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/* mcfokalg.c (find minimum-cost flow with out-of-kilter algorithm) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
*
* Copyright (C) 2009-2016 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 "okalg.h"
int glp_mincost_okalg(glp_graph *G, int v_rhs, int a_low, int a_cap,
int a_cost, double *sol, int a_x, int v_pi)
{ /* find minimum-cost flow with out-of-kilter algorithm */
glp_vertex *v;
glp_arc *a;
int nv, na, i, k, s, t, *tail, *head, *low, *cap, *cost, *x, *pi,
ret;
double sum, temp;
if (v_rhs >= 0 && v_rhs > G->v_size - (int)sizeof(double))
xerror("glp_mincost_okalg: v_rhs = %d; invalid offset\n",
v_rhs);
if (a_low >= 0 && a_low > G->a_size - (int)sizeof(double))
xerror("glp_mincost_okalg: a_low = %d; invalid offset\n",
a_low);
if (a_cap >= 0 && a_cap > G->a_size - (int)sizeof(double))
xerror("glp_mincost_okalg: a_cap = %d; invalid offset\n",
a_cap);
if (a_cost >= 0 && a_cost > G->a_size - (int)sizeof(double))
xerror("glp_mincost_okalg: a_cost = %d; invalid offset\n",
a_cost);
if (a_x >= 0 && a_x > G->a_size - (int)sizeof(double))
xerror("glp_mincost_okalg: a_x = %d; invalid offset\n", a_x);
if (v_pi >= 0 && v_pi > G->v_size - (int)sizeof(double))
xerror("glp_mincost_okalg: v_pi = %d; invalid offset\n", v_pi);
/* s is artificial source node */
s = G->nv + 1;
/* t is artificial sink node */
t = s + 1;
/* nv is the total number of nodes in the resulting network */
nv = t;
/* na is the total number of arcs in the resulting network */
na = G->na + 1;
for (i = 1; i <= G->nv; i++)
{ v = G->v[i];
if (v_rhs >= 0)
memcpy(&temp, (char *)v->data + v_rhs, sizeof(double));
else
temp = 0.0;
if (temp != 0.0) na++;
}
/* allocate working arrays */
tail = xcalloc(1+na, sizeof(int));
head = xcalloc(1+na, sizeof(int));
low = xcalloc(1+na, sizeof(int));
cap = xcalloc(1+na, sizeof(int));
cost = xcalloc(1+na, sizeof(int));
x = xcalloc(1+na, sizeof(int));
pi = xcalloc(1+nv, sizeof(int));
/* construct the resulting network */
k = 0;
/* (original arcs) */
for (i = 1; i <= G->nv; i++)
{ v = G->v[i];
for (a = v->out; a != NULL; a = a->t_next)
{ k++;
tail[k] = a->tail->i;
head[k] = a->head->i;
if (tail[k] == head[k])
{ ret = GLP_EDATA;
goto done;
}
if (a_low >= 0)
memcpy(&temp, (char *)a->data + a_low, sizeof(double));
else
temp = 0.0;
if (!(0.0 <= temp && temp <= (double)INT_MAX &&
temp == floor(temp)))
{ ret = GLP_EDATA;
goto done;
}
low[k] = (int)temp;
if (a_cap >= 0)
memcpy(&temp, (char *)a->data + a_cap, sizeof(double));
else
temp = 1.0;
if (!((double)low[k] <= temp && temp <= (double)INT_MAX &&
temp == floor(temp)))
{ ret = GLP_EDATA;
goto done;
}
cap[k] = (int)temp;
if (a_cost >= 0)
memcpy(&temp, (char *)a->data + a_cost, sizeof(double));
else
temp = 0.0;
if (!(fabs(temp) <= (double)INT_MAX && temp == floor(temp)))
{ ret = GLP_EDATA;
goto done;
}
cost[k] = (int)temp;
}
}
/* (artificial arcs) */
sum = 0.0;
for (i = 1; i <= G->nv; i++)
{ v = G->v[i];
if (v_rhs >= 0)
memcpy(&temp, (char *)v->data + v_rhs, sizeof(double));
else
temp = 0.0;
if (!(fabs(temp) <= (double)INT_MAX && temp == floor(temp)))
{ ret = GLP_EDATA;
goto done;
}
if (temp > 0.0)
{ /* artificial arc from s to original source i */
k++;
tail[k] = s;
head[k] = i;
low[k] = cap[k] = (int)(+temp); /* supply */
cost[k] = 0;
sum += (double)temp;
}
else if (temp < 0.0)
{ /* artificial arc from original sink i to t */
k++;
tail[k] = i;
head[k] = t;
low[k] = cap[k] = (int)(-temp); /* demand */
cost[k] = 0;
}
}
/* (feedback arc from t to s) */
k++;
xassert(k == na);
tail[k] = t;
head[k] = s;
if (sum > (double)INT_MAX)
{ ret = GLP_EDATA;
goto done;
}
low[k] = cap[k] = (int)sum; /* total supply/demand */
cost[k] = 0;
/* find minimal-cost circulation in the resulting network */
ret = okalg(nv, na, tail, head, low, cap, cost, x, pi);
switch (ret)
{ case 0:
/* optimal circulation found */
ret = 0;
break;
case 1:
/* no feasible circulation exists */
ret = GLP_ENOPFS;
break;
case 2:
/* integer overflow occured */
ret = GLP_ERANGE;
goto done;
case 3:
/* optimality test failed (logic error) */
ret = GLP_EFAIL;
goto done;
default:
xassert(ret != ret);
}
/* store solution components */
/* (objective function = the total cost) */
if (sol != NULL)
{ temp = 0.0;
for (k = 1; k <= na; k++)
temp += (double)cost[k] * (double)x[k];
*sol = temp;
}
/* (arc flows) */
if (a_x >= 0)
{ k = 0;
for (i = 1; i <= G->nv; i++)
{ v = G->v[i];
for (a = v->out; a != NULL; a = a->t_next)
{ temp = (double)x[++k];
memcpy((char *)a->data + a_x, &temp, sizeof(double));
}
}
}
/* (node potentials = Lagrange multipliers) */
if (v_pi >= 0)
{ for (i = 1; i <= G->nv; i++)
{ v = G->v[i];
temp = - (double)pi[i];
memcpy((char *)v->data + v_pi, &temp, sizeof(double));
}
}
done: /* free working arrays */
xfree(tail);
xfree(head);
xfree(low);
xfree(cap);
xfree(cost);
xfree(x);
xfree(pi);
return ret;
}
/* eof */
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