1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
|
/* glpios12.c (node selection heuristics) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
*
* Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
* 2009, 2010, 2011, 2013, 2018 Andrew Makhorin, Department for Applied
* Informatics, Moscow Aviation Institute, Moscow, Russia. All rights
* reserved. E-mail: <mao@gnu.org>.
*
* GLPK is free software: you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* GLPK is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
* License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
***********************************************************************/
#include "env.h"
#include "ios.h"
/***********************************************************************
* NAME
*
* ios_choose_node - select subproblem to continue the search
*
* SYNOPSIS
*
* #include "glpios.h"
* int ios_choose_node(glp_tree *T);
*
* DESCRIPTION
*
* The routine ios_choose_node selects a subproblem from the active
* list to continue the search. The choice depends on the backtracking
* technique option.
*
* RETURNS
*
* The routine ios_choose_node return the reference number of the
* subproblem selected. */
static int most_feas(glp_tree *T);
static int best_proj(glp_tree *T);
static int best_node(glp_tree *T);
int ios_choose_node(glp_tree *T)
{ int p;
if (T->parm->bt_tech == GLP_BT_DFS)
{ /* depth first search */
xassert(T->tail != NULL);
p = T->tail->p;
}
else if (T->parm->bt_tech == GLP_BT_BFS)
{ /* breadth first search */
xassert(T->head != NULL);
p = T->head->p;
}
else if (T->parm->bt_tech == GLP_BT_BLB)
{ /* select node with best local bound */
p = best_node(T);
}
else if (T->parm->bt_tech == GLP_BT_BPH)
{ if (T->mip->mip_stat == GLP_UNDEF)
{ /* "most integer feasible" subproblem */
p = most_feas(T);
}
else
{ /* best projection heuristic */
p = best_proj(T);
}
}
else
xassert(T != T);
return p;
}
static int most_feas(glp_tree *T)
{ /* select subproblem whose parent has minimal sum of integer
infeasibilities */
IOSNPD *node;
int p;
double best;
p = 0, best = DBL_MAX;
for (node = T->head; node != NULL; node = node->next)
{ xassert(node->up != NULL);
if (best > node->up->ii_sum)
p = node->p, best = node->up->ii_sum;
}
return p;
}
static int best_proj(glp_tree *T)
{ /* select subproblem using the best projection heuristic */
IOSNPD *root, *node;
int p;
double best, deg, obj;
/* the global bound must exist */
xassert(T->mip->mip_stat == GLP_FEAS);
/* obtain pointer to the root node, which must exist */
root = T->slot[1].node;
xassert(root != NULL);
/* deg estimates degradation of the objective function per unit
of the sum of integer infeasibilities */
xassert(root->ii_sum > 0.0);
deg = (T->mip->mip_obj - root->bound) / root->ii_sum;
/* nothing has been selected so far */
p = 0, best = DBL_MAX;
/* walk through the list of active subproblems */
for (node = T->head; node != NULL; node = node->next)
{ xassert(node->up != NULL);
/* obj estimates optimal objective value if the sum of integer
infeasibilities were zero */
obj = node->up->bound + deg * node->up->ii_sum;
if (T->mip->dir == GLP_MAX) obj = - obj;
/* select the subproblem which has the best estimated optimal
objective value */
if (best > obj) p = node->p, best = obj;
}
return p;
}
static int best_node(glp_tree *T)
{ /* select subproblem with best local bound */
IOSNPD *node, *best = NULL;
double bound, eps;
switch (T->mip->dir)
{ case GLP_MIN:
bound = +DBL_MAX;
for (node = T->head; node != NULL; node = node->next)
if (bound > node->bound) bound = node->bound;
xassert(bound != +DBL_MAX);
eps = 1e-10 * (1.0 + fabs(bound));
for (node = T->head; node != NULL; node = node->next)
{ if (node->bound <= bound + eps)
{ xassert(node->up != NULL);
if (best == NULL ||
#if 1
best->up->ii_sum > node->up->ii_sum) best = node;
#else
best->lp_obj > node->lp_obj) best = node;
#endif
}
}
break;
case GLP_MAX:
bound = -DBL_MAX;
for (node = T->head; node != NULL; node = node->next)
if (bound < node->bound) bound = node->bound;
xassert(bound != -DBL_MAX);
eps = 1e-10 * (1.0 + fabs(bound));
for (node = T->head; node != NULL; node = node->next)
{ if (node->bound >= bound - eps)
{ xassert(node->up != NULL);
if (best == NULL ||
#if 1
best->up->ii_sum > node->up->ii_sum) best = node;
#else
best->lp_obj < node->lp_obj) best = node;
#endif
}
}
break;
default:
xassert(T != T);
}
xassert(best != NULL);
return best->p;
}
/* eof */
|
