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+/* 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 */