static int is_binary(LPX *lp, int j)
{ /* this routine checks if variable x[j] is binary */
return
lpx_get_col_kind(lp, j) == LPX_IV &&
lpx_get_col_type(lp, j) == LPX_DB &&
lpx_get_col_lb(lp, j) == 0.0 && lpx_get_col_ub(lp, j) == 1.0;
}
static void show_status(LPX *prob, int prob_m, int prob_nz)
{ int n, j, count;
double x, tol_int;
/* determine the number of structural variables of integer kind
whose current values are still fractional */
n = lpx_get_num_cols(prob);
tol_int = lpx_get_real_parm(prob, LPX_K_TOLINT);
count = 0;
for (j = 1; j <= n; j++)
{ if (lpx_get_col_kind(prob, j) != LPX_IV) continue;
x = lpx_get_col_prim(prob, j);
if (fabs(x - floor(x + 0.5)) <= tol_int) continue;
count++;
}
print("&%6d: obj = %17.9e frac = %5d cuts = %5d (%d)",
lpx_get_int_parm(prob, LPX_K_ITCNT),
lpx_get_obj_val(prob), count,
lpx_get_num_rows(prob) - prob_m,
lpx_get_num_nz(prob) - prob_nz);
return;
}
int lpx_write_cpxlp(LPX *lp, const char *fname)
{ /* write problem data in CPLEX LP format */
FILE *fp;
int nrows, ncols, i, j, t, len, typx, flag, kind, *ind;
double lb, ub, temp, *val;
char line[1023+1], term[1023+1], rname[255+1], cname[255+1];
print("lpx_write_cpxlp: writing problem data to `%s'...", fname);
/* open the output text file */
fp = xfopen(fname, "w");
if (fp == NULL)
{ print("lpx_write_cpxlp: unable to create `%s' - %s", fname,
strerror(errno));
goto fail;
}
/* determine the number of rows and columns */
nrows = lpx_get_num_rows(lp);
ncols = lpx_get_num_cols(lp);
/* the problem should contain at least one row and one column */
if (!(nrows > 0 && ncols > 0))
fault("lpx_write_cpxlp: problem has no rows/columns");
/* write problem name */
{ const char *name = lpx_get_prob_name(lp);
if (name == NULL) name = "Unknown";
fprintf(fp, "\\* Problem: %s *\\\n", name);
fprintf(fp, "\n");
}
/* allocate working arrays */
ind = xcalloc(1+ncols, sizeof(int));
val = xcalloc(1+ncols, sizeof(double));
/* write the objective function definition and the constraints
section */
for (i = 0; i <= nrows; i++)
{ if (i == 0)
{ switch (lpx_get_obj_dir(lp))
{ case LPX_MIN:
fprintf(fp, "Minimize\n");
break;
case LPX_MAX:
fprintf(fp, "Maximize\n");
break;
default:
xassert(lp != lp);
}
}
else if (i == 1)
{ temp = lpx_get_obj_coef(lp, 0);
if (temp != 0.0)
fprintf(fp, "\\* constant term = %.*g *\\\n", DBL_DIG,
temp);
fprintf(fp, "\n");
fprintf(fp, "Subject To\n");
}
row_name(lp, i, rname);
if (i == 0)
{ len = 0;
for (j = 1; j <= ncols; j++)
{ temp = lpx_get_obj_coef(lp, j);
if (temp != 0.0)
len++, ind[len] = j, val[len] = temp;
}
}
else
{ lpx_get_row_bnds(lp, i, &typx, &lb, &ub);
if (typx == LPX_FR) continue;
len = lpx_get_mat_row(lp, i, ind, val);
}
flag = 0;
more: if (!flag)
sprintf(line, " %s:", rname);
else
sprintf(line, " %*s ", strlen(rname), "");
for (t = 1; t <= len; t++)
{ col_name(lp, ind[t], cname);
if (val[t] == +1.0)
sprintf(term, " + %s", cname);
else if (val[t] == -1.0)
sprintf(term, " - %s", cname);
else if (val[t] > 0.0)
sprintf(term, " + %.*g %s", DBL_DIG, +val[t], cname);
else if (val[t] < 0.0)
sprintf(term, " - %.*g %s", DBL_DIG, -val[t], cname);
else
xassert(lp != lp);
if (strlen(line) + strlen(term) > 72)
fprintf(fp, "%s\n", line), line[0] = '\0';
strcat(line, term);
}
if (len == 0)
{ /* empty row */
sprintf(term, " 0 %s", col_name(lp, 1, cname));
strcat(line, term);
}
if (i > 0)
{ switch (typx)
{ case LPX_LO:
case LPX_DB:
sprintf(term, " >= %.*g", DBL_DIG, lb);
break;
case LPX_UP:
sprintf(term, " <= %.*g", DBL_DIG, ub);
break;
case LPX_FX:
sprintf(term, " = %.*g", DBL_DIG, lb);
break;
default:
xassert(typx != typx);
}
if (strlen(line) + strlen(term) > 72)
fprintf(fp, "%s\n", line), line[0] = '\0';
strcat(line, term);
}
fprintf(fp, "%s\n", line);
if (i > 0 && typx == LPX_DB)
{ /* double-bounded row needs a copy for its upper bound */
flag = 1;
typx = LPX_UP;
goto more;
}
}
/* free working arrays */
xfree(ind);
xfree(val);
/* write the bounds section */
flag = 0;
for (j = 1; j <= ncols; j++)
{ col_name(lp, j, cname);
lpx_get_col_bnds(lp, j, &typx, &lb, &ub);
if (typx == LPX_LO && lb == 0.0) continue;
if (!flag)
{ fprintf(fp, "\n");
fprintf(fp, "Bounds\n");
flag = 1;
}
switch (typx)
{ case LPX_FR:
fprintf(fp, " %s free\n", cname);
break;
case LPX_LO:
fprintf(fp, " %s >= %.*g\n", cname, DBL_DIG, lb);
break;
case LPX_UP:
fprintf(fp, " %s <= %.*g\n", cname, DBL_DIG, ub);
break;
case LPX_DB:
fprintf(fp, " %.*g <= %s <= %.*g\n", DBL_DIG, lb, cname,
DBL_DIG, ub);
break;
case LPX_FX:
fprintf(fp, " %s = %.*g\n", cname, DBL_DIG, lb);
break;
default:
xassert(typx != typx);
}
}
/* write the general section */
if (lpx_get_class(lp) == LPX_MIP)
{ flag = 0;
for (j = 1; j <= ncols; j++)
{ kind = lpx_get_col_kind(lp, j);
if (kind == LPX_CV) continue;
xassert(kind == LPX_IV);
if (!flag)
{ fprintf(fp, "\n");
fprintf(fp, "Generals\n");
flag = 1;
}
fprintf(fp, " %s\n", col_name(lp, j, cname));
}
}
/* write the end keyword */
fprintf(fp, "\n");
fprintf(fp, "End\n");
/* close the output text file */
fflush(fp);
if (ferror(fp))
{ print("lpx_write_cpxlp: write error on `%s' - %s", fname,
strerror(errno));
goto fail;
}
xfclose(fp);
/* return to the calling program */
return 0;
fail: /* the operation failed */
if (fp != NULL) xfclose(fp);
return 1;
}
int lpx_print_prob(LPX *lp, const char *fname)
{ XFILE *fp;
int m, n, mip, i, j, len, t, type, *ndx;
double coef, lb, ub, *val;
char *str, name[255+1];
xprintf("lpx_write_prob: writing problem data to `%s'...\n",
fname);
fp = xfopen(fname, "w");
if (fp == NULL)
{ xprintf("lpx_write_prob: unable to create `%s' - %s\n",
fname, strerror(errno));
goto fail;
}
m = lpx_get_num_rows(lp);
n = lpx_get_num_cols(lp);
mip = (lpx_get_class(lp) == LPX_MIP);
str = (void *)lpx_get_prob_name(lp);
xfprintf(fp, "Problem: %s\n", str == NULL ? "(unnamed)" : str);
xfprintf(fp, "Class: %s\n", !mip ? "LP" : "MIP");
xfprintf(fp, "Rows: %d\n", m);
if (!mip)
xfprintf(fp, "Columns: %d\n", n);
else
xfprintf(fp, "Columns: %d (%d integer, %d binary)\n",
n, lpx_get_num_int(lp), lpx_get_num_bin(lp));
xfprintf(fp, "Non-zeros: %d\n", lpx_get_num_nz(lp));
xfprintf(fp, "\n");
xfprintf(fp, "*** OBJECTIVE FUNCTION ***\n");
xfprintf(fp, "\n");
switch (lpx_get_obj_dir(lp))
{ case LPX_MIN:
xfprintf(fp, "Minimize:");
break;
case LPX_MAX:
xfprintf(fp, "Maximize:");
break;
default:
xassert(lp != lp);
}
str = (void *)lpx_get_obj_name(lp);
xfprintf(fp, " %s\n", str == NULL ? "(unnamed)" : str);
coef = lpx_get_obj_coef(lp, 0);
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
"(constant term)");
for (i = 1; i <= m; i++)
#if 0
{ coef = lpx_get_row_coef(lp, i);
#else
{ coef = 0.0;
#endif
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
row_name(lp, i, name));
}
for (j = 1; j <= n; j++)
{ coef = lpx_get_obj_coef(lp, j);
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
col_name(lp, j, name));
}
xfprintf(fp, "\n");
xfprintf(fp, "*** ROWS (CONSTRAINTS) ***\n");
ndx = xcalloc(1+n, sizeof(int));
val = xcalloc(1+n, sizeof(double));
for (i = 1; i <= m; i++)
{ xfprintf(fp, "\n");
xfprintf(fp, "Row %d: %s", i, row_name(lp, i, name));
lpx_get_row_bnds(lp, i, &type, &lb, &ub);
switch (type)
{ case LPX_FR:
xfprintf(fp, " free");
break;
case LPX_LO:
xfprintf(fp, " >= %.*g", DBL_DIG, lb);
break;
case LPX_UP:
xfprintf(fp, " <= %.*g", DBL_DIG, ub);
break;
case LPX_DB:
xfprintf(fp, " >= %.*g <= %.*g", DBL_DIG, lb, DBL_DIG,
ub);
break;
case LPX_FX:
xfprintf(fp, " = %.*g", DBL_DIG, lb);
break;
default:
xassert(type != type);
}
xfprintf(fp, "\n");
#if 0
coef = lpx_get_row_coef(lp, i);
#else
coef = 0.0;
#endif
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
"(objective)");
len = lpx_get_mat_row(lp, i, ndx, val);
for (t = 1; t <= len; t++)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, val[t],
col_name(lp, ndx[t], name));
}
xfree(ndx);
xfree(val);
xfprintf(fp, "\n");
xfprintf(fp, "*** COLUMNS (VARIABLES) ***\n");
ndx = xcalloc(1+m, sizeof(int));
val = xcalloc(1+m, sizeof(double));
for (j = 1; j <= n; j++)
{ xfprintf(fp, "\n");
xfprintf(fp, "Col %d: %s", j, col_name(lp, j, name));
if (mip)
{ switch (lpx_get_col_kind(lp, j))
{ case LPX_CV:
break;
case LPX_IV:
xfprintf(fp, " integer");
break;
default:
xassert(lp != lp);
}
}
lpx_get_col_bnds(lp, j, &type, &lb, &ub);
switch (type)
{ case LPX_FR:
xfprintf(fp, " free");
break;
case LPX_LO:
xfprintf(fp, " >= %.*g", DBL_DIG, lb);
break;
case LPX_UP:
xfprintf(fp, " <= %.*g", DBL_DIG, ub);
break;
case LPX_DB:
xfprintf(fp, " >= %.*g <= %.*g", DBL_DIG, lb, DBL_DIG,
ub);
break;
case LPX_FX:
xfprintf(fp, " = %.*g", DBL_DIG, lb);
break;
default:
xassert(type != type);
}
xfprintf(fp, "\n");
coef = lpx_get_obj_coef(lp, j);
if (coef != 0.0)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, coef,
"(objective)");
len = lpx_get_mat_col(lp, j, ndx, val);
for (t = 1; t <= len; t++)
xfprintf(fp, "%*.*g %s\n", DBL_DIG+7, DBL_DIG, val[t],
row_name(lp, ndx[t], name));
}
xfree(ndx);
xfree(val);
xfprintf(fp, "\n");
xfprintf(fp, "End of output\n");
xfflush(fp);
if (xferror(fp))
{ xprintf("lpx_write_prob: write error on `%s' - %s\n", fname,
strerror(errno));
goto fail;
}
xfclose(fp);
return 0;
fail: if (fp != NULL) xfclose(fp);
return 1;
}
#undef row_name
#undef col_name
/*----------------------------------------------------------------------
-- lpx_print_sol - write LP problem solution in printable format.
--
-- *Synopsis*
--
-- #include "glplpx.h"
-- int lpx_print_sol(LPX *lp, char *fname);
--
-- *Description*
--
-- The routine lpx_print_sol writes the current basic solution of an LP
-- problem, which is specified by the pointer lp, to a text file, whose
-- name is the character string fname, in printable format.
--
-- Information reported by the routine lpx_print_sol is intended mainly
-- for visual analysis.
--
-- *Returns*
--
-- If the operation was successful, the routine returns zero. Otherwise
-- the routine prints an error message and returns non-zero. */
int lpx_print_sol(LPX *lp, const char *fname)
{ XFILE *fp;
int what, round;
xprintf(
"lpx_print_sol: writing LP problem solution to `%s'...\n",
fname);
fp = xfopen(fname, "w");
if (fp == NULL)
{ xprintf("lpx_print_sol: can't create `%s' - %s\n", fname,
strerror(errno));
goto fail;
}
/* problem name */
{ const char *name;
name = lpx_get_prob_name(lp);
if (name == NULL) name = "";
xfprintf(fp, "%-12s%s\n", "Problem:", name);
}
/* number of rows (auxiliary variables) */
{ int nr;
nr = lpx_get_num_rows(lp);
xfprintf(fp, "%-12s%d\n", "Rows:", nr);
}
/* number of columns (structural variables) */
{ int nc;
nc = lpx_get_num_cols(lp);
xfprintf(fp, "%-12s%d\n", "Columns:", nc);
}
/* number of non-zeros (constraint coefficients) */
{ int nz;
nz = lpx_get_num_nz(lp);
xfprintf(fp, "%-12s%d\n", "Non-zeros:", nz);
}
/* solution status */
{ int status;
status = lpx_get_status(lp);
xfprintf(fp, "%-12s%s\n", "Status:",
status == LPX_OPT ? "OPTIMAL" :
status == LPX_FEAS ? "FEASIBLE" :
status == LPX_INFEAS ? "INFEASIBLE (INTERMEDIATE)" :
status == LPX_NOFEAS ? "INFEASIBLE (FINAL)" :
status == LPX_UNBND ? "UNBOUNDED" :
status == LPX_UNDEF ? "UNDEFINED" : "???");
}
/* objective function */
{ char *name;
int dir;
double obj;
name = (void *)lpx_get_obj_name(lp);
dir = lpx_get_obj_dir(lp);
obj = lpx_get_obj_val(lp);
xfprintf(fp, "%-12s%s%s%.10g %s\n", "Objective:",
name == NULL ? "" : name,
name == NULL ? "" : " = ", obj,
dir == LPX_MIN ? "(MINimum)" :
dir == LPX_MAX ? "(MAXimum)" : "(" "???" ")");
}
/* main sheet */
for (what = 1; what <= 2; what++)
{ int mn, ij;
xfprintf(fp, "\n");
xfprintf(fp, " No. %-12s St Activity Lower bound Upp"
"er bound Marginal\n",
what == 1 ? " Row name" : "Column name");
xfprintf(fp, "------ ------------ -- ------------- -----------"
"-- ------------- -------------\n");
mn = (what == 1 ? lpx_get_num_rows(lp) : lpx_get_num_cols(lp));
for (ij = 1; ij <= mn; ij++)
{ const char *name;
int typx, tagx;
double lb, ub, vx, dx;
if (what == 1)
{ name = lpx_get_row_name(lp, ij);
if (name == NULL) name = "";
lpx_get_row_bnds(lp, ij, &typx, &lb, &ub);
round = lpx_get_int_parm(lp, LPX_K_ROUND);
lpx_set_int_parm(lp, LPX_K_ROUND, 1);
lpx_get_row_info(lp, ij, &tagx, &vx, &dx);
lpx_set_int_parm(lp, LPX_K_ROUND, round);
}
else
{ name = lpx_get_col_name(lp, ij);
if (name == NULL) name = "";
lpx_get_col_bnds(lp, ij, &typx, &lb, &ub);
round = lpx_get_int_parm(lp, LPX_K_ROUND);
lpx_set_int_parm(lp, LPX_K_ROUND, 1);
lpx_get_col_info(lp, ij, &tagx, &vx, &dx);
lpx_set_int_parm(lp, LPX_K_ROUND, round);
}
/* row/column ordinal number */
xfprintf(fp, "%6d ", ij);
/* row column/name */
if (strlen(name) <= 12)
xfprintf(fp, "%-12s ", name);
else
xfprintf(fp, "%s\n%20s", name, "");
/* row/column status */
xfprintf(fp, "%s ",
tagx == LPX_BS ? "B " :
tagx == LPX_NL ? "NL" :
tagx == LPX_NU ? "NU" :
tagx == LPX_NF ? "NF" :
tagx == LPX_NS ? "NS" : "??");
/* row/column primal activity */
xfprintf(fp, "%13.6g ", vx);
/* row/column lower bound */
if (typx == LPX_LO || typx == LPX_DB || typx == LPX_FX)
xfprintf(fp, "%13.6g ", lb);
else
xfprintf(fp, "%13s ", "");
/* row/column upper bound */
if (typx == LPX_UP || typx == LPX_DB)
xfprintf(fp, "%13.6g ", ub);
else if (typx == LPX_FX)
xfprintf(fp, "%13s ", "=");
else
xfprintf(fp, "%13s ", "");
/* row/column dual activity */
if (tagx != LPX_BS)
{ if (dx == 0.0)
xfprintf(fp, "%13s", "< eps");
else
xfprintf(fp, "%13.6g", dx);
}
/* end of line */
xfprintf(fp, "\n");
}
}
xfprintf(fp, "\n");
#if 1
if (lpx_get_prim_stat(lp) != LPX_P_UNDEF &&
lpx_get_dual_stat(lp) != LPX_D_UNDEF)
{ int m = lpx_get_num_rows(lp);
LPXKKT kkt;
xfprintf(fp, "Karush-Kuhn-Tucker optimality conditions:\n\n");
lpx_check_kkt(lp, 1, &kkt);
xfprintf(fp, "KKT.PE: max.abs.err. = %.2e on row %d\n",
kkt.pe_ae_max, kkt.pe_ae_row);
xfprintf(fp, " max.rel.err. = %.2e on row %d\n",
kkt.pe_re_max, kkt.pe_re_row);
switch (kkt.pe_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " PRIMAL SOLUTION IS WRONG\n");
break;
}
xfprintf(fp, "\n");
xfprintf(fp, "KKT.PB: max.abs.err. = %.2e on %s %d\n",
kkt.pb_ae_max, kkt.pb_ae_ind <= m ? "row" : "column",
kkt.pb_ae_ind <= m ? kkt.pb_ae_ind : kkt.pb_ae_ind - m);
xfprintf(fp, " max.rel.err. = %.2e on %s %d\n",
kkt.pb_re_max, kkt.pb_re_ind <= m ? "row" : "column",
kkt.pb_re_ind <= m ? kkt.pb_re_ind : kkt.pb_re_ind - m);
switch (kkt.pb_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " PRIMAL SOLUTION IS INFEASIBLE\n");
break;
}
xfprintf(fp, "\n");
xfprintf(fp, "KKT.DE: max.abs.err. = %.2e on column %d\n",
kkt.de_ae_max, kkt.de_ae_col);
xfprintf(fp, " max.rel.err. = %.2e on column %d\n",
kkt.de_re_max, kkt.de_re_col);
switch (kkt.de_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " DUAL SOLUTION IS WRONG\n");
break;
}
xfprintf(fp, "\n");
xfprintf(fp, "KKT.DB: max.abs.err. = %.2e on %s %d\n",
kkt.db_ae_max, kkt.db_ae_ind <= m ? "row" : "column",
kkt.db_ae_ind <= m ? kkt.db_ae_ind : kkt.db_ae_ind - m);
xfprintf(fp, " max.rel.err. = %.2e on %s %d\n",
kkt.db_re_max, kkt.db_re_ind <= m ? "row" : "column",
kkt.db_re_ind <= m ? kkt.db_re_ind : kkt.db_re_ind - m);
switch (kkt.db_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " DUAL SOLUTION IS INFEASIBLE\n");
break;
}
xfprintf(fp, "\n");
}
#endif
#if 1
if (lpx_get_status(lp) == LPX_UNBND)
{ int m = lpx_get_num_rows(lp);
int k = lpx_get_ray_info(lp);
xfprintf(fp, "Unbounded ray: %s %d\n",
k <= m ? "row" : "column", k <= m ? k : k - m);
xfprintf(fp, "\n");
}
#endif
xfprintf(fp, "End of output\n");
xfflush(fp);
if (xferror(fp))
{ xprintf("lpx_print_sol: can't write to `%s' - %s\n", fname,
strerror(errno));
goto fail;
}
xfclose(fp);
return 0;
fail: if (fp != NULL) xfclose(fp);
return 1;
}
int lpx_print_mip(LPX *lp, const char *fname)
{ XFILE *fp;
int what, round;
#if 0
if (lpx_get_class(lp) != LPX_MIP)
fault("lpx_print_mip: error -- not a MIP problem");
#endif
xprintf(
"lpx_print_mip: writing MIP problem solution to `%s'...\n",
fname);
fp = xfopen(fname, "w");
if (fp == NULL)
{ xprintf("lpx_print_mip: can't create `%s' - %s\n", fname,
strerror(errno));
goto fail;
}
/* problem name */
{ const char *name;
name = lpx_get_prob_name(lp);
if (name == NULL) name = "";
xfprintf(fp, "%-12s%s\n", "Problem:", name);
}
/* number of rows (auxiliary variables) */
{ int nr;
nr = lpx_get_num_rows(lp);
xfprintf(fp, "%-12s%d\n", "Rows:", nr);
}
/* number of columns (structural variables) */
{ int nc, nc_int, nc_bin;
nc = lpx_get_num_cols(lp);
nc_int = lpx_get_num_int(lp);
nc_bin = lpx_get_num_bin(lp);
xfprintf(fp, "%-12s%d (%d integer, %d binary)\n", "Columns:",
nc, nc_int, nc_bin);
}
/* number of non-zeros (constraint coefficients) */
{ int nz;
nz = lpx_get_num_nz(lp);
xfprintf(fp, "%-12s%d\n", "Non-zeros:", nz);
}
/* solution status */
{ int status;
status = lpx_mip_status(lp);
xfprintf(fp, "%-12s%s\n", "Status:",
status == LPX_I_UNDEF ? "INTEGER UNDEFINED" :
status == LPX_I_OPT ? "INTEGER OPTIMAL" :
status == LPX_I_FEAS ? "INTEGER NON-OPTIMAL" :
status == LPX_I_NOFEAS ? "INTEGER EMPTY" : "???");
}
/* objective function */
{ char *name;
int dir;
double mip_obj;
name = (void *)lpx_get_obj_name(lp);
dir = lpx_get_obj_dir(lp);
mip_obj = lpx_mip_obj_val(lp);
xfprintf(fp, "%-12s%s%s%.10g %s\n", "Objective:",
name == NULL ? "" : name,
name == NULL ? "" : " = ", mip_obj,
dir == LPX_MIN ? "(MINimum)" :
dir == LPX_MAX ? "(MAXimum)" : "(" "???" ")");
}
/* main sheet */
for (what = 1; what <= 2; what++)
{ int mn, ij;
xfprintf(fp, "\n");
xfprintf(fp, " No. %-12s Activity Lower bound Upp"
"er bound\n",
what == 1 ? " Row name" : "Column name");
xfprintf(fp, "------ ------------ ------------- -----------"
"-- -------------\n");
mn = (what == 1 ? lpx_get_num_rows(lp) : lpx_get_num_cols(lp));
for (ij = 1; ij <= mn; ij++)
{ const char *name;
int kind, typx;
double lb, ub, vx;
if (what == 1)
{ name = lpx_get_row_name(lp, ij);
if (name == NULL) name = "";
kind = LPX_CV;
lpx_get_row_bnds(lp, ij, &typx, &lb, &ub);
round = lpx_get_int_parm(lp, LPX_K_ROUND);
lpx_set_int_parm(lp, LPX_K_ROUND, 1);
vx = lpx_mip_row_val(lp, ij);
lpx_set_int_parm(lp, LPX_K_ROUND, round);
}
else
{ name = lpx_get_col_name(lp, ij);
if (name == NULL) name = "";
kind = lpx_get_col_kind(lp, ij);
lpx_get_col_bnds(lp, ij, &typx, &lb, &ub);
round = lpx_get_int_parm(lp, LPX_K_ROUND);
lpx_set_int_parm(lp, LPX_K_ROUND, 1);
vx = lpx_mip_col_val(lp, ij);
lpx_set_int_parm(lp, LPX_K_ROUND, round);
}
/* row/column ordinal number */
xfprintf(fp, "%6d ", ij);
/* row column/name */
if (strlen(name) <= 12)
xfprintf(fp, "%-12s ", name);
else
xfprintf(fp, "%s\n%20s", name, "");
/* row/column kind */
xfprintf(fp, "%s ",
kind == LPX_CV ? " " : kind == LPX_IV ? "*" : "?");
/* row/column primal activity */
xfprintf(fp, "%13.6g", vx);
/* row/column lower and upper bounds */
switch (typx)
{ case LPX_FR:
break;
case LPX_LO:
xfprintf(fp, " %13.6g", lb);
break;
case LPX_UP:
xfprintf(fp, " %13s %13.6g", "", ub);
break;
case LPX_DB:
xfprintf(fp, " %13.6g %13.6g", lb, ub);
break;
case LPX_FX:
xfprintf(fp, " %13.6g %13s", lb, "=");
break;
default:
xassert(typx != typx);
}
/* end of line */
xfprintf(fp, "\n");
}
}
xfprintf(fp, "\n");
#if 1
if (lpx_mip_status(lp) != LPX_I_UNDEF)
{ int m = lpx_get_num_rows(lp);
LPXKKT kkt;
xfprintf(fp, "Integer feasibility conditions:\n\n");
lpx_check_int(lp, &kkt);
xfprintf(fp, "INT.PE: max.abs.err. = %.2e on row %d\n",
kkt.pe_ae_max, kkt.pe_ae_row);
xfprintf(fp, " max.rel.err. = %.2e on row %d\n",
kkt.pe_re_max, kkt.pe_re_row);
switch (kkt.pe_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " SOLUTION IS WRONG\n");
break;
}
xfprintf(fp, "\n");
xfprintf(fp, "INT.PB: max.abs.err. = %.2e on %s %d\n",
kkt.pb_ae_max, kkt.pb_ae_ind <= m ? "row" : "column",
kkt.pb_ae_ind <= m ? kkt.pb_ae_ind : kkt.pb_ae_ind - m);
xfprintf(fp, " max.rel.err. = %.2e on %s %d\n",
kkt.pb_re_max, kkt.pb_re_ind <= m ? "row" : "column",
kkt.pb_re_ind <= m ? kkt.pb_re_ind : kkt.pb_re_ind - m);
switch (kkt.pb_quality)
{ case 'H':
xfprintf(fp, " High quality\n");
break;
case 'M':
xfprintf(fp, " Medium quality\n");
break;
case 'L':
xfprintf(fp, " Low quality\n");
break;
default:
xfprintf(fp, " SOLUTION IS INFEASIBLE\n");
break;
}
xfprintf(fp, "\n");
}
#endif
xfprintf(fp, "End of output\n");
xfflush(fp);
if (xferror(fp))
{ xprintf("lpx_print_mip: can't write to `%s' - %s\n", fname,
strerror(errno));
goto fail;
}
xfclose(fp);
return 0;
fail: if (fp != NULL) xfclose(fp);
return 1;
}
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 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_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;
}
double lpx_eval_degrad(LPX *lp, int len, int ind[], double val[],
int type, double rhs)
{ int m = lpx_get_num_rows(lp);
int n = lpx_get_num_cols(lp);
int dir = lpx_get_obj_dir(lp);
int q, k;
double y, delta;
if (lpx_get_dual_stat(lp) != LPX_D_FEAS)
fault("lpx_eval_degrad: LP basis is not dual feasible");
if (!(0 <= len && len <= n))
fault("lpx_eval_degrad: len = %d; invalid row length", len);
if (!(type == LPX_LO || type == LPX_UP))
fault("lpx_eval_degrad: type = %d; invalid row type", type);
/* compute value of the row auxiliary variable */
y = lpx_eval_row(lp, len, ind, val);
/* the inequalitiy constraint is assumed to be violated */
if (!(type == LPX_LO && y < rhs || type == LPX_UP && y > rhs))
fault("lpx_eval_degrad: y = %g, rhs = %g; constraint is not vi"
"olated", y, rhs);
/* transform the row in order to express y through only non-basic
variables: y = alfa[1] * xN[1] + ... + alfa[n] * xN[n] */
len = lpx_transform_row(lp, len, ind, val);
/* in the adjacent basis y would become non-basic, so in case of
'>=' it increases and in case of '<=' it decreases; determine
which non-basic variable x[q], 1 <= q <= m+n, should leave the
basis to keep dual feasibility */
q = lpx_dual_ratio_test(lp, len, ind, val,
type == LPX_LO ? +1 : -1, 1e-7);
/* q = 0 means no adjacent dual feasible basis exist */
if (q == 0) return dir == LPX_MIN ? +DBL_MAX : -DBL_MAX;
/* find the entry corresponding to x[q] in the list */
for (k = 1; k <= len; k++)
if (ind[k] == q) break;
insist(k <= len);
/* dy = alfa[q] * dx[q], so dx[q] = dy / alfa[q], where dy is a
change in y, dx[q] is a change in x[q] */
delta = (rhs - y) / val[k];
#if 0
/* Tomlin noticed that if the variable x[q] is of integer kind,
its change cannot be less than one in the magnitude */
if (q > m && lpx_get_col_kind(lp, q-m) == LPX_IV)
{ /* x[q] is structural integer variable */
if (fabs(delta - floor(delta + 0.5)) > 1e-3)
{ if (delta > 0.0)
delta = ceil(delta); /* +3.14 -> +4 */
else
delta = floor(delta); /* -3.14 -> -4 */
}
}
#endif
/* dz = lambda[q] * dx[q], where dz is a change in the objective
function, lambda[q] is a reduced cost of x[q] */
if (q <= m)
delta *= lpx_get_row_dual(lp, q);
else
delta *= lpx_get_col_dual(lp, q-m);
/* delta must be >= 0 (in case of minimization) or <= 0 (in case
of minimization); however, due to round-off errors and finite
tolerance used to choose x[q], this condition can be slightly
violated */
switch (dir)
{ case LPX_MIN: if (delta < 0.0) delta = 0.0; break;
case LPX_MAX: if (delta > 0.0) delta = 0.0; break;
default: insist(dir != dir);
}
return delta;
}
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;
}
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;
}
