502 lines
81 KiB
HTML
502 lines
81 KiB
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<div class="headertitle"><div class="title">tsp.cc</div></div>
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<a href="tsp_8cc.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>
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<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>
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<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>
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<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>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<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>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<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>
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<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>
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<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>
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<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>
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<div class="line"><a id="l00012" 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 id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// A minimal TSP solver using MathOpt.</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">//</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">// In the Euclidean Traveling Salesperson Problem (TSP), you are given a list of</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">// n cities, each with an (x, y) coordinate, and you must find an order to visit</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// the cities in to minimize the (Euclidean) travel distance.</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">//</span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">// The MIP "cutset" formulation for the problem is as follows:</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">// * Data:</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// n: An integer, the number of cities</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// (x_i, y_i): a pair of floats for each i in 1..n, the location of each</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">// city</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">// d_ij for all (i, j) pairs of cities, the distance between city i and j.</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// * Decision variables:</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// x_ij: A binary variable, indicates if the edge connecting i and j is</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// used. Note that x_ij == x_ji, because the problem is symmetric. We</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// only create variables for i < j, and have x_ji as an alias for</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// x_ij.</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// * MIP model:</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// minimize sum_{i=1}^n sum_{j=1, j < i}^n d_ij * x_ij</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">// s.t. sum_{j=1, j != i}^n x_ij = 2 for all i = 1..n</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// sum_{i in S} sum_{j not in S} x_ij >= 2 for all S subset {1,...,n}</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// |S| >= 3, |S| <= n - 3</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// x_ij in {0, 1}</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// The first set of constraints are called the degree constraints, and the</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// second set of constraints are called the cutset constraints. There are</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// exponentially many cutset, so we cannot add them all at the start of the</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// solve. Instead, we will use a solver callback to view each integer solution</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// and add any violated cutset constraints that exist.</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">//</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// Note that, while there are exponentially many cutset constraints, we can</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// quickly identify violated ones by exploiting that the solution is integer</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// and the degree constraints are all already in the model and satisfied. As a</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// result, the graph n nodes and edges when x_ij = 1 will be a degree two graph,</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// so it will be a collection of cycles. If it is a single large cycle, then the</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// solution is feasible, and if there multiple cycles, then taking the nodes of</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// any cycle as S produces a violated cutset constraint.</span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">//</span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// Note that this is a minimal TSP solution, more sophisticated MIP methods are</span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">// possible.</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> </div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="preprocessor">#include <iostream></span></div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="preprocessor">#include <optional></span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="preprocessor">#include "absl/flags/flag.h"</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="preprocessor">#include "absl/random/random.h"</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="preprocessor">#include "absl/random/uniform_real_distribution.h"</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="preprocessor">#include "absl/strings/str_cat.h"</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="preprocessor">#include "absl/strings/str_join.h"</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="preprocessor">#include "<a class="code" href="base_2file_8h.html">ortools/base/file.h</a>"</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="preprocessor">#include "<a class="code" href="init__google_8h.html">ortools/base/init_google.h</a>"</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</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 id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="preprocessor">#include "<a class="code" href="status__builder_8h.html">ortools/base/status_builder.h</a>"</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="preprocessor">#include "<a class="code" href="base_2status__macros_8h.html">ortools/base/status_macros.h</a>"</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</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 id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="preprocessor">#include "<a class="code" href="port_2proto__utils_8h.html">ortools/port/proto_utils.h</a>"</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> </div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"><a class="line" href="tsp_8cc.html#ab2f5b46a236867410804f4dae7707d3e"> 70</a></span><a class="code hl_function" href="tsp_8cc.html#ab2f5b46a236867410804f4dae7707d3e">ABSL_FLAG</a>(<span class="keywordtype">int</span>, num_cities, 50, <span class="stringliteral">"Number of cities in random TSP."</span>);</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"><a class="line" href="tsp_8cc.html#aae0a4cd20a5753e456ab215ff17332a7"> 71</a></span><a class="code hl_function" href="tsp_8cc.html#ab2f5b46a236867410804f4dae7707d3e">ABSL_FLAG</a>(std::string, output, <span class="stringliteral">""</span>,</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="stringliteral">"Write a svg of the solution here, or to standard out if empty."</span>);</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"><a class="line" href="tsp_8cc.html#a3a33d3a6331cde05f7d80f5cba8af3ce"> 73</a></span><a class="code hl_function" href="tsp_8cc.html#ab2f5b46a236867410804f4dae7707d3e">ABSL_FLAG</a>(<span class="keywordtype">bool</span>, test_instance, <span class="keyword">false</span>,</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="stringliteral">"Solve the test TSP instead of a random instance."</span>);</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"><a class="line" href="tsp_8cc.html#a6d9f66e65d69fb966ccce0a201fcadb4"> 75</a></span><a class="code hl_function" href="tsp_8cc.html#ab2f5b46a236867410804f4dae7707d3e">ABSL_FLAG</a>(<span class="keywordtype">int</span>, threads, 0,</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="stringliteral">"How many threads to solve with, or solver default if <= 0."</span>);</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> </div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research_1_1math__opt.html">math_opt</a> = <a class="code hl_namespace" href="namespaceoperations__research_1_1math__opt.html">operations_research::math_opt</a>;</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="keyword">using</span> Cycle = std::vector<int>;</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> </div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><span class="comment">// Creates variables modeling the undirected edges for the TSP. For every (i, j)</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span><span class="comment">// pair in [0,n) * [0, n), a variable is created only for j < i, but querying</span></div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="comment">// for the variable x_ij with j > i returns x_ji. Querying for x_ii (which does</span></div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span><span class="comment">// not exist) gives a CHECK failure.</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="comment">//</span></div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="comment">// The Model object passed in to create EdgeVariables must outlive this.</span></div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="keyword">class </span>EdgeVariables {</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> EdgeVariables(<a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model.html">math_opt::Model</a>& <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>, <span class="keyword">const</span> <span class="keywordtype">int</span> n) {</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> variables_.resize(n);</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; ++i) {</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> variables_[i].reserve(i);</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < i; ++j) {</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> variables_[i].push_back(</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddBinaryVariable(absl::StrCat(<span class="stringliteral">"e_"</span>, i, <span class="stringliteral">"_"</span>, j)));</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> }</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> }</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> </div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_variable.html">math_opt::Variable</a> get(<span class="keyword">const</span> <span class="keywordtype">int</span> i, <span class="keyword">const</span> <span class="keywordtype">int</span> j)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <a class="code hl_define" href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a>(i, j);</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">return</span> i > j ? variables_[i][j] : variables_[j][i];</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> }</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordtype">int</span> num_cities()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> variables_.size(); }</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> std::vector<std::vector<math_opt::Variable>> variables_;</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span>};</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span><span class="comment">// Produces a random TSP problem where cities have random locations that are</span></div>
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||
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span><span class="comment">// I.I.D Uniform [0, 1].</span></div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span>std::vector<std::pair<double, double>> RandomCities(<span class="keywordtype">int</span> num_cities) {</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> absl::BitGen rand;</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> std::vector<std::pair<double, double>> cities;</div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_cities; ++i) {</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> cities.push_back({absl::Uniform<double>(rand, 0.0, 1.0),</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> absl::Uniform<double>(rand, 0.0, 1.0)});</div>
|
||
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> }</div>
|
||
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordflow">return</span> cities;</div>
|
||
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span>}</div>
|
||
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> </div>
|
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span>std::vector<std::pair<double, double>> TestCities() {</div>
|
||
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordflow">return</span> {{0, 0}, {0, 0.1}, {0.1, 0}, {0.1, 0.1},</div>
|
||
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> {1, 0}, {1, 0.1}, {0.9, 0}, {0.9, 0.1}};</div>
|
||
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span>}</div>
|
||
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
|
||
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="comment">// Given an n city TSP instance, computes the n by n distance matrix using the</span></div>
|
||
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span><span class="comment">// Euclidean distance.</span></div>
|
||
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span>std::vector<std::vector<double>> DistanceMatrix(</div>
|
||
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keyword">const</span> std::vector<std::pair<double, double>>& cities) {</div>
|
||
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_cities = cities.size();</div>
|
||
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> std::vector<std::vector<double>> distance_matrix(</div>
|
||
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> num_cities, std::vector<double>(num_cities, 0.0));</div>
|
||
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < num_cities; ++i) {</div>
|
||
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < num_cities; ++j) {</div>
|
||
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">if</span> (i != j) {</div>
|
||
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keyword">const</span> <span class="keywordtype">double</span> dx = cities[i].first - cities[j].first;</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keyword">const</span> <span class="keywordtype">double</span> dy = cities[i].second - cities[j].second;</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> distance_matrix[i][j] = std::sqrt(dx * dx + dy * dy);</div>
|
||
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> }</div>
|
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</div>
|
||
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> }</div>
|
||
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordflow">return</span> distance_matrix;</div>
|
||
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span>}</div>
|
||
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> </div>
|
||
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span><span class="comment">// Given the EdgeVariables and a var_values containing the value of each edge in</span></div>
|
||
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span><span class="comment">// a solution, returns an n by n boolean matrix of which edges are used (with</span></div>
|
||
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span><span class="comment">// false diagonal elements). It is assumed that var_values are approximately 0-1</span></div>
|
||
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span><span class="comment">// integer.</span></div>
|
||
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span>std::vector<std::vector<bool>> EdgeValues(</div>
|
||
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keyword">const</span> EdgeVariables& edge_vars,</div>
|
||
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_id_map.html">math_opt::VariableMap<double></a>& var_values) {</div>
|
||
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n = edge_vars.num_cities();</div>
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||
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> std::vector<std::vector<bool>> edge_values(n, std::vector<bool>(n, <span class="keyword">false</span>));</div>
|
||
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; ++i) {</div>
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||
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < n; ++j) {</div>
|
||
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="keywordflow">if</span> (i != j) {</div>
|
||
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> edge_values[i][j] = var_values.<a class="code hl_function" href="classoperations__research_1_1math__opt_1_1_id_map.html#ab2a3f17d02b118e3876034e67fdef6d3">at</a>(edge_vars.get(i, j)) > 0.5;</div>
|
||
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> }</div>
|
||
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> }</div>
|
||
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> }</div>
|
||
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="keywordflow">return</span> edge_values;</div>
|
||
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span>}</div>
|
||
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> </div>
|
||
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span><span class="comment">// Given an n by n boolean matrix of edge values, returns a cycle decomposition.</span></div>
|
||
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span><span class="comment">// it is assumed that edge values respects the degree constraints (each row has</span></div>
|
||
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span><span class="comment">// only two true entries). Each cycle is represented as a list of cities with</span></div>
|
||
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span><span class="comment">// no repeats.</span></div>
|
||
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span>std::vector<Cycle> FindCycles(</div>
|
||
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keyword">const</span> std::vector<std::vector<bool>>& edge_values) {</div>
|
||
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// Algorithm: maintain a "visited" bit for each city indicating if we have</span></div>
|
||
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="comment">// formed a cycle containing this city. Consider the cities in order. When you</span></div>
|
||
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="comment">// find an unvisited city, start a new cycle beginning at this city. Then,</span></div>
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||
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="comment">// build the cycle by finding an unvisited neighbor until no such neighbor</span></div>
|
||
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="comment">// exists (every city will have two neighbors, but eventually both will be</span></div>
|
||
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// visited). To find the "unvisited neighbor", we simply do a linear scan</span></div>
|
||
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="comment">// over the cities, checking both the adjacency matrix and the visited bit.</span></div>
|
||
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|
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="comment">//</span></div>
|
||
|
|
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// Note that for this algorithm, in each cycle, the city with lowest index</span></div>
|
||
|
|
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="comment">// will be first, and the cycles will be sorted by their city of lowest index.</span></div>
|
||
|
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="comment">// This is an implementation detail and should not be relied upon.</span></div>
|
||
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n = edge_values.size();</div>
|
||
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> std::vector<Cycle> result;</div>
|
||
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> std::vector<bool> visited(n, <span class="keyword">false</span>);</div>
|
||
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; ++i) {</div>
|
||
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <span class="keywordflow">if</span> (visited[i]) {</div>
|
||
|
|
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="keywordflow">continue</span>;</div>
|
||
|
|
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> }</div>
|
||
|
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> std::vector<int> cycle;</div>
|
||
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> std::optional<int> <a class="code hl_variable" href="constraint__solver_8cc.html#a395f613555f398dd389670bb4c2a4599">next</a> = i;</div>
|
||
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keywordflow">while</span> (<a class="code hl_variable" href="constraint__solver_8cc.html#a395f613555f398dd389670bb4c2a4599">next</a>.has_value()) {</div>
|
||
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> cycle.push_back(*<a class="code hl_variable" href="constraint__solver_8cc.html#a395f613555f398dd389670bb4c2a4599">next</a>);</div>
|
||
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|
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> visited[*<a class="code hl_variable" href="constraint__solver_8cc.html#a395f613555f398dd389670bb4c2a4599">next</a>] = <span class="keyword">true</span>;</div>
|
||
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <span class="keywordtype">int</span> current = *<a class="code hl_variable" href="constraint__solver_8cc.html#a395f613555f398dd389670bb4c2a4599">next</a>;</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <a class="code hl_variable" href="constraint__solver_8cc.html#a395f613555f398dd389670bb4c2a4599">next</a> = std::nullopt;</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// Scan for an unvisited neighbor. We can start at i+1 since we know that</span></div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <span class="comment">// everything from i back is visited.</span></div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < n; ++j) {</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="keywordflow">if</span> (!visited[j] && edge_values[current][j]) {</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <a class="code hl_variable" href="constraint__solver_8cc.html#a395f613555f398dd389670bb4c2a4599">next</a> = j;</div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> }</div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> }</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> }</div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> result.push_back(cycle);</div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> }</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span>}</div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span><span class="comment">// Given a cycle and an EdgeVariables, returns the cutset constraint for the set</span></div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span><span class="comment">// of nodes in cycle.</span></div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span><a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_bounded_linear_expression.html">math_opt::BoundedLinearExpression</a> CutsetConstraint(</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keyword">const</span> Cycle& cycle, <span class="keyword">const</span> EdgeVariables& edge_vars) {</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n = edge_vars.num_cities();</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">const</span> absl::flat_hash_set<int> cycle_as_set(cycle.begin(), cycle.end());</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> std::vector<int> not_in_cycle;</div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; ++i) {</div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keywordflow">if</span> (!cycle_as_set.contains(i)) {</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> not_in_cycle.push_back(i);</div>
|
||
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> }</div>
|
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> }</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> cutset_edges;</div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> in_cycle : cycle) {</div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> out_of_cycle : not_in_cycle) {</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> cutset_edges += edge_vars.get(in_cycle, out_of_cycle);</div>
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||
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> }</div>
|
||
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> }</div>
|
||
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="keywordflow">return</span> cutset_edges >= 2;</div>
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||
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span>}</div>
|
||
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> </div>
|
||
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span><span class="comment">// Solves the TSP by returning the ordering of the cities that minimizes travel</span></div>
|
||
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span><span class="comment">// distance.</span></div>
|
||
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span>absl::StatusOr<Cycle> SolveTsp(</div>
|
||
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <span class="keyword">const</span> std::vector<std::pair<double, double>>& cities) {</div>
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||
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n = cities.size();</div>
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||
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keyword">const</span> std::vector<std::vector<double>> distance_matrix =</div>
|
||
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> DistanceMatrix(cities);</div>
|
||
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <a class="code hl_define" href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a>(n, 3);</div>
|
||
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model.html">math_opt::Model</a> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>(<span class="stringliteral">"tsp"</span>);</div>
|
||
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="keyword">const</span> EdgeVariables edge_vars(<a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>, n);</div>
|
||
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> edge_cost;</div>
|
||
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; ++i) {</div>
|
||
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < n; ++j) {</div>
|
||
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> edge_cost += edge_vars.get(i, j) * distance_matrix[i][j];</div>
|
||
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|
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> }</div>
|
||
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> }</div>
|
||
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.Minimize(edge_cost);</div>
|
||
|
|
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> </div>
|
||
|
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> <span class="comment">// Add the degree constraints</span></div>
|
||
|
|
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < n; ++i) {</div>
|
||
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> neighbors;</div>
|
||
|
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < n; ++j) {</div>
|
||
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> <span class="keywordflow">if</span> (i != j) {</div>
|
||
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> neighbors += edge_vars.get(i, j);</div>
|
||
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|
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> }</div>
|
||
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> }</div>
|
||
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<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddLinearConstraint(neighbors == 2, absl::StrCat(<span class="stringliteral">"n_"</span>, i));</div>
|
||
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> }</div>
|
||
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<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_arguments.html">math_opt::SolveArguments</a> args;</div>
|
||
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> <span class="keyword">const</span> <span class="keywordtype">int</span> threads = absl::GetFlag(FLAGS_threads);</div>
|
||
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keywordflow">if</span> (threads > 0) {</div>
|
||
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> args.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_arguments.html#a527ff4741dd79a20c29dc896d14c5a01">parameters</a>.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_parameters.html#a8112e07adcce45fb4e3dc39b01aa4875">threads</a> = threads;</div>
|
||
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|
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> }</div>
|
||
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span> args.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_arguments.html#a0ca3ed4feca5eeb20a657c584a52244c">callback_registration</a>.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_callback_registration.html#acf4f9b02e62efeacad4c0aa1cbff6a39">events</a>.insert(</div>
|
||
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|
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> math_opt::CallbackEvent::kMipSolution);</div>
|
||
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span> args.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_arguments.html#a0ca3ed4feca5eeb20a657c584a52244c">callback_registration</a>.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_callback_registration.html#a922db711f1c18d9e29f2e85c2fe23541">add_lazy_constraints</a> = <span class="keyword">true</span>;</div>
|
||
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> args.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_arguments.html#a42712c99422eaa2019fa9713b1dc74b9">callback</a> = [&edge_vars](<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_callback_data.html">math_opt::CallbackData</a>& cb_data) {</div>
|
||
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> <span class="comment">// At event CallbackEvent::kMipSolution, a solution is always present.</span></div>
|
||
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(cb_data.solution.has_value());</div>
|
||
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> <span class="keyword">const</span> std::vector<Cycle> cycles =</div>
|
||
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> FindCycles(EdgeValues(edge_vars, *cb_data.solution));</div>
|
||
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_callback_result.html">math_opt::CallbackResult</a> result;</div>
|
||
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> <span class="keywordflow">if</span> (cycles.size() > 1) {</div>
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||
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> Cycle& cycle : cycles) {</div>
|
||
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_callback_result.html#a8225d69ce6f20e86ccfe133c7d80ff1a">AddLazyConstraint</a>(CutsetConstraint(cycle, edge_vars));</div>
|
||
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span> }</div>
|
||
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> }</div>
|
||
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> <span class="keywordflow">return</span> result;</div>
|
||
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> };</div>
|
||
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_result.html">math_opt::SolveResult</a> result,</div>
|
||
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1">math_opt::Solve</a>(<a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>, math_opt::SolverType::kGurobi, args));</div>
|
||
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="keywordflow">if</span> (result.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81">termination</a>.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_termination.html#a36d5365d462f57468ba3a9d8ae6bbec9">reason</a> != math_opt::TerminationReason::kOptimal) {</div>
|
||
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
|
||
|
|
<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> << <span class="stringliteral">"Expected TSP solve terminate with reason optimal, found: "</span></div>
|
||
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> << result.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81">termination</a>;</div>
|
||
|
|
<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> }</div>
|
||
|
|
<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> std::cout << <span class="stringliteral">"Route length: "</span> << result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08">objective_value</a>() << std::endl;</div>
|
||
|
|
<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span> <span class="keyword">const</span> std::vector<Cycle> cycles =</div>
|
||
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> FindCycles(EdgeValues(edge_vars, result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532">variable_values</a>()));</div>
|
||
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(cycles.size(), 1);</div>
|
||
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|
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(cycles[0].size(), n);</div>
|
||
|
|
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> <span class="keywordflow">return</span> cycles[0];</div>
|
||
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span>}</div>
|
||
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> </div>
|
||
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|
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span><span class="comment">// Produces an SVG to draw a route for a TSP.</span></div>
|
||
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span>std::string RouteSvg(<span class="keyword">const</span> std::vector<std::pair<double, double>>& cities,</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> <span class="keyword">const</span> Cycle& cycle) {</div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <span class="keyword">constexpr</span> <span class="keywordtype">int</span> image_px = 1000;</div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <span class="keyword">constexpr</span> <span class="keywordtype">int</span> r = 5;</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span> <span class="keyword">constexpr</span> <span class="keywordtype">int</span> image_plus_border = image_px + 2 * r;</div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> std::vector<std::string> svg_lines;</div>
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||
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> svg_lines.push_back(absl::StrCat(<span class="stringliteral">"<svg width=\""</span>, image_plus_border,</div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> <span class="stringliteral">"\" height=\""</span>, image_plus_border, <span class="stringliteral">"\">"</span>));</div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span> std::vector<std::string> polygon_coords;</div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keywordtype">int</span> city : cycle) {</div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> <span class="keyword">const</span> <span class="keywordtype">int</span> x =</div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(std::round(cities[city].first * image_px)) + r;</div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> <span class="keyword">const</span> <span class="keywordtype">int</span> y =</div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> <span class="keyword">static_cast<</span><span class="keywordtype">int</span><span class="keyword">></span>(std::round(cities[city].second * image_px)) + r;</div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> svg_lines.push_back(absl::StrCat(<span class="stringliteral">"<circle cx=\""</span>, x, <span class="stringliteral">"\" cy=\""</span>, y,</div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> <span class="stringliteral">"\" r=\""</span>, r, <span class="stringliteral">"\" fill=\"blue\" />"</span>));</div>
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<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span> polygon_coords.push_back(absl::StrCat(x, <span class="stringliteral">","</span>, y));</div>
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||
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> }</div>
|
||
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> std::string polygon_coords_string = absl::StrJoin(polygon_coords, <span class="stringliteral">" "</span>);</div>
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||
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> svg_lines.push_back(</div>
|
||
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> absl::StrCat(<span class="stringliteral">"<polygon fill=\"none\" stroke=\"blue\" points=\""</span>,</div>
|
||
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> polygon_coords_string, <span class="stringliteral">"\" />"</span>));</div>
|
||
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> svg_lines.push_back(<span class="stringliteral">"</svg>"</span>);</div>
|
||
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> <span class="keywordflow">return</span> absl::StrJoin(svg_lines, <span class="stringliteral">"\n"</span>);</div>
|
||
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span>}</div>
|
||
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> </div>
|
||
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span><span class="keywordtype">void</span> RealMain() {</div>
|
||
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> std::vector<std::pair<double, double>> cities;</div>
|
||
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> <span class="keywordflow">if</span> (absl::GetFlag(FLAGS_test_instance)) {</div>
|
||
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> cities = TestCities();</div>
|
||
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> } <span class="keywordflow">else</span> {</div>
|
||
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<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> cities = RandomCities(absl::GetFlag(FLAGS_num_cities));</div>
|
||
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> }</div>
|
||
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> absl::StatusOr<Cycle> solution = SolveTsp(cities);</div>
|
||
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> <span class="keywordflow">if</span> (!solution.ok()) {</div>
|
||
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(QFATAL) << solution.status();</div>
|
||
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> }</div>
|
||
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="keyword">const</span> std::string svg = RouteSvg(cities, *solution);</div>
|
||
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> <span class="keywordflow">if</span> (absl::GetFlag(FLAGS_output).empty()) {</div>
|
||
|
|
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> std::cout << svg << std::endl;</div>
|
||
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|
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> } <span class="keywordflow">else</span> {</div>
|
||
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|
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> <a class="code hl_define" href="base_2logging_8h.html#a91223707c1a1a44be1c1757f324eda47">QCHECK_OK</a>(</div>
|
||
|
|
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> <a class="code hl_function" href="namespacefile.html#ae612ac5fffd37d180718bfe45d8ee445">file::SetContents</a>(absl::GetFlag(FLAGS_output), svg, <a class="code hl_function" href="namespacefile.html#a1abdf766bb120d38e7a4dfa200972681">file::Defaults</a>()));</div>
|
||
|
|
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> }</div>
|
||
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span>}</div>
|
||
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|
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> </div>
|
||
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span>} <span class="comment">// namespace</span></div>
|
||
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> </div>
|
||
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"><a class="line" href="tsp_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627"> 347</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="tsp_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 id="l00348" name="l00348"></a><span class="lineno"> 348</span> <a class="code hl_function" href="init__google_8h.html#a16af2bccb0196e1a9bb628559c95b7cb">InitGoogle</a>(argv[0], &argc, &argv, <span class="keyword">true</span>);</div>
|
||
|
|
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> RealMain();</div>
|
||
|
|
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> <span class="keywordflow">return</span> 0;</div>
|
||
|
|
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span>}</div>
|
||
|
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<div class="ttc" id="abase_2file_8h_html"><div class="ttname"><a href="base_2file_8h.html">file.h</a></div></div>
|
||
|
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<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
|
||
|
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<div class="ttc" id="abase_2logging_8h_html_a3e1cfef60e774a81f30eaddf26a3a274"><div class="ttname"><a href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a></div><div class="ttdeci">#define CHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00495">base/logging.h:495</a></div></div>
|
||
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<div class="ttc" id="abase_2logging_8h_html_a7c0ce053b28d53aa4eaf3eb7fb71663b"><div class="ttname"><a href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a></div><div class="ttdeci">#define CHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00703">base/logging.h:703</a></div></div>
|
||
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<div class="ttc" id="abase_2logging_8h_html_a7cc25402ecd7591b4c39934dd656b1f9"><div class="ttname"><a href="base_2logging_8h.html#a7cc25402ecd7591b4c39934dd656b1f9">CHECK_GE</a></div><div class="ttdeci">#define CHECK_GE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00707">base/logging.h:707</a></div></div>
|
||
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<div class="ttc" id="abase_2logging_8h_html_a91223707c1a1a44be1c1757f324eda47"><div class="ttname"><a href="base_2logging_8h.html#a91223707c1a1a44be1c1757f324eda47">QCHECK_OK</a></div><div class="ttdeci">#define QCHECK_OK</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00045">base/logging.h:45</a></div></div>
|
||
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<div class="ttc" id="abase_2logging_8h_html_ab25e01a2942b821d66371fc68d53f2eb"><div class="ttname"><a href="base_2logging_8h.html#ab25e01a2942b821d66371fc68d53f2eb">CHECK_NE</a></div><div class="ttdeci">#define CHECK_NE(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00704">base/logging.h:704</a></div></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#l00420">base/logging.h:420</a></div></div>
|
||
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<div class="ttc" id="abase_2status__macros_8h_html"><div class="ttname"><a href="base_2status__macros_8h.html">status_macros.h</a></div></div>
|
||
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<div class="ttc" id="abase_2status__macros_8h_html_a600de4b8f65fe0a4b1898041634f9011"><div class="ttname"><a href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a></div><div class="ttdeci">#define ASSIGN_OR_RETURN(lhs, rexpr)</div><div class="ttdef"><b>Definition:</b> <a href="base_2status__macros_8h_source.html#l00046">base/status_macros.h:46</a></div></div>
|
||
|
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<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_id_map_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_id_map.html">operations_research::math_opt::IdMap</a></div><div class="ttdef"><b>Definition:</b> <a href="id__map_8h_source.html#l00053">id_map.h:53</a></div></div>
|
||
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<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_id_map_html_ab2a3f17d02b118e3876034e67fdef6d3"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_id_map.html#ab2a3f17d02b118e3876034e67fdef6d3">operations_research::math_opt::IdMap::at</a></div><div class="ttdeci">const V & at(const K &k) const</div><div class="ttdef"><b>Definition:</b> <a href="id__map_8h_source.html#l00480">id_map.h:480</a></div></div>
|
||
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<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_linear_expression_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_linear_expression.html">operations_research::math_opt::LinearExpression</a></div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8h_source.html#l00193">variable_and_expressions.h:193</a></div></div>
|
||
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<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_model_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_model.html">operations_research::math_opt::Model</a></div><div class="ttdef"><b>Definition:</b> <a href="math__opt_2cpp_2model_8h_source.html#l00091">math_opt/cpp/model.h:91</a></div></div>
|
||
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<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_variable_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_variable.html">operations_research::math_opt::Variable</a></div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8h_source.html#l00115">variable_and_expressions.h:115</a></div></div>
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||
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<div class="ttc" id="aconstraint__solver_8cc_html_a395f613555f398dd389670bb4c2a4599"><div class="ttname"><a href="constraint__solver_8cc.html#a395f613555f398dd389670bb4c2a4599">next</a></div><div class="ttdeci">Block * next</div><div class="ttdef"><b>Definition:</b> <a href="constraint__solver_8cc_source.html#l00678">constraint_solver.cc:678</a></div></div>
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||
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<div class="ttc" id="agurobi__interface_8cc_html_a0728f23c9a47655d38e0bf1a2f200bcf"><div class="ttname"><a href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a></div><div class="ttdeci">GRBmodel * model</div><div class="ttdef"><b>Definition:</b> <a href="gurobi__interface_8cc_source.html#l00274">gurobi_interface.cc:274</a></div></div>
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||
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<div class="ttc" id="ainit__google_8h_html"><div class="ttname"><a href="init__google_8h.html">init_google.h</a></div></div>
|
||
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<div class="ttc" id="ainit__google_8h_html_a16af2bccb0196e1a9bb628559c95b7cb"><div class="ttname"><a href="init__google_8h.html#a16af2bccb0196e1a9bb628559c95b7cb">InitGoogle</a></div><div class="ttdeci">void InitGoogle(const char *usage, int *argc, char ***argv, bool deprecated)</div><div class="ttdef"><b>Definition:</b> <a href="init__google_8h_source.html#l00032">init_google.h:32</a></div></div>
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||
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<div class="ttc" id="amath__opt_8h_html"><div class="ttname"><a href="math__opt_8h.html">math_opt.h</a></div></div>
|
||
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<div class="ttc" id="anamespacefile_html_a1abdf766bb120d38e7a4dfa200972681"><div class="ttname"><a href="namespacefile.html#a1abdf766bb120d38e7a4dfa200972681">file::Defaults</a></div><div class="ttdeci">int Defaults()</div><div class="ttdef"><b>Definition:</b> <a href="base_2file_8h_source.html#l00120">base/file.h:120</a></div></div>
|
||
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<div class="ttc" id="anamespacefile_html_ae612ac5fffd37d180718bfe45d8ee445"><div class="ttname"><a href="namespacefile.html#ae612ac5fffd37d180718bfe45d8ee445">file::SetContents</a></div><div class="ttdeci">absl::Status SetContents(const absl::string_view &filename, const absl::string_view &contents, int flags)</div><div class="ttdef"><b>Definition:</b> <a href="base_2file_8cc_source.html#l00196">base/file.cc:196</a></div></div>
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||
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html">operations_research::math_opt</a></div><div class="ttdef"><b>Definition:</b> <a href="arrow__operator__proxy_8h_source.html#l00020">arrow_operator_proxy.h:20</a></div></div>
|
||
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a5767ee23f380e72488d3c7ebf2d742b1"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1">operations_research::math_opt::Solve</a></div><div class="ttdeci">absl::StatusOr< SolveResult > Solve(const Model &model, const SolverType solver_type, const SolveArguments &solve_args, const SolverInitArguments &init_args)</div><div class="ttdef"><b>Definition:</b> <a href="solve_8cc_source.html#l00094">solve.cc:94</a></div></div>
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||
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<div class="ttc" id="anamespaceutil_html_a302ee4bfcb86ea9ed64a193ed0b14648"><div class="ttname"><a href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a></div><div class="ttdeci">StatusBuilder InternalErrorBuilder()</div><div class="ttdef"><b>Definition:</b> <a href="status__builder_8h_source.html#l00084">status_builder.h:84</a></div></div>
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||
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<div class="ttc" id="aport_2proto__utils_8h_html"><div class="ttname"><a href="port_2proto__utils_8h.html">proto_utils.h</a></div></div>
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||
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<div class="ttc" id="astatus__builder_8h_html"><div class="ttname"><a href="status__builder_8h.html">status_builder.h</a></div></div>
|
||
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_bounded_linear_expression_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_bounded_linear_expression.html">operations_research::math_opt::BoundedLinearExpression</a></div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8h_source.html#l00479">variable_and_expressions.h:479</a></div></div>
|
||
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_callback_data_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_callback_data.html">operations_research::math_opt::CallbackData</a></div><div class="ttdef"><b>Definition:</b> <a href="callback_8h_source.html#l00185">callback.h:185</a></div></div>
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||
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_callback_registration_html_a922db711f1c18d9e29f2e85c2fe23541"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_callback_registration.html#a922db711f1c18d9e29f2e85c2fe23541">operations_research::math_opt::CallbackRegistration::add_lazy_constraints</a></div><div class="ttdeci">bool add_lazy_constraints</div><div class="ttdef"><b>Definition:</b> <a href="callback_8h_source.html#l00179">callback.h:179</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_callback_registration_html_acf4f9b02e62efeacad4c0aa1cbff6a39"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_callback_registration.html#acf4f9b02e62efeacad4c0aa1cbff6a39">operations_research::math_opt::CallbackRegistration::events</a></div><div class="ttdeci">absl::flat_hash_set< CallbackEvent > events</div><div class="ttdef"><b>Definition:</b> <a href="callback_8h_source.html#l00161">callback.h:161</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_callback_result_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_callback_result.html">operations_research::math_opt::CallbackResult</a></div><div class="ttdef"><b>Definition:</b> <a href="callback_8h_source.html#l00222">callback.h:222</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_callback_result_html_a8225d69ce6f20e86ccfe133c7d80ff1a"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_callback_result.html#a8225d69ce6f20e86ccfe133c7d80ff1a">operations_research::math_opt::CallbackResult::AddLazyConstraint</a></div><div class="ttdeci">void AddLazyConstraint(BoundedLinearExpression linear_constraint)</div><div class="ttdef"><b>Definition:</b> <a href="callback_8h_source.html#l00243">callback.h:243</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_arguments_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_arguments.html">operations_research::math_opt::SolveArguments</a></div><div class="ttdef"><b>Definition:</b> <a href="solve__arguments_8h_source.html#l00027">solve_arguments.h:27</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_arguments_html_a0ca3ed4feca5eeb20a657c584a52244c"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_arguments.html#a0ca3ed4feca5eeb20a657c584a52244c">operations_research::math_opt::SolveArguments::callback_registration</a></div><div class="ttdeci">CallbackRegistration callback_registration</div><div class="ttdef"><b>Definition:</b> <a href="solve__arguments_8h_source.html#l00054">solve_arguments.h:54</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_arguments_html_a42712c99422eaa2019fa9713b1dc74b9"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_arguments.html#a42712c99422eaa2019fa9713b1dc74b9">operations_research::math_opt::SolveArguments::callback</a></div><div class="ttdeci">Callback callback</div><div class="ttdef"><b>Definition:</b> <a href="solve__arguments_8h_source.html#l00062">solve_arguments.h:62</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_arguments_html_a527ff4741dd79a20c29dc896d14c5a01"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_arguments.html#a527ff4741dd79a20c29dc896d14c5a01">operations_research::math_opt::SolveArguments::parameters</a></div><div class="ttdeci">SolveParameters parameters</div><div class="ttdef"><b>Definition:</b> <a href="solve__arguments_8h_source.html#l00029">solve_arguments.h:29</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_parameters_html_a8112e07adcce45fb4e3dc39b01aa4875"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_parameters.html#a8112e07adcce45fb4e3dc39b01aa4875">operations_research::math_opt::SolveParameters::threads</a></div><div class="ttdeci">std::optional< int32_t > threads</div><div class="ttdef"><b>Definition:</b> <a href="parameters_8h_source.html#l00243">parameters.h:243</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html">operations_research::math_opt::SolveResult</a></div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8h_source.html#l00295">solve_result.h:295</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_a77d1ea96211300e9417b965981953c81"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81">operations_research::math_opt::SolveResult::termination</a></div><div class="ttdeci">Termination termination</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8h_source.html#l00300">solve_result.h:300</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_a84f066c304d8bcbb9567be094feb9b08"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08">operations_research::math_opt::SolveResult::objective_value</a></div><div class="ttdeci">double objective_value() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00358">solve_result.cc:358</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_ac4a6e078f25aa73eec5271d449a12532"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532">operations_research::math_opt::SolveResult::variable_values</a></div><div class="ttdeci">const VariableMap< double > & variable_values() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00369">solve_result.cc:369</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_termination_html_a36d5365d462f57468ba3a9d8ae6bbec9"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_termination.html#a36d5365d462f57468ba3a9d8ae6bbec9">operations_research::math_opt::Termination::reason</a></div><div class="ttdeci">TerminationReason reason</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8h_source.html#l00261">solve_result.h:261</a></div></div>
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<div class="ttc" id="atsp_8cc_html_a3c04138a5bfe5d72780bb7e82a18e627"><div class="ttname"><a href="tsp_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a></div><div class="ttdeci">int main(int argc, char **argv)</div><div class="ttdef"><b>Definition:</b> <a href="tsp_8cc_source.html#l00347">tsp.cc:347</a></div></div>
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