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<a href="integer__programming_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div>
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<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  </div>
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<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// Simple linear programming example</span></div>
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<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>  </div>
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<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor">#include <iostream></span></div>
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<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="preprocessor">#include <limits></span></div>
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<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  </div>
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<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="preprocessor">#include "absl/flags/parse.h"</span></div>
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<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#include "absl/flags/usage.h"</span></div>
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<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div>
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<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#include "absl/status/statusor.h"</span></div>
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<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include "absl/time/time.h"</span></div>
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<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include "<a class="code" href="math__opt_8h.html">ortools/math_opt/cpp/math_opt.h</a>"</span></div>
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<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  </div>
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<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="keyword">namespace </span>{</div>
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<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> using ::operations_research::math_opt::MathOpt;</div>
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<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> using ::operations_research::math_opt::Result;</div>
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<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> using ::operations_research::math_opt::SolveParametersProto;</div>
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<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> using ::operations_research::math_opt::SOLVER_TYPE_GSCIP;</div>
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<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> using ::operations_research::math_opt::SolveResultProto;</div>
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<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> using ::operations_research::math_opt::SolveStatsProto;</div>
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<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> using ::operations_research::math_opt::Variable;</div>
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<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <a class="code" href="namespaceoperations__research_1_1math__opt.html#a252c66967569c5ab1db4b4d356707fb1">using ::operations_research::math_opt::VariableMap</a>;</div>
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<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  </div>
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<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> constexpr <span class="keywordtype">double</span> <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a> = std::numeric_limits<double>::infinity();</div>
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<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  </div>
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<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment">// Model and solve the problem:</span></div>
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<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment">// max x + 10 * y</span></div>
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<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment">// s.t. x + 7 * y <= 17.5</span></div>
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<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment">// x <= 3.5</span></div>
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<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment">// x in {0.0, 1.0, 2.0, ...,</span></div>
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<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment">// y in {0.0, 1.0, 2.0, ...,</span></div>
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<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment">//</span></div>
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<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keywordtype">void</span> SolveSimpleMIP() {</div>
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<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  MathOpt optimizer(SOLVER_TYPE_GSCIP, <span class="stringliteral">"Integer programming example"</span>);</div>
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<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  </div>
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<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="comment">// Variables</span></div>
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<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keyword">const</span> Variable x = optimizer.AddIntegerVariable(0.0, <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>, <span class="stringliteral">"x"</span>);</div>
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<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keyword">const</span> Variable y = optimizer.AddIntegerVariable(0.0, <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>, <span class="stringliteral">"y"</span>);</div>
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<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  </div>
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<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">// Constraints</span></div>
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<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  optimizer.AddLinearConstraint(x + 7 * y <= 17.5, <span class="stringliteral">"c1"</span>);</div>
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<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  optimizer.AddLinearConstraint(x <= 3.5, <span class="stringliteral">"c2"</span>);</div>
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<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
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<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// Objective</span></div>
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<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  optimizer.objective().Maximize(x + 10 * y);</div>
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<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  </div>
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<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  std::cout << <span class="stringliteral">"Num variables: "</span> << optimizer.num_variables() << std::endl;</div>
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<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  std::cout << <span class="stringliteral">"Num constraints: "</span> << optimizer.num_linear_constraints()</div>
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<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  << std::endl;</div>
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<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  </div>
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<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">const</span> Result result = optimizer.Solve(SolveParametersProto()).value();</div>
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<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  </div>
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<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// Check for warnings.</span></div>
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<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& warning : result.warnings) {</div>
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<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <a class="code" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code" href="log__severity_8h.html#ac9bcbe19995a8140cd4ec61773cd6e67">ERROR</a>) << <span class="stringliteral">"Solver warning: "</span> << warning << std::endl;</div>
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<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  }</div>
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<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">// Check that the problem has an optimal solution.</span></div>
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<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <a class="code" href="base_2logging_8h.html#acdd435d10e595c91b6861a233b8e8432">QCHECK_EQ</a>(result.termination_reason, <a class="code" href="namespaceoperations__research_1_1data_1_1vbp.html#a4604191fbd84a43686f44c25d7bd0161a2579881e7c83261bc21bafb5a5c92cad">SolveResultProto::OPTIMAL</a>)</div>
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<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  << <span class="stringliteral">"Failed to find an optimal solution: "</span> << result.termination_detail;</div>
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<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  </div>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  std::cout << <span class="stringliteral">"Problem solved in "</span> << result.solve_time() << std::endl;</div>
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<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  std::cout << <span class="stringliteral">"Objective value: "</span> << result.objective_value() << std::endl;</div>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  </div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> x_val = result.variable_values().at(x);</div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> y_val = result.variable_values().at(y);</div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  </div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  std::cout << <span class="stringliteral">"Variable values: [x="</span> << x_val << <span class="stringliteral">", y="</span> << y_val << <span class="stringliteral">"]"</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  << std::endl;</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keyword">const</span> SolveStatsProto& stat = result.solve_stats;</div>
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<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  std::cout << <span class="stringliteral">"Simplex iterations: "</span> << stat.simplex_iterations() << std::endl;</div>
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<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  std::cout << <span class="stringliteral">"Barrier iterations: "</span> << stat.barrier_iterations() << std::endl;</div>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  std::cout << <span class="stringliteral">"Branch and bound nodes: "</span> << stat.node_count() << std::endl;</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> }</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> } <span class="comment">// namespace</span></div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  </div>
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<div class="line"><a name="l00088"></a><span class="lineno"><a class="line" href="integer__programming_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627"> 88</a></span> <span class="keywordtype">int</span> <a class="code" href="integer__programming_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span>** argv) {</div>
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<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <a class="code" href="namespacegoogle.html#a1749056ff206ebc4f581e6bc0bae841d">google::InitGoogleLogging</a>(argv[0]);</div>
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<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> absl::ParseCommandLine(argc, argv);</div>
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<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  SolveSimpleMIP();</div>
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<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> }</div>
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<div class="ttc" id="abase_2logging_8h_html_accad43a85d781d53381cd53a9894b6ae"><div class="ttname"><a href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a></div><div class="ttdeci">#define LOG(severity)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00423">base/logging.h:423</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_acdd435d10e595c91b6861a233b8e8432"><div class="ttname"><a href="base_2logging_8h.html#acdd435d10e595c91b6861a233b8e8432">QCHECK_EQ</a></div><div class="ttdeci">#define QCHECK_EQ</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00040">base/logging.h:40</a></div></div>
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<div class="ttc" id="ainteger__programming_8cc_html_a3c04138a5bfe5d72780bb7e82a18e627"><div class="ttname"><a href="integer__programming_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a></div><div class="ttdeci">int main(int argc, char **argv)</div><div class="ttdef"><b>Definition:</b> <a href="integer__programming_8cc_source.html#l00088">integer_programming.cc:88</a></div></div>
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<div class="ttc" id="alog__severity_8h_html_ac9bcbe19995a8140cd4ec61773cd6e67"><div class="ttname"><a href="log__severity_8h.html#ac9bcbe19995a8140cd4ec61773cd6e67">ERROR</a></div><div class="ttdeci">const int ERROR</div><div class="ttdef"><b>Definition:</b> <a href="log__severity_8h_source.html#l00032">log_severity.h:32</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1data_1_1vbp_html_a4604191fbd84a43686f44c25d7bd0161a2579881e7c83261bc21bafb5a5c92cad"><div class="ttname"><a href="namespaceoperations__research_1_1data_1_1vbp.html#a4604191fbd84a43686f44c25d7bd0161a2579881e7c83261bc21bafb5a5c92cad">operations_research::data::vbp::OPTIMAL</a></div><div class="ttdeci">@ OPTIMAL</div><div class="ttdef"><b>Definition:</b> <a href="vector__bin__packing_8pb_8h_source.html#l00088">vector_bin_packing.pb.h:88</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a252c66967569c5ab1db4b4d356707fb1"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a252c66967569c5ab1db4b4d356707fb1">operations_research::math_opt::VariableMap</a></div><div class="ttdeci">IdMap< Variable, V > VariableMap</div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8h_source.html#l00141">variable_and_expressions.h:141</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_ad9f50c9313b35cc1e8887057dc4d9645"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">operations_research::math_opt::kInf</a></div><div class="ttdeci">constexpr double kInf</div><div class="ttdef"><b>Definition:</b> <a href="ids__validator_8cc_source.html#l00035">ids_validator.cc:35</a></div></div>
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