You can not select more than 25 topics Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
 
 
 
 

222 lines
9.2 KiB

/* spychuzc.c */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
*
* Copyright (C) 2015 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 "env.h"
#include "spychuzc.h"
/***********************************************************************
* spy_chuzc_std - choose non-basic variable (dual textbook ratio test)
*
* This routine implements an improved dual textbook ratio test to
* choose non-basic variable xN[q].
*
* Current reduced costs of non-basic variables should be placed in the
* array locations d[1], ..., d[n-m]. Note that d[j] is a value of dual
* basic variable lambdaN[j] in the current basis.
*
* The parameter s specifies the sign of bound violation for basic
* variable xB[p] chosen: s = +1.0 means that xB[p] violates its lower
* bound, so dual non-basic variable lambdaB[p] = lambda^+B[p]
* increases, and s = -1.0 means that xB[p] violates its upper bound,
* so dual non-basic variable lambdaB[p] = lambda^-B[p] decreases.
* (Thus, the dual ray parameter theta = s * lambdaB[p] >= 0.)
*
* Elements of p-th simplex table row t[p] = (t[p,j]) corresponding
* to basic variable xB[p] should be placed in the array locations
* trow[1], ..., trow[n-m].
*
* The parameter tol_piv specifies a tolerance for elements of the
* simplex table row t[p]. If |t[p,j]| < tol_piv, dual basic variable
* lambdaN[j] is skipped, i.e. it is assumed that it does not depend on
* the dual ray parameter theta.
*
* The parameters tol and tol1 specify tolerances used to increase the
* choice freedom by simulating an artificial degeneracy as follows.
* If lambdaN[j] = lambda^+N[j] >= 0 and d[j] <= +delta[j], or if
* lambdaN[j] = lambda^-N[j] <= 0 and d[j] >= -delta[j], where
* delta[j] = tol + tol1 * |cN[j]|, cN[j] is objective coefficient at
* xN[j], then it is assumed that reduced cost d[j] is equal to zero.
*
* The routine determines the index 1 <= q <= n-m of non-basic variable
* xN[q], for which corresponding dual basic variable lambda^+N[j] or
* lambda^-N[j] reaches its zero bound first on increasing the dual ray
* parameter theta, and returns p on exit. And if theta may increase
* unlimitedly, the routine returns zero. */
int spy_chuzc_std(SPXLP *lp, const double d[/*1+n-m*/],
double s, const double trow[/*1+n-m*/], double tol_piv,
double tol, double tol1)
{ int m = lp->m;
int n = lp->n;
double *c = lp->c;
double *l = lp->l;
double *u = lp->u;
int *head = lp->head;
char *flag = lp->flag;
int j, k, q;
double alfa, biga, delta, teta, teta_min;
xassert(s == +1.0 || s == -1.0);
/* nothing is chosen so far */
q = 0, teta_min = DBL_MAX, biga = 0.0;
/* walk thru the list of non-basic variables */
for (j = 1; j <= n-m; j++)
{ k = head[m+j]; /* x[k] = xN[j] */
/* if xN[j] is fixed variable, skip it */
if (l[k] == u[k])
continue;
alfa = s * trow[j];
if (alfa >= +tol_piv && !flag[j])
{ /* xN[j] is either free or has its lower bound active, so
* lambdaN[j] = d[j] >= 0 decreases down to zero */
delta = tol + tol1 * (c[k] >= 0.0 ? +c[k] : -c[k]);
/* determine theta on which lambdaN[j] reaches zero */
teta = (d[j] < +delta ? 0.0 : d[j] / alfa);
}
else if (alfa <= -tol_piv && (l[k] == -DBL_MAX || flag[j]))
{ /* xN[j] is either free or has its upper bound active, so
* lambdaN[j] = d[j] <= 0 increases up to zero */
delta = tol + tol1 * (c[k] >= 0.0 ? +c[k] : -c[k]);
/* determine theta on which lambdaN[j] reaches zero */
teta = (d[j] > -delta ? 0.0 : d[j] / alfa);
}
else
{ /* lambdaN[j] cannot reach zero on increasing theta */
continue;
}
/* choose non-basic variable xN[q] by corresponding dual basic
* variable lambdaN[q] for which theta is minimal */
xassert(teta >= 0.0);
alfa = (alfa >= 0.0 ? +alfa : -alfa);
if (teta_min > teta || (teta_min == teta && biga < alfa))
q = j, teta_min = teta, biga = alfa;
}
return q;
}
/***********************************************************************
* spy_chuzc_harris - choose non-basic var. (dual Harris' ratio test)
*
* This routine implements dual Harris' ratio test to choose non-basic
* variable xN[q].
*
* All the parameters, except tol and tol1, as well as the returned
* value have the same meaning as for the routine spx_chuzr_std (see
* above).
*
* The parameters tol and tol1 specify tolerances on zero bound
* violations for reduced costs of non-basic variables. For reduced
* cost d[j] the tolerance is delta[j] = tol + tol1 |cN[j]|, where
* cN[j] is objective coefficient at non-basic variable xN[j]. */
int spy_chuzc_harris(SPXLP *lp, const double d[/*1+n-m*/],
double s, const double trow[/*1+n-m*/], double tol_piv,
double tol, double tol1)
{ int m = lp->m;
int n = lp->n;
double *c = lp->c;
double *l = lp->l;
double *u = lp->u;
int *head = lp->head;
char *flag = lp->flag;
int j, k, q;
double alfa, biga, delta, teta, teta_min;
xassert(s == +1.0 || s == -1.0);
/*--------------------------------------------------------------*/
/* first pass: determine teta_min for relaxed bounds */
/*--------------------------------------------------------------*/
teta_min = DBL_MAX;
/* walk thru the list of non-basic variables */
for (j = 1; j <= n-m; j++)
{ k = head[m+j]; /* x[k] = xN[j] */
/* if xN[j] is fixed variable, skip it */
if (l[k] == u[k])
continue;
alfa = s * trow[j];
if (alfa >= +tol_piv && !flag[j])
{ /* xN[j] is either free or has its lower bound active, so
* lambdaN[j] = d[j] >= 0 decreases down to zero */
delta = tol + tol1 * (c[k] >= 0.0 ? +c[k] : -c[k]);
/* determine theta on which lambdaN[j] reaches -delta */
teta = ((d[j] < 0.0 ? 0.0 : d[j]) + delta) / alfa;
}
else if (alfa <= -tol_piv && (l[k] == -DBL_MAX || flag[j]))
{ /* xN[j] is either free or has its upper bound active, so
* lambdaN[j] = d[j] <= 0 increases up to zero */
delta = tol + tol1 * (c[k] >= 0.0 ? +c[k] : -c[k]);
/* determine theta on which lambdaN[j] reaches +delta */
teta = ((d[j] > 0.0 ? 0.0 : d[j]) - delta) / alfa;
}
else
{ /* lambdaN[j] cannot reach zero on increasing theta */
continue;
}
xassert(teta >= 0.0);
if (teta_min > teta)
teta_min = teta;
}
/*--------------------------------------------------------------*/
/* second pass: choose non-basic variable xN[q] */
/*--------------------------------------------------------------*/
if (teta_min == DBL_MAX)
{ /* theta may increase unlimitedly */
q = 0;
goto done;
}
/* nothing is chosen so far */
q = 0, biga = 0.0;
/* walk thru the list of non-basic variables */
for (j = 1; j <= n-m; j++)
{ k = head[m+j]; /* x[k] = xN[j] */
/* if xN[j] is fixed variable, skip it */
if (l[k] == u[k])
continue;
alfa = s * trow[j];
if (alfa >= +tol_piv && !flag[j])
{ /* xN[j] is either free or has its lower bound active, so
* lambdaN[j] = d[j] >= 0 decreases down to zero */
/* determine theta on which lambdaN[j] reaches zero */
teta = d[j] / alfa;
}
else if (alfa <= -tol_piv && (l[k] == -DBL_MAX || flag[j]))
{ /* xN[j] is either free or has its upper bound active, so
* lambdaN[j] = d[j] <= 0 increases up to zero */
/* determine theta on which lambdaN[j] reaches zero */
teta = d[j] / alfa;
}
else
{ /* lambdaN[j] cannot reach zero on increasing theta */
continue;
}
/* choose non-basic variable for which theta is not greater
* than theta_min determined for relaxed bounds and which has
* best (largest in magnitude) pivot */
alfa = (alfa >= 0.0 ? +alfa : -alfa);
if (teta <= teta_min && biga < alfa)
q = j, biga = alfa;
}
/* something must be chosen */
xassert(1 <= q && q <= n-m);
done: return q;
}
/* eof */