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