1 | /* -*- mode: C++; indent-tabs-mode: nil; -*- |
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2 | * |
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3 | * This file is a part of LEMON, a generic C++ optimization library. |
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4 | * |
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5 | * Copyright (C) 2003-2010 |
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6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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8 | * |
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9 | * Permission to use, modify and distribute this software is granted |
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10 | * provided that this copyright notice appears in all copies. For |
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11 | * precise terms see the accompanying LICENSE file. |
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12 | * |
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13 | * This software is provided "AS IS" with no warranty of any kind, |
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14 | * express or implied, and with no claim as to its suitability for any |
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15 | * purpose. |
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16 | * |
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17 | */ |
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18 | |
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19 | #ifndef LEMON_OPT2_TSP_H |
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20 | #define LEMON_OPT2_TSP_H |
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21 | |
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22 | /// \ingroup tsp |
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23 | /// \file |
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24 | /// \brief 2-opt algorithm for symmetric TSP. |
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25 | |
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26 | #include <vector> |
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27 | #include <lemon/full_graph.h> |
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28 | |
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29 | namespace lemon { |
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30 | |
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31 | /// \ingroup tsp |
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32 | /// |
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33 | /// \brief 2-opt algorithm for symmetric TSP. |
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34 | /// |
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35 | /// Opt2Tsp implements the 2-opt heuristic for solving |
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36 | /// symmetric \ref tsp "TSP". |
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37 | /// |
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38 | /// This algorithm starts with an initial tour and iteratively improves it. |
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39 | /// At each step, it removes two edges and the reconnects the created two |
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40 | /// paths in the other way if the resulting tour is shorter. |
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41 | /// The algorithm finishes when no such 2-opt move can be applied, and so |
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42 | /// the tour is 2-optimal. |
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43 | /// |
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44 | /// If no starting tour is given to the \ref run() function, then the |
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45 | /// algorithm uses the node sequence determined by the node IDs. |
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46 | /// Oherwise, it starts with the given tour. |
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47 | /// |
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48 | /// This is a rather slow but effective method. |
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49 | /// Its typical usage is the improvement of the result of a fast tour |
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50 | /// construction heuristic (e.g. the InsertionTsp algorithm). |
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51 | /// |
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52 | /// \tparam CM Type of the cost map. |
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53 | template <typename CM> |
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54 | class Opt2Tsp |
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55 | { |
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56 | public: |
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57 | |
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58 | /// Type of the cost map |
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59 | typedef CM CostMap; |
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60 | /// Type of the edge costs |
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61 | typedef typename CM::Value Cost; |
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62 | |
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63 | private: |
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64 | |
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65 | GRAPH_TYPEDEFS(FullGraph); |
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66 | |
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67 | const FullGraph &_gr; |
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68 | const CostMap &_cost; |
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69 | Cost _sum; |
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70 | std::vector<int> _plist; |
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71 | std::vector<Node> _path; |
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72 | |
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73 | public: |
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74 | |
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75 | /// \brief Constructor |
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76 | /// |
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77 | /// Constructor. |
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78 | /// \param gr The \ref FullGraph "full graph" the algorithm runs on. |
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79 | /// \param cost The cost map. |
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80 | Opt2Tsp(const FullGraph &gr, const CostMap &cost) |
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81 | : _gr(gr), _cost(cost) {} |
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82 | |
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83 | /// \name Execution Control |
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84 | /// @{ |
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85 | |
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86 | /// \brief Runs the algorithm from scratch. |
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87 | /// |
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88 | /// This function runs the algorithm starting from the tour that is |
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89 | /// determined by the node ID sequence. |
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90 | /// |
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91 | /// \return The total cost of the found tour. |
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92 | Cost run() { |
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93 | _path.clear(); |
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94 | |
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95 | if (_gr.nodeNum() == 0) return _sum = 0; |
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96 | else if (_gr.nodeNum() == 1) { |
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97 | _path.push_back(_gr(0)); |
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98 | return _sum = 0; |
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99 | } |
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100 | else if (_gr.nodeNum() == 2) { |
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101 | _path.push_back(_gr(0)); |
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102 | _path.push_back(_gr(1)); |
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103 | return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))]; |
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104 | } |
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105 | |
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106 | _plist.resize(2*_gr.nodeNum()); |
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107 | for (int i = 1; i < _gr.nodeNum()-1; ++i) { |
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108 | _plist[2*i] = i-1; |
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109 | _plist[2*i+1] = i+1; |
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110 | } |
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111 | _plist[0] = _gr.nodeNum()-1; |
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112 | _plist[1] = 1; |
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113 | _plist[2*_gr.nodeNum()-2] = _gr.nodeNum()-2; |
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114 | _plist[2*_gr.nodeNum()-1] = 0; |
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115 | |
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116 | return start(); |
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117 | } |
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118 | |
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119 | /// \brief Runs the algorithm starting from the given tour. |
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120 | /// |
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121 | /// This function runs the algorithm starting from the given tour. |
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122 | /// |
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123 | /// \param tour The tour as a path structure. It must be a |
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124 | /// \ref checkPath() "valid path" containing excactly n arcs. |
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125 | /// |
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126 | /// \return The total cost of the found tour. |
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127 | template <typename Path> |
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128 | Cost run(const Path& tour) { |
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129 | _path.clear(); |
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130 | |
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131 | if (_gr.nodeNum() == 0) return _sum = 0; |
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132 | else if (_gr.nodeNum() == 1) { |
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133 | _path.push_back(_gr(0)); |
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134 | return _sum = 0; |
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135 | } |
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136 | else if (_gr.nodeNum() == 2) { |
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137 | _path.push_back(_gr(0)); |
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138 | _path.push_back(_gr(1)); |
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139 | return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))]; |
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140 | } |
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141 | |
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142 | _plist.resize(2*_gr.nodeNum()); |
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143 | typename Path::ArcIt it(tour); |
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144 | int first = _gr.id(_gr.source(it)), |
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145 | prev = first, |
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146 | curr = _gr.id(_gr.target(it)), |
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147 | next = -1; |
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148 | _plist[2*first+1] = curr; |
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149 | for (++it; it != INVALID; ++it) { |
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150 | next = _gr.id(_gr.target(it)); |
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151 | _plist[2*curr] = prev; |
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152 | _plist[2*curr+1] = next; |
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153 | prev = curr; |
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154 | curr = next; |
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155 | } |
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156 | _plist[2*first] = prev; |
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157 | |
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158 | return start(); |
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159 | } |
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160 | |
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161 | /// \brief Runs the algorithm starting from the given tour. |
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162 | /// |
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163 | /// This function runs the algorithm starting from the given tour |
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164 | /// (node sequence). |
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165 | /// |
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166 | /// \param tour A vector that stores all <tt>Node</tt>s of the graph |
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167 | /// in the desired order. |
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168 | /// |
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169 | /// \return The total cost of the found tour. |
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170 | Cost run(const std::vector<Node>& tour) { |
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171 | _path.clear(); |
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172 | |
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173 | if (_gr.nodeNum() == 0) return _sum = 0; |
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174 | else if (_gr.nodeNum() == 1) { |
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175 | _path.push_back(_gr(0)); |
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176 | return _sum = 0; |
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177 | } |
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178 | else if (_gr.nodeNum() == 2) { |
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179 | _path.push_back(_gr(0)); |
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180 | _path.push_back(_gr(1)); |
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181 | return _sum = 2 * _cost[_gr.edge(_gr(0), _gr(1))]; |
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182 | } |
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183 | |
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184 | _plist.resize(2*_gr.nodeNum()); |
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185 | typename std::vector<Node>::const_iterator it = tour.begin(); |
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186 | int first = _gr.id(*it), |
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187 | prev = first, |
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188 | curr = _gr.id(*(++it)), |
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189 | next = -1; |
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190 | _plist[2*first+1] = curr; |
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191 | for (++it; it != tour.end(); ++it) { |
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192 | next = _gr.id(*it); |
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193 | _plist[2*curr] = prev; |
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194 | _plist[2*curr+1] = next; |
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195 | prev = curr; |
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196 | curr = next; |
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197 | } |
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198 | _plist[2*first] = curr; |
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199 | _plist[2*curr] = prev; |
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200 | _plist[2*curr+1] = first; |
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201 | |
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202 | return start(); |
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203 | } |
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204 | |
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205 | /// @} |
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206 | |
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207 | /// \name Query Functions |
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208 | /// @{ |
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209 | |
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210 | /// \brief The total cost of the found tour. |
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211 | /// |
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212 | /// This function returns the total cost of the found tour. |
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213 | /// |
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214 | /// \pre run() must be called before using this function. |
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215 | Cost tourCost() const { |
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216 | return _sum; |
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217 | } |
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218 | |
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219 | /// \brief Returns a const reference to the node sequence of the |
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220 | /// found tour. |
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221 | /// |
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222 | /// This function returns a const reference to a vector |
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223 | /// that stores the node sequence of the found tour. |
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224 | /// |
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225 | /// \pre run() must be called before using this function. |
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226 | const std::vector<Node>& tourNodes() const { |
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227 | return _path; |
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228 | } |
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229 | |
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230 | /// \brief Gives back the node sequence of the found tour. |
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231 | /// |
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232 | /// This function copies the node sequence of the found tour into |
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233 | /// an STL container through the given output iterator. The |
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234 | /// <tt>value_type</tt> of the container must be <tt>FullGraph::Node</tt>. |
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235 | /// For example, |
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236 | /// \code |
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237 | /// std::vector<FullGraph::Node> nodes(countNodes(graph)); |
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238 | /// tsp.tourNodes(nodes.begin()); |
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239 | /// \endcode |
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240 | /// or |
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241 | /// \code |
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242 | /// std::list<FullGraph::Node> nodes; |
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243 | /// tsp.tourNodes(std::back_inserter(nodes)); |
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244 | /// \endcode |
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245 | /// |
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246 | /// \pre run() must be called before using this function. |
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247 | template <typename Iterator> |
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248 | void tourNodes(Iterator out) const { |
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249 | std::copy(_path.begin(), _path.end(), out); |
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250 | } |
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251 | |
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252 | /// \brief Gives back the found tour as a path. |
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253 | /// |
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254 | /// This function copies the found tour as a list of arcs/edges into |
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255 | /// the given \ref concept::Path "path structure". |
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256 | /// |
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257 | /// \pre run() must be called before using this function. |
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258 | template <typename Path> |
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259 | void tour(Path &path) const { |
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260 | path.clear(); |
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261 | for (int i = 0; i < int(_path.size()) - 1; ++i) { |
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262 | path.addBack(_gr.arc(_path[i], _path[i+1])); |
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263 | } |
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264 | if (int(_path.size()) >= 2) { |
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265 | path.addBack(_gr.arc(_path.back(), _path.front())); |
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266 | } |
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267 | } |
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268 | |
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269 | /// @} |
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270 | |
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271 | private: |
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272 | |
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273 | // Iterator class for the linked list storage of the tour |
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274 | class PathListIt { |
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275 | public: |
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276 | PathListIt(const std::vector<int> &pl, int i=0) |
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277 | : plist(&pl), act(i), last(pl[2*act]) {} |
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278 | PathListIt(const std::vector<int> &pl, int i, int l) |
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279 | : plist(&pl), act(i), last(l) {} |
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280 | |
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281 | int nextIndex() const { |
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282 | return (*plist)[2*act] == last ? 2*act+1 : 2*act; |
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283 | } |
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284 | |
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285 | int prevIndex() const { |
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286 | return (*plist)[2*act] == last ? 2*act : 2*act+1; |
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287 | } |
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288 | |
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289 | int next() const { |
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290 | int x = (*plist)[2*act]; |
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291 | return x == last ? (*plist)[2*act+1] : x; |
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292 | } |
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293 | |
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294 | int prev() const { |
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295 | return last; |
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296 | } |
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297 | |
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298 | PathListIt& operator++() { |
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299 | int tmp = act; |
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300 | act = next(); |
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301 | last = tmp; |
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302 | return *this; |
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303 | } |
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304 | |
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305 | operator int() const { |
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306 | return act; |
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307 | } |
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308 | |
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309 | private: |
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310 | const std::vector<int> *plist; |
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311 | int act; |
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312 | int last; |
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313 | }; |
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314 | |
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315 | // Checks and applies 2-opt move (if it improves the tour) |
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316 | bool checkOpt2(const PathListIt& i, const PathListIt& j) { |
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317 | Node u = _gr.nodeFromId(i), |
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318 | un = _gr.nodeFromId(i.next()), |
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319 | v = _gr.nodeFromId(j), |
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320 | vn = _gr.nodeFromId(j.next()); |
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321 | |
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322 | if (_cost[_gr.edge(u, un)] + _cost[_gr.edge(v, vn)] > |
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323 | _cost[_gr.edge(u, v)] + _cost[_gr.edge(un, vn)]) |
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324 | { |
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325 | _plist[PathListIt(_plist, i.next(), i).prevIndex()] = j.next(); |
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326 | _plist[PathListIt(_plist, j.next(), j).prevIndex()] = i.next(); |
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327 | |
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328 | _plist[i.nextIndex()] = j; |
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329 | _plist[j.nextIndex()] = i; |
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330 | |
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331 | return true; |
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332 | } |
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333 | |
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334 | return false; |
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335 | } |
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336 | |
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337 | // Executes the algorithm from the initial tour |
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338 | Cost start() { |
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339 | |
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340 | restart_search: |
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341 | for (PathListIt i(_plist); true; ++i) { |
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342 | PathListIt j = i; |
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343 | if (++j == 0 || ++j == 0) break; |
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344 | for (; j != 0 && j != i.prev(); ++j) { |
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345 | if (checkOpt2(i, j)) |
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346 | goto restart_search; |
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347 | } |
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348 | } |
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349 | |
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350 | PathListIt i(_plist); |
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351 | _path.push_back(_gr.nodeFromId(i)); |
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352 | for (++i; i != 0; ++i) |
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353 | _path.push_back(_gr.nodeFromId(i)); |
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354 | |
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355 | _sum = _cost[_gr.edge(_path.back(), _path.front())]; |
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356 | for (int i = 0; i < int(_path.size())-1; ++i) { |
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357 | _sum += _cost[_gr.edge(_path[i], _path[i+1])]; |
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358 | } |
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359 | |
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360 | return _sum; |
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361 | } |
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362 | |
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363 | }; |
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364 | |
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365 | }; // namespace lemon |
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366 | |
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367 | #endif |
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