<ahref="optimization_8h.html">Go to the documentation of this file.</a><divclass="fragment"><divclass="line"><aid="l00001"name="l00001"></a><spanclass="lineno"> 1</span><spanclass="comment">// Copyright 2010-2021 Google LLC</span></div>
<divclass="line"><aid="l00002"name="l00002"></a><spanclass="lineno"> 2</span><spanclass="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
<divclass="line"><aid="l00003"name="l00003"></a><spanclass="lineno"> 3</span><spanclass="comment">// you may not use this file except in compliance with the License.</span></div>
<divclass="line"><aid="l00004"name="l00004"></a><spanclass="lineno"> 4</span><spanclass="comment">// You may obtain a copy of the License at</span></div>
<divclass="line"><aid="l00008"name="l00008"></a><spanclass="lineno"> 8</span><spanclass="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<divclass="line"><aid="l00009"name="l00009"></a><spanclass="lineno"> 9</span><spanclass="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
<divclass="line"><aid="l00010"name="l00010"></a><spanclass="lineno"> 10</span><spanclass="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<divclass="line"><aid="l00011"name="l00011"></a><spanclass="lineno"> 11</span><spanclass="comment">// See the License for the specific language governing permissions and</span></div>
<divclass="line"><aid="l00012"name="l00012"></a><spanclass="lineno"> 12</span><spanclass="comment">// limitations under the License.</span></div>
<divclass="line"><aid="l00035"name="l00035"></a><spanclass="lineno"> 35</span><spanclass="comment">// Like MinimizeCore() with a slower but strictly better heuristic. This</span></div>
<divclass="line"><aid="l00036"name="l00036"></a><spanclass="lineno"> 36</span><spanclass="comment">// algorithm should produce a minimal core with respect to propagation. We put</span></div>
<divclass="line"><aid="l00037"name="l00037"></a><spanclass="lineno"> 37</span><spanclass="comment">// each literal of the initial core "last" at least once, so if such literal can</span></div>
<divclass="line"><aid="l00038"name="l00038"></a><spanclass="lineno"> 38</span><spanclass="comment">// be inferred by propagation by any subset of the other literal, it will be</span></div>
<divclass="line"><aid="l00041"name="l00041"></a><spanclass="lineno"> 41</span><spanclass="comment">// Note that the literal of the minimized core will stay in the same order.</span></div>
<divclass="line"><aid="l00043"name="l00043"></a><spanclass="lineno"> 43</span><spanclass="comment">// TODO(user): Avoid spending too much time trying to minimize a core.</span></div>
<divclass="line"><aid="l00047"name="l00047"></a><spanclass="lineno"> 47</span><spanclass="comment">// Because the Solve*() functions below are also used in scripts that requires a</span></div>
<divclass="line"><aid="l00048"name="l00048"></a><spanclass="lineno"> 48</span><spanclass="comment">// special output format, we use this to tell them whether or not to use the</span></div>
<divclass="line"><aid="l00049"name="l00049"></a><spanclass="lineno"> 49</span><spanclass="comment">// default logging framework or simply stdout. Most users should just use</span></div>
<divclass="line"><aid="l00053"name="l00053"></a><spanclass="lineno"> 53</span><spanclass="comment">// All the Solve*() functions below reuse the SatSolver::Status with a slightly</span></div>
<divclass="line"><aid="l00054"name="l00054"></a><spanclass="lineno"> 54</span><spanclass="comment">// different meaning:</span></div>
<divclass="line"><aid="l00055"name="l00055"></a><spanclass="lineno"> 55</span><spanclass="comment">// - FEASIBLE: The problem has been solved to optimality.</span></div>
<divclass="line"><aid="l00056"name="l00056"></a><spanclass="lineno"> 56</span><spanclass="comment">// - INFEASIBLE: Same meaning, the decision version is already unsat.</span></div>
<divclass="line"><aid="l00057"name="l00057"></a><spanclass="lineno"> 57</span><spanclass="comment">// - LIMIT_REACHED: we may have some feasible solution (if solution is</span></div>
<divclass="line"><aid="l00058"name="l00058"></a><spanclass="lineno"> 58</span><spanclass="comment">// non-empty), but the optimality is not proven.</span></div>
<divclass="line"><aid="l00060"name="l00060"></a><spanclass="lineno"> 60</span><spanclass="comment">// Implements the "Fu & Malik" algorithm described in:</span></div>
<divclass="line"><aid="l00062"name="l00062"></a><spanclass="lineno"> 62</span><spanclass="comment">// International Conference on Theory and Applications of Satisfiability</span></div>
<divclass="line"><aid="l00065"name="l00065"></a><spanclass="lineno"> 65</span><spanclass="comment">// This algorithm requires all the objective weights to be the same (CHECKed)</span></div>
<divclass="line"><aid="l00066"name="l00066"></a><spanclass="lineno"> 66</span><spanclass="comment">// and currently only works on minimization problems. The problem is assumed to</span></div>
<divclass="line"><aid="l00067"name="l00067"></a><spanclass="lineno"> 67</span><spanclass="comment">// be already loaded into the given solver.</span></div>
<divclass="line"><aid="l00069"name="l00069"></a><spanclass="lineno"> 69</span><spanclass="comment">// TODO(user): double-check the correctness if the objective coefficients are</span></div>
<divclass="line"><aid="l00076"name="l00076"></a><spanclass="lineno"> 76</span><spanclass="comment">// The WPM1 algorithm is a generalization of the Fu & Malik algorithm to</span></div>
<divclass="line"><aid="l00077"name="l00077"></a><spanclass="lineno"> 77</span><spanclass="comment">// weighted problems. Note that if all objective weights are the same, this is</span></div>
<divclass="line"><aid="l00078"name="l00078"></a><spanclass="lineno"> 78</span><spanclass="comment">// almost the same as SolveWithFuMalik() but the encoding of the constraints is</span></div>
<divclass="line"><aid="l00082"name="l00082"></a><spanclass="lineno"> 82</span><spanclass="comment">// through satisfiability testing. In: Proc. of the 12th Int. Conf. on Theory and</span></div>
<divclass="line"><aid="l00083"name="l00083"></a><spanclass="lineno"> 83</span><spanclass="comment">// Applications of Satisfiability Testing (SAT’09). pp. 427-440 (2009)</span></div>
<divclass="line"><aid="l00088"name="l00088"></a><spanclass="lineno"> 88</span><spanclass="comment">// Solves num_times the decision version of the given problem with different</span></div>
<divclass="line"><aid="l00089"name="l00089"></a><spanclass="lineno"> 89</span><spanclass="comment">// random parameters. Keep the best solution (regarding the objective) and</span></div>
<divclass="line"><aid="l00090"name="l00090"></a><spanclass="lineno"> 90</span><spanclass="comment">// returns it in solution. The problem is assumed to be already loaded into the</span></div>
<divclass="line"><aid="l00091"name="l00091"></a><spanclass="lineno"> 91</span><spanclass="comment">// given solver.</span></div>
<divclass="line"><aid="l00096"name="l00096"></a><spanclass="lineno"> 96</span><spanclass="comment">// Starts by solving the decision version of the given LinearBooleanProblem and</span></div>
<divclass="line"><aid="l00097"name="l00097"></a><spanclass="lineno"> 97</span><spanclass="comment">// then simply add a constraint to find a lower objective that the current best</span></div>
<divclass="line"><aid="l00098"name="l00098"></a><spanclass="lineno"> 98</span><spanclass="comment">// solution and repeat until the problem becomes unsat.</span></div>
<divclass="line"><aid="l00100"name="l00100"></a><spanclass="lineno"> 100</span><spanclass="comment">// The problem is assumed to be already loaded into the given solver. If</span></div>
<divclass="line"><aid="l00101"name="l00101"></a><spanclass="lineno"> 101</span><spanclass="comment">// solution is initially a feasible solution, the search will starts from there.</span></div>
<divclass="line"><aid="l00102"name="l00102"></a><spanclass="lineno"> 102</span><spanclass="comment">// solution will be updated with the best solution found so far.</span></div>
<divclass="line"><aid="l00108"name="l00108"></a><spanclass="lineno"> 108</span><spanclass="comment">// Similar algorithm as the one used by qmaxsat, this is a linear scan with the</span></div>
<divclass="line"><aid="l00109"name="l00109"></a><spanclass="lineno"> 109</span><spanclass="comment">// at-most k constraint encoded in SAT. This only works on problems with</span></div>
<divclass="line"><aid="l00115"name="l00115"></a><spanclass="lineno"> 115</span><spanclass="comment">// This is an original algorithm. It is a mix between the cardinality encoding</span></div>
<divclass="line"><aid="l00116"name="l00116"></a><spanclass="lineno"> 116</span><spanclass="comment">// and the Fu & Malik algorithm. It also works on general weighted instances.</span></div>
<divclass="line"><aid="l00121"name="l00121"></a><spanclass="lineno"> 121</span><spanclass="comment">// Model-based API to minimize a given IntegerVariable by solving a sequence of</span></div>
<divclass="line"><aid="l00122"name="l00122"></a><spanclass="lineno"> 122</span><spanclass="comment">// decision problem. Each problem is solved using SolveIntegerProblem(). Returns</span></div>
<divclass="line"><aid="l00123"name="l00123"></a><spanclass="lineno"> 123</span><spanclass="comment">// the status of the last solved decision problem.</span></div>
<divclass="line"><aid="l00125"name="l00125"></a><spanclass="lineno"> 125</span><spanclass="comment">// The feasible_solution_observer function will be called each time a new</span></div>
<divclass="line"><aid="l00126"name="l00126"></a><spanclass="lineno"> 126</span><spanclass="comment">// feasible solution is found.</span></div>
<divclass="line"><aid="l00128"name="l00128"></a><spanclass="lineno"> 128</span><spanclass="comment">// Note that this function will resume the search from the current state of the</span></div>
<divclass="line"><aid="l00129"name="l00129"></a><spanclass="lineno"> 129</span><spanclass="comment">// solver, and it is up to the client to backtrack to the root node if needed.</span></div>
<divclass="line"><aid="l00134"name="l00134"></a><spanclass="lineno"> 134</span><spanclass="comment">// Use a low conflict limit and performs a binary search to try to restrict the</span></div>
<divclass="line"><aid="l00135"name="l00135"></a><spanclass="lineno"> 135</span><spanclass="comment">// domain of objective_var.</span></div>
<divclass="line"><aid="l00140"name="l00140"></a><spanclass="lineno"> 140</span><spanclass="comment">// Same as MinimizeIntegerVariableWithLinearScanAndLazyEncoding() but use</span></div>
<divclass="line"><aid="l00141"name="l00141"></a><spanclass="lineno"> 141</span><spanclass="comment">// a core-based approach instead. Note that the given objective_var is just used</span></div>
<divclass="line"><aid="l00142"name="l00142"></a><spanclass="lineno"> 142</span><spanclass="comment">// for reporting the lower-bound/upper-bound and do not need to be linked with</span></div>
<divclass="line"><aid="l00143"name="l00143"></a><spanclass="lineno"> 143</span><spanclass="comment">// its linear representation.</span></div>
<divclass="line"><aid="l00145"name="l00145"></a><spanclass="lineno"> 145</span><spanclass="comment">// Unlike MinimizeIntegerVariableWithLinearScanAndLazyEncoding() this function</span></div>
<divclass="line"><aid="l00146"name="l00146"></a><spanclass="lineno"> 146</span><spanclass="comment">// just return the last solver status. In particular if it is INFEASIBLE but</span></div>
<divclass="line"><aid="l00147"name="l00147"></a><spanclass="lineno"> 147</span><spanclass="comment">// feasible_solution_observer() was called, it means we are at OPTIMAL.</span></div>
<divclass="line"><aid="l00156"name="l00156"></a><spanclass="lineno"> 156</span><spanclass="comment">// TODO(user): Change the algo slighlty to allow resuming from the last</span></div>
<divclass="line"><aid="l00157"name="l00157"></a><spanclass="lineno"> 157</span><spanclass="comment">// aborted position. Currently, the search is "resumable", but it will restart</span></div>
<divclass="line"><aid="l00158"name="l00158"></a><spanclass="lineno"> 158</span><spanclass="comment">// some of the work already done, so it might just never find anything.</span></div>
<divclass="line"><aid="l00161"name="l00161"></a><spanclass="lineno"> 161</span><spanclass="comment">// A different way to encode the objective as core are found. This one do</span></div>
<divclass="line"><aid="l00162"name="l00162"></a><spanclass="lineno"> 162</span><spanclass="comment">// not introduce IntegerVariable and encode everything in Boolean.</span></div>
<divclass="line"><aid="l00164"name="l00164"></a><spanclass="lineno"> 164</span><spanclass="comment">// It seems to be more powerful, but it isn't completely implemented yet.</span></div>
<divclass="line"><aid="l00166"name="l00166"></a><spanclass="lineno"> 166</span><spanclass="comment">// - Make it work for integer variable in the objective.</span></div>
<divclass="line"><aid="l00167"name="l00167"></a><spanclass="lineno"> 167</span><spanclass="comment">// - Only call it if the objective domain is not too large?</span></div>
<divclass="line"><aid="l00168"name="l00168"></a><spanclass="lineno"> 168</span><spanclass="comment">// - Support resuming for interleaved search.</span></div>
<divclass="line"><aid="l00169"name="l00169"></a><spanclass="lineno"> 169</span><spanclass="comment">// - Implement all core heurisitics.</span></div>
<divclass="line"><aid="l00181"name="l00181"></a><spanclass="lineno"> 181</span><spanclass="keywordtype">int</span> depth; <spanclass="comment">// Only for logging/debugging.</span></div>
<divclass="line"><aid="l00184"name="l00184"></a><spanclass="lineno"> 184</span><spanclass="comment">// An upper bound on the optimal solution if we were to optimize only this</span></div>
<divclass="line"><aid="l00185"name="l00185"></a><spanclass="lineno"> 185</span><spanclass="comment">// term. This is used by the cover optimization code.</span></div>
<divclass="line"><aid="l00189"name="l00189"></a><spanclass="lineno"> 189</span><spanclass="comment">// This will be called each time a feasible solution is found. Returns false</span></div>
<divclass="line"><aid="l00190"name="l00190"></a><spanclass="lineno"> 190</span><spanclass="comment">// if a conflict was detected while trying to constrain the objective to a</span></div>
<divclass="line"><aid="l00194"name="l00194"></a><spanclass="lineno"> 194</span><spanclass="comment">// Use the gap an implied bounds to propagated the bounds of the objective</span></div>
<divclass="line"><aid="l00195"name="l00195"></a><spanclass="lineno"> 195</span><spanclass="comment">// variables and of its terms.</span></div>
<divclass="line"><aid="l00198"name="l00198"></a><spanclass="lineno"> 198</span><spanclass="comment">// Heuristic that aim to find the "real" lower bound of the objective on each</span></div>
<divclass="line"><aid="l00199"name="l00199"></a><spanclass="lineno"> 199</span><spanclass="comment">// core by using a linear scan optimization approach.</span></div>
<divclass="line"><aid="l00202"name="l00202"></a><spanclass="lineno"> 202</span><spanclass="comment">// Computes the next stratification threshold.</span></div>
<divclass="line"><aid="l00203"name="l00203"></a><spanclass="lineno"> 203</span><spanclass="comment">// Sets it to zero if all the assumptions where already considered.</span></div>
<divclass="line"><aid="l00206"name="l00206"></a><spanclass="lineno"> 206</span><spanclass="comment">// If we have an "at most one can be false" between literals with a positive</span></div>
<divclass="line"><aid="l00207"name="l00207"></a><spanclass="lineno"> 207</span><spanclass="comment">// cost, you then know that at least n - 1 will contribute to the cost, and</span></div>
<divclass="line"><aid="l00208"name="l00208"></a><spanclass="lineno"> 208</span><spanclass="comment">// you can increase the objective lower bound. This is the same as having</span></div>
<divclass="line"><aid="l00209"name="l00209"></a><spanclass="lineno"> 209</span><spanclass="comment">// a real "at most one" constraint on the negation of such literals.</span></div>
<divclass="line"><aid="l00211"name="l00211"></a><spanclass="lineno"> 211</span><spanclass="comment">// This detects such "at most ones" and rewrite the objective accordingly.</span></div>
<divclass="line"><aid="l00212"name="l00212"></a><spanclass="lineno"> 212</span><spanclass="comment">// For each at most one, the rewrite create a new Boolean variable and update</span></div>
<divclass="line"><aid="l00213"name="l00213"></a><spanclass="lineno"> 213</span><spanclass="comment">// the cost so that the trivial objective lower bound reflect the increase.</span></div>
<divclass="line"><aid="l00215"name="l00215"></a><spanclass="lineno"> 215</span><spanclass="comment">// TODO(user) : Code that as a general presolve rule? I am not sure adding</span></div>
<divclass="line"><aid="l00216"name="l00216"></a><spanclass="lineno"> 216</span><spanclass="comment">// the extra Booleans is always a good idea though. Especially since the LP</span></div>
<divclass="line"><aid="l00217"name="l00217"></a><spanclass="lineno"> 217</span><spanclass="comment">// will see the same lower bound that what is computed by this.</span></div>
<divclass="line"><aid="l00235"name="l00235"></a><spanclass="lineno"> 235</span><spanclass="comment">// This is used to not add the objective equation more than once if we</span></div>
<divclass="line"><aid="l00236"name="l00236"></a><spanclass="lineno"> 236</span><spanclass="comment">// solve in "chunk".</span></div>
<divclass="line"><aid="l00239"name="l00239"></a><spanclass="lineno"> 239</span><spanclass="comment">// Set to true when we need to abort early.</span></div>
<divclass="line"><aid="l00241"name="l00241"></a><spanclass="lineno"> 241</span><spanclass="comment">// TODO(user): This is only used for the stop after first solution parameter</span></div>
<divclass="line"><aid="l00242"name="l00242"></a><spanclass="lineno"> 242</span><spanclass="comment">// which should likely be handled differently by simply using the normal way</span></div>
<divclass="line"><aid="l00243"name="l00243"></a><spanclass="lineno"> 243</span><spanclass="comment">// to stop a solver from the feasible solution callback.</span></div>
<divclass="ttc"id="aclassoperations__research_1_1_time_limit_html"><divclass="ttname"><ahref="classoperations__research_1_1_time_limit.html">operations_research::TimeLimit</a></div><divclass="ttdoc">A simple class to enforce both an elapsed time limit and a deterministic time limit in the same threa...</div><divclass="ttdef"><b>Definition:</b><ahref="time__limit_8h_source.html#l00106">time_limit.h:106</a></div></div>
<divclass="ttc"id="aclassoperations__research_1_1sat_1_1_model_html"><divclass="ttname"><ahref="classoperations__research_1_1sat_1_1_model.html">operations_research::sat::Model</a></div><divclass="ttdoc">Class that owns everything related to a particular optimization model.</div><divclass="ttdef"><b>Definition:</b><ahref="sat_2model_8h_source.html#l00042">sat/model.h:42</a></div></div>
<divclass="ttc"id="anamespaceoperations__research_html"><divclass="ttname"><ahref="namespaceoperations__research.html">operations_research</a></div><divclass="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><divclass="ttdef"><b>Definition:</b><ahref="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
