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_INSERTION_TSP_H |
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20 | #define LEMON_INSERTION_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 Insertion algorithm for symmetric TSP |
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25 | |
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26 | #include <vector> |
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27 | #include <functional> |
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28 | #include <lemon/full_graph.h> |
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29 | #include <lemon/maps.h> |
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30 | #include <lemon/random.h> |
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31 | |
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32 | namespace lemon { |
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33 | |
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34 | /// \ingroup tsp |
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35 | /// |
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36 | /// \brief Insertion algorithm for symmetric TSP. |
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37 | /// |
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38 | /// InsertionTsp implements the insertion heuristic for solving |
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39 | /// symmetric \ref tsp "TSP". |
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40 | /// |
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41 | /// This is a fast and effective tour construction method that has |
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42 | /// many variants. |
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43 | /// It starts with a subtour containing a few nodes of the graph and it |
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44 | /// iteratively inserts the other nodes into this subtour according to a |
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45 | /// certain node selection rule. |
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46 | /// |
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47 | /// This method is among the fastest TSP algorithms, and it typically |
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48 | /// provides quite good solutions (usually much better than |
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49 | /// \ref NearestNeighborTsp and \ref GreedyTsp). |
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50 | /// |
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51 | /// InsertionTsp implements four different node selection rules, |
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52 | /// from which the most effective one (\e farthest \e node \e selection) |
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53 | /// is used by default. |
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54 | /// With this choice, the algorithm runs in O(n<sup>2</sup>) time. |
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55 | /// For more information, see \ref SelectionRule. |
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56 | /// |
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57 | /// \tparam CM Type of the cost map. |
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58 | template <typename CM> |
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59 | class InsertionTsp |
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60 | { |
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61 | public: |
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62 | |
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63 | /// Type of the cost map |
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64 | typedef CM CostMap; |
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65 | /// Type of the edge costs |
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66 | typedef typename CM::Value Cost; |
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67 | |
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68 | private: |
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69 | |
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70 | GRAPH_TYPEDEFS(FullGraph); |
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71 | |
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72 | const FullGraph &_gr; |
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73 | const CostMap &_cost; |
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74 | std::vector<Node> _notused; |
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75 | std::vector<Node> _tour; |
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76 | Cost _sum; |
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77 | |
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78 | public: |
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79 | |
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80 | /// \brief Constants for specifying the node selection rule. |
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81 | /// |
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82 | /// Enum type containing constants for specifying the node selection |
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83 | /// rule for the \ref run() function. |
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84 | /// |
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85 | /// During the algorithm, nodes are selected for addition to the current |
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86 | /// subtour according to the applied rule. |
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87 | /// The FARTHEST method is one of the fastest selection rules, and |
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88 | /// it is typically the most effective, thus it is the default |
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89 | /// option. The RANDOM rule usually gives slightly worse results, |
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90 | /// but it is more robust. |
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91 | /// |
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92 | /// The desired selection rule can be specified as a parameter of the |
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93 | /// \ref run() function. |
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94 | enum SelectionRule { |
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95 | |
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96 | /// An unvisited node having minimum distance from the current |
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97 | /// subtour is selected at each step. |
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98 | /// The algorithm runs in O(n<sup>2</sup>) time using this |
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99 | /// selection rule. |
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100 | NEAREST, |
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101 | |
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102 | /// An unvisited node having maximum distance from the current |
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103 | /// subtour is selected at each step. |
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104 | /// The algorithm runs in O(n<sup>2</sup>) time using this |
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105 | /// selection rule. |
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106 | FARTHEST, |
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107 | |
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108 | /// An unvisited node whose insertion results in the least |
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109 | /// increase of the subtour's total cost is selected at each step. |
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110 | /// The algorithm runs in O(n<sup>3</sup>) time using this |
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111 | /// selection rule, but in most cases, it is almost as fast as |
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112 | /// with other rules. |
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113 | CHEAPEST, |
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114 | |
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115 | /// An unvisited node is selected randomly without any evaluation |
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116 | /// at each step. |
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117 | /// The global \ref rnd "random number generator instance" is used. |
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118 | /// You can seed it before executing the algorithm, if you |
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119 | /// would like to. |
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120 | /// The algorithm runs in O(n<sup>2</sup>) time using this |
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121 | /// selection rule. |
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122 | RANDOM |
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123 | }; |
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124 | |
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125 | public: |
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126 | |
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127 | /// \brief Constructor |
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128 | /// |
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129 | /// Constructor. |
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130 | /// \param gr The \ref FullGraph "full graph" the algorithm runs on. |
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131 | /// \param cost The cost map. |
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132 | InsertionTsp(const FullGraph &gr, const CostMap &cost) |
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133 | : _gr(gr), _cost(cost) {} |
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134 | |
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135 | /// \name Execution Control |
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136 | /// @{ |
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137 | |
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138 | /// \brief Runs the algorithm. |
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139 | /// |
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140 | /// This function runs the algorithm. |
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141 | /// |
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142 | /// \param rule The node selection rule. For more information, see |
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143 | /// \ref SelectionRule. |
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144 | /// |
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145 | /// \return The total cost of the found tour. |
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146 | Cost run(SelectionRule rule = FARTHEST) { |
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147 | _tour.clear(); |
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148 | |
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149 | if (_gr.nodeNum() == 0) return _sum = 0; |
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150 | else if (_gr.nodeNum() == 1) { |
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151 | _tour.push_back(_gr(0)); |
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152 | return _sum = 0; |
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153 | } |
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154 | |
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155 | switch (rule) { |
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156 | case NEAREST: |
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157 | init(true); |
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158 | start<ComparingSelection<std::less<Cost> >, |
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159 | DefaultInsertion>(); |
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160 | break; |
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161 | case FARTHEST: |
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162 | init(false); |
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163 | start<ComparingSelection<std::greater<Cost> >, |
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164 | DefaultInsertion>(); |
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165 | break; |
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166 | case CHEAPEST: |
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167 | init(true); |
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168 | start<CheapestSelection, CheapestInsertion>(); |
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169 | break; |
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170 | case RANDOM: |
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171 | init(true); |
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172 | start<RandomSelection, DefaultInsertion>(); |
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173 | break; |
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174 | } |
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175 | return _sum; |
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176 | } |
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177 | |
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178 | /// @} |
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179 | |
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180 | /// \name Query Functions |
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181 | /// @{ |
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182 | |
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183 | /// \brief The total cost of the found tour. |
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184 | /// |
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185 | /// This function returns the total cost of the found tour. |
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186 | /// |
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187 | /// \pre run() must be called before using this function. |
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188 | Cost tourCost() const { |
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189 | return _sum; |
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190 | } |
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191 | |
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192 | /// \brief Returns a const reference to the node sequence of the |
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193 | /// found tour. |
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194 | /// |
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195 | /// This function returns a const reference to a vector |
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196 | /// that stores the node sequence of the found tour. |
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197 | /// |
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198 | /// \pre run() must be called before using this function. |
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199 | const std::vector<Node>& tourNodes() const { |
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200 | return _tour; |
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201 | } |
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202 | |
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203 | /// \brief Gives back the node sequence of the found tour. |
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204 | /// |
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205 | /// This function copies the node sequence of the found tour into |
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206 | /// an STL container through the given output iterator. The |
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207 | /// <tt>value_type</tt> of the container must be <tt>FullGraph::Node</tt>. |
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208 | /// For example, |
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209 | /// \code |
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210 | /// std::vector<FullGraph::Node> nodes(countNodes(graph)); |
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211 | /// tsp.tourNodes(nodes.begin()); |
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212 | /// \endcode |
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213 | /// or |
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214 | /// \code |
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215 | /// std::list<FullGraph::Node> nodes; |
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216 | /// tsp.tourNodes(std::back_inserter(nodes)); |
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217 | /// \endcode |
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218 | /// |
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219 | /// \pre run() must be called before using this function. |
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220 | template <typename Iterator> |
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221 | void tourNodes(Iterator out) const { |
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222 | std::copy(_tour.begin(), _tour.end(), out); |
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223 | } |
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224 | |
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225 | /// \brief Gives back the found tour as a path. |
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226 | /// |
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227 | /// This function copies the found tour as a list of arcs/edges into |
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228 | /// the given \ref concept::Path "path structure". |
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229 | /// |
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230 | /// \pre run() must be called before using this function. |
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231 | template <typename Path> |
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232 | void tour(Path &path) const { |
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233 | path.clear(); |
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234 | for (int i = 0; i < int(_tour.size()) - 1; ++i) { |
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235 | path.addBack(_gr.arc(_tour[i], _tour[i+1])); |
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236 | } |
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237 | if (int(_tour.size()) >= 2) { |
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238 | path.addBack(_gr.arc(_tour.back(), _tour.front())); |
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239 | } |
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240 | } |
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241 | |
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242 | /// @} |
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243 | |
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244 | private: |
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245 | |
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246 | // Initializes the algorithm |
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247 | void init(bool min) { |
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248 | Edge min_edge = min ? mapMin(_gr, _cost) : mapMax(_gr, _cost); |
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249 | |
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250 | _tour.clear(); |
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251 | _tour.push_back(_gr.u(min_edge)); |
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252 | _tour.push_back(_gr.v(min_edge)); |
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253 | |
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254 | _notused.clear(); |
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255 | for (NodeIt n(_gr); n!=INVALID; ++n) { |
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256 | if (n != _gr.u(min_edge) && n != _gr.v(min_edge)) { |
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257 | _notused.push_back(n); |
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258 | } |
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259 | } |
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260 | |
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261 | _sum = _cost[min_edge] * 2; |
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262 | } |
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263 | |
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264 | // Executes the algorithm |
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265 | template <class SelectionFunctor, class InsertionFunctor> |
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266 | void start() { |
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267 | SelectionFunctor selectNode(_gr, _cost, _tour, _notused); |
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268 | InsertionFunctor insertNode(_gr, _cost, _tour, _sum); |
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269 | |
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270 | for (int i=0; i<_gr.nodeNum()-2; ++i) { |
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271 | insertNode.insert(selectNode.select()); |
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272 | } |
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273 | |
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274 | _sum = _cost[_gr.edge(_tour.back(), _tour.front())]; |
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275 | for (int i = 0; i < int(_tour.size())-1; ++i) { |
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276 | _sum += _cost[_gr.edge(_tour[i], _tour[i+1])]; |
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277 | } |
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278 | } |
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279 | |
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280 | |
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281 | // Implementation of the nearest and farthest selection rule |
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282 | template <typename Comparator> |
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283 | class ComparingSelection { |
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284 | public: |
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285 | ComparingSelection(const FullGraph &gr, const CostMap &cost, |
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286 | std::vector<Node> &tour, std::vector<Node> ¬used) |
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287 | : _gr(gr), _cost(cost), _tour(tour), _notused(notused), |
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288 | _dist(gr, 0), _compare() |
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289 | { |
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290 | // Compute initial distances for the unused nodes |
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291 | for (unsigned int i=0; i<_notused.size(); ++i) { |
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292 | Node u = _notused[i]; |
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293 | Cost min_dist = _cost[_gr.edge(u, _tour[0])]; |
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294 | for (unsigned int j=1; j<_tour.size(); ++j) { |
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295 | Cost curr = _cost[_gr.edge(u, _tour[j])]; |
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296 | if (curr < min_dist) { |
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297 | min_dist = curr; |
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298 | } |
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299 | } |
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300 | _dist[u] = min_dist; |
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301 | } |
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302 | } |
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303 | |
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304 | Node select() { |
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305 | |
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306 | // Select an used node with minimum distance |
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307 | Cost ins_dist = 0; |
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308 | int ins_node = -1; |
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309 | for (unsigned int i=0; i<_notused.size(); ++i) { |
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310 | Cost curr = _dist[_notused[i]]; |
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311 | if (_compare(curr, ins_dist) || ins_node == -1) { |
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312 | ins_dist = curr; |
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313 | ins_node = i; |
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314 | } |
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315 | } |
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316 | |
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317 | // Remove the selected node from the unused vector |
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318 | Node sn = _notused[ins_node]; |
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319 | _notused[ins_node] = _notused.back(); |
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320 | _notused.pop_back(); |
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321 | |
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322 | // Update the distances of the remaining nodes |
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323 | for (unsigned int i=0; i<_notused.size(); ++i) { |
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324 | Node u = _notused[i]; |
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325 | Cost nc = _cost[_gr.edge(sn, u)]; |
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326 | if (nc < _dist[u]) { |
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327 | _dist[u] = nc; |
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328 | } |
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329 | } |
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330 | |
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331 | return sn; |
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332 | } |
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333 | |
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334 | private: |
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335 | const FullGraph &_gr; |
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336 | const CostMap &_cost; |
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337 | std::vector<Node> &_tour; |
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338 | std::vector<Node> &_notused; |
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339 | FullGraph::NodeMap<Cost> _dist; |
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340 | Comparator _compare; |
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341 | }; |
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342 | |
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343 | // Implementation of the cheapest selection rule |
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344 | class CheapestSelection { |
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345 | private: |
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346 | Cost costDiff(Node u, Node v, Node w) const { |
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347 | return |
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348 | _cost[_gr.edge(u, w)] + |
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349 | _cost[_gr.edge(v, w)] - |
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350 | _cost[_gr.edge(u, v)]; |
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351 | } |
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352 | |
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353 | public: |
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354 | CheapestSelection(const FullGraph &gr, const CostMap &cost, |
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355 | std::vector<Node> &tour, std::vector<Node> ¬used) |
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356 | : _gr(gr), _cost(cost), _tour(tour), _notused(notused), |
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357 | _ins_cost(gr, 0), _ins_pos(gr, -1) |
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358 | { |
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359 | // Compute insertion cost and position for the unused nodes |
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360 | for (unsigned int i=0; i<_notused.size(); ++i) { |
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361 | Node u = _notused[i]; |
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362 | Cost min_cost = costDiff(_tour.back(), _tour.front(), u); |
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363 | int min_pos = 0; |
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364 | for (unsigned int j=1; j<_tour.size(); ++j) { |
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365 | Cost curr_cost = costDiff(_tour[j-1], _tour[j], u); |
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366 | if (curr_cost < min_cost) { |
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367 | min_cost = curr_cost; |
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368 | min_pos = j; |
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369 | } |
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370 | } |
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371 | _ins_cost[u] = min_cost; |
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372 | _ins_pos[u] = min_pos; |
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373 | } |
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374 | } |
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375 | |
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376 | Cost select() { |
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377 | |
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378 | // Select an used node with minimum insertion cost |
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379 | Cost min_cost = 0; |
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380 | int min_node = -1; |
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381 | for (unsigned int i=0; i<_notused.size(); ++i) { |
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382 | Cost curr_cost = _ins_cost[_notused[i]]; |
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383 | if (curr_cost < min_cost || min_node == -1) { |
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384 | min_cost = curr_cost; |
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385 | min_node = i; |
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386 | } |
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387 | } |
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388 | |
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389 | // Remove the selected node from the unused vector |
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390 | Node sn = _notused[min_node]; |
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391 | _notused[min_node] = _notused.back(); |
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392 | _notused.pop_back(); |
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393 | |
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394 | // Insert the selected node into the tour |
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395 | const int ipos = _ins_pos[sn]; |
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396 | _tour.insert(_tour.begin() + ipos, sn); |
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397 | |
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398 | // Update the insertion cost and position of the remaining nodes |
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399 | for (unsigned int i=0; i<_notused.size(); ++i) { |
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400 | Node u = _notused[i]; |
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401 | Cost curr_cost = _ins_cost[u]; |
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402 | int curr_pos = _ins_pos[u]; |
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403 | |
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404 | int ipos_prev = ipos == 0 ? _tour.size()-1 : ipos-1; |
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405 | int ipos_next = ipos == int(_tour.size())-1 ? 0 : ipos+1; |
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406 | Cost nc1 = costDiff(_tour[ipos_prev], _tour[ipos], u); |
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407 | Cost nc2 = costDiff(_tour[ipos], _tour[ipos_next], u); |
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408 | |
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409 | if (nc1 <= curr_cost || nc2 <= curr_cost) { |
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410 | // A new position is better than the old one |
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411 | if (nc1 <= nc2) { |
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412 | curr_cost = nc1; |
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413 | curr_pos = ipos; |
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414 | } else { |
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415 | curr_cost = nc2; |
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416 | curr_pos = ipos_next; |
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417 | } |
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418 | } |
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419 | else { |
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420 | if (curr_pos == ipos) { |
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421 | // The minimum should be found again |
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422 | curr_cost = costDiff(_tour.back(), _tour.front(), u); |
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423 | curr_pos = 0; |
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424 | for (unsigned int j=1; j<_tour.size(); ++j) { |
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425 | Cost tmp_cost = costDiff(_tour[j-1], _tour[j], u); |
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426 | if (tmp_cost < curr_cost) { |
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427 | curr_cost = tmp_cost; |
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428 | curr_pos = j; |
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429 | } |
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430 | } |
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431 | } |
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432 | else if (curr_pos > ipos) { |
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433 | ++curr_pos; |
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434 | } |
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435 | } |
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436 | |
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437 | _ins_cost[u] = curr_cost; |
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438 | _ins_pos[u] = curr_pos; |
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439 | } |
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440 | |
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441 | return min_cost; |
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442 | } |
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443 | |
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444 | private: |
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445 | const FullGraph &_gr; |
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446 | const CostMap &_cost; |
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447 | std::vector<Node> &_tour; |
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448 | std::vector<Node> &_notused; |
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449 | FullGraph::NodeMap<Cost> _ins_cost; |
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450 | FullGraph::NodeMap<int> _ins_pos; |
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451 | }; |
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452 | |
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453 | // Implementation of the random selection rule |
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454 | class RandomSelection { |
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455 | public: |
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456 | RandomSelection(const FullGraph &, const CostMap &, |
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457 | std::vector<Node> &, std::vector<Node> ¬used) |
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458 | : _notused(notused) {} |
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459 | |
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460 | Node select() const { |
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461 | const int index = rnd[_notused.size()]; |
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462 | Node n = _notused[index]; |
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463 | _notused[index] = _notused.back(); |
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464 | _notused.pop_back(); |
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465 | return n; |
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466 | } |
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467 | |
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468 | private: |
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469 | std::vector<Node> &_notused; |
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470 | }; |
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471 | |
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472 | |
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473 | // Implementation of the default insertion method |
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474 | class DefaultInsertion { |
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475 | private: |
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476 | Cost costDiff(Node u, Node v, Node w) const { |
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477 | return |
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478 | _cost[_gr.edge(u, w)] + |
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479 | _cost[_gr.edge(v, w)] - |
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480 | _cost[_gr.edge(u, v)]; |
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481 | } |
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482 | |
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483 | public: |
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484 | DefaultInsertion(const FullGraph &gr, const CostMap &cost, |
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485 | std::vector<Node> &tour, Cost &total_cost) : |
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486 | _gr(gr), _cost(cost), _tour(tour), _total(total_cost) {} |
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487 | |
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488 | void insert(Node n) const { |
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489 | int min = 0; |
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490 | Cost min_val = |
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491 | costDiff(_tour.front(), _tour.back(), n); |
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492 | |
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493 | for (unsigned int i=1; i<_tour.size(); ++i) { |
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494 | Cost tmp = costDiff(_tour[i-1], _tour[i], n); |
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495 | if (tmp < min_val) { |
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496 | min = i; |
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497 | min_val = tmp; |
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498 | } |
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499 | } |
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500 | |
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501 | _tour.insert(_tour.begin()+min, n); |
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502 | _total += min_val; |
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503 | } |
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504 | |
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505 | private: |
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506 | const FullGraph &_gr; |
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507 | const CostMap &_cost; |
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508 | std::vector<Node> &_tour; |
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509 | Cost &_total; |
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510 | }; |
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511 | |
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512 | // Implementation of a special insertion method for the cheapest |
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513 | // selection rule |
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514 | class CheapestInsertion { |
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515 | TEMPLATE_GRAPH_TYPEDEFS(FullGraph); |
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516 | public: |
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517 | CheapestInsertion(const FullGraph &, const CostMap &, |
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518 | std::vector<Node> &, Cost &total_cost) : |
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519 | _total(total_cost) {} |
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520 | |
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521 | void insert(Cost diff) const { |
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522 | _total += diff; |
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523 | } |
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524 | |
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525 | private: |
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526 | Cost &_total; |
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527 | }; |
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528 | |
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529 | }; |
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530 | |
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531 | }; // namespace lemon |
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532 | |
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533 | #endif |
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