689 lines
134 KiB
HTML
689 lines
134 KiB
HTML
<!-- HTML header for doxygen 1.8.18-->
|
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
|
|
<html xmlns="http://www.w3.org/1999/xhtml">
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
|
|
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
|
|
<meta name="generator" content="Doxygen 1.9.2"/>
|
|
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
|
<title>OR-Tools: cuts.h Source File</title>
|
|
<link href="tabs.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="jquery.js"></script>
|
|
<script type="text/javascript" src="dynsections.js"></script>
|
|
<link href="navtree.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="resize.js"></script>
|
|
<script type="text/javascript" src="navtreedata.js"></script>
|
|
<script type="text/javascript" src="navtree.js"></script>
|
|
<link href="search/search.css" rel="stylesheet" type="text/css"/>
|
|
<script type="text/javascript" src="search/searchdata.js"></script>
|
|
<script type="text/javascript" src="search/search.js"></script>
|
|
<link href="doxygen.css" rel="stylesheet" type="text/css" />
|
|
<link href="styleSheet.tmp.css" rel="stylesheet" type="text/css"/>
|
|
</head>
|
|
<body>
|
|
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
|
|
<div id="titlearea">
|
|
<table cellspacing="0" cellpadding="0">
|
|
<tbody>
|
|
<tr style="height: 56px;">
|
|
<td id="projectlogo"><img alt="Logo" src="orLogo.png"/></td>
|
|
<td id="projectalign" style="padding-left: 0.5em;">
|
|
<div id="projectname">OR-Tools
|
|
 <span id="projectnumber">9.1</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
<!-- end header part -->
|
|
<!-- Generated by Doxygen 1.9.2 -->
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
|
|
var searchBox = new SearchBox("searchBox", "search",'Search','.html');
|
|
/* @license-end */
|
|
</script>
|
|
<script type="text/javascript" src="menudata.js"></script>
|
|
<script type="text/javascript" src="menu.js"></script>
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
|
|
$(function() {
|
|
initMenu('',true,false,'search.php','Search');
|
|
$(document).ready(function() { init_search(); });
|
|
});
|
|
/* @license-end */
|
|
</script>
|
|
<div id="main-nav"></div>
|
|
</div><!-- top -->
|
|
<div id="side-nav" class="ui-resizable side-nav-resizable">
|
|
<div id="nav-tree">
|
|
<div id="nav-tree-contents">
|
|
<div id="nav-sync" class="sync"></div>
|
|
</div>
|
|
</div>
|
|
<div id="splitbar" style="-moz-user-select:none;"
|
|
class="ui-resizable-handle">
|
|
</div>
|
|
</div>
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:d3d9a9a6595521f9666a5e94cc830dab83b65699&dn=expat.txt MIT */
|
|
$(document).ready(function(){initNavTree('cuts_8h_source.html',''); initResizable(); });
|
|
/* @license-end */
|
|
</script>
|
|
<div id="doc-content">
|
|
<!-- window showing the filter options -->
|
|
<div id="MSearchSelectWindow"
|
|
onmouseover="return searchBox.OnSearchSelectShow()"
|
|
onmouseout="return searchBox.OnSearchSelectHide()"
|
|
onkeydown="return searchBox.OnSearchSelectKey(event)">
|
|
</div>
|
|
|
|
<!-- iframe showing the search results (closed by default) -->
|
|
<div id="MSearchResultsWindow">
|
|
<iframe src="javascript:void(0)" frameborder="0"
|
|
name="MSearchResults" id="MSearchResults">
|
|
</iframe>
|
|
</div>
|
|
|
|
<div class="header">
|
|
<div class="headertitle"><div class="title">cuts.h</div></div>
|
|
</div><!--header-->
|
|
<div class="contents">
|
|
<a href="cuts_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
|
|
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
|
|
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
|
|
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
|
|
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
|
|
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
|
|
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
|
|
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
|
|
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
|
|
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
|
|
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
|
|
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#ifndef OR_TOOLS_SAT_CUTS_H_</span></div>
|
|
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#define OR_TOOLS_SAT_CUTS_H_</span></div>
|
|
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
|
|
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <functional></span></div>
|
|
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="preprocessor">#include <string></span></div>
|
|
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="preprocessor">#include <utility></span></div>
|
|
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#include <vector></span></div>
|
|
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> </div>
|
|
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include "<a class="code" href="int__type_8h.html">ortools/base/int_type.h</a>"</span></div>
|
|
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "<a class="code" href="strong__vector_8h.html">ortools/base/strong_vector.h</a>"</span></div>
|
|
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include "<a class="code" href="implied__bounds_8h.html">ortools/sat/implied_bounds.h</a>"</span></div>
|
|
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include "<a class="code" href="integer_8h.html">ortools/sat/integer.h</a>"</span></div>
|
|
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include "<a class="code" href="sat_2linear__constraint_8h.html">ortools/sat/linear_constraint.h</a>"</span></div>
|
|
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include "<a class="code" href="linear__constraint__manager_8h.html">ortools/sat/linear_constraint_manager.h</a>"</span></div>
|
|
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include "<a class="code" href="sat_2model_8h.html">ortools/sat/model.h</a>"</span></div>
|
|
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="preprocessor">#include "<a class="code" href="time__limit_8h.html">ortools/util/time_limit.h</a>"</span></div>
|
|
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> </div>
|
|
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research.html">operations_research</a> {</div>
|
|
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="keyword">namespace </span>sat {</div>
|
|
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
|
|
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// A "cut" generator on a set of IntegerVariable.</span></div>
|
|
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// The generate_cuts() function will usually be called with the current LP</span></div>
|
|
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// optimal solution (but should work for any lp_values). Note that a</span></div>
|
|
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// CutGenerator should:</span></div>
|
|
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// - Only look at the lp_values positions that corresponds to its 'vars' or</span></div>
|
|
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// their negation.</span></div>
|
|
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// - Only add cuts in term of the same variables or their negation.</span></div>
|
|
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_cut_generator.html"> 42</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1sat_1_1_cut_generator.html">CutGenerator</a> {</div>
|
|
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_cut_generator.html#a73e4094f2d4e2adbe5e8d79a5b61fcd1"> 43</a></span> std::vector<IntegerVariable> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_cut_generator.html#a73e4094f2d4e2adbe5e8d79a5b61fcd1">vars</a>;</div>
|
|
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> std::function<bool(</div>
|
|
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
|
|
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_linear_constraint_manager.html">LinearConstraintManager</a>* manager)></div>
|
|
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_cut_generator.html#a79779673f2fe909d104c37f3b7cc5a48"> 47</a></span> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_cut_generator.html#a79779673f2fe909d104c37f3b7cc5a48">generate_cuts</a>;</div>
|
|
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span>};</div>
|
|
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> </div>
|
|
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// Given an upper-bounded linear relation (sum terms <= ub), this algorithm</span></div>
|
|
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// inspects the integer variable appearing in the sum and try to replace each of</span></div>
|
|
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// them by a tight lower bound (>= coeff * binary + lb) using the implied bound</span></div>
|
|
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// repository. By tight, we mean that it will take the same value under the</span></div>
|
|
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// current LP solution.</span></div>
|
|
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// We use a class to reuse memory of the tmp terms.</span></div>
|
|
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html"> 57</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html">ImpliedBoundsProcessor</a> {</div>
|
|
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <span class="keyword">public</span>:</div>
|
|
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <span class="comment">// We will only replace IntegerVariable appearing in lp_vars_.</span></div>
|
|
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#acc1b04e5f7e2423d189a70388e177e97"> 60</a></span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#acc1b04e5f7e2423d189a70388e177e97">ImpliedBoundsProcessor</a>(absl::Span<const IntegerVariable> lp_vars_,</div>
|
|
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_integer_trail.html">IntegerTrail</a>* integer_trail,</div>
|
|
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_implied_bounds.html">ImpliedBounds</a>* implied_bounds)</div>
|
|
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> : lp_vars_(lp_vars_.begin(), lp_vars_.end()),</div>
|
|
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> integer_trail_(integer_trail),</div>
|
|
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> implied_bounds_(implied_bounds) {}</div>
|
|
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> </div>
|
|
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// See if some of the implied bounds equation are violated and add them to</span></div>
|
|
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// the IB cut pool if it is the case.</span></div>
|
|
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// Important: This must be called before we process any constraints with a</span></div>
|
|
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// different lp_values or level zero bounds.</span></div>
|
|
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#ab354ebe396f7f5ad0c79ff2a928d9a40">RecomputeCacheAndSeparateSomeImpliedBoundCuts</a>(</div>
|
|
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values);</div>
|
|
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
|
|
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// Processes and updates the given cut.</span></div>
|
|
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a7fb8d0b24091252e79aea6e5666f29e8">ProcessUpperBoundedConstraint</a>(</div>
|
|
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
|
|
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>* cut);</div>
|
|
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
|
|
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// Same as ProcessUpperBoundedConstraint() but instead of just using</span></div>
|
|
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// var >= coeff * binary + lb we use var == slack + coeff * binary + lb where</span></div>
|
|
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// slack is a new temporary variable that we create.</span></div>
|
|
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// The new slack will be such that slack_infos[(slack - first_slack) / 2]</span></div>
|
|
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="comment">// contains its definition so that we can properly handle it in the cut</span></div>
|
|
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// generation and substitute it back later.</span></div>
|
|
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html"> 87</a></span> <span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html">SlackInfo</a> {</div>
|
|
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> <span class="comment">// This slack is equal to sum of terms + offset.</span></div>
|
|
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a250583d63e8184c6f9f4deba1125e6bb"> 89</a></span> std::vector<std::pair<IntegerVariable, IntegerValue>> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a250583d63e8184c6f9f4deba1125e6bb">terms</a>;</div>
|
|
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#acd07f8397a2e61932c8ee17a4e300e23"> 90</a></span> IntegerValue <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#acd07f8397a2e61932c8ee17a4e300e23">offset</a>;</div>
|
|
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> </div>
|
|
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// The slack bounds and current lp_value.</span></div>
|
|
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a0ee34e5c6fbf075def1a6c2f0c42d040"> 93</a></span> IntegerValue <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a0ee34e5c6fbf075def1a6c2f0c42d040">lb</a> = IntegerValue(0);</div>
|
|
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a6e2915dc7e5345d6959390b53f026c5f"> 94</a></span> IntegerValue <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a6e2915dc7e5345d6959390b53f026c5f">ub</a> = IntegerValue(0);</div>
|
|
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#adb47ac0cff7c9dc4dc5f101d38a91185"> 95</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#adb47ac0cff7c9dc4dc5f101d38a91185">lp_value</a> = 0.0;</div>
|
|
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> };</div>
|
|
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a135d2e8757ef674942be0b1d6f46f75b">ProcessUpperBoundedConstraintWithSlackCreation</a>(</div>
|
|
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordtype">bool</span> substitute_only_inner_variables, IntegerVariable first_slack,</div>
|
|
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
|
|
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>* cut, std::vector<SlackInfo>* slack_infos);</div>
|
|
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> </div>
|
|
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// Only used for debugging.</span></div>
|
|
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="comment">//</span></div>
|
|
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// Substituting back the slack created by the function above should give</span></div>
|
|
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// exactly the same cut as the original one.</span></div>
|
|
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#ab1b4642341faf5ff972b02f034d88f21">DebugSlack</a>(IntegerVariable first_slack,</div>
|
|
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>& initial_cut,</div>
|
|
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>& cut,</div>
|
|
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">const</span> std::vector<SlackInfo>& info);</div>
|
|
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> </div>
|
|
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// Add a new variable that could be used in the new cuts.</span></div>
|
|
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="comment">// Note that the cache must be computed to take this into account.</span></div>
|
|
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a07e1de12d9a4b00c96911544e72b86d4"> 113</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a07e1de12d9a4b00c96911544e72b86d4">AddLpVariable</a>(IntegerVariable <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>) { lp_vars_.insert(<a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>); }</div>
|
|
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> </div>
|
|
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// Once RecomputeCacheAndSeparateSomeImpliedBoundCuts() has been called,</span></div>
|
|
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> <span class="comment">// we can get the best implied bound for each variables.</span></div>
|
|
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html"> 117</a></span> <span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html">BestImpliedBoundInfo</a> {</div>
|
|
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a9231f58e9d0f2dafc65c9eb41c979028"> 118</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a9231f58e9d0f2dafc65c9eb41c979028">bool_lp_value</a> = 0.0;</div>
|
|
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#ac11e010c276514d6402c772d0651f82f"> 119</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#ac11e010c276514d6402c772d0651f82f">slack_lp_value</a> = std::numeric_limits<double>::infinity();</div>
|
|
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a6d2822d5e07c3716efcdf73a4ae5eafc"> 120</a></span> <span class="keywordtype">bool</span> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a6d2822d5e07c3716efcdf73a4ae5eafc">is_positive</a>;</div>
|
|
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a2c25b894240115eebb2e75e2d8491a79"> 121</a></span> IntegerValue <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a2c25b894240115eebb2e75e2d8491a79">bound_diff</a>;</div>
|
|
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a871eaa421116e3c7cd440b6299d0b74d"> 122</a></span> IntegerVariable <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a871eaa421116e3c7cd440b6299d0b74d">bool_var</a> = <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a5bd8c44473618b7eafd33ba978db2f06">kNoIntegerVariable</a>;</div>
|
|
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> };</div>
|
|
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html">BestImpliedBoundInfo</a> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#abb0b7cc2e259fc8ebe8fd3dd55816b75">GetCachedImpliedBoundInfo</a>(IntegerVariable <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>);</div>
|
|
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> </div>
|
|
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// As we compute the best implied bounds for each variable, we add violated</span></div>
|
|
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// cuts here.</span></div>
|
|
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a25ce3a542ac1e183148844cb649069fd"> 128</a></span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_top_n_cuts.html">TopNCuts</a>& <a class="code hl_function" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a25ce3a542ac1e183148844cb649069fd">IbCutPool</a>() { <span class="keywordflow">return</span> ib_cut_pool_; }</div>
|
|
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
|
|
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keyword">private</span>:</div>
|
|
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> BestImpliedBoundInfo ComputeBestImpliedBound(</div>
|
|
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> IntegerVariable <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>,</div>
|
|
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values);</div>
|
|
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
|
|
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> absl::flat_hash_set<IntegerVariable> lp_vars_;</div>
|
|
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keyword">mutable</span> absl::flat_hash_map<IntegerVariable, BestImpliedBoundInfo> cache_;</div>
|
|
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> </div>
|
|
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_top_n_cuts.html">TopNCuts</a> ib_cut_pool_ = <a class="code hl_class" href="classoperations__research_1_1sat_1_1_top_n_cuts.html">TopNCuts</a>(50);</div>
|
|
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> </div>
|
|
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="comment">// Data from the constructor.</span></div>
|
|
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_integer_trail.html">IntegerTrail</a>* integer_trail_;</div>
|
|
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_implied_bounds.html">ImpliedBounds</a>* implied_bounds_;</div>
|
|
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> </div>
|
|
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="comment">// Temporary memory used by ProcessUpperBoundedConstraint().</span></div>
|
|
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keyword">mutable</span> std::vector<std::pair<IntegerVariable, IntegerValue>> tmp_terms_;</div>
|
|
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span>};</div>
|
|
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> </div>
|
|
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span><span class="comment">// Visible for testing. Returns a function f on integers such that:</span></div>
|
|
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="comment">// - f is non-decreasing.</span></div>
|
|
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="comment">// - f is super-additive: f(a) + f(b) <= f(a + b)</span></div>
|
|
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span><span class="comment">// - 1 <= f(divisor) <= max_scaling</span></div>
|
|
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span><span class="comment">// - For all x, f(x * divisor) = x * f(divisor)</span></div>
|
|
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span><span class="comment">// - For all x, f(x * divisor + remainder) = x * f(divisor)</span></div>
|
|
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span><span class="comment">// Preconditions:</span></div>
|
|
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span><span class="comment">// - 0 <= remainder < divisor.</span></div>
|
|
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="comment">// - 1 <= max_scaling.</span></div>
|
|
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span><span class="comment">// This is used in IntegerRoundingCut() and is responsible for "strengthening"</span></div>
|
|
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span><span class="comment">// the cut. Just taking f(x) = x / divisor result in the non-strengthened cut</span></div>
|
|
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span><span class="comment">// and using any function that stricly dominate this one is better.</span></div>
|
|
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span><span class="comment">// Algorithm:</span></div>
|
|
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span><span class="comment">// - We first scale by a factor t so that rhs_remainder >= divisor / 2.</span></div>
|
|
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span><span class="comment">// - Then, if max_scaling == 2, we use the function described</span></div>
|
|
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span><span class="comment">// in "Strenghtening Chvatal-Gomory cuts and Gomory fractional cuts", Adam N.</span></div>
|
|
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span><span class="comment">// Letchfrod, Andrea Lodi.</span></div>
|
|
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="comment">// - Otherwise, we use a generalization of this which is a discretized version</span></div>
|
|
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="comment">// of the classical MIR rounding function that only take the value of the</span></div>
|
|
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="comment">// form "an_integer / max_scaling". As max_scaling goes to infinity, this</span></div>
|
|
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="comment">// converge to the real-valued MIR function.</span></div>
|
|
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span><span class="comment">// Note that for each value of max_scaling we will get a different function.</span></div>
|
|
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span><span class="comment">// And that there is no dominance relation between any of these functions. So</span></div>
|
|
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span><span class="comment">// it could be nice to try to generate a cut using different values of</span></div>
|
|
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span><span class="comment">// max_scaling.</span></div>
|
|
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span>IntegerValue <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a44bd0a015c444c2e2d58a002a09a1ea5">GetFactorT</a>(IntegerValue rhs_remainder, IntegerValue divisor,</div>
|
|
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> IntegerValue max_t);</div>
|
|
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span>std::function<IntegerValue(IntegerValue)> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a8e30df8580d6914abba28f43b6e4e667">GetSuperAdditiveRoundingFunction</a>(</div>
|
|
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> IntegerValue rhs_remainder, IntegerValue divisor, IntegerValue t,</div>
|
|
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> IntegerValue max_scaling);</div>
|
|
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> </div>
|
|
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span><span class="comment">// Given an upper bounded linear constraint, this function tries to transform it</span></div>
|
|
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span><span class="comment">// to a valid cut that violate the given LP solution using integer rounding.</span></div>
|
|
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span><span class="comment">// Note that the returned cut might not always violate the LP solution, in which</span></div>
|
|
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span><span class="comment">// case it can be discarded.</span></div>
|
|
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span><span class="comment">// What this does is basically take the integer division of the constraint by an</span></div>
|
|
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span><span class="comment">// integer. If the coefficients where doubles, this would be the same as scaling</span></div>
|
|
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span><span class="comment">// the constraint and then rounding. We choose the coefficient of the most</span></div>
|
|
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span><span class="comment">// fractional variable (rescaled by its coefficient) as the divisor, but there</span></div>
|
|
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span><span class="comment">// are other possible alternatives.</span></div>
|
|
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span><span class="comment">// Note that if the constraint is tight under the given lp solution, and if</span></div>
|
|
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span><span class="comment">// there is a unique variable not at one of its bounds and fractional, then we</span></div>
|
|
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span><span class="comment">// are guaranteed to generate a cut that violate the current LP solution. This</span></div>
|
|
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span><span class="comment">// should be the case for Chvatal-Gomory base constraints modulo our loss of</span></div>
|
|
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span><span class="comment">// precision while doing exact integer computations.</span></div>
|
|
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span><span class="comment">// Precondition:</span></div>
|
|
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span><span class="comment">// - We assumes that the given initial constraint is tight using the given lp</span></div>
|
|
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span><span class="comment">// values. This could be relaxed, but for now it should always be the case, so</span></div>
|
|
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span><span class="comment">// we log a message and abort if not, to ease debugging.</span></div>
|
|
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span><span class="comment">// - The IntegerVariable of the cuts are not used here. We assumes that the</span></div>
|
|
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span><span class="comment">// first three vectors are in one to one correspondence with the initial order</span></div>
|
|
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span><span class="comment">// of the variable in the cut.</span></div>
|
|
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span><span class="comment">// TODO(user): There is a bunch of heuristic involved here, and we could spend</span></div>
|
|
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span><span class="comment">// more effort tunning them. In particular, one can try many heuristics and keep</span></div>
|
|
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span><span class="comment">// the best looking cut (or more than one). This is not on the critical code</span></div>
|
|
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span><span class="comment">// path, so we can spend more effort in finding good cuts.</span></div>
|
|
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_rounding_options.html"> 212</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1sat_1_1_rounding_options.html">RoundingOptions</a> {</div>
|
|
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_rounding_options.html#a01db407e90fac1c31c6705758a057908"> 213</a></span> IntegerValue <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_rounding_options.html#a01db407e90fac1c31c6705758a057908">max_scaling</a> = IntegerValue(60);</div>
|
|
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span>};</div>
|
|
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html"> 215</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html">IntegerRoundingCutHelper</a> {</div>
|
|
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keyword">public</span>:</div>
|
|
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keywordtype">void</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a66c8e6dc26260b69dcdf7668925dc3aa">ComputeCut</a>(<a class="code hl_struct" href="structoperations__research_1_1sat_1_1_rounding_options.html">RoundingOptions</a> options, <span class="keyword">const</span> std::vector<double>& lp_values,</div>
|
|
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">const</span> std::vector<IntegerValue>& <a class="code hl_variable" href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a>,</div>
|
|
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <span class="keyword">const</span> std::vector<IntegerValue>& <a class="code hl_variable" href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a>,</div>
|
|
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <a class="code hl_class" href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html">ImpliedBoundsProcessor</a>* ib_processor, <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>* cut);</div>
|
|
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> </div>
|
|
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <span class="comment">// Returns the number of implied bound lifted Booleans in the last</span></div>
|
|
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="comment">// ComputeCut() call. Useful for investigation.</span></div>
|
|
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a4f879f884fd170f77c9024aee023feb2"> 224</a></span> <span class="keywordtype">int</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a4f879f884fd170f77c9024aee023feb2">NumLiftedBooleans</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_lifted_booleans_; }</div>
|
|
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> </div>
|
|
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="keyword">private</span>:</div>
|
|
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="comment">// The helper is just here to reuse the memory for these vectors.</span></div>
|
|
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> std::vector<int> relevant_indices_;</div>
|
|
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> std::vector<double> relevant_lp_values_;</div>
|
|
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> std::vector<IntegerValue> relevant_coeffs_;</div>
|
|
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> std::vector<IntegerValue> relevant_bound_diffs_;</div>
|
|
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> std::vector<IntegerValue> divisors_;</div>
|
|
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> std::vector<std::pair<int, IntegerValue>> adjusted_coeffs_;</div>
|
|
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> std::vector<IntegerValue> remainders_;</div>
|
|
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> std::vector<bool> change_sign_at_postprocessing_;</div>
|
|
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> std::vector<IntegerValue> rs_;</div>
|
|
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> std::vector<IntegerValue> best_rs_;</div>
|
|
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> </div>
|
|
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keywordtype">int</span> num_lifted_booleans_ = 0;</div>
|
|
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> std::vector<std::pair<IntegerVariable, IntegerValue>> tmp_terms_;</div>
|
|
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span>};</div>
|
|
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> </div>
|
|
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span><span class="comment">// Helper to find knapsack or flow cover cuts (not yet implemented).</span></div>
|
|
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html"> 244</a></span><span class="keyword">class </span><a class="code hl_class" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html">CoverCutHelper</a> {</div>
|
|
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keyword">public</span>:</div>
|
|
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="comment">// Try to find a cut with a knapsack heuristic.</span></div>
|
|
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="comment">// If this returns true, you can get the cut via cut().</span></div>
|
|
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="keywordtype">bool</span> <a class="code hl_function" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ad86e161bb994fe49fa9c4298ebb5ae2d">TrySimpleKnapsack</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a> base_ct,</div>
|
|
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <span class="keyword">const</span> std::vector<double>& lp_values,</div>
|
|
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keyword">const</span> std::vector<IntegerValue>& <a class="code hl_variable" href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a>,</div>
|
|
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keyword">const</span> std::vector<IntegerValue>& <a class="code hl_variable" href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a>);</div>
|
|
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> </div>
|
|
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="comment">// If successful, info about the last generated cut.</span></div>
|
|
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#aab767e578fedc6ebe0b264c003671a55"> 254</a></span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>* <a class="code hl_function" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#aab767e578fedc6ebe0b264c003671a55">mutable_cut</a>() { <span class="keywordflow">return</span> &cut_; }</div>
|
|
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#a4dbdfea287fc5d8f740860d985499645"> 255</a></span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_linear_constraint.html">LinearConstraint</a>& <a class="code hl_function" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#a4dbdfea287fc5d8f740860d985499645">cut</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> cut_; }</div>
|
|
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> </div>
|
|
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="comment">// Single line of text that we append to the cut log line.</span></div>
|
|
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"><a class="line" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ac3816c1571dfd130851ed09c79224360"> 258</a></span> <span class="keyword">const</span> std::string <a class="code hl_function" href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ac3816c1571dfd130851ed09c79224360">Info</a>() { <span class="keywordflow">return</span> absl::StrCat(<span class="stringliteral">"lift="</span>, num_lifting_); }</div>
|
|
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> </div>
|
|
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <span class="keyword">private</span>:</div>
|
|
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> <span class="keyword">struct </span>Term {</div>
|
|
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="keywordtype">int</span> <a class="code hl_variable" href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a>;</div>
|
|
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="keywordtype">double</span> dist_to_max_value;</div>
|
|
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> IntegerValue positive_coeff; <span class="comment">// abs(coeff in original constraint).</span></div>
|
|
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> IntegerValue diff;</div>
|
|
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> };</div>
|
|
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> std::vector<Term> terms_;</div>
|
|
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> std::vector<bool> in_cut_;</div>
|
|
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> </div>
|
|
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> LinearConstraint cut_;</div>
|
|
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <span class="keywordtype">int</span> num_lifting_;</div>
|
|
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span>};</div>
|
|
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> </div>
|
|
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span><span class="comment">// If a variable is away from its upper bound by more than value 1.0, then it</span></div>
|
|
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span><span class="comment">// cannot be part of a cover that will violate the lp solution. This method</span></div>
|
|
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span><span class="comment">// returns a reduced constraint by removing such variables from the given</span></div>
|
|
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span><span class="comment">// constraint.</span></div>
|
|
<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span>LinearConstraint <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a1de556a1559f25bd0819655d375f6c8e">GetPreprocessedLinearConstraint</a>(</div>
|
|
<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> <span class="keyword">const</span> LinearConstraint& constraint,</div>
|
|
<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
|
|
<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
|
|
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> </div>
|
|
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span><span class="comment">// Returns true if sum of all the variables in the given constraint is less than</span></div>
|
|
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span><span class="comment">// or equal to constraint upper bound. This method assumes that all the</span></div>
|
|
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span><span class="comment">// coefficients are non negative.</span></div>
|
|
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ac8b530afe36cf1521c919ca43429926d">ConstraintIsTriviallyTrue</a>(<span class="keyword">const</span> LinearConstraint& constraint,</div>
|
|
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
|
|
<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> </div>
|
|
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span><span class="comment">// If the left variables in lp solution satisfies following inequality, we prove</span></div>
|
|
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span><span class="comment">// that there does not exist any knapsack cut which is violated by the solution.</span></div>
|
|
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span><span class="comment">// Let |Cmin| = smallest possible cover size.</span></div>
|
|
<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span><span class="comment">// Let S = smallest (var_ub - lp_values[var]) first |Cmin| variables.</span></div>
|
|
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span><span class="comment">// Let cut lower bound = sum_(var in S)(var_ub - lp_values[var])</span></div>
|
|
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span><span class="comment">// For any cover,</span></div>
|
|
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span><span class="comment">// If cut lower bound >= 1</span></div>
|
|
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span><span class="comment">// ==> sum_(var in S)(var_ub - lp_values[var]) >= 1</span></div>
|
|
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span><span class="comment">// ==> sum_(var in cover)(var_ub - lp_values[var]) >= 1</span></div>
|
|
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span><span class="comment">// ==> The solution already satisfies cover. Since this is true for all covers,</span></div>
|
|
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span><span class="comment">// this method returns false in such cases.</span></div>
|
|
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span><span class="comment">// This method assumes that the constraint is preprocessed and has only non</span></div>
|
|
<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span><span class="comment">// negative coefficients.</span></div>
|
|
<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a588b516182cd6d5d8c048dfd76bc5523">CanBeFilteredUsingCutLowerBound</a>(</div>
|
|
<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> <span class="keyword">const</span> LinearConstraint& preprocessed_constraint,</div>
|
|
<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
|
|
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
|
|
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> </div>
|
|
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span><span class="comment">// Struct to help compute upper bound for knapsack instance.</span></div>
|
|
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_knapsack_item.html"> 308</a></span><span class="keyword">struct </span><a class="code hl_struct" href="structoperations__research_1_1sat_1_1_knapsack_item.html">KnapsackItem</a> {</div>
|
|
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c"> 309</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c">profit</a>;</div>
|
|
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513"> 310</a></span> <span class="keywordtype">double</span> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513">weight</a>;</div>
|
|
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1_knapsack_item.html#aa51ab05fd43c2d0962967f9d889c7bb7"> 311</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="structoperations__research_1_1sat_1_1_knapsack_item.html#aa51ab05fd43c2d0962967f9d889c7bb7">operator></a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1sat_1_1_knapsack_item.html">KnapsackItem</a>& other)<span class="keyword"> const </span>{</div>
|
|
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c">profit</a> * other.<a class="code hl_variable" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513">weight</a> > other.<a class="code hl_variable" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c">profit</a> * <a class="code hl_variable" href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513">weight</a>;</div>
|
|
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> }</div>
|
|
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span>};</div>
|
|
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> </div>
|
|
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span><span class="comment">// Gets upper bound on profit for knapsack instance by solving the linear</span></div>
|
|
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span><span class="comment">// relaxation.</span></div>
|
|
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span><span class="keywordtype">double</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a457076abfb3071fca80b8175363e3dfa">GetKnapsackUpperBound</a>(std::vector<KnapsackItem> items, <span class="keywordtype">double</span> <a class="code hl_variable" href="routing__flow_8cc.html#a2acb49f4df5288066c43610bede123ec">capacity</a>);</div>
|
|
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> </div>
|
|
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span><span class="comment">// Returns true if the linear relaxation upper bound for the knapsack instance</span></div>
|
|
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span><span class="comment">// shows that this constraint cannot be used to form a cut. This method assumes</span></div>
|
|
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span><span class="comment">// that all the coefficients are non negative.</span></div>
|
|
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a8c8db245a613f2fb46d917cd78100f83">CanBeFilteredUsingKnapsackUpperBound</a>(</div>
|
|
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> <span class="keyword">const</span> LinearConstraint& constraint,</div>
|
|
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
|
|
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
|
|
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> </div>
|
|
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span><span class="comment">// Returns true if the given constraint passes all the filters described above.</span></div>
|
|
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span><span class="comment">// This method assumes that the constraint is preprocessed and has only non</span></div>
|
|
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span><span class="comment">// negative coefficients.</span></div>
|
|
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a32f0016572d69bfcd1f3af811b2043ad">CanFormValidKnapsackCover</a>(</div>
|
|
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="keyword">const</span> LinearConstraint& preprocessed_constraint,</div>
|
|
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
|
|
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> <span class="keyword">const</span> IntegerTrail& integer_trail);</div>
|
|
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> </div>
|
|
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span><span class="comment">// Converts the given constraint into canonical knapsack form (described</span></div>
|
|
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span><span class="comment">// below) and adds it to 'knapsack_constraints'.</span></div>
|
|
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span><span class="comment">// Canonical knapsack form:</span></div>
|
|
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span><span class="comment">// - Constraint has finite upper bound.</span></div>
|
|
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span><span class="comment">// - All coefficients are positive.</span></div>
|
|
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span><span class="comment">// For constraint with finite lower bound, this method also adds the negation of</span></div>
|
|
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span><span class="comment">// the given constraint after converting it to canonical knapsack form.</span></div>
|
|
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span><span class="keywordtype">void</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a06e2118f6735d033f7f43a939abe558d">ConvertToKnapsackForm</a>(<span class="keyword">const</span> LinearConstraint& constraint,</div>
|
|
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> std::vector<LinearConstraint>* knapsack_constraints,</div>
|
|
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> IntegerTrail* integer_trail);</div>
|
|
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> </div>
|
|
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span><span class="comment">// Returns true if the cut is lifted. Lifting procedure is described below.</span></div>
|
|
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span><span class="comment">// First we decide a lifting sequence for the binary variables which are not</span></div>
|
|
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span><span class="comment">// already in cut. We lift the cut for each lifting candidate one by one.</span></div>
|
|
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span><span class="comment">// Given the original constraint where the lifting candidate is fixed to one, we</span></div>
|
|
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span><span class="comment">// compute the maximum value the cut can take and still be feasible using a</span></div>
|
|
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span><span class="comment">// knapsack problem. We can then lift the variable in the cut using the</span></div>
|
|
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span><span class="comment">// difference between the cut upper bound and this maximum value.</span></div>
|
|
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span><span class="keywordtype">bool</span> <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#accb737ae1fad15d6798a4b8bc27cea51">LiftKnapsackCut</a>(</div>
|
|
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> <span class="keyword">const</span> LinearConstraint& constraint,</div>
|
|
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="keyword">const</span> <a class="code hl_class" href="classabsl_1_1_strong_vector.html">absl::StrongVector<IntegerVariable, double></a>& lp_values,</div>
|
|
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> <span class="keyword">const</span> std::vector<IntegerValue>& cut_vars_original_coefficients,</div>
|
|
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> <span class="keyword">const</span> IntegerTrail& integer_trail, <a class="code hl_class" href="classoperations__research_1_1_time_limit.html">TimeLimit</a>* <a class="code hl_variable" href="cp__model__solver_8cc.html#aec8af5c1be4e1b6d4330e1161028de21">time_limit</a>,</div>
|
|
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> LinearConstraint* cut);</div>
|
|
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> </div>
|
|
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span><span class="comment">// A cut generator that creates knpasack cover cuts.</span></div>
|
|
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span><span class="comment">// For a constraint of type</span></div>
|
|
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span><span class="comment">// \sum_{i=1..n}(a_i * x_i) <= b</span></div>
|
|
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span><span class="comment">// where x_i are integer variables with upper bound u_i, a cover of size k is a</span></div>
|
|
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span><span class="comment">// subset C of {1 , .. , n} such that \sum_{c \in C}(a_c * u_c) > b.</span></div>
|
|
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span><span class="comment">// A knapsack cover cut is a constraint of the form</span></div>
|
|
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span><span class="comment">// \sum_{c \in C}(u_c - x_c) >= 1</span></div>
|
|
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span><span class="comment">// which is equivalent to \sum_{c \in C}(x_c) <= \sum_{c \in C}(u_c) - 1.</span></div>
|
|
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span><span class="comment">// In other words, in a feasible solution, at least some of the variables do</span></div>
|
|
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span><span class="comment">// not take their maximum value.</span></div>
|
|
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span><span class="comment">// If all x_i are binary variables then the cover cut becomes</span></div>
|
|
<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span><span class="comment">// \sum_{c \in C}(x_c) <= |C| - 1.</span></div>
|
|
<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span><span class="comment">// The major difficulty for generating Knapsack cover cuts is finding a minimal</span></div>
|
|
<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</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 id="l00381" name="l00381"></a><span class="lineno"> 381</span><span class="comment">// heuristically generate the cover but the following method that uses a</span></div>
|
|
<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span><span class="comment">// solution of the LP relaxation of the constraint works the best.</span></div>
|
|
<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span><span class="comment">// Look at a given linear relaxation solution for the integer problem x'</span></div>
|
|
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span><span class="comment">// and try to solve the following knapsack problem:</span></div>
|
|
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span><span class="comment">// Minimize \sum_{i=1..n}(z_i * (u_i - x_i')),</span></div>
|
|
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span><span class="comment">// such that \sum_{i=1..n}(a_i * u_i * z_i) > b,</span></div>
|
|
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span><span class="comment">// where z_i is a binary decision variable and x_i' are values of the variables</span></div>
|
|
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span><span class="comment">// in the given relaxation solution x'. If the objective of the optimal solution</span></div>
|
|
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span><span class="comment">// of this problem is less than 1, this algorithm does not generate any cuts.</span></div>
|
|
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span><span class="comment">// Otherwise, it adds a knapsack cover cut in the form</span></div>
|
|
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span><span class="comment">// \sum_{i=1..n}(z_i' * x_i) <= cb,</span></div>
|
|
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span><span class="comment">// where z_i' is the value of z_i in the optimal solution of the above</span></div>
|
|
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span><span class="comment">// problem and cb is the upper bound for the cut constraint. Note that the above</span></div>
|
|
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span><span class="comment">// problem can be converted into a standard kanpsack form by replacing z_i by 1</span></div>
|
|
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span><span class="comment">// - y_i. In that case the problem becomes</span></div>
|
|
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span><span class="comment">// Maximize \sum_{i=1..n}((u_i - x_i') * (y_i - 1)),</span></div>
|
|
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span><span class="comment">// such that</span></div>
|
|
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span><span class="comment">// \sum_{i=1..n}(a_i * u_i * y_i) <= \sum_{i=1..n}(a_i * u_i) - b - 1.</span></div>
|
|
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span><span class="comment">// Solving this knapsack instance would help us find the smallest cover with</span></div>
|
|
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span><span class="comment">// maximum LP violation.</span></div>
|
|
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span><span class="comment">// Cut strengthning:</span></div>
|
|
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span><span class="comment">// Let lambda = \sum_{c \in C}(a_c * u_c) - b and max_coeff = \max_{c</span></div>
|
|
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span><span class="comment">// \in C}(a_c), then cut can be strengthened as</span></div>
|
|
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span><span class="comment">// \sum_{c \in C}(u_c - x_c) >= ceil(lambda / max_coeff)</span></div>
|
|
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span><span class="comment">// For further information about knapsack cover cuts see</span></div>
|
|
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span><span class="comment">// A. Atamtürk, Cover and Pack Inequalities for (Mixed) Integer Programming</span></div>
|
|
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span><span class="comment">// Annals of Operations Research Volume 139, Issue 1 , pp 21-38, 2005.</span></div>
|
|
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span><span class="comment">// TODO(user): Implement cut lifting.</span></div>
|
|
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span>CutGenerator <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ac158f737c8653b1fc1bd294ea2d3412d">CreateKnapsackCoverCutGenerator</a>(</div>
|
|
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <span class="keyword">const</span> std::vector<LinearConstraint>& base_constraints,</div>
|
|
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> <span class="keyword">const</span> std::vector<IntegerVariable>& vars, Model* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> </div>
|
|
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span><span class="comment">// A cut generator for z = x * y (x and y >= 0).</span></div>
|
|
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span>CutGenerator <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#af11d52b4cc77e85f6a523f04642229f3">CreatePositiveMultiplicationCutGenerator</a>(IntegerVariable z,</div>
|
|
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> IntegerVariable x,</div>
|
|
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> IntegerVariable y,</div>
|
|
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <span class="keywordtype">int</span> linearization_level,</div>
|
|
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> Model* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> </div>
|
|
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span><span class="comment">// A cut generator for y = x ^ 2 (x >= 0).</span></div>
|
|
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span><span class="comment">// It will dynamically add a linear inequality to push y closer to the parabola.</span></div>
|
|
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span>CutGenerator <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a19a67428513beb394b652edf75b32216">CreateSquareCutGenerator</a>(IntegerVariable y, IntegerVariable x,</div>
|
|
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> <span class="keywordtype">int</span> linearization_level, Model* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> </div>
|
|
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</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 id="l00430" name="l00430"></a><span class="lineno"> 430</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 id="l00431" name="l00431"></a><span class="lineno"> 431</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 id="l00432" name="l00432"></a><span class="lineno"> 432</span><span class="comment">// D. The cut generator first sorts the variables based on LP values and adds</span></div>
|
|
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span><span class="comment">// cuts of the form described above if they are violated by lp solution. Note</span></div>
|
|
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span><span class="comment">// that all the fixed variables are ignored while generating cuts.</span></div>
|
|
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span>CutGenerator <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a7feb76be212dca01ffe7ba3a0391e118">CreateAllDifferentCutGenerator</a>(</div>
|
|
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> <span class="keyword">const</span> std::vector<IntegerVariable>& vars, Model* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> </div>
|
|
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span><span class="comment">// Consider the Lin Max constraint with d expressions and n variables in the</span></div>
|
|
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span><span class="comment">// form: target = max {exprs[k] = Sum (wki * xi + bk)}. k in {1,..,d}.</span></div>
|
|
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span><span class="comment">// Li = lower bound of xi</span></div>
|
|
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span><span class="comment">// Ui = upper bound of xi.</span></div>
|
|
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span><span class="comment">// Let zk be in {0,1} for all k in {1,..,d}.</span></div>
|
|
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span><span class="comment">// The target = exprs[k] when zk = 1.</span></div>
|
|
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span><span class="comment">// The following is a valid linearization for Lin Max.</span></div>
|
|
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span><span class="comment">// target >= exprs[k], for all k in {1,..,d}</span></div>
|
|
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span><span class="comment">// target <= Sum (wli * xi) + Sum((Nlk + bk) * zk), for all l in {1,..,d}</span></div>
|
|
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span><span class="comment">// Where Nlk is a large number defined as:</span></div>
|
|
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span><span class="comment">// Nlk = Sum (max((wki - wli)*Li, (wki - wli)*Ui))</span></div>
|
|
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span><span class="comment">// = Sum (max corner difference for variable i, target expr l, max expr k)</span></div>
|
|
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span><span class="comment">// Consider a partition of variables xi into set {1,..,d} as I.</span></div>
|
|
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span><span class="comment">// i.e. I(i) = j means xi is mapped to jth index.</span></div>
|
|
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span><span class="comment">// The following inequality is valid and sharp cut for the lin max constraint</span></div>
|
|
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span><span class="comment">// described above.</span></div>
|
|
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</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 id="l00458" name="l00458"></a><span class="lineno"> 458</span><span class="comment">// + Sum(k=1..d)(bk * zk) ,</span></div>
|
|
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span><span class="comment">// Where MPlusCoefficient_ki = max((wki - wI(i)i) * Li,</span></div>
|
|
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span><span class="comment">// (wki - wI(i)i) * Ui)</span></div>
|
|
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span><span class="comment">// = max corner difference for variable i,</span></div>
|
|
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span><span class="comment">// target expr I(i), max expr k.</span></div>
|
|
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span><span class="comment">// For detailed proof of validity, refer</span></div>
|
|
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span><span class="comment">// Reference: "Strong mixed-integer programming formulations for trained neural</span></div>
|
|
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span><span class="comment">// networks" by Ross Anderson et. (https://arxiv.org/pdf/1811.01988.pdf).</span></div>
|
|
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span><span class="comment">// In the cut generator, we compute the most violated partition I by computing</span></div>
|
|
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</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 id="l00470" name="l00470"></a><span class="lineno"> 470</span><span class="comment">// for each variable for each partition index. We choose the partition index</span></div>
|
|
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span><span class="comment">// that gives lowest rhs value for a given variable.</span></div>
|
|
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span><span class="comment">//</span></div>
|
|
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span><span class="comment">// Note: This cut generator requires all expressions to contain only positive</span></div>
|
|
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span><span class="comment">// vars.</span></div>
|
|
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span>CutGenerator <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a7fea62548e11ae728e506874f767bdd3">CreateLinMaxCutGenerator</a>(</div>
|
|
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> <span class="keyword">const</span> IntegerVariable target, <span class="keyword">const</span> std::vector<LinearExpression>& exprs,</div>
|
|
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> <span class="keyword">const</span> std::vector<IntegerVariable>& z_vars, Model* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> </div>
|
|
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span><span class="comment">// Helper for the affine max constraint.</span></div>
|
|
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span>LinearConstraint <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#a88fabb0f851ff07d459b8be401162601">BuildMaxAffineUpConstraint</a>(</div>
|
|
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> <span class="keyword">const</span> LinearExpression& target, IntegerVariable <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>,</div>
|
|
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> <span class="keyword">const</span> std::vector<std::pair<IntegerValue, IntegerValue>>& affines,</div>
|
|
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> Model* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> </div>
|
|
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span><span class="comment">// By definition, the Max of affine functions is convex. The linear polytope is</span></div>
|
|
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span><span class="comment">// bounded by all affine functions on the bottom, and by a single hyperplane</span></div>
|
|
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span><span class="comment">// that join the two points at the extreme of the var domain, and their y-values</span></div>
|
|
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span><span class="comment">// of the max of the affine functions.</span></div>
|
|
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span>CutGenerator <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#ab782d6f91aefca5ee81c3b622e862875">CreateMaxAffineCutGenerator</a>(</div>
|
|
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> LinearExpression target, IntegerVariable <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>,</div>
|
|
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> std::vector<std::pair<IntegerValue, IntegerValue>> affines,</div>
|
|
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> <span class="keyword">const</span> std::string cut_name, Model* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> </div>
|
|
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span><span class="comment">// Extracts the variables that have a Literal view from base variables and</span></div>
|
|
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span><span class="comment">// create a generator that will returns constraint of the form "at_most_one"</span></div>
|
|
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span><span class="comment">// between such literals.</span></div>
|
|
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span>CutGenerator <a class="code hl_function" href="namespaceoperations__research_1_1sat.html#adf176ac81e34e8fd124d823ee0033f1a">CreateCliqueCutGenerator</a>(</div>
|
|
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> <span class="keyword">const</span> std::vector<IntegerVariable>& base_variables, Model* <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>);</div>
|
|
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span> </div>
|
|
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span>} <span class="comment">// namespace sat</span></div>
|
|
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span>} <span class="comment">// namespace operations_research</span></div>
|
|
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> </div>
|
|
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span><span class="preprocessor">#endif </span><span class="comment">// OR_TOOLS_SAT_CUTS_H_</span></div>
|
|
<div class="ttc" id="aclassabsl_1_1_strong_vector_html"><div class="ttname"><a href="classabsl_1_1_strong_vector.html">absl::StrongVector< IntegerVariable, double ></a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1_time_limit_html"><div class="ttname"><a href="classoperations__research_1_1_time_limit.html">operations_research::TimeLimit</a></div><div class="ttdoc">A simple class to enforce both an elapsed time limit and a deterministic time limit in the same threa...</div><div class="ttdef"><b>Definition:</b> <a href="time__limit_8h_source.html#l00105">time_limit.h:105</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html">operations_research::sat::CoverCutHelper</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00244">cuts.h:244</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html_a4dbdfea287fc5d8f740860d985499645"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#a4dbdfea287fc5d8f740860d985499645">operations_research::sat::CoverCutHelper::cut</a></div><div class="ttdeci">const LinearConstraint & cut() const</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00255">cuts.h:255</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html_aab767e578fedc6ebe0b264c003671a55"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#aab767e578fedc6ebe0b264c003671a55">operations_research::sat::CoverCutHelper::mutable_cut</a></div><div class="ttdeci">LinearConstraint * mutable_cut()</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00254">cuts.h:254</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html_ac3816c1571dfd130851ed09c79224360"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ac3816c1571dfd130851ed09c79224360">operations_research::sat::CoverCutHelper::Info</a></div><div class="ttdeci">const std::string Info()</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00258">cuts.h:258</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_cover_cut_helper_html_ad86e161bb994fe49fa9c4298ebb5ae2d"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_cover_cut_helper.html#ad86e161bb994fe49fa9c4298ebb5ae2d">operations_research::sat::CoverCutHelper::TrySimpleKnapsack</a></div><div class="ttdeci">bool TrySimpleKnapsack(const LinearConstraint base_ct, const std::vector< double > &lp_values, const std::vector< IntegerValue > &lower_bounds, const std::vector< IntegerValue > &upper_bounds)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01168">cuts.cc:1168</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds.html">operations_research::sat::ImpliedBounds</a></div><div class="ttdef"><b>Definition:</b> <a href="implied__bounds_8h_source.html#l00078">implied_bounds.h:78</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html">operations_research::sat::ImpliedBoundsProcessor</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00057">cuts.h:57</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_a07e1de12d9a4b00c96911544e72b86d4"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a07e1de12d9a4b00c96911544e72b86d4">operations_research::sat::ImpliedBoundsProcessor::AddLpVariable</a></div><div class="ttdeci">void AddLpVariable(IntegerVariable var)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00113">cuts.h:113</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_a135d2e8757ef674942be0b1d6f46f75b"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a135d2e8757ef674942be0b1d6f46f75b">operations_research::sat::ImpliedBoundsProcessor::ProcessUpperBoundedConstraintWithSlackCreation</a></div><div class="ttdeci">void ProcessUpperBoundedConstraintWithSlackCreation(bool substitute_only_inner_variables, IntegerVariable first_slack, const absl::StrongVector< IntegerVariable, double > &lp_values, LinearConstraint *cut, std::vector< SlackInfo > *slack_infos)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01593">cuts.cc:1593</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_a25ce3a542ac1e183148844cb649069fd"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a25ce3a542ac1e183148844cb649069fd">operations_research::sat::ImpliedBoundsProcessor::IbCutPool</a></div><div class="ttdeci">TopNCuts & IbCutPool()</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00128">cuts.h:128</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_a7fb8d0b24091252e79aea6e5666f29e8"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#a7fb8d0b24091252e79aea6e5666f29e8">operations_research::sat::ImpliedBoundsProcessor::ProcessUpperBoundedConstraint</a></div><div class="ttdeci">void ProcessUpperBoundedConstraint(const absl::StrongVector< IntegerVariable, double > &lp_values, LinearConstraint *cut)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01500">cuts.cc:1500</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_ab1b4642341faf5ff972b02f034d88f21"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#ab1b4642341faf5ff972b02f034d88f21">operations_research::sat::ImpliedBoundsProcessor::DebugSlack</a></div><div class="ttdeci">bool DebugSlack(IntegerVariable first_slack, const LinearConstraint &initial_cut, const LinearConstraint &cut, const std::vector< SlackInfo > &info)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01726">cuts.cc:1726</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_ab354ebe396f7f5ad0c79ff2a928d9a40"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#ab354ebe396f7f5ad0c79ff2a928d9a40">operations_research::sat::ImpliedBoundsProcessor::RecomputeCacheAndSeparateSomeImpliedBoundCuts</a></div><div class="ttdeci">void RecomputeCacheAndSeparateSomeImpliedBoundCuts(const absl::StrongVector< IntegerVariable, double > &lp_values)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01583">cuts.cc:1583</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_abb0b7cc2e259fc8ebe8fd3dd55816b75"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#abb0b7cc2e259fc8ebe8fd3dd55816b75">operations_research::sat::ImpliedBoundsProcessor::GetCachedImpliedBoundInfo</a></div><div class="ttdeci">BestImpliedBoundInfo GetCachedImpliedBoundInfo(IntegerVariable var)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01509">cuts.cc:1509</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_implied_bounds_processor_html_acc1b04e5f7e2423d189a70388e177e97"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_implied_bounds_processor.html#acc1b04e5f7e2423d189a70388e177e97">operations_research::sat::ImpliedBoundsProcessor::ImpliedBoundsProcessor</a></div><div class="ttdeci">ImpliedBoundsProcessor(absl::Span< const IntegerVariable > lp_vars_, IntegerTrail *integer_trail, ImpliedBounds *implied_bounds)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00060">cuts.h:60</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_rounding_cut_helper_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html">operations_research::sat::IntegerRoundingCutHelper</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00215">cuts.h:215</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_rounding_cut_helper_html_a4f879f884fd170f77c9024aee023feb2"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a4f879f884fd170f77c9024aee023feb2">operations_research::sat::IntegerRoundingCutHelper::NumLiftedBooleans</a></div><div class="ttdeci">int NumLiftedBooleans() const</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00224">cuts.h:224</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_rounding_cut_helper_html_a66c8e6dc26260b69dcdf7668925dc3aa"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_rounding_cut_helper.html#a66c8e6dc26260b69dcdf7668925dc3aa">operations_research::sat::IntegerRoundingCutHelper::ComputeCut</a></div><div class="ttdeci">void ComputeCut(RoundingOptions options, const std::vector< double > &lp_values, const std::vector< IntegerValue > &lower_bounds, const std::vector< IntegerValue > &upper_bounds, ImpliedBoundsProcessor *ib_processor, LinearConstraint *cut)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00720">cuts.cc:720</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_integer_trail_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_integer_trail.html">operations_research::sat::IntegerTrail</a></div><div class="ttdef"><b>Definition:</b> <a href="integer_8h_source.html#l00574">integer.h:574</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_linear_constraint_manager_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_linear_constraint_manager.html">operations_research::sat::LinearConstraintManager</a></div><div class="ttdef"><b>Definition:</b> <a href="linear__constraint__manager_8h_source.html#l00043">linear_constraint_manager.h:43</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1_top_n_cuts_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1_top_n_cuts.html">operations_research::sat::TopNCuts</a></div><div class="ttdef"><b>Definition:</b> <a href="linear__constraint__manager_8h_source.html#l00294">linear_constraint_manager.h:294</a></div></div>
|
|
<div class="ttc" id="acp__model__solver_8cc_html_aec8af5c1be4e1b6d4330e1161028de21"><div class="ttname"><a href="cp__model__solver_8cc.html#aec8af5c1be4e1b6d4330e1161028de21">time_limit</a></div><div class="ttdeci">ModelSharedTimeLimit * time_limit</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__solver_8cc_source.html#l02013">cp_model_solver.cc:2013</a></div></div>
|
|
<div class="ttc" id="aexpr__array_8cc_html_a472a99923cbe11ae7b5a5d157d9ad465"><div class="ttname"><a href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a></div><div class="ttdeci">IntVar * var</div><div class="ttdef"><b>Definition:</b> <a href="expr__array_8cc_source.html#l01874">expr_array.cc:1874</a></div></div>
|
|
<div class="ttc" id="agurobi__interface_8cc_html_a0728f23c9a47655d38e0bf1a2f200bcf"><div class="ttname"><a href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a></div><div class="ttdeci">GRBmodel * model</div><div class="ttdef"><b>Definition:</b> <a href="gurobi__interface_8cc_source.html#l00273">gurobi_interface.cc:273</a></div></div>
|
|
<div class="ttc" id="aimplied__bounds_8h_html"><div class="ttname"><a href="implied__bounds_8h.html">implied_bounds.h</a></div></div>
|
|
<div class="ttc" id="aint__type_8h_html"><div class="ttname"><a href="int__type_8h.html">int_type.h</a></div></div>
|
|
<div class="ttc" id="ainteger_8h_html"><div class="ttname"><a href="integer_8h.html">integer.h</a></div></div>
|
|
<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>
|
|
<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#l00393">cuts.cc:393</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a19a67428513beb394b652edf75b32216"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a19a67428513beb394b652edf75b32216">operations_research::sat::CreateSquareCutGenerator</a></div><div class="ttdeci">CutGenerator CreateSquareCutGenerator(IntegerVariable y, IntegerVariable x, int linearization_level, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01428">cuts.cc:1428</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a1de556a1559f25bd0819655d375f6c8e"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a1de556a1559f25bd0819655d375f6c8e">operations_research::sat::GetPreprocessedLinearConstraint</a></div><div class="ttdeci">LinearConstraint GetPreprocessedLinearConstraint(const LinearConstraint &constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00255">cuts.cc:255</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a32f0016572d69bfcd1f3af811b2043ad"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a32f0016572d69bfcd1f3af811b2043ad">operations_research::sat::CanFormValidKnapsackCover</a></div><div class="ttdeci">bool CanFormValidKnapsackCover(const LinearConstraint &preprocessed_constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00375">cuts.cc:375</a></div></div>
|
|
<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#l00624">cuts.cc:624</a></div></div>
|
|
<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#l00323">cuts.cc:323</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a588b516182cd6d5d8c048dfd76bc5523"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a588b516182cd6d5d8c048dfd76bc5523">operations_research::sat::CanBeFilteredUsingCutLowerBound</a></div><div class="ttdeci">bool CanBeFilteredUsingCutLowerBound(const LinearConstraint &preprocessed_constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00295">cuts.cc:295</a></div></div>
|
|
<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>
|
|
<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#l01917">cuts.cc:1917</a></div></div>
|
|
<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#l01819">cuts.cc:1819</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a88fabb0f851ff07d459b8be401162601"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a88fabb0f851ff07d459b8be401162601">operations_research::sat::BuildMaxAffineUpConstraint</a></div><div class="ttdeci">LinearConstraint BuildMaxAffineUpConstraint(const LinearExpression &target, IntegerVariable var, const std::vector< std::pair< IntegerValue, IntegerValue > > &affines, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l02001">cuts.cc:2001</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a8c8db245a613f2fb46d917cd78100f83"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a8c8db245a613f2fb46d917cd78100f83">operations_research::sat::CanBeFilteredUsingKnapsackUpperBound</a></div><div class="ttdeci">bool CanBeFilteredUsingKnapsackUpperBound(const LinearConstraint &constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const IntegerTrail &integer_trail)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00341">cuts.cc:341</a></div></div>
|
|
<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#l00632">cuts.cc:632</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_ab782d6f91aefca5ee81c3b622e862875"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#ab782d6f91aefca5ee81c3b622e862875">operations_research::sat::CreateMaxAffineCutGenerator</a></div><div class="ttdeci">CutGenerator CreateMaxAffineCutGenerator(LinearExpression target, IntegerVariable var, std::vector< std::pair< IntegerValue, IntegerValue > > affines, const std::string cut_name, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l02037">cuts.cc:2037</a></div></div>
|
|
<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#l00443">cuts.cc:443</a></div></div>
|
|
<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#l00279">cuts.cc:279</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_accb737ae1fad15d6798a4b8bc27cea51"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#accb737ae1fad15d6798a4b8bc27cea51">operations_research::sat::LiftKnapsackCut</a></div><div class="ttdeci">bool LiftKnapsackCut(const LinearConstraint &constraint, const absl::StrongVector< IntegerVariable, double > &lp_values, const std::vector< IntegerValue > &cut_vars_original_coefficients, const IntegerTrail &integer_trail, TimeLimit *time_limit, LinearConstraint *cut)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l00176">cuts.cc:176</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_adf176ac81e34e8fd124d823ee0033f1a"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#adf176ac81e34e8fd124d823ee0033f1a">operations_research::sat::CreateCliqueCutGenerator</a></div><div class="ttdeci">CutGenerator CreateCliqueCutGenerator(const std::vector< IntegerVariable > &base_variables, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l02059">cuts.cc:2059</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_af11d52b4cc77e85f6a523f04642229f3"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#af11d52b4cc77e85f6a523f04642229f3">operations_research::sat::CreatePositiveMultiplicationCutGenerator</a></div><div class="ttdeci">CutGenerator CreatePositiveMultiplicationCutGenerator(IntegerVariable z, IntegerVariable x, IntegerVariable y, int linearization_level, Model *model)</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8cc_source.html#l01341">cuts.cc:1341</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_html"><div class="ttname"><a href="namespaceoperations__research.html">operations_research</a></div><div class="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
|
|
<div class="ttc" id="apack_8cc_html_a750b5d744c39a06bfb13e6eb010e35d0"><div class="ttname"><a href="pack_8cc.html#a750b5d744c39a06bfb13e6eb010e35d0">index</a></div><div class="ttdeci">int index</div><div class="ttdef"><b>Definition:</b> <a href="pack_8cc_source.html#l00509">pack.cc:509</a></div></div>
|
|
<div class="ttc" id="arouting__flow_8cc_html_a2acb49f4df5288066c43610bede123ec"><div class="ttname"><a href="routing__flow_8cc.html#a2acb49f4df5288066c43610bede123ec">capacity</a></div><div class="ttdeci">int64_t capacity</div><div class="ttdef"><b>Definition:</b> <a href="routing__flow_8cc_source.html#l00151">routing_flow.cc:151</a></div></div>
|
|
<div class="ttc" id="asat_2linear__constraint_8h_html"><div class="ttname"><a href="sat_2linear__constraint_8h.html">linear_constraint.h</a></div></div>
|
|
<div class="ttc" id="asat_2lp__utils_8cc_html_a561d7bf12fc7674b3fe0ad2ba2e175a0"><div class="ttname"><a href="sat_2lp__utils_8cc.html#a561d7bf12fc7674b3fe0ad2ba2e175a0">lower_bounds</a></div><div class="ttdeci">std::vector< double > lower_bounds</div><div class="ttdef"><b>Definition:</b> <a href="sat_2lp__utils_8cc_source.html#l00497">sat/lp_utils.cc:497</a></div></div>
|
|
<div class="ttc" id="asat_2lp__utils_8cc_html_a88215c8581662c40eec0fb8621c44af3"><div class="ttname"><a href="sat_2lp__utils_8cc.html#a88215c8581662c40eec0fb8621c44af3">upper_bounds</a></div><div class="ttdeci">std::vector< double > upper_bounds</div><div class="ttdef"><b>Definition:</b> <a href="sat_2lp__utils_8cc_source.html#l00498">sat/lp_utils.cc:498</a></div></div>
|
|
<div class="ttc" id="asat_2model_8h_html"><div class="ttname"><a href="sat_2model_8h.html">model.h</a></div></div>
|
|
<div class="ttc" id="astrong__vector_8h_html"><div class="ttname"><a href="strong__vector_8h.html">strong_vector.h</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_cut_generator_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_cut_generator.html">operations_research::sat::CutGenerator</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00042">cuts.h:42</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_cut_generator_html_a73e4094f2d4e2adbe5e8d79a5b61fcd1"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_cut_generator.html#a73e4094f2d4e2adbe5e8d79a5b61fcd1">operations_research::sat::CutGenerator::vars</a></div><div class="ttdeci">std::vector< IntegerVariable > vars</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00043">cuts.h:43</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_cut_generator_html_a79779673f2fe909d104c37f3b7cc5a48"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_cut_generator.html#a79779673f2fe909d104c37f3b7cc5a48">operations_research::sat::CutGenerator::generate_cuts</a></div><div class="ttdeci">std::function< bool(const absl::StrongVector< IntegerVariable, double > &lp_values, LinearConstraintManager *manager)> generate_cuts</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00047">cuts.h:47</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00117">cuts.h:117</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_a2c25b894240115eebb2e75e2d8491a79"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a2c25b894240115eebb2e75e2d8491a79">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::bound_diff</a></div><div class="ttdeci">IntegerValue bound_diff</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00121">cuts.h:121</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_a6d2822d5e07c3716efcdf73a4ae5eafc"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a6d2822d5e07c3716efcdf73a4ae5eafc">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::is_positive</a></div><div class="ttdeci">bool is_positive</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00120">cuts.h:120</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_a871eaa421116e3c7cd440b6299d0b74d"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a871eaa421116e3c7cd440b6299d0b74d">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::bool_var</a></div><div class="ttdeci">IntegerVariable bool_var</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00122">cuts.h:122</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_a9231f58e9d0f2dafc65c9eb41c979028"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#a9231f58e9d0f2dafc65c9eb41c979028">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::bool_lp_value</a></div><div class="ttdeci">double bool_lp_value</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00118">cuts.h:118</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info_html_ac11e010c276514d6402c772d0651f82f"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_best_implied_bound_info.html#ac11e010c276514d6402c772d0651f82f">operations_research::sat::ImpliedBoundsProcessor::BestImpliedBoundInfo::slack_lp_value</a></div><div class="ttdeci">double slack_lp_value</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00119">cuts.h:119</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html">operations_research::sat::ImpliedBoundsProcessor::SlackInfo</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00087">cuts.h:87</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_a0ee34e5c6fbf075def1a6c2f0c42d040"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a0ee34e5c6fbf075def1a6c2f0c42d040">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::lb</a></div><div class="ttdeci">IntegerValue lb</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00093">cuts.h:93</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_a250583d63e8184c6f9f4deba1125e6bb"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a250583d63e8184c6f9f4deba1125e6bb">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::terms</a></div><div class="ttdeci">std::vector< std::pair< IntegerVariable, IntegerValue > > terms</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00089">cuts.h:89</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_a6e2915dc7e5345d6959390b53f026c5f"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#a6e2915dc7e5345d6959390b53f026c5f">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::ub</a></div><div class="ttdeci">IntegerValue ub</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00094">cuts.h:94</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_acd07f8397a2e61932c8ee17a4e300e23"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#acd07f8397a2e61932c8ee17a4e300e23">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::offset</a></div><div class="ttdeci">IntegerValue offset</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00090">cuts.h:90</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info_html_adb47ac0cff7c9dc4dc5f101d38a91185"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_implied_bounds_processor_1_1_slack_info.html#adb47ac0cff7c9dc4dc5f101d38a91185">operations_research::sat::ImpliedBoundsProcessor::SlackInfo::lp_value</a></div><div class="ttdeci">double lp_value</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00095">cuts.h:95</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_knapsack_item_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_knapsack_item.html">operations_research::sat::KnapsackItem</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00308">cuts.h:308</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_knapsack_item_html_a3ff84545f00a56ba7584b2a7f2cef69c"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_knapsack_item.html#a3ff84545f00a56ba7584b2a7f2cef69c">operations_research::sat::KnapsackItem::profit</a></div><div class="ttdeci">double profit</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00309">cuts.h:309</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_knapsack_item_html_a99108733d00274978a4979dc072bd513"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_knapsack_item.html#a99108733d00274978a4979dc072bd513">operations_research::sat::KnapsackItem::weight</a></div><div class="ttdeci">double weight</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00310">cuts.h:310</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_knapsack_item_html_aa51ab05fd43c2d0962967f9d889c7bb7"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_knapsack_item.html#aa51ab05fd43c2d0962967f9d889c7bb7">operations_research::sat::KnapsackItem::operator></a></div><div class="ttdeci">bool operator>(const KnapsackItem &other) const</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00311">cuts.h:311</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_linear_constraint_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_linear_constraint.html">operations_research::sat::LinearConstraint</a></div><div class="ttdef"><b>Definition:</b> <a href="sat_2linear__constraint_8h_source.html#l00033">sat/linear_constraint.h:33</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_rounding_options_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_rounding_options.html">operations_research::sat::RoundingOptions</a></div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00212">cuts.h:212</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1_rounding_options_html_a01db407e90fac1c31c6705758a057908"><div class="ttname"><a href="structoperations__research_1_1sat_1_1_rounding_options.html#a01db407e90fac1c31c6705758a057908">operations_research::sat::RoundingOptions::max_scaling</a></div><div class="ttdeci">IntegerValue max_scaling</div><div class="ttdef"><b>Definition:</b> <a href="cuts_8h_source.html#l00213">cuts.h:213</a></div></div>
|
|
<div class="ttc" id="atime__limit_8h_html"><div class="ttname"><a href="time__limit_8h.html">time_limit.h</a></div></div>
|
|
</div><!-- fragment --></div><!-- contents -->
|
|
</div><!-- doc-content -->
|
|
<!-- HTML footer for doxygen 1.8.18-->
|
|
<!-- start footer part -->
|
|
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
|
|
<ul>
|
|
<li class="navelem"><a class="el" href="dir_a7cc1eeded8f693d0da6c729bc88c45a.html">ortools</a></li><li class="navelem"><a class="el" href="dir_dddac007a45022d9da6ea1dee012c3b9.html">sat</a></li><li class="navelem"><a class="el" href="cuts_8h.html">cuts.h</a></li>
|
|
<li class="footer">Generated by
|
|
<a href="http://www.doxygen.org/index.html">
|
|
<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.9.2 </li>
|
|
</ul>
|
|
</div>
|
|
</body>
|
|
</html>
|