void lpx_get_col_info(glp_prob *lp, int j, int *tagx, double *vx,
double *dx)
{ /* obtain column solution information */
if (tagx != NULL) *tagx = lpx_get_col_stat(lp, j);
if (vx != NULL) *vx = lpx_get_col_prim(lp, j);
if (dx != NULL) *dx = lpx_get_col_dual(lp, j);
return;
}
void lpx_eval_b_dual(LPX *lp, double row_dual[], double col_dual[])
{ int i, j, k, m, n, len, *ind;
double dj, *cB, *pi, *val;
if (!lpx_is_b_avail(lp))
xfault("lpx_eval_b_dual: LP basis is not available\n");
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* store zero reduced costs of basic auxiliary and structural
variables and build the vector cB of objective coefficients at
basic variables */
cB = xcalloc(1+m, sizeof(double));
for (i = 1; i <= m; i++)
{ k = lpx_get_b_info(lp, i);
/* xB[i] is k-th original variable */
xassert(1 <= k && k <= m+n);
if (k <= m)
{ row_dual[k] = 0.0;
cB[i] = 0.0;
}
else
{ col_dual[k-m] = 0.0;
cB[i] = lpx_get_obj_coef(lp, k-m);
}
}
/* solve the system B'*pi = cB to compute the vector pi */
pi = cB, lpx_btran(lp, pi);
/* compute reduced costs of non-basic auxiliary variables */
for (i = 1; i <= m; i++)
{ if (lpx_get_row_stat(lp, i) != LPX_BS)
row_dual[i] = - pi[i];
}
/* compute reduced costs of non-basic structural variables */
ind = xcalloc(1+m, sizeof(int));
val = xcalloc(1+m, sizeof(double));
for (j = 1; j <= n; j++)
{ if (lpx_get_col_stat(lp, j) != LPX_BS)
{ dj = lpx_get_obj_coef(lp, j);
len = lpx_get_mat_col(lp, j, ind, val);
for (k = 1; k <= len; k++) dj += val[k] * pi[ind[k]];
col_dual[j] = dj;
}
}
xfree(ind);
xfree(val);
xfree(cB);
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;
}
int lpx_dual_ratio_test(LPX *lp, int len, const int ind[],
const double val[], int how, double tol)
{ int k, m, n, t, q, tagx;
double dir, alfa_j, abs_alfa_j, big, eps, cbar_j, temp, teta;
if (!lpx_is_b_avail(lp))
xfault("lpx_dual_ratio_test: LP basis is not available\n");
if (lpx_get_dual_stat(lp) != LPX_D_FEAS)
xfault("lpx_dual_ratio_test: current basic solution is not dua"
"l feasible\n");
if (!(how == +1 || how == -1))
xfault("lpx_dual_ratio_test: how = %d; invalid parameter\n",
how);
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
dir = (lpx_get_obj_dir(lp) == LPX_MIN ? +1.0 : -1.0);
/* 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 row */
if (!(0.0 < tol && tol < 1.0))
xfault("lpx_dual_ratio_test: tol = %g; invalid tolerance\n",
tol);
eps = tol * (1.0 + big);
/* initial settings */
q = 0, teta = DBL_MAX, big = 0.0;
/* walk through the entries of the specified row */
for (t = 1; t <= len; t++)
{ /* get ordinal number of non-basic variable */
k = ind[t];
if (!(1 <= k && k <= m+n))
xfault("lpx_dual_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_dual_ratio_test: ind[%d] = %d; basic variable n"
"ot allowed\n", t, k);
/* determine unscaled reduced cost of the non-basic variable
x[k] = xN[j] in the current basic solution */
if (k <= m)
cbar_j = lpx_get_row_dual(lp, k);
else
cbar_j = lpx_get_col_dual(lp, k-m);
/* determine influence coefficient at the non-basic variable
x[k] = xN[j] in the explicitly specified row and turn to
the case of increasing the variable y in order to simplify
program logic */
alfa_j = (how > 0 ? +val[t] : -val[t]);
abs_alfa_j = (alfa_j > 0.0 ? +alfa_j : -alfa_j);
/* analyze main cases */
switch (tagx)
{ case LPX_NL:
/* xN[j] is on its lower bound */
if (alfa_j < +eps) continue;
temp = (dir * cbar_j) / alfa_j;
break;
case LPX_NU:
/* xN[j] is on its upper bound */
if (alfa_j > -eps) continue;
temp = (dir * cbar_j) / alfa_j;
break;
case LPX_NF:
/* xN[j] is non-basic free variable */
if (abs_alfa_j < eps) continue;
temp = 0.0;
break;
case LPX_NS:
/* xN[j] is non-basic fixed variable */
continue;
default:
xassert(tagx != tagx);
}
/* if the reduced cost of the variable xN[j] violates its zero
bound (slightly, because the current basis is assumed to be
dual feasible), temp is negative; we can think this happens
due to round-off errors and the reduced cost is exact zero;
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_j)
q = k, teta = temp, big = abs_alfa_j;
}
/* return the ordinal number of the chosen non-basic variable */
return q;
}
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_transform_row(LPX *lp, int len, int ind[], double val[])
{ int i, j, k, m, n, t, lll, *iii;
double alfa, *a, *aB, *rho, *vvv;
if (!lpx_is_b_avail(lp))
xfault("lpx_transform_row: LP basis is not available\n");
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
/* unpack the row to be transformed to the array a */
a = xcalloc(1+n, sizeof(double));
for (j = 1; j <= n; j++) a[j] = 0.0;
if (!(0 <= len && len <= n))
xfault("lpx_transform_row: len = %d; invalid row length\n",
len);
for (t = 1; t <= len; t++)
{ j = ind[t];
if (!(1 <= j && j <= n))
xfault("lpx_transform_row: ind[%d] = %d; column index out o"
"f range\n", t, j);
if (val[t] == 0.0)
xfault("lpx_transform_row: val[%d] = 0; zero coefficient no"
"t allowed\n", t);
if (a[j] != 0.0)
xfault("lpx_transform_row: ind[%d] = %d; duplicate column i"
"ndices not allowed\n", t, j);
a[j] = val[t];
}
/* construct the vector aB */
aB = xcalloc(1+m, sizeof(double));
for (i = 1; i <= m; i++)
{ k = lpx_get_b_info(lp, i);
/* xB[i] is k-th original variable */
xassert(1 <= k && k <= m+n);
aB[i] = (k <= m ? 0.0 : a[k-m]);
}
/* solve the system B'*rho = aB to compute the vector rho */
rho = aB, lpx_btran(lp, rho);
/* compute coefficients at non-basic auxiliary variables */
len = 0;
for (i = 1; i <= m; i++)
{ if (lpx_get_row_stat(lp, i) != LPX_BS)
{ alfa = - rho[i];
if (alfa != 0.0)
{ len++;
ind[len] = i;
val[len] = alfa;
}
}
}
/* compute coefficients at non-basic structural variables */
iii = xcalloc(1+m, sizeof(int));
vvv = xcalloc(1+m, sizeof(double));
for (j = 1; j <= n; j++)
{ if (lpx_get_col_stat(lp, j) != LPX_BS)
{ alfa = a[j];
lll = lpx_get_mat_col(lp, j, iii, vvv);
for (t = 1; t <= lll; t++) alfa += vvv[t] * rho[iii[t]];
if (alfa != 0.0)
{ len++;
ind[len] = m+j;
val[len] = alfa;
}
}
}
xassert(len <= n);
xfree(iii);
xfree(vvv);
xfree(aB);
xfree(a);
return len;
}
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;
}
static void gen_gomory_cut(LPX *prob, int maxlen)
{ int m = lpx_get_num_rows(prob);
int n = lpx_get_num_cols(prob);
int i, j, k, len, cut_j, *ind;
double x, d, r, temp, cut_d, cut_r, *val, *work;
insist(lpx_get_status(prob) == LPX_OPT);
/* allocate working arrays */
ind = ucalloc(1+n, sizeof(int));
val = ucalloc(1+n, sizeof(double));
work = ucalloc(1+m+n, sizeof(double));
/* nothing is chosen so far */
cut_j = 0; cut_d = 0.0; cut_r = 0.0;
/* look through all structural variables */
for (j = 1; j <= n; j++)
{ /* if the variable is continuous, skip it */
if (lpx_get_col_kind(prob, j) != LPX_IV) continue;
/* if the variable is non-basic, skip it */
if (lpx_get_col_stat(prob, j) != LPX_BS) continue;
/* if the variable is fixed, skip it */
if (lpx_get_col_type(prob, j) == LPX_FX) continue;
/* obtain current primal value of the variable */
x = lpx_get_col_prim(prob, j);
/* if the value is close enough to nearest integer, skip the
variable */
if (fabs(x - floor(x + 0.5)) < 1e-4) continue;
/* compute the row of the simplex table corresponding to the
variable */
len = lpx_eval_tab_row(prob, m+j, ind, val);
len = lpx_remove_tiny(len, ind, NULL, val, 1e-10);
/* generate Gomory's mixed integer cut:
a[1]*x[1] + ... + a[n]*x[n] >= b */
len = lpx_gomory_cut(prob, len, ind, val, work);
if (len < 0) continue;
insist(0 <= len && len <= n);
len = lpx_remove_tiny(len, ind, NULL, val, 1e-10);
if (fabs(val[0]) < 1e-10) val[0] = 0.0;
/* if the cut is too long, skip it */
if (len > maxlen) continue;
/* if the cut contains coefficients with too large magnitude,
do not use it to prevent numeric instability */
for (k = 0; k <= len; k++) /* including rhs */
if (fabs(val[k]) > 1e+6) break;
if (k <= len) continue;
/* at the current point the cut inequality is violated, i.e.
the residual b - (a[1]*x[1] + ... + a[n]*x[n]) > 0; note
that for Gomory's cut the residual is less than 1.0 */
/* in order not to depend on the magnitude of coefficients we
use scaled residual:
r = [b - (a[1]*x[1] + ... + a[n]*x[n])] / max(1, |a[j]|) */
temp = 1.0;
for (k = 1; k <= len; k++)
if (temp < fabs(val[k])) temp = fabs(val[k]);
r = (val[0] - lpx_eval_row(prob, len, ind, val)) / temp;
if (r < 1e-5) continue;
/* estimate degradation (worsening) of the objective function
by one dual simplex step if the cut row would be introduced
in the problem */
d = lpx_eval_degrad(prob, len, ind, val, LPX_LO, val[0]);
/* ignore the sign of degradation */
d = fabs(d);
/* which cut should be used? there are two basic cases:
1) if the degradation is non-zero, we are interested in a
cut providing maximal degradation;
2) if the degradation is zero (i.e. a non-basic variable
which would enter the basis in the adjacent vertex has
zero reduced cost), we are interested in a cut providing
maximal scaled residual;
in both cases it is desired that the cut length (the number
of inequality coefficients) is possibly short */
/* if both degradation and scaled residual are small, skip the
cut */
if (d < 0.001 && r < 0.001)
continue;
/* if there is no cut chosen, choose this cut */
else if (cut_j == 0)
;
/* if this cut provides stronger degradation and has shorter
length, choose it */
else if (cut_d != 0.0 && cut_d < d)
;
/* if this cut provides larger scaled residual and has shorter
length, choose it */
else if (cut_d == 0.0 && cut_r < r)
;
/* otherwise skip the cut */
else
continue;
/* save attributes of the cut choosen */
cut_j = j, cut_r = r, cut_d = d;
}
/* if a cut has been chosen, include it to the problem */
if (cut_j != 0)
{ j = cut_j;
/* compute the row of the simplex table */
len = lpx_eval_tab_row(prob, m+j, ind, val);
len = lpx_remove_tiny(len, ind, NULL, val, 1e-10);
/* generate the cut */
len = lpx_gomory_cut(prob, len, ind, val, work);
insist(0 <= len && len <= n);
len = lpx_remove_tiny(len, ind, NULL, val, 1e-10);
if (fabs(val[0]) < 1e-10) val[0] = 0.0;
/* include the corresponding row in the problem */
i = lpx_add_rows(prob, 1);
lpx_set_row_bnds(prob, i, LPX_LO, val[0], 0.0);
lpx_set_mat_row(prob, i, len, ind, val);
}
/* free working arrays */
ufree(ind);
ufree(val);
ufree(work);
return;
}