265 lines
39 KiB
HTML
265 lines
39 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 1.8.18"/>
|
|
<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
|
<title>OR-Tools: linear_relaxation.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">8.0</span>
|
|
</div>
|
|
</td>
|
|
</tr>
|
|
</tbody>
|
|
</table>
|
|
</div>
|
|
<!-- end header part -->
|
|
<!-- Generated by Doxygen 1.8.18 -->
|
|
<script type="text/javascript">
|
|
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
var searchBox = new SearchBox("searchBox", "search",false,'Search');
|
|
/* @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:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
$(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:cf05388f2679ee054f2beb29a391d25f4e673ac3&dn=gpl-2.0.txt GPL-v2 */
|
|
$(document).ready(function(){initNavTree('linear__relaxation_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">linear_relaxation.h</div> </div>
|
|
</div><!--header-->
|
|
<div class="contents">
|
|
<a href="linear__relaxation_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 Google LLC</span></div>
|
|
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
|
|
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
|
|
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
|
|
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
|
|
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
|
|
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
|
|
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
|
|
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
|
|
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
|
|
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
|
|
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#ifndef OR_TOOLS_SAT_LINEAR_RELAXATION_H_</span></div>
|
|
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor">#define OR_TOOLS_SAT_LINEAR_RELAXATION_H_</span></div>
|
|
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  </div>
|
|
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <vector></span></div>
|
|
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  </div>
|
|
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "<a class="code" href="cp__model__loader_8h.html">ortools/sat/cp_model_loader.h</a>"</span></div>
|
|
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "<a class="code" href="integer_8h.html">ortools/sat/integer.h</a>"</span></div>
|
|
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "<a class="code" href="linear__constraint_8h.html">ortools/sat/linear_constraint.h</a>"</span></div>
|
|
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "<a class="code" href="linear__programming__constraint_8h.html">ortools/sat/linear_programming_constraint.h</a>"</span></div>
|
|
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include "<a class="code" href="sat_2model_8h.html">ortools/sat/model.h</a>"</span></div>
|
|
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  </div>
|
|
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="keyword">namespace </span><a class="code" href="namespaceoperations__research.html">operations_research</a> {</div>
|
|
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">namespace </span>sat {</div>
|
|
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  </div>
|
|
<div class="line"><a name="l00028"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1LinearRelaxation.html"> 28</a></span> <span class="keyword">struct </span><a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html">LinearRelaxation</a> {</div>
|
|
<div class="line"><a name="l00029"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1LinearRelaxation.html#a787dea05b34122764c7fb5fd13e9a1c9"> 29</a></span>  std::vector<LinearConstraint> <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html#a787dea05b34122764c7fb5fd13e9a1c9">linear_constraints</a>;</div>
|
|
<div class="line"><a name="l00030"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1LinearRelaxation.html#a0bffb74eb458b339aa75f20b6c982a60"> 30</a></span>  std::vector<std::vector<Literal>> <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html#a0bffb74eb458b339aa75f20b6c982a60">at_most_ones</a>;</div>
|
|
<div class="line"><a name="l00031"></a><span class="lineno"><a class="line" href="structoperations__research_1_1sat_1_1LinearRelaxation.html#ae6fdc05264dc58e553116fe3d9dbe236"> 31</a></span>  std::vector<CutGenerator> <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html#ae6fdc05264dc58e553116fe3d9dbe236">cut_generators</a>;</div>
|
|
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> };</div>
|
|
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  </div>
|
|
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// If the given IntegerVariable is fully encoded (li <=> var == xi), adds to the</span></div>
|
|
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">// constraints vector the following linear relaxation of its encoding:</span></div>
|
|
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment">// - Sum li == 1</span></div>
|
|
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment">// - Sum li * xi == var</span></div>
|
|
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// Note that all the literal (li) of the encoding must have an IntegerView,</span></div>
|
|
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// otherwise this function just does nothing.</span></div>
|
|
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// Returns false, if the relaxation couldn't be added because this variable</span></div>
|
|
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// was not fully encoded or not all its associated literal had a view.</span></div>
|
|
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="keywordtype">bool</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a5564bcb1461ad3cbce7f744c3fb58c6b">AppendFullEncodingRelaxation</a>(IntegerVariable <a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1sat_1_1Model.html">Model</a>& <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
|
|
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html">LinearRelaxation</a>* relaxation);</div>
|
|
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
|
|
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment">// When the set of (li <=> var == xi) do not cover the full domain of xi, we</span></div>
|
|
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// do something a bit more involved. Let min/max the min and max value of the</span></div>
|
|
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">// domain of var that is NOT part of the encoding. We add:</span></div>
|
|
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">// - Sum li <= 1</span></div>
|
|
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment">// - (Sum li * xi) + (1 - Sum li) * min <= var</span></div>
|
|
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// - var <= (Sum li * xi) + (1 - Sum li) * max</span></div>
|
|
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// Note that if it turns out that the partial encoding is full, this will just</span></div>
|
|
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment">// use the same encoding as AppendFullEncodingRelaxation(). Any literal that</span></div>
|
|
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">// do not have an IntegerView will be skipped, there is no point adding them</span></div>
|
|
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment">// to the LP if they are not used in any other constraint, the relaxation will</span></div>
|
|
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment">// have the same "power" without them.</span></div>
|
|
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#aa490b08ec514e9c567ff098d53353db1">AppendPartialEncodingRelaxation</a>(IntegerVariable <a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>, <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1sat_1_1Model.html">Model</a>& <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
|
|
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html">LinearRelaxation</a>* relaxation);</div>
|
|
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
|
|
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// This is a different relaxation that use a partial set of literal li such that</span></div>
|
|
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="comment">// (li <=> var >= xi). In which case we use the following encoding:</span></div>
|
|
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">// - li >= l_{i+1} for all possible i. Note that the xi need to be sorted.</span></div>
|
|
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment">// - var >= min + l0 * (x0 - min) + Sum_{i>0} li * (xi - x_{i-1})</span></div>
|
|
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// - and same as above for NegationOf(var) for the upper bound.</span></div>
|
|
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// Like for AppendPartialEncodingRelaxation() we skip any li that do not have</span></div>
|
|
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// an integer view.</span></div>
|
|
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#aff14a4092356fceea657393b7b234b7f">AppendPartialGreaterThanEncodingRelaxation</a>(IntegerVariable <a class="code" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>,</div>
|
|
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1sat_1_1Model.html">Model</a>& <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
|
|
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html">LinearRelaxation</a>* relaxation);</div>
|
|
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  </div>
|
|
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// Adds linearization of different types of constraints.</span></div>
|
|
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a94739087f86f5e1b7679d5371d4d9f4b">TryToLinearizeConstraint</a>(<span class="keyword">const</span> CpModelProto& <a class="code" href="cp__model__solver_8cc.html#a6ac76d8a372013f67c4973012948ec84">model_proto</a>,</div>
|
|
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keyword">const</span> ConstraintProto& <a class="code" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>, <a class="code" href="classoperations__research_1_1sat_1_1Model.html">Model</a>* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
|
|
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordtype">int</span> linearization_level,</div>
|
|
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html">LinearRelaxation</a>* relaxation);</div>
|
|
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  </div>
|
|
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment">// Adds linearization of no overlap constraints. For each pair of intervals, we</span></div>
|
|
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">// add linear constraints enforcing precedence of one over other. We check the</span></div>
|
|
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// bounds and only linearize the pairs which are intersecting. We ignore the</span></div>
|
|
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment">// intervals with enforcement literal. Note that we might create new variables</span></div>
|
|
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment">// for each pair of intervals and this might cause addition of quadratic number</span></div>
|
|
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// of new variables.</span></div>
|
|
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#acc7b292198fce358615d0295cd1c3078">AppendNoOverlapRelaxation</a>(<span class="keyword">const</span> CpModelProto& <a class="code" href="cp__model__solver_8cc.html#a6ac76d8a372013f67c4973012948ec84">model_proto</a>,</div>
|
|
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keyword">const</span> ConstraintProto& <a class="code" href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a>,</div>
|
|
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordtype">int</span> linearization_level, <a class="code" href="classoperations__research_1_1sat_1_1Model.html">Model</a>* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
|
|
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html">LinearRelaxation</a>* relaxation);</div>
|
|
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  </div>
|
|
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment">// Adds linearization of int max constraints. This can also be used to linearize</span></div>
|
|
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// int min with negated variables.</span></div>
|
|
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a69d42878d739b511b1abd4843592cdb3">AppendMaxRelaxation</a>(IntegerVariable target,</div>
|
|
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keyword">const</span> std::vector<IntegerVariable>& vars,</div>
|
|
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordtype">int</span> linearization_level, <a class="code" href="classoperations__research_1_1sat_1_1Model.html">Model</a>* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
|
|
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html">LinearRelaxation</a>* relaxation);</div>
|
|
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  </div>
|
|
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment">// Adds linearization of int max constraints. Returns a vector of z vars such</span></div>
|
|
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// that: z_vars[l] == 1 <=> target = exprs[l].</span></div>
|
|
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// Consider the Lin Max constraint with d expressions and n variables in the</span></div>
|
|
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment">// form: target = max {exprs[l] = Sum (wli * xi + bl)}. l in {1,..,d}.</span></div>
|
|
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment">// Li = lower bound of xi</span></div>
|
|
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment">// Ui = upper bound of xi.</span></div>
|
|
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment">// Let zl be in {0,1} for all l in {1,..,d}.</span></div>
|
|
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// The target = exprs[l] when zl = 1.</span></div>
|
|
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <span class="comment">//</span></div>
|
|
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment">// The following is a valid linearization for Lin Max.</span></div>
|
|
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span> <span class="comment">// target >= exprs[l], for all l in {1,..,d}</span></div>
|
|
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// target <= Sum_i(wki * xi) + Sum_l((Nkl + bl) * zl), for all k in {1,..,d}</span></div>
|
|
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// Where Nkl is a large number defined as:</span></div>
|
|
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// Nkl = Sum_i(max((wli - wki)*Li, (wli - wki)*Ui))</span></div>
|
|
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span> <span class="comment">// = Sum (max corner difference for variable i, target expr k, max expr l)</span></div>
|
|
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment">// Reference: "Strong mixed-integer programming formulations for trained neural</span></div>
|
|
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment">// networks" by Ross Anderson et. (https://arxiv.org/pdf/1811.01988.pdf).</span></div>
|
|
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> <span class="comment">// TODO(user): Support linear expression as target.</span></div>
|
|
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> std::vector<IntegerVariable> <a class="code" href="namespaceoperations__research_1_1sat.html#a130634b7e74e7c3eee64967e6bd5bb15">AppendLinMaxRelaxation</a>(</div>
|
|
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  IntegerVariable target, <span class="keyword">const</span> std::vector<LinearExpression>& exprs,</div>
|
|
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <a class="code" href="classoperations__research_1_1sat_1_1Model.html">Model</a>* <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>, <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html">LinearRelaxation</a>* relaxation);</div>
|
|
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div>
|
|
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// Appends linear constraints to the relaxation. This also handles the</span></div>
|
|
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment">// relaxation of linear constraints with enforcement literals.</span></div>
|
|
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment">// A linear constraint lb <= ax <= ub with enforcement literals {ei} is relaxed</span></div>
|
|
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> <span class="comment">// as following.</span></div>
|
|
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="comment">// lb <= (Sum Negated(ei) * (lb - implied_lb)) + ax <= inf</span></div>
|
|
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> <span class="comment">// -inf <= (Sum Negated(ei) * (ub - implied_ub)) + ax <= ub</span></div>
|
|
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span> <span class="comment">// Where implied_lb and implied_ub are trivial lower and upper bounds of the</span></div>
|
|
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// constraint.</span></div>
|
|
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="keywordtype">void</span> <a class="code" href="namespaceoperations__research_1_1sat.html#a1d3cc11409a085647b7fb94b62a82ae5">AppendLinearConstraintRelaxation</a>(<span class="keyword">const</span> ConstraintProto& constraint_proto,</div>
|
|
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> linearization_level,</div>
|
|
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">const</span> <a class="code" href="classoperations__research_1_1sat_1_1Model.html">Model</a>& <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>,</div>
|
|
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <a class="code" href="structoperations__research_1_1sat_1_1LinearRelaxation.html">LinearRelaxation</a>* relaxation);</div>
|
|
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  </div>
|
|
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span> } <span class="comment">// namespace sat</span></div>
|
|
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> } <span class="comment">// namespace operations_research</span></div>
|
|
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  </div>
|
|
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="preprocessor">#endif // OR_TOOLS_SAT_LINEAR_RELAXATION_H_</span></div>
|
|
</div><!-- fragment --></div><!-- contents -->
|
|
</div><!-- doc-content -->
|
|
<div class="ttc" id="aexpr__array_8cc_html_a472a99923cbe11ae7b5a5d157d9ad465"><div class="ttname"><a href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a></div><div class="ttdeci">IntVar * var</div><div class="ttdef"><b>Definition:</b> <a href="expr__array_8cc_source.html#l01858">expr_array.cc:1858</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1LinearRelaxation_html"><div class="ttname"><a href="structoperations__research_1_1sat_1_1LinearRelaxation.html">operations_research::sat::LinearRelaxation</a></div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8h_source.html#l00028">linear_relaxation.h:28</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a5564bcb1461ad3cbce7f744c3fb58c6b"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a5564bcb1461ad3cbce7f744c3fb58c6b">operations_research::sat::AppendFullEncodingRelaxation</a></div><div class="ttdeci">bool AppendFullEncodingRelaxation(IntegerVariable var, const Model &model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00032">linear_relaxation.cc:32</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_acc7b292198fce358615d0295cd1c3078"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#acc7b292198fce358615d0295cd1c3078">operations_research::sat::AppendNoOverlapRelaxation</a></div><div class="ttdeci">void AppendNoOverlapRelaxation(const CpModelProto &model_proto, const ConstraintProto &ct, int linearization_level, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00483">linear_relaxation.cc:483</a></div></div>
|
|
<div class="ttc" id="alinear__constraint_8h_html"><div class="ttname"><a href="linear__constraint_8h.html">linear_constraint.h</a></div></div>
|
|
<div class="ttc" id="acp__model__solver_8cc_html_a6ac76d8a372013f67c4973012948ec84"><div class="ttname"><a href="cp__model__solver_8cc.html#a6ac76d8a372013f67c4973012948ec84">model_proto</a></div><div class="ttdeci">CpModelProto const * model_proto</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__solver_8cc_source.html#l02023">cp_model_solver.cc:2023</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="anamespaceoperations__research_1_1sat_html_a130634b7e74e7c3eee64967e6bd5bb15"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a130634b7e74e7c3eee64967e6bd5bb15">operations_research::sat::AppendLinMaxRelaxation</a></div><div class="ttdeci">std::vector< IntegerVariable > AppendLinMaxRelaxation(IntegerVariable target, const std::vector< LinearExpression > &exprs, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00628">linear_relaxation.cc:628</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">The vehicle routing library lets one model and solve generic vehicle routing problems ranging from th...</div><div class="ttdef"><b>Definition:</b> <a href="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
|
|
<div class="ttc" id="aclassoperations__research_1_1sat_1_1Model_html"><div class="ttname"><a href="classoperations__research_1_1sat_1_1Model.html">operations_research::sat::Model</a></div><div class="ttdoc">Class that owns everything related to a particular optimization model.</div><div class="ttdef"><b>Definition:</b> <a href="sat_2model_8h_source.html#l00038">sat/model.h:38</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_aa490b08ec514e9c567ff098d53353db1"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#aa490b08ec514e9c567ff098d53353db1">operations_research::sat::AppendPartialEncodingRelaxation</a></div><div class="ttdeci">void AppendPartialEncodingRelaxation(IntegerVariable var, const Model &model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00109">linear_relaxation.cc:109</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1LinearRelaxation_html_ae6fdc05264dc58e553116fe3d9dbe236"><div class="ttname"><a href="structoperations__research_1_1sat_1_1LinearRelaxation.html#ae6fdc05264dc58e553116fe3d9dbe236">operations_research::sat::LinearRelaxation::cut_generators</a></div><div class="ttdeci">std::vector< CutGenerator > cut_generators</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8h_source.html#l00031">linear_relaxation.h:31</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a69d42878d739b511b1abd4843592cdb3"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a69d42878d739b511b1abd4843592cdb3">operations_research::sat::AppendMaxRelaxation</a></div><div class="ttdeci">void AppendMaxRelaxation(IntegerVariable target, const std::vector< IntegerVariable > &vars, int linearization_level, Model *model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00554">linear_relaxation.cc:554</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1LinearRelaxation_html_a787dea05b34122764c7fb5fd13e9a1c9"><div class="ttname"><a href="structoperations__research_1_1sat_1_1LinearRelaxation.html#a787dea05b34122764c7fb5fd13e9a1c9">operations_research::sat::LinearRelaxation::linear_constraints</a></div><div class="ttdeci">std::vector< LinearConstraint > linear_constraints</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8h_source.html#l00029">linear_relaxation.h:29</a></div></div>
|
|
<div class="ttc" id="ademon__profiler_8cc_html_a05da18ca9c7b657a4a6ea24e07c9b695"><div class="ttname"><a href="demon__profiler_8cc.html#a05da18ca9c7b657a4a6ea24e07c9b695">ct</a></div><div class="ttdeci">const Constraint * ct</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00042">demon_profiler.cc:42</a></div></div>
|
|
<div class="ttc" id="astructoperations__research_1_1sat_1_1LinearRelaxation_html_a0bffb74eb458b339aa75f20b6c982a60"><div class="ttname"><a href="structoperations__research_1_1sat_1_1LinearRelaxation.html#a0bffb74eb458b339aa75f20b6c982a60">operations_research::sat::LinearRelaxation::at_most_ones</a></div><div class="ttdeci">std::vector< std::vector< Literal > > at_most_ones</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8h_source.html#l00030">linear_relaxation.h:30</a></div></div>
|
|
<div class="ttc" id="agurobi__interface_8cc_html_a0728f23c9a47655d38e0bf1a2f200bcf"><div class="ttname"><a href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a></div><div class="ttdeci">GRBmodel * model</div><div class="ttdef"><b>Definition:</b> <a href="gurobi__interface_8cc_source.html#l00195">gurobi_interface.cc:195</a></div></div>
|
|
<div class="ttc" id="acp__model__loader_8h_html"><div class="ttname"><a href="cp__model__loader_8h.html">cp_model_loader.h</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a1d3cc11409a085647b7fb94b62a82ae5"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a1d3cc11409a085647b7fb94b62a82ae5">operations_research::sat::AppendLinearConstraintRelaxation</a></div><div class="ttdeci">void AppendLinearConstraintRelaxation(const ConstraintProto &constraint_proto, const int linearization_level, const Model &model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00725">linear_relaxation.cc:725</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_aff14a4092356fceea657393b7b234b7f"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#aff14a4092356fceea657393b7b234b7f">operations_research::sat::AppendPartialGreaterThanEncodingRelaxation</a></div><div class="ttdeci">void AppendPartialGreaterThanEncodingRelaxation(IntegerVariable var, const Model &model, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00184">linear_relaxation.cc:184</a></div></div>
|
|
<div class="ttc" id="anamespaceoperations__research_1_1sat_html_a94739087f86f5e1b7679d5371d4d9f4b"><div class="ttname"><a href="namespaceoperations__research_1_1sat.html#a94739087f86f5e1b7679d5371d4d9f4b">operations_research::sat::TryToLinearizeConstraint</a></div><div class="ttdeci">void TryToLinearizeConstraint(const CpModelProto &model_proto, const ConstraintProto &ct, Model *model, int linearization_level, LinearRelaxation *relaxation)</div><div class="ttdef"><b>Definition:</b> <a href="linear__relaxation_8cc_source.html#l00314">linear_relaxation.cc:314</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__programming__constraint_8h_html"><div class="ttname"><a href="linear__programming__constraint_8h.html">linear_programming_constraint.h</a></div></div>
|
|
<!-- 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="linear__relaxation_8h.html">linear_relaxation.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> 1.8.18 </li>
|
|
</ul>
|
|
</div>
|
|
</body>
|
|
</html>
|