Пример #1
0
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;
}
Пример #2
0
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;
}
Пример #3
0
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;
}
Пример #4
0
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;
}
Пример #5
0
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;
}
Пример #6
0
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;
}
Пример #7
0
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;
}
Пример #8
0
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;
}
Пример #9
0
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;
}
Пример #10
0
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;
}