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270 lines
8.8 KiB
270 lines
8.8 KiB
/* glpini02.c */
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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 "env.h"
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#include "prob.h"
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struct var
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{ /* structural variable */
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int j;
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/* ordinal number */
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double q;
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/* penalty value */
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};
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static int fcmp(const void *ptr1, const void *ptr2)
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{ /* this routine is passed to the qsort() function */
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struct var *col1 = (void *)ptr1, *col2 = (void *)ptr2;
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if (col1->q < col2->q) return -1;
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if (col1->q > col2->q) return +1;
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return 0;
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}
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static int get_column(glp_prob *lp, int j, int ind[], double val[])
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{ /* Bixby's algorithm assumes that the constraint matrix is scaled
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such that the maximum absolute value in every non-zero row and
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column is 1 */
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int k, len;
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double big;
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len = glp_get_mat_col(lp, j, ind, val);
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big = 0.0;
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for (k = 1; k <= len; k++)
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if (big < fabs(val[k])) big = fabs(val[k]);
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if (big == 0.0) big = 1.0;
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for (k = 1; k <= len; k++) val[k] /= big;
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return len;
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}
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static void cpx_basis(glp_prob *lp)
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{ /* main routine */
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struct var *C, *C2, *C3, *C4;
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int m, n, i, j, jk, k, l, ll, t, n2, n3, n4, type, len, *I, *r,
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*ind;
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double alpha, gamma, cmax, temp, *v, *val;
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xprintf("Constructing initial basis...\n");
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/* determine the number of rows and columns */
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m = glp_get_num_rows(lp);
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n = glp_get_num_cols(lp);
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/* allocate working arrays */
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C = xcalloc(1+n, sizeof(struct var));
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I = xcalloc(1+m, sizeof(int));
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r = xcalloc(1+m, sizeof(int));
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v = xcalloc(1+m, sizeof(double));
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ind = xcalloc(1+m, sizeof(int));
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val = xcalloc(1+m, sizeof(double));
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/* make all auxiliary variables non-basic */
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for (i = 1; i <= m; i++)
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{ if (glp_get_row_type(lp, i) != GLP_DB)
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glp_set_row_stat(lp, i, GLP_NS);
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else if (fabs(glp_get_row_lb(lp, i)) <=
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fabs(glp_get_row_ub(lp, i)))
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glp_set_row_stat(lp, i, GLP_NL);
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else
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glp_set_row_stat(lp, i, GLP_NU);
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}
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/* make all structural variables non-basic */
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for (j = 1; j <= n; j++)
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{ if (glp_get_col_type(lp, j) != GLP_DB)
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glp_set_col_stat(lp, j, GLP_NS);
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else if (fabs(glp_get_col_lb(lp, j)) <=
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fabs(glp_get_col_ub(lp, j)))
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glp_set_col_stat(lp, j, GLP_NL);
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else
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glp_set_col_stat(lp, j, GLP_NU);
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}
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/* C2 is a set of free structural variables */
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n2 = 0, C2 = C + 0;
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for (j = 1; j <= n; j++)
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{ type = glp_get_col_type(lp, j);
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if (type == GLP_FR)
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{ n2++;
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C2[n2].j = j;
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C2[n2].q = 0.0;
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}
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}
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/* C3 is a set of structural variables having excatly one (lower
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or upper) bound */
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n3 = 0, C3 = C2 + n2;
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for (j = 1; j <= n; j++)
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{ type = glp_get_col_type(lp, j);
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if (type == GLP_LO)
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{ n3++;
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C3[n3].j = j;
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C3[n3].q = + glp_get_col_lb(lp, j);
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}
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else if (type == GLP_UP)
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{ n3++;
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C3[n3].j = j;
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C3[n3].q = - glp_get_col_ub(lp, j);
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}
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}
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/* C4 is a set of structural variables having both (lower and
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upper) bounds */
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n4 = 0, C4 = C3 + n3;
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for (j = 1; j <= n; j++)
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{ type = glp_get_col_type(lp, j);
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if (type == GLP_DB)
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{ n4++;
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C4[n4].j = j;
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C4[n4].q = glp_get_col_lb(lp, j) - glp_get_col_ub(lp, j);
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}
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}
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/* compute gamma = max{|c[j]|: 1 <= j <= n} */
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gamma = 0.0;
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for (j = 1; j <= n; j++)
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{ temp = fabs(glp_get_obj_coef(lp, j));
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if (gamma < temp) gamma = temp;
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}
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/* compute cmax */
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cmax = (gamma == 0.0 ? 1.0 : 1000.0 * gamma);
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/* compute final penalty for all structural variables within sets
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C2, C3, and C4 */
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switch (glp_get_obj_dir(lp))
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{ case GLP_MIN: temp = +1.0; break;
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case GLP_MAX: temp = -1.0; break;
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default: xassert(lp != lp);
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}
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for (k = 1; k <= n2+n3+n4; k++)
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{ j = C[k].j;
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C[k].q += (temp * glp_get_obj_coef(lp, j)) / cmax;
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}
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/* sort structural variables within C2, C3, and C4 in ascending
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order of penalty value */
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qsort(C2+1, n2, sizeof(struct var), fcmp);
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for (k = 1; k < n2; k++) xassert(C2[k].q <= C2[k+1].q);
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qsort(C3+1, n3, sizeof(struct var), fcmp);
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for (k = 1; k < n3; k++) xassert(C3[k].q <= C3[k+1].q);
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qsort(C4+1, n4, sizeof(struct var), fcmp);
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for (k = 1; k < n4; k++) xassert(C4[k].q <= C4[k+1].q);
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/*** STEP 1 ***/
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for (i = 1; i <= m; i++)
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{ type = glp_get_row_type(lp, i);
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if (type != GLP_FX)
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{ /* row i is either free or inequality constraint */
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glp_set_row_stat(lp, i, GLP_BS);
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I[i] = 1;
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r[i] = 1;
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}
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else
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{ /* row i is equality constraint */
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I[i] = 0;
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r[i] = 0;
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}
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v[i] = +DBL_MAX;
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}
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/*** STEP 2 ***/
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for (k = 1; k <= n2+n3+n4; k++)
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{ jk = C[k].j;
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len = get_column(lp, jk, ind, val);
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/* let alpha = max{|A[l,jk]|: r[l] = 0} and let l' be such
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that alpha = |A[l',jk]| */
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alpha = 0.0, ll = 0;
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for (t = 1; t <= len; t++)
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{ l = ind[t];
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if (r[l] == 0 && alpha < fabs(val[t]))
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alpha = fabs(val[t]), ll = l;
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}
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if (alpha >= 0.99)
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{ /* B := B union {jk} */
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glp_set_col_stat(lp, jk, GLP_BS);
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I[ll] = 1;
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v[ll] = alpha;
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/* r[l] := r[l] + 1 for all l such that |A[l,jk]| != 0 */
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for (t = 1; t <= len; t++)
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{ l = ind[t];
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if (val[t] != 0.0) r[l]++;
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}
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/* continue to the next k */
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continue;
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}
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/* if |A[l,jk]| > 0.01 * v[l] for some l, continue to the
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next k */
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for (t = 1; t <= len; t++)
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{ l = ind[t];
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if (fabs(val[t]) > 0.01 * v[l]) break;
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}
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if (t <= len) continue;
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/* otherwise, let alpha = max{|A[l,jk]|: I[l] = 0} and let l'
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be such that alpha = |A[l',jk]| */
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alpha = 0.0, ll = 0;
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for (t = 1; t <= len; t++)
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{ l = ind[t];
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if (I[l] == 0 && alpha < fabs(val[t]))
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alpha = fabs(val[t]), ll = l;
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}
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/* if alpha = 0, continue to the next k */
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if (alpha == 0.0) continue;
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/* B := B union {jk} */
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glp_set_col_stat(lp, jk, GLP_BS);
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I[ll] = 1;
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v[ll] = alpha;
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/* r[l] := r[l] + 1 for all l such that |A[l,jk]| != 0 */
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for (t = 1; t <= len; t++)
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{ l = ind[t];
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if (val[t] != 0.0) r[l]++;
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}
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}
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/*** STEP 3 ***/
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/* add an artificial variable (auxiliary variable for equality
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constraint) to cover each remaining uncovered row */
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for (i = 1; i <= m; i++)
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if (I[i] == 0) glp_set_row_stat(lp, i, GLP_BS);
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/* free working arrays */
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xfree(C);
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xfree(I);
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xfree(r);
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xfree(v);
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xfree(ind);
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xfree(val);
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return;
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}
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/***********************************************************************
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* NAME
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*
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* glp_cpx_basis - construct Bixby's initial LP basis
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*
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* SYNOPSIS
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*
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* void glp_cpx_basis(glp_prob *lp);
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*
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* DESCRIPTION
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*
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* The routine glp_cpx_basis constructs an advanced initial basis for
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* the specified problem object.
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*
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* The routine is based on Bixby's algorithm described in the paper:
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*
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* Robert E. Bixby. Implementing the Simplex Method: The Initial Basis.
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* ORSA Journal on Computing, Vol. 4, No. 3, 1992, pp. 267-84. */
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void glp_cpx_basis(glp_prob *lp)
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{ if (lp->m == 0 || lp->n == 0)
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glp_std_basis(lp);
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else
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cpx_basis(lp);
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return;
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}
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/* eof */
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