1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/glpios05.c Mon Dec 06 13:09:21 2010 +0100
1.3 @@ -0,0 +1,281 @@
1.4 +/* glpios05.c (Gomory's mixed integer cut generator) */
1.5 +
1.6 +/***********************************************************************
1.7 +* This code is part of GLPK (GNU Linear Programming Kit).
1.8 +*
1.9 +* Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
1.10 +* 2009, 2010 Andrew Makhorin, Department for Applied Informatics,
1.11 +* Moscow Aviation Institute, Moscow, Russia. All rights reserved.
1.12 +* E-mail: <mao@gnu.org>.
1.13 +*
1.14 +* GLPK is free software: you can redistribute it and/or modify it
1.15 +* under the terms of the GNU General Public License as published by
1.16 +* the Free Software Foundation, either version 3 of the License, or
1.17 +* (at your option) any later version.
1.18 +*
1.19 +* GLPK is distributed in the hope that it will be useful, but WITHOUT
1.20 +* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
1.21 +* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
1.22 +* License for more details.
1.23 +*
1.24 +* You should have received a copy of the GNU General Public License
1.25 +* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
1.26 +***********************************************************************/
1.27 +
1.28 +#include "glpios.h"
1.29 +
1.30 +/***********************************************************************
1.31 +* NAME
1.32 +*
1.33 +* ios_gmi_gen - generate Gomory's mixed integer cuts.
1.34 +*
1.35 +* SYNOPSIS
1.36 +*
1.37 +* #include "glpios.h"
1.38 +* void ios_gmi_gen(glp_tree *tree, IOSPOOL *pool);
1.39 +*
1.40 +* DESCRIPTION
1.41 +*
1.42 +* The routine ios_gmi_gen generates Gomory's mixed integer cuts for
1.43 +* the current point and adds them to the cut pool. */
1.44 +
1.45 +#define MAXCUTS 50
1.46 +/* maximal number of cuts to be generated for one round */
1.47 +
1.48 +struct worka
1.49 +{ /* Gomory's cut generator working area */
1.50 + int *ind; /* int ind[1+n]; */
1.51 + double *val; /* double val[1+n]; */
1.52 + double *phi; /* double phi[1+m+n]; */
1.53 +};
1.54 +
1.55 +#define f(x) ((x) - floor(x))
1.56 +/* compute fractional part of x */
1.57 +
1.58 +static void gen_cut(glp_tree *tree, struct worka *worka, int j)
1.59 +{ /* this routine tries to generate Gomory's mixed integer cut for
1.60 + specified structural variable x[m+j] of integer kind, which is
1.61 + basic and has fractional value in optimal solution to current
1.62 + LP relaxation */
1.63 + glp_prob *mip = tree->mip;
1.64 + int m = mip->m;
1.65 + int n = mip->n;
1.66 + int *ind = worka->ind;
1.67 + double *val = worka->val;
1.68 + double *phi = worka->phi;
1.69 + int i, k, len, kind, stat;
1.70 + double lb, ub, alfa, beta, ksi, phi1, rhs;
1.71 + /* compute row of the simplex tableau, which (row) corresponds
1.72 + to specified basic variable xB[i] = x[m+j]; see (23) */
1.73 + len = glp_eval_tab_row(mip, m+j, ind, val);
1.74 + /* determine beta[i], which a value of xB[i] in optimal solution
1.75 + to current LP relaxation; note that this value is the same as
1.76 + if it would be computed with formula (27); it is assumed that
1.77 + beta[i] is fractional enough */
1.78 + beta = mip->col[j]->prim;
1.79 + /* compute cut coefficients phi and right-hand side rho, which
1.80 + correspond to formula (30); dense format is used, because rows
1.81 + of the simplex tableau is usually dense */
1.82 + for (k = 1; k <= m+n; k++) phi[k] = 0.0;
1.83 + rhs = f(beta); /* initial value of rho; see (28), (32) */
1.84 + for (j = 1; j <= len; j++)
1.85 + { /* determine original number of non-basic variable xN[j] */
1.86 + k = ind[j];
1.87 + xassert(1 <= k && k <= m+n);
1.88 + /* determine the kind, bounds and current status of xN[j] in
1.89 + optimal solution to LP relaxation */
1.90 + if (k <= m)
1.91 + { /* auxiliary variable */
1.92 + GLPROW *row = mip->row[k];
1.93 + kind = GLP_CV;
1.94 + lb = row->lb;
1.95 + ub = row->ub;
1.96 + stat = row->stat;
1.97 + }
1.98 + else
1.99 + { /* structural variable */
1.100 + GLPCOL *col = mip->col[k-m];
1.101 + kind = col->kind;
1.102 + lb = col->lb;
1.103 + ub = col->ub;
1.104 + stat = col->stat;
1.105 + }
1.106 + /* xN[j] cannot be basic */
1.107 + xassert(stat != GLP_BS);
1.108 + /* determine row coefficient ksi[i,j] at xN[j]; see (23) */
1.109 + ksi = val[j];
1.110 + /* if ksi[i,j] is too large in the magnitude, do not generate
1.111 + the cut */
1.112 + if (fabs(ksi) > 1e+05) goto fini;
1.113 + /* if ksi[i,j] is too small in the magnitude, skip it */
1.114 + if (fabs(ksi) < 1e-10) goto skip;
1.115 + /* compute row coefficient alfa[i,j] at y[j]; see (26) */
1.116 + switch (stat)
1.117 + { case GLP_NF:
1.118 + /* xN[j] is free (unbounded) having non-zero ksi[i,j];
1.119 + do not generate the cut */
1.120 + goto fini;
1.121 + case GLP_NL:
1.122 + /* xN[j] has active lower bound */
1.123 + alfa = - ksi;
1.124 + break;
1.125 + case GLP_NU:
1.126 + /* xN[j] has active upper bound */
1.127 + alfa = + ksi;
1.128 + break;
1.129 + case GLP_NS:
1.130 + /* xN[j] is fixed; skip it */
1.131 + goto skip;
1.132 + default:
1.133 + xassert(stat != stat);
1.134 + }
1.135 + /* compute cut coefficient phi'[j] at y[j]; see (21), (28) */
1.136 + switch (kind)
1.137 + { case GLP_IV:
1.138 + /* y[j] is integer */
1.139 + if (fabs(alfa - floor(alfa + 0.5)) < 1e-10)
1.140 + { /* alfa[i,j] is close to nearest integer; skip it */
1.141 + goto skip;
1.142 + }
1.143 + else if (f(alfa) <= f(beta))
1.144 + phi1 = f(alfa);
1.145 + else
1.146 + phi1 = (f(beta) / (1.0 - f(beta))) * (1.0 - f(alfa));
1.147 + break;
1.148 + case GLP_CV:
1.149 + /* y[j] is continuous */
1.150 + if (alfa >= 0.0)
1.151 + phi1 = + alfa;
1.152 + else
1.153 + phi1 = (f(beta) / (1.0 - f(beta))) * (- alfa);
1.154 + break;
1.155 + default:
1.156 + xassert(kind != kind);
1.157 + }
1.158 + /* compute cut coefficient phi[j] at xN[j] and update right-
1.159 + hand side rho; see (31), (32) */
1.160 + switch (stat)
1.161 + { case GLP_NL:
1.162 + /* xN[j] has active lower bound */
1.163 + phi[k] = + phi1;
1.164 + rhs += phi1 * lb;
1.165 + break;
1.166 + case GLP_NU:
1.167 + /* xN[j] has active upper bound */
1.168 + phi[k] = - phi1;
1.169 + rhs -= phi1 * ub;
1.170 + break;
1.171 + default:
1.172 + xassert(stat != stat);
1.173 + }
1.174 +skip: ;
1.175 + }
1.176 + /* now the cut has the form sum_k phi[k] * x[k] >= rho, where cut
1.177 + coefficients are stored in the array phi in dense format;
1.178 + x[1,...,m] are auxiliary variables, x[m+1,...,m+n] are struc-
1.179 + tural variables; see (30) */
1.180 + /* eliminate auxiliary variables in order to express the cut only
1.181 + through structural variables; see (33) */
1.182 + for (i = 1; i <= m; i++)
1.183 + { GLPROW *row;
1.184 + GLPAIJ *aij;
1.185 + if (fabs(phi[i]) < 1e-10) continue;
1.186 + /* auxiliary variable x[i] has non-zero cut coefficient */
1.187 + row = mip->row[i];
1.188 + /* x[i] cannot be fixed */
1.189 + xassert(row->type != GLP_FX);
1.190 + /* substitute x[i] = sum_j a[i,j] * x[m+j] */
1.191 + for (aij = row->ptr; aij != NULL; aij = aij->r_next)
1.192 + phi[m+aij->col->j] += phi[i] * aij->val;
1.193 + }
1.194 + /* convert the final cut to sparse format and substitute fixed
1.195 + (structural) variables */
1.196 + len = 0;
1.197 + for (j = 1; j <= n; j++)
1.198 + { GLPCOL *col;
1.199 + if (fabs(phi[m+j]) < 1e-10) continue;
1.200 + /* structural variable x[m+j] has non-zero cut coefficient */
1.201 + col = mip->col[j];
1.202 + if (col->type == GLP_FX)
1.203 + { /* eliminate x[m+j] */
1.204 + rhs -= phi[m+j] * col->lb;
1.205 + }
1.206 + else
1.207 + { len++;
1.208 + ind[len] = j;
1.209 + val[len] = phi[m+j];
1.210 + }
1.211 + }
1.212 + if (fabs(rhs) < 1e-12) rhs = 0.0;
1.213 + /* if the cut inequality seems to be badly scaled, reject it to
1.214 + avoid numeric difficulties */
1.215 + for (k = 1; k <= len; k++)
1.216 + { if (fabs(val[k]) < 1e-03) goto fini;
1.217 + if (fabs(val[k]) > 1e+03) goto fini;
1.218 + }
1.219 + /* add the cut to the cut pool for further consideration */
1.220 +#if 0
1.221 + ios_add_cut_row(tree, pool, GLP_RF_GMI, len, ind, val, GLP_LO,
1.222 + rhs);
1.223 +#else
1.224 + glp_ios_add_row(tree, NULL, GLP_RF_GMI, 0, len, ind, val, GLP_LO,
1.225 + rhs);
1.226 +#endif
1.227 +fini: return;
1.228 +}
1.229 +
1.230 +struct var { int j; double f; };
1.231 +
1.232 +static int fcmp(const void *p1, const void *p2)
1.233 +{ const struct var *v1 = p1, *v2 = p2;
1.234 + if (v1->f > v2->f) return -1;
1.235 + if (v1->f < v2->f) return +1;
1.236 + return 0;
1.237 +}
1.238 +
1.239 +void ios_gmi_gen(glp_tree *tree)
1.240 +{ /* main routine to generate Gomory's cuts */
1.241 + glp_prob *mip = tree->mip;
1.242 + int m = mip->m;
1.243 + int n = mip->n;
1.244 + struct var *var;
1.245 + int k, nv, j, size;
1.246 + struct worka _worka, *worka = &_worka;
1.247 + /* allocate working arrays */
1.248 + var = xcalloc(1+n, sizeof(struct var));
1.249 + worka->ind = xcalloc(1+n, sizeof(int));
1.250 + worka->val = xcalloc(1+n, sizeof(double));
1.251 + worka->phi = xcalloc(1+m+n, sizeof(double));
1.252 + /* build the list of integer structural variables, which are
1.253 + basic and have fractional value in optimal solution to current
1.254 + LP relaxation */
1.255 + nv = 0;
1.256 + for (j = 1; j <= n; j++)
1.257 + { GLPCOL *col = mip->col[j];
1.258 + double frac;
1.259 + if (col->kind != GLP_IV) continue;
1.260 + if (col->type == GLP_FX) continue;
1.261 + if (col->stat != GLP_BS) continue;
1.262 + frac = f(col->prim);
1.263 + if (!(0.05 <= frac && frac <= 0.95)) continue;
1.264 + /* add variable to the list */
1.265 + nv++, var[nv].j = j, var[nv].f = frac;
1.266 + }
1.267 + /* order the list by descending fractionality */
1.268 + qsort(&var[1], nv, sizeof(struct var), fcmp);
1.269 + /* try to generate cuts by one for each variable in the list, but
1.270 + not more than MAXCUTS cuts */
1.271 + size = glp_ios_pool_size(tree);
1.272 + for (k = 1; k <= nv; k++)
1.273 + { if (glp_ios_pool_size(tree) - size >= MAXCUTS) break;
1.274 + gen_cut(tree, worka, var[k].j);
1.275 + }
1.276 + /* free working arrays */
1.277 + xfree(var);
1.278 + xfree(worka->ind);
1.279 + xfree(worka->val);
1.280 + xfree(worka->phi);
1.281 + return;
1.282 +}
1.283 +
1.284 +/* eof */