1 | /* -*- C++ -*- |
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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) 2003-2007 |
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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_CSP_H |
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20 | #define LEMON_CSP_H |
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21 | |
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22 | ///\ingroup approx |
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23 | ///\file |
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24 | ///\brief Algorithm for the Resource Constrained Shortest Path problem. |
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25 | /// |
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26 | |
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27 | #include <lemon/list_graph.h> |
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28 | #include <lemon/graph_utils.h> |
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29 | #include <lemon/error.h> |
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30 | #include <lemon/maps.h> |
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31 | #include <lemon/tolerance.h> |
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32 | #include <lemon/dijkstra.h> |
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33 | #include <lemon/path.h> |
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34 | #include <lemon/counter.h> |
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35 | namespace lemon { |
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36 | |
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37 | ///\ingroup approx |
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38 | /// |
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39 | ///\brief Algorithms for the Resource Constrained Shortest Path Problem |
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40 | /// |
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41 | ///The Resource Constrained Shortest (Least Cost) Path problem is the |
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42 | ///following. We are given a directed graph with two additive weightings |
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43 | ///on the edges, referred as \e cost and \e delay. In addition, |
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44 | ///a source and a destination node \e s and \e t and a delay |
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45 | ///constraint \e D is given. A path \e p is called \e feasible |
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46 | ///if <em>delay(p)\<=D</em>. Then, the task is to find the least cost |
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47 | ///feasible path. |
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48 | /// |
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49 | template<class Graph, |
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50 | class CM=typename Graph:: template EdgeMap<double>, |
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51 | class DM=CM> |
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52 | class ConstrainedShortestPath |
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53 | { |
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54 | public: |
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55 | |
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56 | GRAPH_TYPEDEFS(typename Graph); |
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57 | |
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58 | typedef SimplePath<Graph> Path; |
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59 | |
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60 | private: |
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61 | |
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62 | const Graph &_g; |
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63 | Tolerance<double> tol; |
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64 | |
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65 | const CM &_cost; |
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66 | const DM &_delay; |
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67 | |
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68 | class CoMap |
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69 | { |
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70 | const CM &_cost; |
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71 | const DM &_delay; |
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72 | double _lambda; |
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73 | public: |
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74 | typedef typename CM::Key Key; |
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75 | typedef double Value; |
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76 | CoMap(const CM &c, const DM &d) :_cost(c), _delay(d), _lambda(0) {} |
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77 | double lambda() const { return _lambda; } |
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78 | void lambda(double l) { _lambda=l; } |
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79 | Value operator[](Key &e) const |
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80 | { |
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81 | return _cost[e]+_lambda*_delay[e]; |
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82 | } |
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83 | }; |
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84 | |
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85 | CoMap _co_map; |
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86 | |
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87 | |
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88 | Dijkstra<Graph, CoMap> _dij; |
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89 | |
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90 | public: |
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91 | |
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92 | /// \brief Constructor |
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93 | |
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94 | ///Constructor |
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95 | /// |
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96 | ConstrainedShortestPath(const Graph &g, const CM &ct, const DM &dl) |
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97 | : _g(g), _cost(ct), _delay(dl), |
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98 | _co_map(ct, dl), _dij(_g,_co_map) {} |
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99 | |
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100 | |
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101 | ///Compute the cost of a path |
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102 | double cost(const Path &p) const |
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103 | { |
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104 | double s=0; |
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105 | // Path r; |
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106 | for(typename Path::EdgeIt e(p);e!=INVALID;++e) s+=_cost[e]; |
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107 | return s; |
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108 | } |
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109 | |
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110 | ///Compute the delay of a path |
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111 | double delay(const Path &p) const |
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112 | { |
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113 | double s=0; |
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114 | for(typename Path::EdgeIt e(p);e!=INVALID;++e) s+=_delay[e]; |
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115 | return s; |
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116 | } |
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117 | |
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118 | ///Runs the LARAC algorithm |
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119 | |
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120 | ///This function runs a Lagrange relaxation based heuristic to find |
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121 | ///a delay constrained least cost path. |
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122 | ///\param s source node |
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123 | ///\param t target node |
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124 | ///\param delta upper bound on the delta |
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125 | ///\retval lo_bo a lower bound on the optimal solution |
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126 | ///\return the found path or an empty |
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127 | Path larac(Node s, Node t, double delta, double &lo_bo) |
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128 | { |
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129 | double lambda=0; |
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130 | double cp,cq,dp,dq,cr,dr; |
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131 | Path p; |
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132 | Path q; |
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133 | Path r; |
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134 | { |
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135 | Dijkstra<Graph,CM> dij(_g,_cost); |
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136 | dij.run(s,t); |
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137 | if(!dij.reached(t)) return Path(); |
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138 | p=dij.path(t); |
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139 | cp=cost(p); |
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140 | dp=delay(p); |
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141 | } |
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142 | if(delay(p)<=delta) return p; |
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143 | { |
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144 | Dijkstra<Graph,DM> dij(_g,_delay); |
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145 | dij.run(s,t); |
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146 | q=dij.path(t); |
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147 | cq=cost(q); |
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148 | dq=delay(q); |
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149 | } |
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150 | if(delay(q)>delta) return Path(); |
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151 | while (true) { |
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152 | lambda=(cp-cq)/(dq-dp); |
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153 | _co_map.lambda(lambda); |
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154 | _dij.run(s,t); |
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155 | r=_dij.path(t); |
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156 | cr=cost(r); |
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157 | dr=delay(r); |
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158 | if(!tol.less(cr+lambda*dr,cp+lambda*dp)) { |
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159 | lo_bo=cq+lambda*(dq-delta); |
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160 | return q; |
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161 | } |
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162 | else if(tol.less(dr,delta)) |
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163 | { |
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164 | q=r; |
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165 | cq=cr; |
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166 | dq=dr; |
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167 | } |
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168 | else if(tol.less(delta,dr)) |
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169 | { |
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170 | p=r; |
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171 | cp=cr; |
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172 | dp=dr; |
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173 | } |
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174 | else return r; |
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175 | } |
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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 | } //END OF NAMESPACE LEMON |
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181 | |
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182 | #endif |
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