1 | /* glpios12.c (node selection heuristics) */ |
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2 | |
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3 | /*********************************************************************** |
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4 | * This code is part of GLPK (GNU Linear Programming Kit). |
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5 | * |
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6 | * Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, |
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7 | * 2009, 2010 Andrew Makhorin, Department for Applied Informatics, |
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8 | * Moscow Aviation Institute, Moscow, Russia. All rights reserved. |
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9 | * E-mail: <mao@gnu.org>. |
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10 | * |
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11 | * GLPK is free software: you can redistribute it and/or modify it |
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12 | * under the terms of the GNU General Public License as published by |
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13 | * the Free Software Foundation, either version 3 of the License, or |
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14 | * (at your option) any later version. |
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15 | * |
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16 | * GLPK is distributed in the hope that it will be useful, but WITHOUT |
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17 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
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18 | * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public |
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19 | * License for more details. |
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20 | * |
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21 | * You should have received a copy of the GNU General Public License |
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22 | * along with GLPK. If not, see <http://www.gnu.org/licenses/>. |
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23 | ***********************************************************************/ |
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24 | |
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25 | #include "glpios.h" |
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26 | |
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27 | /*********************************************************************** |
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28 | * NAME |
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29 | * |
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30 | * ios_choose_node - select subproblem to continue the search |
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31 | * |
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32 | * SYNOPSIS |
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33 | * |
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34 | * #include "glpios.h" |
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35 | * int ios_choose_node(glp_tree *T); |
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36 | * |
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37 | * DESCRIPTION |
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38 | * |
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39 | * The routine ios_choose_node selects a subproblem from the active |
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40 | * list to continue the search. The choice depends on the backtracking |
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41 | * technique option. |
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42 | * |
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43 | * RETURNS |
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44 | * |
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45 | * The routine ios_choose_node return the reference number of the |
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46 | * subproblem selected. */ |
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47 | |
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48 | static int most_feas(glp_tree *T); |
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49 | static int best_proj(glp_tree *T); |
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50 | static int best_node(glp_tree *T); |
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51 | |
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52 | int ios_choose_node(glp_tree *T) |
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53 | { int p; |
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54 | if (T->parm->bt_tech == GLP_BT_DFS) |
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55 | { /* depth first search */ |
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56 | xassert(T->tail != NULL); |
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57 | p = T->tail->p; |
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58 | } |
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59 | else if (T->parm->bt_tech == GLP_BT_BFS) |
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60 | { /* breadth first search */ |
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61 | xassert(T->head != NULL); |
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62 | p = T->head->p; |
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63 | } |
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64 | else if (T->parm->bt_tech == GLP_BT_BLB) |
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65 | { /* select node with best local bound */ |
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66 | p = best_node(T); |
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67 | } |
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68 | else if (T->parm->bt_tech == GLP_BT_BPH) |
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69 | { if (T->mip->mip_stat == GLP_UNDEF) |
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70 | { /* "most integer feasible" subproblem */ |
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71 | p = most_feas(T); |
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72 | } |
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73 | else |
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74 | { /* best projection heuristic */ |
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75 | p = best_proj(T); |
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76 | } |
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77 | } |
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78 | else |
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79 | xassert(T != T); |
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80 | return p; |
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81 | } |
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82 | |
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83 | static int most_feas(glp_tree *T) |
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84 | { /* select subproblem whose parent has minimal sum of integer |
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85 | infeasibilities */ |
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86 | IOSNPD *node; |
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87 | int p; |
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88 | double best; |
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89 | p = 0, best = DBL_MAX; |
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90 | for (node = T->head; node != NULL; node = node->next) |
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91 | { xassert(node->up != NULL); |
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92 | if (best > node->up->ii_sum) |
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93 | p = node->p, best = node->up->ii_sum; |
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94 | } |
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95 | return p; |
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96 | } |
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97 | |
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98 | static int best_proj(glp_tree *T) |
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99 | { /* select subproblem using the best projection heuristic */ |
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100 | IOSNPD *root, *node; |
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101 | int p; |
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102 | double best, deg, obj; |
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103 | /* the global bound must exist */ |
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104 | xassert(T->mip->mip_stat == GLP_FEAS); |
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105 | /* obtain pointer to the root node, which must exist */ |
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106 | root = T->slot[1].node; |
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107 | xassert(root != NULL); |
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108 | /* deg estimates degradation of the objective function per unit |
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109 | of the sum of integer infeasibilities */ |
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110 | xassert(root->ii_sum > 0.0); |
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111 | deg = (T->mip->mip_obj - root->bound) / root->ii_sum; |
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112 | /* nothing has been selected so far */ |
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113 | p = 0, best = DBL_MAX; |
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114 | /* walk through the list of active subproblems */ |
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115 | for (node = T->head; node != NULL; node = node->next) |
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116 | { xassert(node->up != NULL); |
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117 | /* obj estimates optimal objective value if the sum of integer |
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118 | infeasibilities were zero */ |
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119 | obj = node->up->bound + deg * node->up->ii_sum; |
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120 | if (T->mip->dir == GLP_MAX) obj = - obj; |
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121 | /* select the subproblem which has the best estimated optimal |
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122 | objective value */ |
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123 | if (best > obj) p = node->p, best = obj; |
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124 | } |
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125 | return p; |
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126 | } |
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127 | |
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128 | static int best_node(glp_tree *T) |
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129 | { /* select subproblem with best local bound */ |
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130 | IOSNPD *node, *best = NULL; |
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131 | double bound, eps; |
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132 | switch (T->mip->dir) |
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133 | { case GLP_MIN: |
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134 | bound = +DBL_MAX; |
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135 | for (node = T->head; node != NULL; node = node->next) |
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136 | if (bound > node->bound) bound = node->bound; |
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137 | xassert(bound != +DBL_MAX); |
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138 | eps = 0.001 * (1.0 + fabs(bound)); |
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139 | for (node = T->head; node != NULL; node = node->next) |
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140 | { if (node->bound <= bound + eps) |
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141 | { xassert(node->up != NULL); |
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142 | if (best == NULL || |
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143 | #if 1 |
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144 | best->up->ii_sum > node->up->ii_sum) best = node; |
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145 | #else |
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146 | best->lp_obj > node->lp_obj) best = node; |
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147 | #endif |
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148 | } |
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149 | } |
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150 | break; |
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151 | case GLP_MAX: |
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152 | bound = -DBL_MAX; |
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153 | for (node = T->head; node != NULL; node = node->next) |
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154 | if (bound < node->bound) bound = node->bound; |
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155 | xassert(bound != -DBL_MAX); |
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156 | eps = 0.001 * (1.0 + fabs(bound)); |
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157 | for (node = T->head; node != NULL; node = node->next) |
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158 | { if (node->bound >= bound - eps) |
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159 | { xassert(node->up != NULL); |
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160 | if (best == NULL || |
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161 | #if 1 |
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162 | best->up->ii_sum > node->up->ii_sum) best = node; |
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163 | #else |
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164 | best->lp_obj < node->lp_obj) best = node; |
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165 | #endif |
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166 | } |
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167 | } |
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168 | break; |
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169 | default: |
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170 | xassert(T != T); |
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171 | } |
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172 | xassert(best != NULL); |
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173 | return best->p; |
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174 | } |
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175 | |
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176 | /* eof */ |
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