/* glpios05.c (Gomory's mixed integer cut generator) */

 /***********************************************************************

 *  This code is part of GLPK (GNU Linear Programming Kit).

 *

 *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,

 *  2009, 2010 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 "glpios.h"

 /***********************************************************************

 *  NAME

 *

 *  ios_gmi_gen - generate Gomory's mixed integer cuts.

 *

 *  SYNOPSIS

 *

 *  #include "glpios.h"

 *  void ios_gmi_gen(glp_tree *tree, IOSPOOL *pool);

 *

 *  DESCRIPTION

 *

 *  The routine ios_gmi_gen generates Gomory's mixed integer cuts for

 *  the current point and adds them to the cut pool. */

 #define MAXCUTS 50

 /* maximal number of cuts to be generated for one round */

 struct worka

 {     /* Gomory's cut generator working area */

       int *ind; /* int ind[1+n]; */

       double *val; /* double val[1+n]; */

       double *phi; /* double phi[1+m+n]; */

 };

 #define f(x) ((x) - floor(x))

 /* compute fractional part of x */

 static void gen_cut(glp_tree *tree, struct worka *worka, int j)

 {     /* this routine tries to generate Gomory's mixed integer cut for

          specified structural variable x[m+j] of integer kind, which is

          basic and has fractional value in optimal solution to current

          LP relaxation */

       glp_prob *mip = tree->mip;

       int m = mip->m;

       int n = mip->n;

       int *ind = worka->ind;

       double *val = worka->val;

       double *phi = worka->phi;

       int i, k, len, kind, stat;

       double lb, ub, alfa, beta, ksi, phi1, rhs;

       /* compute row of the simplex tableau, which (row) corresponds

          to specified basic variable xB[i] = x[m+j]; see (23) */

       len = glp_eval_tab_row(mip, m+j, ind, val);

       /* determine beta[i], which a value of xB[i] in optimal solution

          to current LP relaxation; note that this value is the same as

          if it would be computed with formula (27); it is assumed that

          beta[i] is fractional enough */

       beta = mip->col[j]->prim;

       /* compute cut coefficients phi and right-hand side rho, which

          correspond to formula (30); dense format is used, because rows

          of the simplex tableau is usually dense */

       for (k = 1; k <= m+n; k++) phi[k] = 0.0;

       rhs = f(beta); /* initial value of rho; see (28), (32) */

       for (j = 1; j <= len; j++)

       {  /* determine original number of non-basic variable xN[j] */

          k = ind[j];

          xassert(1 <= k && k <= m+n);

          /* determine the kind, bounds and current status of xN[j] in

             optimal solution to LP relaxation */

          if (k <= m)

          {  /* auxiliary variable */

             GLPROW *row = mip->row[k];

             kind = GLP_CV;

             lb = row->lb;

             ub = row->ub;

             stat = row->stat;

          }

          else

          {  /* structural variable */

             GLPCOL *col = mip->col[k-m];

             kind = col->kind;

             lb = col->lb;

             ub = col->ub;

             stat = col->stat;

          }

          /* xN[j] cannot be basic */

          xassert(stat != GLP_BS);

          /* determine row coefficient ksi[i,j] at xN[j]; see (23) */

          ksi = val[j];

          /* if ksi[i,j] is too large in the magnitude, do not generate

             the cut */

          if (fabs(ksi) > 1e+05) goto fini;

          /* if ksi[i,j] is too small in the magnitude, skip it */

          if (fabs(ksi) < 1e-10) goto skip;

          /* compute row coefficient alfa[i,j] at y[j]; see (26) */

          switch (stat)

          {  case GLP_NF:

                /* xN[j] is free (unbounded) having non-zero ksi[i,j];

                   do not generate the cut */

                goto fini;

             case GLP_NL:

                /* xN[j] has active lower bound */

                alfa = - ksi;

                break;

             case GLP_NU:

                /* xN[j] has active upper bound */

                alfa = + ksi;

                break;

             case GLP_NS:

                /* xN[j] is fixed; skip it */

                goto skip;

             default:

                xassert(stat != stat);

          }

          /* compute cut coefficient phi'[j] at y[j]; see (21), (28) */

          switch (kind)

          {  case GLP_IV:

                /* y[j] is integer */

                if (fabs(alfa - floor(alfa + 0.5)) < 1e-10)

                {  /* alfa[i,j] is close to nearest integer; skip it */

                   goto skip;

                }

                else if (f(alfa) <= f(beta))

                   phi1 = f(alfa);

                else

                   phi1 = (f(beta) / (1.0 - f(beta))) * (1.0 - f(alfa));

                break;

             case GLP_CV:

                /* y[j] is continuous */

                if (alfa >= 0.0)

                   phi1 = + alfa;

                else

                   phi1 = (f(beta) / (1.0 - f(beta))) * (- alfa);

                break;

             default:

                xassert(kind != kind);

          }

          /* compute cut coefficient phi[j] at xN[j] and update right-

             hand side rho; see (31), (32) */

          switch (stat)

          {  case GLP_NL:

                /* xN[j] has active lower bound */

                phi[k] = + phi1;

                rhs += phi1 * lb;

                break;

             case GLP_NU:

                /* xN[j] has active upper bound */

                phi[k] = - phi1;

                rhs -= phi1 * ub;

                break;

             default:

                xassert(stat != stat);

          }

 skip:    ;

       }

       /* now the cut has the form sum_k phi[k] * x[k] >= rho, where cut

          coefficients are stored in the array phi in dense format;

          x[1,...,m] are auxiliary variables, x[m+1,...,m+n] are struc-

          tural variables; see (30) */

       /* eliminate auxiliary variables in order to express the cut only

          through structural variables; see (33) */

       for (i = 1; i <= m; i++)

       {  GLPROW *row;

          GLPAIJ *aij;

          if (fabs(phi[i]) < 1e-10) continue;

          /* auxiliary variable x[i] has non-zero cut coefficient */

          row = mip->row[i];

          /* x[i] cannot be fixed */

          xassert(row->type != GLP_FX);

          /* substitute x[i] = sum_j a[i,j] * x[m+j] */

          for (aij = row->ptr; aij != NULL; aij = aij->r_next)

             phi[m+aij->col->j] += phi[i] * aij->val;

       }

       /* convert the final cut to sparse format and substitute fixed

          (structural) variables */

       len = 0;

       for (j = 1; j <= n; j++)

       {  GLPCOL *col;

          if (fabs(phi[m+j]) < 1e-10) continue;

          /* structural variable x[m+j] has non-zero cut coefficient */

          col = mip->col[j];

          if (col->type == GLP_FX)

          {  /* eliminate x[m+j] */

             rhs -= phi[m+j] * col->lb;

          }

          else

          {  len++;

             ind[len] = j;

             val[len] = phi[m+j];

          }

       }

       if (fabs(rhs) < 1e-12) rhs = 0.0;

       /* if the cut inequality seems to be badly scaled, reject it to

          avoid numeric difficulties */

       for (k = 1; k <= len; k++)

       {  if (fabs(val[k]) < 1e-03) goto fini;

          if (fabs(val[k]) > 1e+03) goto fini;

       }

       /* add the cut to the cut pool for further consideration */

 #if 0

       ios_add_cut_row(tree, pool, GLP_RF_GMI, len, ind, val, GLP_LO,

          rhs);

 #else

       glp_ios_add_row(tree, NULL, GLP_RF_GMI, 0, len, ind, val, GLP_LO,

          rhs);

 #endif

 fini: return;

 }

 struct var { int j; double f; };

 static int fcmp(const void *p1, const void *p2)

 {     const struct var *v1 = p1, *v2 = p2;

       if (v1->f > v2->f) return -1;

       if (v1->f < v2->f) return +1;

       return 0;

 }

 void ios_gmi_gen(glp_tree *tree)

 {     /* main routine to generate Gomory's cuts */

       glp_prob *mip = tree->mip;

       int m = mip->m;

       int n = mip->n;

       struct var *var;

       int k, nv, j, size;

       struct worka _worka, *worka = &_worka;

       /* allocate working arrays */

       var = xcalloc(1+n, sizeof(struct var));

       worka->ind = xcalloc(1+n, sizeof(int));

       worka->val = xcalloc(1+n, sizeof(double));

       worka->phi = xcalloc(1+m+n, sizeof(double));

       /* build the list of integer structural variables, which are

          basic and have fractional value in optimal solution to current

          LP relaxation */

       nv = 0;

       for (j = 1; j <= n; j++)

       {  GLPCOL *col = mip->col[j];

          double frac;

          if (col->kind != GLP_IV) continue;

          if (col->type == GLP_FX) continue;

          if (col->stat != GLP_BS) continue;

          frac = f(col->prim);

          if (!(0.05 <= frac && frac <= 0.95)) continue;

          /* add variable to the list */

          nv++, var[nv].j = j, var[nv].f = frac;

       }

       /* order the list by descending fractionality */

       qsort(&var[1], nv, sizeof(struct var), fcmp);

       /* try to generate cuts by one for each variable in the list, but

          not more than MAXCUTS cuts */

       size = glp_ios_pool_size(tree);

       for (k = 1; k <= nv; k++)

       {  if (glp_ios_pool_size(tree) - size >= MAXCUTS) break;

          gen_cut(tree, worka, var[k].j);

       }

       /* free working arrays */

       xfree(var);

       xfree(worka->ind);

       xfree(worka->val);

       xfree(worka->phi);

       return;

 }

 /* eof */