void lpx_get_row_bnds(glp_prob *lp, int i, int *typx, double *lb,
double *ub)
{ /* retrieve row bounds */
if (typx != NULL) *typx = lpx_get_row_type(lp, i);
if (lb != NULL) *lb = lpx_get_row_lb(lp, i);
if (ub != NULL) *ub = lpx_get_row_ub(lp, i);
return;
}
static double get_row_ub(LPX *lp, int i)
{ /* this routine returns upper bound of row i or +DBL_MAX if the
row has no upper bound */
double ub;
switch (lpx_get_row_type(lp, i))
{ case LPX_FR:
case LPX_LO:
ub = +DBL_MAX;
break;
case LPX_UP:
case LPX_DB:
case LPX_FX:
ub = lpx_get_row_ub(lp, i);
break;
default:
xassert(lp != lp);
}
return ub;
}
static void transform(struct dsa *dsa)
{ /* transform original LP to standard formulation */
LPX *lp = dsa->lp;
int orig_m = dsa->orig_m;
int orig_n = dsa->orig_n;
int *ref = dsa->ref;
int m = dsa->m;
int n = dsa->n;
double *b = dsa->b;
double *c = dsa->c;
int i, j, k, type, t, ii, len, *ind;
double lb, ub, coef, rii, sjj, *val;
/* initialize components of transformed LP */
dsa->ne = 0;
for (i = 1; i <= m; i++) b[i] = 0.0;
c[0] = lpx_get_obj_coef(lp, 0);
for (j = 1; j <= n; j++) c[j] = 0.0;
/* i and j are, respectively, ordinal number of current row and
ordinal number of current column in transformed LP */
i = j = 0;
/* transform rows (auxiliary variables) */
for (k = 1; k <= orig_m; k++)
{ type = lpx_get_row_type(lp, k);
rii = lpx_get_rii(lp, k);
lb = lpx_get_row_lb(lp, k) * rii;
ub = lpx_get_row_ub(lp, k) * rii;
switch (type)
{
case LPX_FR:
/* source: -inf < (L.F.) < +inf */
/* result: ignore free row */
ref[k] = 0;
break;
case LPX_LO:
/* source: lb <= (L.F.) < +inf */
/* result: (L.F.) - x' = lb, x' >= 0 */
i++;
j++;
ref[k] = i;
new_coef(dsa, i, j, -1.0);
b[i] = lb;
break;
case LPX_UP:
/* source: -inf < (L.F.) <= ub */
/* result: (L.F.) + x' = ub, x' >= 0 */
i++;
j++;
ref[k] = i;
new_coef(dsa, i, j, +1.0);
b[i] = ub;
break;
case LPX_DB:
/* source: lb <= (L.F.) <= ub */
/* result: (L.F.) - x' = lb, x' + x'' = ub - lb */
i++;
j++;
ref[k] = i;
new_coef(dsa, i, j, -1.0);
b[i] = lb;
i++;
new_coef(dsa, i, j, +1.0);
j++;
new_coef(dsa, i, j, +1.0);
b[i] = ub - lb;
break;
case LPX_FX:
/* source: (L.F.) = lb */
/* result: (L.F.) = lb */
i++;
ref[k] = i;
b[i] = lb;
break;
default:
insist(type != type);
}
}
/* transform columns (structural variables) */
ind = ucalloc(1+orig_m, sizeof(int));
val = ucalloc(1+orig_m, sizeof(double));
for (k = 1; k <= orig_n; k++)
{ type = lpx_get_col_type(lp, k);
sjj = lpx_get_sjj(lp, k);
lb = lpx_get_col_lb(lp, k) / sjj;
ub = lpx_get_col_ub(lp, k) / sjj;
coef = lpx_get_obj_coef(lp, k) * sjj;
len = lpx_get_mat_col(lp, k, ind, val);
for (t = 1; t <= len; t++)
val[t] *= (lpx_get_rii(lp, ind[t]) * sjj);
switch (type)
{
case LPX_FR:
/* source: -inf < x < +inf */
/* result: x = x' - x'', x' >= 0, x'' >= 0 */
j++;
ref[orig_m+k] = j;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0) new_coef(dsa, ii, j, +val[t]);
}
c[j] = +coef;
j++;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0) new_coef(dsa, ii, j, -val[t]);
}
c[j] = -coef;
break;
case LPX_LO:
/* source: lb <= x < +inf */
/* result: x = lb + x', x' >= 0 */
j++;
ref[orig_m+k] = j;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0)
{ new_coef(dsa, ii, j, val[t]);
b[ii] -= val[t] * lb;
}
}
c[j] = +coef;
c[0] += c[j] * lb;
break;
case LPX_UP:
/* source: -inf < x <= ub */
/* result: x = ub - x', x' >= 0 */
j++;
ref[orig_m+k] = j;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0)
{ new_coef(dsa, ii, j, -val[t]);
b[ii] -= val[t] * ub;
}
}
c[j] = -coef;
c[0] -= c[j] * ub;
break;
case LPX_DB:
/* source: lb <= x <= ub */
/* result: x = lb + x', x' + x'' = ub - lb */
j++;
ref[orig_m+k] = j;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0)
{ new_coef(dsa, ii, j, val[t]);
b[ii] -= val[t] * lb;
}
}
c[j] = +coef;
c[0] += c[j] * lb;
i++;
new_coef(dsa, i, j, +1.0);
j++;
new_coef(dsa, i, j, +1.0);
b[i] = ub - lb;
break;
case LPX_FX:
/* source: x = lb */
/* result: just substitute */
ref[orig_m+k] = 0;
for (t = 1; t <= len; t++)
{ ii = ref[ind[t]];
if (ii != 0) b[ii] -= val[t] * lb;
}
c[0] += coef * lb;
break;
default:
insist(type != type);
}
}
ufree(ind);
ufree(val);
/* end of transformation */
insist(i == m && j == n);
/* change the objective sign in case of maximization */
if (lpx_get_obj_dir(lp) == LPX_MAX)
for (j = 0; j <= n; j++) c[j] = -c[j];
return;
}
int lpx_integer(LPX *mip)
{ int m = lpx_get_num_rows(mip);
int n = lpx_get_num_cols(mip);
MIPTREE *tree;
LPX *lp;
int ret, i, j, stat, type, len, *ind;
double lb, ub, coef, *val;
#if 0
/* the problem must be of MIP class */
if (lpx_get_class(mip) != LPX_MIP)
{ print("lpx_integer: problem is not of MIP class");
ret = LPX_E_FAULT;
goto done;
}
#endif
/* an optimal solution of LP relaxation must be known */
if (lpx_get_status(mip) != LPX_OPT)
{ print("lpx_integer: optimal solution of LP relaxation required"
);
ret = LPX_E_FAULT;
goto done;
}
/* bounds of all integer variables must be integral */
for (j = 1; j <= n; j++)
{ if (lpx_get_col_kind(mip, j) != LPX_IV) continue;
type = lpx_get_col_type(mip, j);
if (type == LPX_LO || type == LPX_DB || type == LPX_FX)
{ lb = lpx_get_col_lb(mip, j);
if (lb != floor(lb))
{ print("lpx_integer: integer column %d has non-integer lo"
"wer bound or fixed value %g", j, lb);
ret = LPX_E_FAULT;
goto done;
}
}
if (type == LPX_UP || type == LPX_DB)
{ ub = lpx_get_col_ub(mip, j);
if (ub != floor(ub))
{ print("lpx_integer: integer column %d has non-integer up"
"per bound %g", j, ub);
ret = LPX_E_FAULT;
goto done;
}
}
}
/* it seems all is ok */
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 2)
print("Integer optimization begins...");
/* create the branch-and-bound tree */
tree = mip_create_tree(m, n, lpx_get_obj_dir(mip));
/* set up column kinds */
for (j = 1; j <= n; j++)
tree->int_col[j] = (lpx_get_col_kind(mip, j) == LPX_IV);
/* access the LP relaxation template */
lp = tree->lp;
/* set up the objective function */
tree->int_obj = 1;
for (j = 0; j <= tree->n; j++)
{ coef = lpx_get_obj_coef(mip, j);
lpx_set_obj_coef(lp, j, coef);
if (coef != 0.0 && !(tree->int_col[j] && coef == floor(coef)))
tree->int_obj = 0;
}
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 2 && tree->int_obj)
print("Objective function is integral");
/* set up the constraint matrix */
ind = xcalloc(1+n, sizeof(int));
val = xcalloc(1+n, sizeof(double));
for (i = 1; i <= m; i++)
{ len = lpx_get_mat_row(mip, i, ind, val);
lpx_set_mat_row(lp, i, len, ind, val);
}
xfree(ind);
xfree(val);
/* set up scaling matrices */
for (i = 1; i <= m; i++)
lpx_set_rii(lp, i, lpx_get_rii(mip, i));
for (j = 1; j <= n; j++)
lpx_set_sjj(lp, j, lpx_get_sjj(mip, j));
/* revive the root subproblem */
mip_revive_node(tree, 1);
/* set up row attributes for the root subproblem */
for (i = 1; i <= m; i++)
{ type = lpx_get_row_type(mip, i);
lb = lpx_get_row_lb(mip, i);
ub = lpx_get_row_ub(mip, i);
stat = lpx_get_row_stat(mip, i);
lpx_set_row_bnds(lp, i, type, lb, ub);
lpx_set_row_stat(lp, i, stat);
}
/* set up column attributes for the root subproblem */
for (j = 1; j <= n; j++)
{ type = lpx_get_col_type(mip, j);
lb = lpx_get_col_lb(mip, j);
ub = lpx_get_col_ub(mip, j);
stat = lpx_get_col_stat(mip, j);
lpx_set_col_bnds(lp, j, type, lb, ub);
lpx_set_col_stat(lp, j, stat);
}
/* freeze the root subproblem */
mip_freeze_node(tree);
/* inherit some control parameters and statistics */
tree->msg_lev = lpx_get_int_parm(mip, LPX_K_MSGLEV);
if (tree->msg_lev > 2) tree->msg_lev = 2;
tree->branch = lpx_get_int_parm(mip, LPX_K_BRANCH);
tree->btrack = lpx_get_int_parm(mip, LPX_K_BTRACK);
tree->tol_int = lpx_get_real_parm(mip, LPX_K_TOLINT);
tree->tol_obj = lpx_get_real_parm(mip, LPX_K_TOLOBJ);
tree->tm_lim = lpx_get_real_parm(mip, LPX_K_TMLIM);
lpx_set_int_parm(lp, LPX_K_BFTYPE, lpx_get_int_parm(mip,
LPX_K_BFTYPE));
lpx_set_int_parm(lp, LPX_K_PRICE, lpx_get_int_parm(mip,
LPX_K_PRICE));
lpx_set_real_parm(lp, LPX_K_RELAX, lpx_get_real_parm(mip,
LPX_K_RELAX));
lpx_set_real_parm(lp, LPX_K_TOLBND, lpx_get_real_parm(mip,
LPX_K_TOLBND));
lpx_set_real_parm(lp, LPX_K_TOLDJ, lpx_get_real_parm(mip,
LPX_K_TOLDJ));
lpx_set_real_parm(lp, LPX_K_TOLPIV, lpx_get_real_parm(mip,
LPX_K_TOLPIV));
lpx_set_int_parm(lp, LPX_K_ITLIM, lpx_get_int_parm(mip,
LPX_K_ITLIM));
lpx_set_int_parm(lp, LPX_K_ITCNT, lpx_get_int_parm(mip,
LPX_K_ITCNT));
/* reset the status of MIP solution */
lpx_put_mip_soln(mip, LPX_I_UNDEF, NULL, NULL);
/* try solving the problem */
ret = mip_driver(tree);
/* if an integer feasible solution has been found, copy it to the
MIP problem object */
if (tree->found)
lpx_put_mip_soln(mip, LPX_I_FEAS, &tree->mipx[0],
&tree->mipx[m]);
/* copy back statistics about spent resources */
lpx_set_real_parm(mip, LPX_K_TMLIM, tree->tm_lim);
lpx_set_int_parm(mip, LPX_K_ITLIM, lpx_get_int_parm(lp,
LPX_K_ITLIM));
lpx_set_int_parm(mip, LPX_K_ITCNT, lpx_get_int_parm(lp,
LPX_K_ITCNT));
/* analyze exit code reported by the mip driver */
switch (ret)
{ case MIP_E_OK:
if (tree->found)
{ if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 3)
print("INTEGER OPTIMAL SOLUTION FOUND");
lpx_put_mip_soln(mip, LPX_I_OPT, NULL, NULL);
}
else
{ if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 3)
print("PROBLEM HAS NO INTEGER FEASIBLE SOLUTION");
lpx_put_mip_soln(mip, LPX_I_NOFEAS, NULL, NULL);
}
ret = LPX_E_OK;
break;
case MIP_E_ITLIM:
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 3)
print("ITERATIONS LIMIT EXCEEDED; SEARCH TERMINATED");
ret = LPX_E_ITLIM;
break;
case MIP_E_TMLIM:
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 3)
print("TIME LIMIT EXCEEDED; SEARCH TERMINATED");
ret = LPX_E_TMLIM;
break;
case MIP_E_ERROR:
if (lpx_get_int_parm(mip, LPX_K_MSGLEV) >= 1)
print("lpx_integer: cannot solve current LP relaxation");
ret = LPX_E_SING;
break;
default:
xassert(ret != ret);
}
/* delete the branch-and-bound tree */
mip_delete_tree(tree);
done: /* return to the application program */
return ret;
}
void lpx_check_int(LPX *lp, LPXKKT *kkt)
{ int m = lpx_get_num_rows(lp);
int n = lpx_get_num_cols(lp);
int *ind, i, len, t, j, k, type;
double *val, xR_i, g_i, xS_j, temp, lb, ub, x_k, h_k;
/*--------------------------------------------------------------*/
/* compute largest absolute and relative errors and corresponding
row indices for the condition (KKT.PE) */
kkt->pe_ae_max = 0.0, kkt->pe_ae_row = 0;
kkt->pe_re_max = 0.0, kkt->pe_re_row = 0;
ind = xcalloc(1+n, sizeof(int));
val = xcalloc(1+n, sizeof(double));
for (i = 1; i <= m; i++)
{ /* determine xR[i] */
xR_i = lpx_mip_row_val(lp, i);
/* g[i] := xR[i] */
g_i = xR_i;
/* g[i] := g[i] - (i-th row of A) * xS */
len = lpx_get_mat_row(lp, i, ind, val);
for (t = 1; t <= len; t++)
{ j = ind[t];
/* determine xS[j] */
xS_j = lpx_mip_col_val(lp, j);
/* g[i] := g[i] - a[i,j] * xS[j] */
g_i -= val[t] * xS_j;
}
/* determine absolute error */
temp = fabs(g_i);
if (kkt->pe_ae_max < temp)
kkt->pe_ae_max = temp, kkt->pe_ae_row = i;
/* determine relative error */
temp /= (1.0 + fabs(xR_i));
if (kkt->pe_re_max < temp)
kkt->pe_re_max = temp, kkt->pe_re_row = i;
}
xfree(ind);
xfree(val);
/* estimate the solution quality */
if (kkt->pe_re_max <= 1e-9)
kkt->pe_quality = 'H';
else if (kkt->pe_re_max <= 1e-6)
kkt->pe_quality = 'M';
else if (kkt->pe_re_max <= 1e-3)
kkt->pe_quality = 'L';
else
kkt->pe_quality = '?';
/*--------------------------------------------------------------*/
/* compute largest absolute and relative errors and corresponding
variable indices for the condition (KKT.PB) */
kkt->pb_ae_max = 0.0, kkt->pb_ae_ind = 0;
kkt->pb_re_max = 0.0, kkt->pb_re_ind = 0;
for (k = 1; k <= m+n; k++)
{ /* determine x[k] */
if (k <= m)
{ i = k;
type = lpx_get_row_type(lp, i);
lb = lpx_get_row_lb(lp, i);
ub = lpx_get_row_ub(lp, i);
x_k = lpx_mip_row_val(lp, i);
}
else
{ j = k - m;
type = lpx_get_col_type(lp, j);
lb = lpx_get_col_lb(lp, j);
ub = lpx_get_col_ub(lp, j);
x_k = lpx_mip_col_val(lp, j);
}
/* compute h[k] */
h_k = 0.0;
switch (type)
{ case LPX_FR:
break;
case LPX_LO:
if (x_k < lb) h_k = x_k - lb;
break;
case LPX_UP:
if (x_k > ub) h_k = x_k - ub;
break;
case LPX_DB:
case LPX_FX:
if (x_k < lb) h_k = x_k - lb;
if (x_k > ub) h_k = x_k - ub;
break;
default:
xassert(type != type);
}
/* determine absolute error */
temp = fabs(h_k);
if (kkt->pb_ae_max < temp)
kkt->pb_ae_max = temp, kkt->pb_ae_ind = k;
/* determine relative error */
temp /= (1.0 + fabs(x_k));
if (kkt->pb_re_max < temp)
kkt->pb_re_max = temp, kkt->pb_re_ind = k;
}
/* estimate the solution quality */
if (kkt->pb_re_max <= 1e-9)
kkt->pb_quality = 'H';
else if (kkt->pb_re_max <= 1e-6)
kkt->pb_quality = 'M';
else if (kkt->pb_re_max <= 1e-3)
kkt->pb_quality = 'L';
else
kkt->pb_quality = '?';
return;
}
void ipp_load_orig(IPP *ipp, LPX *orig)
{ IPPROW **row;
IPPCOL *col;
int i, j, k, type, len, *ind;
double lb, ub, *val;
/* save some information about the original problem */
ipp->orig_m = lpx_get_num_rows(orig);
ipp->orig_n = lpx_get_num_cols(orig);
ipp->orig_nnz = lpx_get_num_nz(orig);
ipp->orig_dir = lpx_get_obj_dir(orig);
/* allocate working arrays */
row = xcalloc(1+ipp->orig_m, sizeof(IPPROW *));
ind = xcalloc(1+ipp->orig_m, sizeof(int));
val = xcalloc(1+ipp->orig_m, sizeof(double));
/* copy rows of the original problem into the workspace */
for (i = 1; i <= ipp->orig_m; i++)
{ type = lpx_get_row_type(orig, i);
if (type == LPX_FR || type == LPX_UP)
lb = -DBL_MAX;
else
lb = lpx_get_row_lb(orig, i);
if (type == LPX_FR || type == LPX_LO)
ub = +DBL_MAX;
else
ub = lpx_get_row_ub(orig, i);
row[i] = ipp_add_row(ipp, lb, ub);
}
/* copy columns of the original problem into the workspace; each
column created in the workspace is assigned a reference number
which is its ordinal number in the original problem */
for (j = 1; j <= ipp->orig_n; j++)
{ type = lpx_get_col_type(orig, j);
if (type == LPX_FR || type == LPX_UP)
lb = -DBL_MAX;
else
lb = lpx_get_col_lb(orig, j);
if (type == LPX_FR || type == LPX_LO)
ub = +DBL_MAX;
else
ub = lpx_get_col_ub(orig, j);
col = ipp_add_col(ipp, lpx_get_col_kind(orig, j) == LPX_IV,
lb, ub, lpx_get_obj_coef(orig, j));
len = lpx_get_mat_col(orig, j, ind, val);
for (k = 1; k <= len; k++)
ipp_add_aij(ipp, row[ind[k]], col, val[k]);
}
/* copy the constant term of the original objective function */
ipp->c0 = lpx_get_obj_coef(orig, 0);
/* if the original problem is maximization, change the sign of
the objective function, because the transformed problem to be
processed by the presolver must be minimization */
if (ipp->orig_dir == LPX_MAX)
{ for (col = ipp->col_ptr; col != NULL; col = col->next)
col->c = - col->c;
ipp->c0 = - ipp->c0;
}
/* free working arrays */
xfree(row);
xfree(ind);
xfree(val);
return;
}
int lpx_prim_ratio_test(LPX *lp, int len, const int ind[],
const double val[], int how, double tol)
{ int i, k, m, n, p, t, typx, tagx;
double alfa_i, abs_alfa_i, big, eps, bbar_i, lb_i, ub_i, temp,
teta;
if (!lpx_is_b_avail(lp))
xfault("lpx_prim_ratio_test: LP basis is not available\n");
if (lpx_get_prim_stat(lp) != LPX_P_FEAS)
xfault("lpx_prim_ratio_test: current basic solution is not pri"
"mal feasible\n");
if (!(how == +1 || how == -1))
xfault("lpx_prim_ratio_test: how = %d; invalid parameter\n",
how);
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* compute the largest absolute value of the specified influence
coefficients */
big = 0.0;
for (t = 1; t <= len; t++)
{ temp = val[t];
if (temp < 0.0) temp = - temp;
if (big < temp) big = temp;
}
/* compute the absolute tolerance eps used to skip small entries
of the column */
if (!(0.0 < tol && tol < 1.0))
xfault("lpx_prim_ratio_test: tol = %g; invalid tolerance\n",
tol);
eps = tol * (1.0 + big);
/* initial settings */
p = 0, teta = DBL_MAX, big = 0.0;
/* walk through the entries of the specified column */
for (t = 1; t <= len; t++)
{ /* get the ordinal number of basic variable */
k = ind[t];
if (!(1 <= k && k <= m+n))
xfault("lpx_prim_ratio_test: ind[%d] = %d; variable number "
"out of range\n", t, k);
if (k <= m)
tagx = lpx_get_row_stat(lp, k);
else
tagx = lpx_get_col_stat(lp, k-m);
if (tagx != LPX_BS)
xfault("lpx_prim_ratio_test: ind[%d] = %d; non-basic variab"
"le not allowed\n", t, k);
/* determine index of the variable x[k] in the vector xB */
if (k <= m)
i = lpx_get_row_b_ind(lp, k);
else
i = lpx_get_col_b_ind(lp, k-m);
xassert(1 <= i && i <= m);
/* determine unscaled bounds and value of the basic variable
xB[i] in the current basic solution */
if (k <= m)
{ typx = lpx_get_row_type(lp, k);
lb_i = lpx_get_row_lb(lp, k);
ub_i = lpx_get_row_ub(lp, k);
bbar_i = lpx_get_row_prim(lp, k);
}
else
{ typx = lpx_get_col_type(lp, k-m);
lb_i = lpx_get_col_lb(lp, k-m);
ub_i = lpx_get_col_ub(lp, k-m);
bbar_i = lpx_get_col_prim(lp, k-m);
}
/* determine influence coefficient for the basic variable
x[k] = xB[i] in the explicitly specified column and turn to
the case of increasing the variable y in order to simplify
the program logic */
alfa_i = (how > 0 ? +val[t] : -val[t]);
abs_alfa_i = (alfa_i > 0.0 ? +alfa_i : -alfa_i);
/* analyze main cases */
switch (typx)
{ case LPX_FR:
/* xB[i] is free variable */
continue;
case LPX_LO:
lo: /* xB[i] has an lower bound */
if (alfa_i > - eps) continue;
temp = (lb_i - bbar_i) / alfa_i;
break;
case LPX_UP:
up: /* xB[i] has an upper bound */
if (alfa_i < + eps) continue;
temp = (ub_i - bbar_i) / alfa_i;
break;
case LPX_DB:
/* xB[i] has both lower and upper bounds */
if (alfa_i < 0.0) goto lo; else goto up;
case LPX_FX:
/* xB[i] is fixed variable */
if (abs_alfa_i < eps) continue;
temp = 0.0;
break;
default:
xassert(typx != typx);
}
/* if the value of the variable xB[i] violates its lower or
upper bound (slightly, because the current basis is assumed
to be primal feasible), temp is negative; we can think this
happens due to round-off errors and the value is exactly on
the bound; this allows replacing temp by zero */
if (temp < 0.0) temp = 0.0;
/* apply the minimal ratio test */
if (teta > temp || teta == temp && big < abs_alfa_i)
p = k, teta = temp, big = abs_alfa_i;
}
/* return the ordinal number of the chosen basic variable */
return p;
}
void lpx_eval_b_prim(LPX *lp, double row_prim[], double col_prim[])
{ int i, j, k, m, n, stat, len, *ind;
double xN, *NxN, *xB, *val;
if (!lpx_is_b_avail(lp))
xfault("lpx_eval_b_prim: LP basis is not available\n");
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* store values of non-basic auxiliary and structural variables
and compute the right-hand side vector (-N*xN) */
NxN = xcalloc(1+m, sizeof(double));
for (i = 1; i <= m; i++) NxN[i] = 0.0;
/* walk through auxiliary variables */
for (i = 1; i <= m; i++)
{ /* obtain status of i-th auxiliary variable */
stat = lpx_get_row_stat(lp, i);
/* if it is basic, skip it */
if (stat == LPX_BS) continue;
/* i-th auxiliary variable is non-basic; get its value */
switch (stat)
{ case LPX_NL: xN = lpx_get_row_lb(lp, i); break;
case LPX_NU: xN = lpx_get_row_ub(lp, i); break;
case LPX_NF: xN = 0.0; break;
case LPX_NS: xN = lpx_get_row_lb(lp, i); break;
default: xassert(lp != lp);
}
/* store the value of non-basic auxiliary variable */
row_prim[i] = xN;
/* and add corresponding term to the right-hand side vector */
NxN[i] -= xN;
}
/* walk through structural variables */
ind = xcalloc(1+m, sizeof(int));
val = xcalloc(1+m, sizeof(double));
for (j = 1; j <= n; j++)
{ /* obtain status of j-th structural variable */
stat = lpx_get_col_stat(lp, j);
/* if it basic, skip it */
if (stat == LPX_BS) continue;
/* j-th structural variable is non-basic; get its value */
switch (stat)
{ case LPX_NL: xN = lpx_get_col_lb(lp, j); break;
case LPX_NU: xN = lpx_get_col_ub(lp, j); break;
case LPX_NF: xN = 0.0; break;
case LPX_NS: xN = lpx_get_col_lb(lp, j); break;
default: xassert(lp != lp);
}
/* store the value of non-basic structural variable */
col_prim[j] = xN;
/* and add corresponding term to the right-hand side vector */
if (xN != 0.0)
{ len = lpx_get_mat_col(lp, j, ind, val);
for (k = 1; k <= len; k++) NxN[ind[k]] += val[k] * xN;
}
}
xfree(ind);
xfree(val);
/* solve the system B*xB = (-N*xN) to compute the vector xB */
xB = NxN, lpx_ftran(lp, xB);
/* store values of basic auxiliary and structural variables */
for (i = 1; i <= m; i++)
{ k = lpx_get_b_info(lp, i);
xassert(1 <= k && k <= m+n);
if (k <= m)
row_prim[k] = xB[i];
else
col_prim[k-m] = xB[i];
}
xfree(NxN);
return;
}
int lpx_warm_up(LPX *lp)
{ int m, n, j, k, ret, type, stat, p_stat, d_stat;
double lb, ub, prim, dual, tol_bnd, tol_dj, dir;
double *row_prim, *row_dual, *col_prim, *col_dual, sum;
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* reinvert the basis matrix, if necessary */
if (lpx_is_b_avail(lp))
ret = LPX_E_OK;
else
{ if (m == 0 || n == 0)
{ ret = LPX_E_EMPTY;
goto done;
}
#if 0
ret = lpx_invert(lp);
switch (ret)
{ case 0:
ret = LPX_E_OK;
break;
case 1:
case 2:
ret = LPX_E_SING;
goto done;
case 3:
ret = LPX_E_BADB;
goto done;
default:
xassert(ret != ret);
}
#else
switch (glp_factorize(lp))
{ case 0:
ret = LPX_E_OK;
break;
case GLP_EBADB:
ret = LPX_E_BADB;
goto done;
case GLP_ESING:
case GLP_ECOND:
ret = LPX_E_SING;
goto done;
default:
xassert(lp != lp);
}
#endif
}
/* allocate working arrays */
row_prim = xcalloc(1+m, sizeof(double));
row_dual = xcalloc(1+m, sizeof(double));
col_prim = xcalloc(1+n, sizeof(double));
col_dual = xcalloc(1+n, sizeof(double));
/* compute primal basic solution components */
lpx_eval_b_prim(lp, row_prim, col_prim);
/* determine primal status of basic solution */
tol_bnd = 3.0 * lpx_get_real_parm(lp, LPX_K_TOLBND);
p_stat = LPX_P_FEAS;
for (k = 1; k <= m+n; k++)
{ if (k <= m)
{ type = lpx_get_row_type(lp, k);
lb = lpx_get_row_lb(lp, k);
ub = lpx_get_row_ub(lp, k);
prim = row_prim[k];
}
else
{ type = lpx_get_col_type(lp, k-m);
lb = lpx_get_col_lb(lp, k-m);
ub = lpx_get_col_ub(lp, k-m);
prim = col_prim[k-m];
}
if (type == LPX_LO || type == LPX_DB || type == LPX_FX)
{ /* variable x[k] has lower bound */
if (prim < lb - tol_bnd * (1.0 + fabs(lb)))
{ p_stat = LPX_P_INFEAS;
break;
}
}
if (type == LPX_UP || type == LPX_DB || type == LPX_FX)
{ /* variable x[k] has upper bound */
if (prim > ub + tol_bnd * (1.0 + fabs(ub)))
{ p_stat = LPX_P_INFEAS;
break;
}
}
}
/* compute dual basic solution components */
lpx_eval_b_dual(lp, row_dual, col_dual);
/* determine dual status of basic solution */
tol_dj = 3.0 * lpx_get_real_parm(lp, LPX_K_TOLDJ);
dir = (lpx_get_obj_dir(lp) == LPX_MIN ? +1.0 : -1.0);
d_stat = LPX_D_FEAS;
for (k = 1; k <= m+n; k++)
{ if (k <= m)
{ stat = lpx_get_row_stat(lp, k);
dual = row_dual[k];
}
else
{ stat = lpx_get_col_stat(lp, k-m);
dual = col_dual[k-m];
}
if (stat == LPX_BS || stat == LPX_NL || stat == LPX_NF)
{ /* reduced cost of x[k] must be non-negative (minimization)
or non-positive (maximization) */
if (dir * dual < - tol_dj)
{ d_stat = LPX_D_INFEAS;
break;
}
}
if (stat == LPX_BS || stat == LPX_NU || stat == LPX_NF)
{ /* reduced cost of x[k] must be non-positive (minimization)
or non-negative (maximization) */
if (dir * dual > + tol_dj)
{ d_stat = LPX_D_INFEAS;
break;
}
}
}
/* store basic solution components */
p_stat = p_stat - LPX_P_UNDEF + GLP_UNDEF;
d_stat = d_stat - LPX_D_UNDEF + GLP_UNDEF;
sum = lpx_get_obj_coef(lp, 0);
for (j = 1; j <= n; j++)
sum += lpx_get_obj_coef(lp, j) * col_prim[j];
glp_put_solution(lp, 0, &p_stat, &d_stat, &sum,
NULL, row_prim, row_dual, NULL, col_prim, col_dual);
xassert(lpx_is_b_avail(lp));
/* free working arrays */
xfree(row_prim);
xfree(row_dual);
xfree(col_prim);
xfree(col_dual);
done: /* return to the calling program */
return ret;
}
int lpx_gomory_cut(LPX *lp, int len, int ind[], double val[],
double work[])
{ int m = lpx_get_num_rows(lp);
int n = lpx_get_num_cols(lp);
int k, t, stat;
double lb, ub, *alfa, beta, alfa_j, f0, fj, *a, b, a_j;
/* on entry the specified row of the simplex table has the form:
y = alfa[1]*xN[1] + ... + alfa[n]*xN[n];
convert this row to the form:
y + alfa'[1]*xN'[1] + ... + alfa'[n]*xN'[n] = beta,
where all new (stroked) non-basic variables are non-negative
(this is not needed for y, because it has integer bounds and
only fractional part of beta is used); note that beta is the
value of y in the current basic solution */
alfa = val;
beta = 0.0;
for (t = 1; t <= len; t++)
{ /* get index of some non-basic variable x[k] = xN[j] */
k = ind[t];
if (!(1 <= k && k <= m+n))
fault("lpx_gomory_cut: ind[%d] = %d; variable number out of"
" range", t, k);
/* get the original influence coefficient alfa[j] */
alfa_j = alfa[t];
/* obtain status and bounds of x[k] = xN[j] */
if (k <= m)
{ stat = lpx_get_row_stat(lp, k);
lb = lpx_get_row_lb(lp, k);
ub = lpx_get_row_ub(lp, k);
}
else
{ stat = lpx_get_col_stat(lp, k-m);
lb = lpx_get_col_lb(lp, k-m);
ub = lpx_get_col_ub(lp, k-m);
}
/* perform conversion */
if (stat == LPX_BS)
fault("lpx_gomory_cut: ind[%d] = %d; variable must be non-b"
"asic", t, k);
switch (stat)
{ case LPX_NL:
/* xN[j] is on its lower bound */
/* substitute xN[j] = lb[k] + xN'[j] */
alfa[t] = - alfa_j;
beta += alfa_j * lb;
break;
case LPX_NU:
/* xN[j] is on its upper bound */
/* substitute xN[j] = ub[k] - xN'[j] */
alfa[t] = + alfa_j;
beta += alfa_j * ub;
break;
case LPX_NF:
/* xN[j] is free non-basic variable */
return -1;
case LPX_NS:
/* xN[j] is fixed non-basic variable */
/* substitute xN[j] = lb[k] */
alfa[t] = 0.0;
beta += alfa_j * lb;
break;
default:
insist(stat != stat);
}
}
/* now the converted row of the simplex table has the form:
y + alfa'[1]*xN'[1] + ... + alfa'[n]*xN'[n] = beta,
where all xN'[j] >= 0; generate Gomory's mixed integer cut in
the form of inequality:
a'[1]*xN'[1] + ... + a'[n]*xN'[n] >= b' */
a = val;
/* f0 is fractional part of beta, where beta is the value of the
variable y in the current basic solution; if f0 is close to
zero or to one, i.e. if y is near to a closest integer point,
the corresponding cutting plane may be unreliable */
f0 = beta - floor(beta);
if (!(0.00001 <= f0 && f0 <= 0.99999)) return -2;
for (t = 1; t <= len; t++)
{ alfa_j = alfa[t];
if (alfa_j == 0.0)
{ a[t] = 0.0;
continue;
}
k = ind[t];
insist(1 <= k && k <= m+n);
if (k > m && lpx_get_col_kind(lp, k-m) == LPX_IV)
{ /* xN[j] is integer */
fj = alfa_j - floor(alfa_j);
if (fj <= f0)
a[t] = fj;
else
a[t] = (f0 / (1.0 - f0)) * (1.0 - fj);
}
else
{ /* xN[j] is continuous */
if (alfa_j > 0.0)
a[t] = alfa_j;
else
a[t] = - (f0 / (1.0 - f0)) * alfa_j;
}
}
b = f0;
/* now the generated cutting plane has the form of an inequality:
a'[1]*xN'[1] + ... + a'[n]*xN'[n] >= b';
convert this inequality back to the form expressed through the
original non-basic variables:
a[1]*xN[1] + ... + a[n]*xN[n] >= b */
for (t = 1; t <= len; t++)
{ a_j = a[t];
if (a_j == 0.0) continue;
k = ind[t]; /* x[k] = xN[j] */
/* obtain status and bounds of x[k] = xN[j] */
if (k <= m)
{ stat = lpx_get_row_stat(lp, k);
lb = lpx_get_row_lb(lp, k);
ub = lpx_get_row_ub(lp, k);
}
else
{ stat = lpx_get_col_stat(lp, k-m);
lb = lpx_get_col_lb(lp, k-m);
ub = lpx_get_col_ub(lp, k-m);
}
/* perform conversion */
switch (stat)
{ case LPX_NL:
/* xN[j] is on its lower bound */
/* substitute xN'[j] = xN[j] - lb[k] */
val[t] = + a_j;
b += a_j * lb;
break;
case LPX_NU:
/* xN[j] is on its upper bound */
/* substitute xN'[j] = ub[k] - xN[j] */
val[t] = - a_j;
b -= a_j * ub;
break;
default:
insist(stat != stat);
}
}
/* substitute auxiliary (non-basic) variables to the generated
inequality constraint a[1]*xN[1] + ... + a[n]*xN[n] >= b using
the equality constraints of the specified LP problem object in
order to express the generated constraint through structural
variables only */
len = lpx_reduce_form(lp, len, ind, val, work);
/* store the right-hand side */
ind[0] = 0, val[0] = b;
/* return to the calling program */
return len;
}
int lpx_intopt(LPX *_mip)
{ IPP *ipp = NULL;
LPX *orig = _mip, *prob = NULL;
int orig_m, orig_n, i, j, ret, i_stat;
/* the problem must be of MIP class */
if (lpx_get_class(orig) != LPX_MIP)
{ print("lpx_intopt: problem is not of MIP class");
ret = LPX_E_FAULT;
goto done;
}
/* the problem must have at least one row and one column */
orig_m = lpx_get_num_rows(orig);
orig_n = lpx_get_num_cols(orig);
if (!(orig_m > 0 && orig_n > 0))
{ print("lpx_intopt: problem has no rows/columns");
ret = LPX_E_FAULT;
goto done;
}
/* check that each double-bounded row and column has bounds */
for (i = 1; i <= orig_m; i++)
{ if (lpx_get_row_type(orig, i) == LPX_DB)
{ if (lpx_get_row_lb(orig, i) >= lpx_get_row_ub(orig, i))
{ print("lpx_intopt: row %d has incorrect bounds", i);
ret = LPX_E_FAULT;
goto done;
}
}
}
for (j = 1; j <= orig_n; j++)
{ if (lpx_get_col_type(orig, j) == LPX_DB)
{ if (lpx_get_col_lb(orig, j) >= lpx_get_col_ub(orig, j))
{ print("lpx_intopt: column %d has incorrect bounds", j);
ret = LPX_E_FAULT;
goto done;
}
}
}
/* bounds of all integer variables must be integral */
for (j = 1; j <= orig_n; j++)
{ int type;
double lb, ub;
if (lpx_get_col_kind(orig, j) != LPX_IV) continue;
type = lpx_get_col_type(orig, j);
if (type == LPX_LO || type == LPX_DB || type == LPX_FX)
{ lb = lpx_get_col_lb(orig, j);
if (lb != floor(lb))
{ print("lpx_intopt: integer column %d has non-integer low"
"er bound or fixed value %g", j, lb);
ret = LPX_E_FAULT;
goto done;
}
}
if (type == LPX_UP || type == LPX_DB)
{ ub = lpx_get_col_ub(orig, j);
if (ub != floor(ub))
{ print("lpx_intopt: integer column %d has non-integer upp"
"er bound %g", j, ub);
ret = LPX_E_FAULT;
goto done;
}
}
}
/* reset the status of MIP solution */
lpx_put_mip_soln(orig, LPX_I_UNDEF, NULL, NULL);
/* create MIP presolver workspace */
ipp = ipp_create_wksp();
/* load the original problem into the presolver workspace */
ipp_load_orig(ipp, orig);
/* perform basic MIP presolve analysis */
switch (ipp_basic_tech(ipp))
{ case 0:
/* no infeasibility is detected */
break;
case 1:
nopfs: /* primal infeasibility is detected */
print("PROBLEM HAS NO PRIMAL FEASIBLE SOLUTION");
ret = LPX_E_NOPFS;
goto done;
case 2:
/* dual infeasibility is detected */
nodfs: print("LP RELAXATION HAS NO DUAL FEASIBLE SOLUTION");
ret = LPX_E_NODFS;
goto done;
default:
insist(ipp != ipp);
}
/* reduce column bounds */
switch (ipp_reduce_bnds(ipp))
{ case 0: break;
case 1: goto nopfs;
default: insist(ipp != ipp);
}
/* perform basic MIP presolve analysis */
switch (ipp_basic_tech(ipp))
{ case 0: break;
case 1: goto nopfs;
case 2: goto nodfs;
default: insist(ipp != ipp);
}
/* replace general integer variables by sum of binary variables,
if required */
if (lpx_get_int_parm(orig, LPX_K_BINARIZE))
ipp_binarize(ipp);
/* perform coefficient reduction */
ipp_reduction(ipp);
/* if the resultant problem is empty, it has an empty solution,
which is optimal */
if (ipp->row_ptr == NULL || ipp->col_ptr == NULL)
{ insist(ipp->row_ptr == NULL);
insist(ipp->col_ptr == NULL);
print("Objective value = %.10g",
ipp->orig_dir == LPX_MIN ? +ipp->c0 : -ipp->c0);
print("INTEGER OPTIMAL SOLUTION FOUND BY MIP PRESOLVER");
/* allocate recovered solution segment */
ipp->col_stat = ucalloc(1+ipp->ncols, sizeof(int));
ipp->col_mipx = ucalloc(1+ipp->ncols, sizeof(double));
for (j = 1; j <= ipp->ncols; j++) ipp->col_stat[j] = 0;
/* perform MIP postsolve processing */
ipp_postsolve(ipp);
/* unload recovered MIP solution and store it in the original
problem object */
ipp_unload_sol(ipp, orig, LPX_I_OPT);
ret = LPX_E_OK;
goto done;
}
/* build resultant MIP problem object */
prob = ipp_build_prob(ipp);
/* display some statistics */
{ int m = lpx_get_num_rows(prob);
int n = lpx_get_num_cols(prob);
int nnz = lpx_get_num_nz(prob);
int ni = lpx_get_num_int(prob);
int nb = lpx_get_num_bin(prob);
char s[50];
print("lpx_intopt: presolved MIP has %d row%s, %d column%s, %d"
" non-zero%s", m, m == 1 ? "" : "s", n, n == 1 ? "" : "s",
nnz, nnz == 1 ? "" : "s");
if (nb == 0)
strcpy(s, "none of");
else if (ni == 1 && nb == 1)
strcpy(s, "");
else if (nb == 1)
strcpy(s, "one of");
else if (nb == ni)
strcpy(s, "all of");
else
sprintf(s, "%d of", nb);
print("lpx_intopt: %d integer column%s, %s which %s binary",
ni, ni == 1 ? "" : "s", s, nb == 1 ? "is" : "are");
}
/* inherit some control parameters and statistics */
lpx_set_int_parm(prob, LPX_K_PRICE, lpx_get_int_parm(orig,
LPX_K_PRICE));
lpx_set_real_parm(prob, LPX_K_RELAX, lpx_get_real_parm(orig,
LPX_K_RELAX));
lpx_set_real_parm(prob, LPX_K_TOLBND, lpx_get_real_parm(orig,
LPX_K_TOLBND));
lpx_set_real_parm(prob, LPX_K_TOLDJ, lpx_get_real_parm(orig,
LPX_K_TOLDJ));
lpx_set_real_parm(prob, LPX_K_TOLPIV, lpx_get_real_parm(orig,
LPX_K_TOLPIV));
lpx_set_int_parm(prob, LPX_K_ITLIM, lpx_get_int_parm(orig,
LPX_K_ITLIM));
lpx_set_int_parm(prob, LPX_K_ITCNT, lpx_get_int_parm(orig,
LPX_K_ITCNT));
lpx_set_real_parm(prob, LPX_K_TMLIM, lpx_get_real_parm(orig,
LPX_K_TMLIM));
lpx_set_int_parm(prob, LPX_K_BRANCH, lpx_get_int_parm(orig,
LPX_K_BRANCH));
lpx_set_int_parm(prob, LPX_K_BTRACK, lpx_get_int_parm(orig,
LPX_K_BTRACK));
lpx_set_real_parm(prob, LPX_K_TOLINT, lpx_get_real_parm(orig,
LPX_K_TOLINT));
lpx_set_real_parm(prob, LPX_K_TOLOBJ, lpx_get_real_parm(orig,
LPX_K_TOLOBJ));
/* build an advanced initial basis */
lpx_adv_basis(prob);
/* solve LP relaxation */
print("Solving LP relaxation...");
switch (lpx_simplex(prob))
{ case LPX_E_OK:
break;
case LPX_E_ITLIM:
ret = LPX_E_ITLIM;
goto done;
case LPX_E_TMLIM:
ret = LPX_E_TMLIM;
goto done;
default:
print("lpx_intopt: cannot solve LP relaxation");
ret = LPX_E_SING;
goto done;
}
/* analyze status of the basic solution */
switch (lpx_get_status(prob))
{ case LPX_OPT:
break;
case LPX_NOFEAS:
ret = LPX_E_NOPFS;
goto done;
case LPX_UNBND:
ret = LPX_E_NODFS;
goto done;
default:
insist(prob != prob);
}
/* generate cutting planes, if necessary */
if (lpx_get_int_parm(orig, LPX_K_USECUTS))
{ ret = generate_cuts(prob);
if (ret != LPX_E_OK) goto done;
}
/* call the branch-and-bound solver */
ret = lpx_integer(prob);
/* determine status of MIP solution */
i_stat = lpx_mip_status(prob);
if (i_stat == LPX_I_OPT || i_stat == LPX_I_FEAS)
{ /* load MIP solution of the resultant problem into presolver
workspace */
ipp_load_sol(ipp, prob);
/* perform MIP postsolve processing */
ipp_postsolve(ipp);
/* unload recovered MIP solution and store it in the original
problem object */
ipp_unload_sol(ipp, orig, i_stat);
}
else
{ /* just set the status of MIP solution */
lpx_put_mip_soln(orig, i_stat, NULL, NULL);
}
done: /* copy back statistics about spent resources */
if (prob != NULL)
{ lpx_set_int_parm(orig, LPX_K_ITLIM, lpx_get_int_parm(prob,
LPX_K_ITLIM));
lpx_set_int_parm(orig, LPX_K_ITCNT, lpx_get_int_parm(prob,
LPX_K_ITCNT));
lpx_set_real_parm(orig, LPX_K_TMLIM, lpx_get_real_parm(prob,
LPX_K_TMLIM));
}
/* delete the resultant problem object */
if (prob != NULL) lpx_delete_prob(prob);
/* delete MIP presolver workspace */
if (ipp != NULL) ipp_delete_wksp(ipp);
return ret;
}