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282 lines
10 KiB
282 lines
10 KiB
/* glpios11.c (process cuts stored in the local cut pool) */
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/***********************************************************************
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* This code is part of GLPK (GNU Linear Programming Kit).
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*
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* Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
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* 2009, 2010, 2011, 2013 Andrew Makhorin, Department for Applied
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* Informatics, Moscow Aviation Institute, Moscow, Russia. All rights
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* reserved. E-mail: <mao@gnu.org>.
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*
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* GLPK is free software: you can redistribute it and/or modify it
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* under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* GLPK is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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* License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
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***********************************************************************/
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#include "draft.h"
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#include "env.h"
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#include "glpios.h"
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/***********************************************************************
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* NAME
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*
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* ios_process_cuts - process cuts stored in the local cut pool
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*
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* SYNOPSIS
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*
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* #include "glpios.h"
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* void ios_process_cuts(glp_tree *T);
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*
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* DESCRIPTION
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*
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* The routine ios_process_cuts analyzes each cut currently stored in
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* the local cut pool, which must be non-empty, and either adds the cut
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* to the current subproblem or just discards it. All cuts are assumed
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* to be locally valid. On exit the local cut pool remains unchanged.
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*
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* REFERENCES
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*
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* 1. E.Balas, S.Ceria, G.Cornuejols, "Mixed 0-1 Programming by
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* Lift-and-Project in a Branch-and-Cut Framework", Management Sc.,
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* 42 (1996) 1229-1246.
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*
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* 2. G.Andreello, A.Caprara, and M.Fischetti, "Embedding Cuts in
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* a Branch&Cut Framework: a Computational Study with {0,1/2}-Cuts",
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* Preliminary Draft, October 28, 2003, pp.6-8. */
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struct info
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{ /* estimated cut efficiency */
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IOSCUT *cut;
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/* pointer to cut in the cut pool */
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char flag;
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/* if this flag is set, the cut is included into the current
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subproblem */
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double eff;
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/* cut efficacy (normalized residual) */
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double deg;
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/* lower bound to objective degradation */
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};
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static int fcmp(const void *arg1, const void *arg2)
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{ const struct info *info1 = arg1, *info2 = arg2;
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if (info1->deg == 0.0 && info2->deg == 0.0)
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{ if (info1->eff > info2->eff) return -1;
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if (info1->eff < info2->eff) return +1;
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}
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else
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{ if (info1->deg > info2->deg) return -1;
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if (info1->deg < info2->deg) return +1;
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}
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return 0;
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}
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static double parallel(IOSCUT *a, IOSCUT *b, double work[]);
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void ios_process_cuts(glp_tree *T)
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{ IOSPOOL *pool;
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IOSCUT *cut;
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IOSAIJ *aij;
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struct info *info;
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int k, kk, max_cuts, len, ret, *ind;
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double *val, *work;
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/* the current subproblem must exist */
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xassert(T->curr != NULL);
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/* the pool must exist and be non-empty */
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pool = T->local;
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xassert(pool != NULL);
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xassert(pool->size > 0);
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/* allocate working arrays */
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info = xcalloc(1+pool->size, sizeof(struct info));
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ind = xcalloc(1+T->n, sizeof(int));
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val = xcalloc(1+T->n, sizeof(double));
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work = xcalloc(1+T->n, sizeof(double));
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for (k = 1; k <= T->n; k++) work[k] = 0.0;
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/* build the list of cuts stored in the cut pool */
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for (k = 0, cut = pool->head; cut != NULL; cut = cut->next)
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k++, info[k].cut = cut, info[k].flag = 0;
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xassert(k == pool->size);
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/* estimate efficiency of all cuts in the cut pool */
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for (k = 1; k <= pool->size; k++)
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{ double temp, dy, dz;
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cut = info[k].cut;
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/* build the vector of cut coefficients and compute its
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Euclidean norm */
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len = 0; temp = 0.0;
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for (aij = cut->ptr; aij != NULL; aij = aij->next)
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{ xassert(1 <= aij->j && aij->j <= T->n);
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len++, ind[len] = aij->j, val[len] = aij->val;
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temp += aij->val * aij->val;
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}
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if (temp < DBL_EPSILON * DBL_EPSILON) temp = DBL_EPSILON;
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/* transform the cut to express it only through non-basic
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(auxiliary and structural) variables */
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len = glp_transform_row(T->mip, len, ind, val);
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/* determine change in the cut value and in the objective
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value for the adjacent basis by simulating one step of the
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dual simplex */
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ret = _glp_analyze_row(T->mip, len, ind, val, cut->type,
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cut->rhs, 1e-9, NULL, NULL, NULL, NULL, &dy, &dz);
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/* determine normalized residual and lower bound to objective
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degradation */
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if (ret == 0)
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{ info[k].eff = fabs(dy) / sqrt(temp);
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/* if some reduced costs violates (slightly) their zero
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bounds (i.e. have wrong signs) due to round-off errors,
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dz also may have wrong sign being close to zero */
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if (T->mip->dir == GLP_MIN)
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{ if (dz < 0.0) dz = 0.0;
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info[k].deg = + dz;
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}
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else /* GLP_MAX */
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{ if (dz > 0.0) dz = 0.0;
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info[k].deg = - dz;
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}
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}
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else if (ret == 1)
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{ /* the constraint is not violated at the current point */
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info[k].eff = info[k].deg = 0.0;
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}
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else if (ret == 2)
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{ /* no dual feasible adjacent basis exists */
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info[k].eff = 1.0;
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info[k].deg = DBL_MAX;
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}
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else
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xassert(ret != ret);
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/* if the degradation is too small, just ignore it */
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if (info[k].deg < 0.01) info[k].deg = 0.0;
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}
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/* sort the list of cuts by decreasing objective degradation and
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then by decreasing efficacy */
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qsort(&info[1], pool->size, sizeof(struct info), fcmp);
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/* only first (most efficient) max_cuts in the list are qualified
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as candidates to be added to the current subproblem */
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max_cuts = (T->curr->level == 0 ? 90 : 10);
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if (max_cuts > pool->size) max_cuts = pool->size;
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/* add cuts to the current subproblem */
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#if 0
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xprintf("*** adding cuts ***\n");
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#endif
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for (k = 1; k <= max_cuts; k++)
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{ int i, len;
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/* if this cut seems to be inefficient, skip it */
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if (info[k].deg < 0.01 && info[k].eff < 0.01) continue;
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/* if the angle between this cut and every other cut included
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in the current subproblem is small, skip this cut */
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for (kk = 1; kk < k; kk++)
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{ if (info[kk].flag)
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{ if (parallel(info[k].cut, info[kk].cut, work) > 0.90)
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break;
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}
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}
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if (kk < k) continue;
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/* add this cut to the current subproblem */
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#if 0
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xprintf("eff = %g; deg = %g\n", info[k].eff, info[k].deg);
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#endif
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cut = info[k].cut, info[k].flag = 1;
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i = glp_add_rows(T->mip, 1);
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if (cut->name != NULL)
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glp_set_row_name(T->mip, i, cut->name);
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xassert(T->mip->row[i]->origin == GLP_RF_CUT);
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T->mip->row[i]->klass = cut->klass;
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len = 0;
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for (aij = cut->ptr; aij != NULL; aij = aij->next)
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len++, ind[len] = aij->j, val[len] = aij->val;
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glp_set_mat_row(T->mip, i, len, ind, val);
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xassert(cut->type == GLP_LO || cut->type == GLP_UP);
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glp_set_row_bnds(T->mip, i, cut->type, cut->rhs, cut->rhs);
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}
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/* free working arrays */
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xfree(info);
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xfree(ind);
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xfree(val);
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xfree(work);
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return;
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}
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#if 0
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/***********************************************************************
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* Given a cut a * x >= b (<= b) the routine efficacy computes the cut
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* efficacy as follows:
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*
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* eff = d * (a * x~ - b) / ||a||,
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*
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* where d is -1 (in case of '>= b') or +1 (in case of '<= b'), x~ is
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* the vector of values of structural variables in optimal solution to
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* LP relaxation of the current subproblem, ||a|| is the Euclidean norm
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* of the vector of cut coefficients.
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*
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* If the cut is violated at point x~, the efficacy eff is positive,
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* and its value is the Euclidean distance between x~ and the cut plane
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* a * x = b in the space of structural variables.
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*
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* Following geometrical intuition, it is quite natural to consider
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* this distance as a first-order measure of the expected efficacy of
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* the cut: the larger the distance the better the cut [1]. */
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static double efficacy(glp_tree *T, IOSCUT *cut)
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{ glp_prob *mip = T->mip;
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IOSAIJ *aij;
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double s = 0.0, t = 0.0, temp;
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for (aij = cut->ptr; aij != NULL; aij = aij->next)
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{ xassert(1 <= aij->j && aij->j <= mip->n);
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s += aij->val * mip->col[aij->j]->prim;
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t += aij->val * aij->val;
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}
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temp = sqrt(t);
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if (temp < DBL_EPSILON) temp = DBL_EPSILON;
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if (cut->type == GLP_LO)
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temp = (s >= cut->rhs ? 0.0 : (cut->rhs - s) / temp);
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else if (cut->type == GLP_UP)
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temp = (s <= cut->rhs ? 0.0 : (s - cut->rhs) / temp);
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else
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xassert(cut != cut);
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return temp;
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}
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#endif
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/***********************************************************************
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* Given two cuts a1 * x >= b1 (<= b1) and a2 * x >= b2 (<= b2) the
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* routine parallel computes the cosine of angle between the cut planes
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* a1 * x = b1 and a2 * x = b2 (which is the acute angle between two
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* normals to these planes) in the space of structural variables as
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* follows:
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*
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* cos phi = (a1' * a2) / (||a1|| * ||a2||),
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*
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* where (a1' * a2) is a dot product of vectors of cut coefficients,
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* ||a1|| and ||a2|| are Euclidean norms of vectors a1 and a2.
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*
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* Note that requirement cos phi = 0 forces the cuts to be orthogonal,
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* i.e. with disjoint support, while requirement cos phi <= 0.999 means
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* only avoiding duplicate (parallel) cuts [1]. */
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static double parallel(IOSCUT *a, IOSCUT *b, double work[])
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{ IOSAIJ *aij;
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double s = 0.0, sa = 0.0, sb = 0.0, temp;
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for (aij = a->ptr; aij != NULL; aij = aij->next)
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{ work[aij->j] = aij->val;
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sa += aij->val * aij->val;
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}
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for (aij = b->ptr; aij != NULL; aij = aij->next)
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{ s += work[aij->j] * aij->val;
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sb += aij->val * aij->val;
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}
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for (aij = a->ptr; aij != NULL; aij = aij->next)
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work[aij->j] = 0.0;
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temp = sqrt(sa) * sqrt(sb);
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if (temp < DBL_EPSILON * DBL_EPSILON) temp = DBL_EPSILON;
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return s / temp;
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}
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/* eof */
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