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/* mcfrelax.c (find minimum-cost flow with RELAX-IV) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
*
* Copyright (C) 2013-2016 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 "glpk.h"
#include "relax4.h"
static int overflow(int u, int v)
{ /* check for integer overflow on computing u + v */
if (u > 0 && v > 0 && u + v < 0) return 1;
if (u < 0 && v < 0 && u + v > 0) return 1;
return 0;
}
int glp_mincost_relax4(glp_graph *G, int v_rhs, int a_low, int a_cap,
int a_cost, int crash, double *sol, int a_x, int a_rc)
{ /* find minimum-cost flow with Bertsekas-Tseng relaxation method
(RELAX-IV) */
glp_vertex *v;
glp_arc *a;
struct relax4_csa csa;
int i, k, large, n, na, ret;
double cap, cost, low, rc, rhs, sum, x;
if (v_rhs >= 0 && v_rhs > G->v_size - (int)sizeof(double))
xerror("glp_mincost_relax4: v_rhs = %d; invalid offset\n",
v_rhs);
if (a_low >= 0 && a_low > G->a_size - (int)sizeof(double))
xerror("glp_mincost_relax4: a_low = %d; invalid offset\n",
a_low);
if (a_cap >= 0 && a_cap > G->a_size - (int)sizeof(double))
xerror("glp_mincost_relax4: a_cap = %d; invalid offset\n",
a_cap);
if (a_cost >= 0 && a_cost > G->a_size - (int)sizeof(double))
xerror("glp_mincost_relax4: a_cost = %d; invalid offset\n",
a_cost);
if (a_x >= 0 && a_x > G->a_size - (int)sizeof(double))
xerror("glp_mincost_relax4: a_x = %d; invalid offset\n",
a_x);
if (a_rc >= 0 && a_rc > G->a_size - (int)sizeof(double))
xerror("glp_mincost_relax4: a_rc = %d; invalid offset\n",
a_rc);
csa.n = n = G->nv; /* number of nodes */
csa.na = na = G->na; /* number of arcs */
csa.large = large = INT_MAX / 4;
csa.repeat = 0;
csa.crash = crash;
/* allocate working arrays */
csa.startn = xcalloc(1+na, sizeof(int));
csa.endn = xcalloc(1+na, sizeof(int));
csa.fou = xcalloc(1+n, sizeof(int));
csa.nxtou = xcalloc(1+na, sizeof(int));
csa.fin = xcalloc(1+n, sizeof(int));
csa.nxtin = xcalloc(1+na, sizeof(int));
csa.rc = xcalloc(1+na, sizeof(int));
csa.u = xcalloc(1+na, sizeof(int));
csa.dfct = xcalloc(1+n, sizeof(int));
csa.x = xcalloc(1+na, sizeof(int));
csa.label = xcalloc(1+n, sizeof(int));
csa.prdcsr = xcalloc(1+n, sizeof(int));
csa.save = xcalloc(1+na, sizeof(int));
csa.tfstou = xcalloc(1+n, sizeof(int));
csa.tnxtou = xcalloc(1+na, sizeof(int));
csa.tfstin = xcalloc(1+n, sizeof(int));
csa.tnxtin = xcalloc(1+na, sizeof(int));
csa.nxtqueue = xcalloc(1+n, sizeof(int));
csa.scan = xcalloc(1+n, sizeof(char));
csa.mark = xcalloc(1+n, sizeof(char));
if (crash)
{ csa.extend_arc = xcalloc(1+n, sizeof(int));
csa.sb_level = xcalloc(1+n, sizeof(int));
csa.sb_arc = xcalloc(1+n, sizeof(int));
}
else
{ csa.extend_arc = NULL;
csa.sb_level = NULL;
csa.sb_arc = NULL;
}
/* scan nodes */
for (i = 1; i <= n; i++)
{ v = G->v[i];
/* get supply at i-th node */
if (v_rhs >= 0)
memcpy(&rhs, (char *)v->data + v_rhs, sizeof(double));
else
rhs = 0.0;
if (!(fabs(rhs) <= (double)large && rhs == floor(rhs)))
{ ret = GLP_EDATA;
goto done;
}
/* set demand at i-th node */
csa.dfct[i] = -(int)rhs;
}
/* scan arcs */
k = 0;
for (i = 1; i <= n; i++)
{ v = G->v[i];
for (a = v->out; a != NULL; a = a->t_next)
{ k++;
/* set endpoints of k-th arc */
if (a->tail->i == a->head->i)
{ /* self-loops not allowed */
ret = GLP_EDATA;
goto done;
}
csa.startn[k] = a->tail->i;
csa.endn[k] = a->head->i;
/* set per-unit cost for k-th arc flow */
if (a_cost >= 0)
memcpy(&cost, (char *)a->data + a_cost, sizeof(double));
else
cost = 0.0;
if (!(fabs(cost) <= (double)large && cost == floor(cost)))
{ ret = GLP_EDATA;
goto done;
}
csa.rc[k] = (int)cost;
/* get lower bound for k-th arc flow */
if (a_low >= 0)
memcpy(&low, (char *)a->data + a_low, sizeof(double));
else
low = 0.0;
if (!(0.0 <= low && low <= (double)large &&
low == floor(low)))
{ ret = GLP_EDATA;
goto done;
}
/* get upper bound for k-th arc flow */
if (a_cap >= 0)
memcpy(&cap, (char *)a->data + a_cap, sizeof(double));
else
cap = 1.0;
if (!(low <= cap && cap <= (double)large &&
cap == floor(cap)))
{ ret = GLP_EDATA;
goto done;
}
/* substitute x = x' + low, where 0 <= x' <= cap - low */
csa.u[k] = (int)(cap - low);
/* correct demands at endpoints of k-th arc */
if (overflow(csa.dfct[a->tail->i], +low))
{ ret = GLP_ERANGE;
goto done;
}
#if 0 /* 29/IX-2017 */
csa.dfct[a->tail->i] += low;
#else
csa.dfct[a->tail->i] += (int)low;
#endif
if (overflow(csa.dfct[a->head->i], -low))
{ ret = GLP_ERANGE;
goto done;
}
#if 0 /* 29/IX-2017 */
csa.dfct[a->head->i] -= low;
#else
csa.dfct[a->head->i] -= (int)low;
#endif
}
}
/* construct linked list for network topology */
relax4_inidat(&csa);
/* find minimum-cost flow */
ret = relax4(&csa);
if (ret != 0)
{ /* problem is found to be infeasible */
xassert(1 <= ret && ret <= 8);
ret = GLP_ENOPFS;
goto done;
}
/* store solution */
sum = 0.0;
k = 0;
for (i = 1; i <= n; i++)
{ v = G->v[i];
for (a = v->out; a != NULL; a = a->t_next)
{ k++;
/* get lower bound for k-th arc flow */
if (a_low >= 0)
memcpy(&low, (char *)a->data + a_low, sizeof(double));
else
low = 0.0;
/* store original flow x = x' + low thru k-th arc */
x = (double)csa.x[k] + low;
if (a_x >= 0)
memcpy((char *)a->data + a_x, &x, sizeof(double));
/* store reduced cost for k-th arc flow */
rc = (double)csa.rc[k];
if (a_rc >= 0)
memcpy((char *)a->data + a_rc, &rc, sizeof(double));
/* get per-unit cost for k-th arc flow */
if (a_cost >= 0)
memcpy(&cost, (char *)a->data + a_cost, sizeof(double));
else
cost = 0.0;
/* compute the total cost */
sum += cost * x;
}
}
/* store the total cost */
if (sol != NULL)
*sol = sum;
done: /* free working arrays */
xfree(csa.startn);
xfree(csa.endn);
xfree(csa.fou);
xfree(csa.nxtou);
xfree(csa.fin);
xfree(csa.nxtin);
xfree(csa.rc);
xfree(csa.u);
xfree(csa.dfct);
xfree(csa.x);
xfree(csa.label);
xfree(csa.prdcsr);
xfree(csa.save);
xfree(csa.tfstou);
xfree(csa.tnxtou);
xfree(csa.tfstin);
xfree(csa.tnxtin);
xfree(csa.nxtqueue);
xfree(csa.scan);
xfree(csa.mark);
if (crash)
{ xfree(csa.extend_arc);
xfree(csa.sb_level);
xfree(csa.sb_arc);
}
return ret;
}
/* eof */
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