int ssx_driver(SSX *ssx)
{ int m = ssx->m;
int *type = ssx->type;
mpq_t *lb = ssx->lb;
mpq_t *ub = ssx->ub;
int *Q_col = ssx->Q_col;
mpq_t *bbar = ssx->bbar;
int i, k, ret;
ssx->tm_beg = xtime();
/* factorize the initial basis matrix */
if (ssx_factorize(ssx))
{ xprintf("Initial basis matrix is singular\n");
ret = 7;
goto done;
}
/* compute values of basic variables */
ssx_eval_bbar(ssx);
/* check if the initial basic solution is primal feasible */
for (i = 1; i <= m; i++)
{ int t;
k = Q_col[i]; /* x[k] = xB[i] */
t = type[k];
if (t == SSX_LO || t == SSX_DB || t == SSX_FX)
{ /* x[k] has lower bound */
if (mpq_cmp(bbar[i], lb[k]) < 0)
{ /* which is violated */
break;
}
}
if (t == SSX_UP || t == SSX_DB || t == SSX_FX)
{ /* x[k] has upper bound */
if (mpq_cmp(bbar[i], ub[k]) > 0)
{ /* which is violated */
break;
}
}
}
if (i > m)
{ /* no basic variable violates its bounds */
ret = 0;
goto skip;
}
/* phase I: find primal feasible solution */
ret = ssx_phase_I(ssx);
switch (ret)
{ case 0:
ret = 0;
break;
case 1:
//xprintf("PROBLEM HAS NO FEASIBLE SOLUTION\n");
ret = 1;
break;
case 2:
xprintf("ITERATIONS LIMIT EXCEEDED; SEARCH TERMINATED\n");
ret = 3;
break;
case 3:
xprintf("TIME LIMIT EXCEEDED; SEARCH TERMINATED\n");
ret = 5;
break;
default:
xassert(ret != ret);
}
/* compute values of basic variables (actually only the objective
value needs to be computed) */
ssx_eval_bbar(ssx);
skip: /* compute simplex multipliers */
ssx_eval_pi(ssx);
/* compute reduced costs of non-basic variables */
ssx_eval_cbar(ssx);
/* if phase I failed, do not start phase II */
if (ret != 0) goto done;
/* phase II: find optimal solution */
ret = ssx_phase_II(ssx);
switch (ret)
{ case 0:
//xprintf("OPTIMAL SOLUTION FOUND\n");
ret = 0;
break;
case 1:
//xprintf("PROBLEM HAS UNBOUNDED SOLUTION\n");
ret = 2;
break;
case 2:
xprintf("ITERATIONS LIMIT EXCEEDED; SEARCH TERMINATED\n");
ret = 4;
break;
case 3:
xprintf("TIME LIMIT EXCEEDED; SEARCH TERMINATED\n");
ret = 6;
break;
default:
xassert(ret != ret);
}
done: /* decrease the time limit by the spent amount of time */
if (ssx->tm_lim >= 0.0)
#if 0
{ ssx->tm_lim -= utime() - ssx->tm_beg;
#else
{ ssx->tm_lim -= xdifftime(xtime(), ssx->tm_beg);
#endif
if (ssx->tm_lim < 0.0) ssx->tm_lim = 0.0;
}
return ret;
}
void ssx_change_basis(SSX *ssx)
{ int m = ssx->m;
int n = ssx->n;
int *type = ssx->type;
int *stat = ssx->stat;
int *Q_row = ssx->Q_row;
int *Q_col = ssx->Q_col;
int p = ssx->p;
int q = ssx->q;
int p_stat = ssx->p_stat;
int k, kp, kq;
if (p < 0)
{ /* special case: xN[q] goes to its opposite bound */
xassert(1 <= q && q <= n);
k = Q_col[m+q]; /* x[k] = xN[q] */
xassert(type[k] == SSX_DB);
switch (stat[k])
{ case SSX_NL:
stat[k] = SSX_NU;
break;
case SSX_NU:
stat[k] = SSX_NL;
break;
default:
xassert(stat != stat);
}
}
else
{ /* xB[p] leaves the basis, xN[q] enters the basis */
xassert(1 <= p && p <= m);
xassert(1 <= q && q <= n);
kp = Q_col[p]; /* x[kp] = xB[p] */
kq = Q_col[m+q]; /* x[kq] = xN[q] */
/* check non-basic status of xB[p] which becomes xN[q] */
switch (type[kp])
{ case SSX_FR:
xassert(p_stat == SSX_NF);
break;
case SSX_LO:
xassert(p_stat == SSX_NL);
break;
case SSX_UP:
xassert(p_stat == SSX_NU);
break;
case SSX_DB:
xassert(p_stat == SSX_NL || p_stat == SSX_NU);
break;
case SSX_FX:
xassert(p_stat == SSX_NS);
break;
default:
xassert(type != type);
}
/* swap xB[p] and xN[q] */
stat[kp] = (char)p_stat, stat[kq] = SSX_BS;
Q_row[kp] = m+q, Q_row[kq] = p;
Q_col[p] = kq, Q_col[m+q] = kp;
/* update factorization of the basis matrix */
if (bfx_update(ssx->binv, p))
{ if (ssx_factorize(ssx))
xassert(("Internal error: basis matrix is singular", 0));
}
}
return;
}