ImpliedBoundsProcessor_html_a01eca8210872034b3bca100ad24ecb23"><div class="ttname"><a href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#a01eca8210872034b3bca100ad24ecb23">operations_research::sat::ImpliedBoundsProcessor::ProcessUpperBoundedConstraintWithSlackCreation</a></div><div class="ttdeci">void ProcessUpperBoundedConstraintWithSlackCreation(bool substitute_only_inner_variables, IntegerVariable first_slack, const gtl::ITIVector< IntegerVariable, double > &lp_values, LinearConstraint *cut, std::vector< SlackInfo > *slack_infos, std::vector< LinearConstraint > *implied_bound_cuts) const</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01391">cuts.cc:1391</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#l00288">sat/lp_utils.cc:288</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#l00303">cuts.cc:303</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#l01823">cuts.cc:1823</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1IntegerRoundingCutHelper_html_a66c8e6dc26260b69dcdf7668925dc3aa"><div class="ttname"><a href="classoperations__research_1_1sat_1_1IntegerRoundingCutHelper.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#l00692">cuts.cc:692</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1CutGenerator_html_ac64771783f46031abe2052d745e8b0a7"><div class="ttname"><a href="structoperations__research_1_1sat_1_1CutGenerator.html#ac64771783f46031abe2052d745e8b0a7">operations_research::sat::CutGenerator::generate_cuts</a></div><div class="ttdeci">std::function< void(const gtl::ITIVector< IntegerVariable, double > &lp_values, LinearConstraintManager *manager)> generate_cuts</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00044">cuts.h:44</a></div></div>
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<div class="ttc" id="aclassgtl_1_1ITIVector_html"><div class="ttname"><a href="classgtl_1_1ITIVector.html">gtl::ITIVector< IntegerVariable, double ></a></div></div>
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<div class="ttc" id="arouting__flow_8cc_html_adf3be22c64f10c0783c0cf277e857adf"><div class="ttname"><a href="routing__flow_8cc.html#adf3be22c64f10c0783c0cf277e857adf">capacity</a></div><div class="ttdeci">int64 capacity</div><div class="ttdef"><b>Definition:</b> <a href="routing__flow_8cc_source.html#l00129">routing_flow.cc:129</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1CutGenerator_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1CutGenerator.html">operations_research::sat::CutGenerator</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00040">cuts.h:40</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo_html_adb47ac0cff7c9dc4dc5f101d38a91185"><div class="ttname"><a href="structoperations__research_1_1sat_1_1ImpliedBoundsProcessor_1_1SlackInfo.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#l00084">cuts.h:84</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#l00289">sat/lp_utils.cc:289</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#l00422">cuts.cc:422</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1sat_1_1ImpliedBoundsProcessor_html_a19e26dd5481c4a596ad8e6458d13a25c"><div class="ttname"><a href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.html#a19e26dd5481c4a596ad8e6458d13a25c">operations_research::sat::ImpliedBoundsProcessor::ProcessUpperBoundedConstraint</a></div><div class="ttdeci">void ProcessUpperBoundedConstraint(const gtl::ITIVector< IntegerVariable, double > &lp_values, LinearConstraint *cut) const</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01303">cuts.cc:1303</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#l00259">cuts.cc:259</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="aclassoperations__research_1_1sat_1_1ImpliedBoundsProcessor_html_abb0b7cc2e259fc8ebe8fd3dd55816b75"><div class="ttname"><a href="classoperations__research_1_1sat_1_1ImpliedBoundsProcessor.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#l01312">cuts.cc:1312</a></div></div>
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