/* glpapi13.c (branch-and-bound interface routines) */

 /***********************************************************************

 *  This code is part of GLPK (GNU Linear Programming Kit).

 *

 *  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,

 *  2009, 2010 Andrew Makhorin, Department for Applied Informatics,

 *  Moscow Aviation Institute, Moscow, Russia. All rights reserved.

 *  E-mail: <mao@gnu.org>.

 *

 *  GLPK is free software: you can redistribute it and/or modify it

 *  under the terms of the GNU General Public License as published by

 *  the Free Software Foundation, either version 3 of the License, or

 *  (at your option) any later version.

 *

 *  GLPK is distributed in the hope that it will be useful, but WITHOUT

 *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY

 *  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public

 *  License for more details.

 *

 *  You should have received a copy of the GNU General Public License

 *  along with GLPK. If not, see <http://www.gnu.org/licenses/>.

 ***********************************************************************/

 #include "glpios.h"

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_reason - determine reason for calling the callback routine

 *

 *  SYNOPSIS

 *

 *  glp_ios_reason(glp_tree *tree);

 *

 *  RETURNS

 *

 *  The routine glp_ios_reason returns a code, which indicates why the

 *  user-defined callback routine is being called. */

 int glp_ios_reason(glp_tree *tree)

 {     return

          tree->reason;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_get_prob - access the problem object

 *

 *  SYNOPSIS

 *

 *  glp_prob *glp_ios_get_prob(glp_tree *tree);

 *

 *  DESCRIPTION

 *

 *  The routine glp_ios_get_prob can be called from the user-defined

 *  callback routine to access the problem object, which is used by the

 *  MIP solver. It is the original problem object passed to the routine

 *  glp_intopt if the MIP presolver is not used; otherwise it is an

 *  internal problem object built by the presolver. If the current

 *  subproblem exists, LP segment of the problem object corresponds to

 *  its LP relaxation.

 *

 *  RETURNS

 *

 *  The routine glp_ios_get_prob returns a pointer to the problem object

 *  used by the MIP solver. */

 glp_prob *glp_ios_get_prob(glp_tree *tree)

 {     return

          tree->mip;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_tree_size - determine size of the branch-and-bound tree

 *

 *  SYNOPSIS

 *

 *  void glp_ios_tree_size(glp_tree *tree, int *a_cnt, int *n_cnt,

 *     int *t_cnt);

 *

 *  DESCRIPTION

 *

 *  The routine glp_ios_tree_size stores the following three counts which

 *  characterize the current size of the branch-and-bound tree:

 *

 *  a_cnt is the current number of active nodes, i.e. the current size of

 *        the active list;

 *

 *  n_cnt is the current number of all (active and inactive) nodes;

 *

 *  t_cnt is the total number of nodes including those which have been

 *        already removed from the tree. This count is increased whenever

 *        a new node appears in the tree and never decreased.

 *

 *  If some of the parameters a_cnt, n_cnt, t_cnt is a null pointer, the

 *  corresponding count is not stored. */

 void glp_ios_tree_size(glp_tree *tree, int *a_cnt, int *n_cnt,

       int *t_cnt)

 {     if (a_cnt != NULL) *a_cnt = tree->a_cnt;

       if (n_cnt != NULL) *n_cnt = tree->n_cnt;

       if (t_cnt != NULL) *t_cnt = tree->t_cnt;

       return;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_curr_node - determine current active subproblem

 *

 *  SYNOPSIS

 *

 *  int glp_ios_curr_node(glp_tree *tree);

 *

 *  RETURNS

 *

 *  The routine glp_ios_curr_node returns the reference number of the

 *  current active subproblem. However, if the current subproblem does

 *  not exist, the routine returns zero. */

 int glp_ios_curr_node(glp_tree *tree)

 {     IOSNPD *node;

       /* obtain pointer to the current subproblem */

       node = tree->curr;

       /* return its reference number */

       return node == NULL ? 0 : node->p;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_next_node - determine next active subproblem

 *

 *  SYNOPSIS

 *

 *  int glp_ios_next_node(glp_tree *tree, int p);

 *

 *  RETURNS

 *

 *  If the parameter p is zero, the routine glp_ios_next_node returns

 *  the reference number of the first active subproblem. However, if the

 *  tree is empty, zero is returned.

 *

 *  If the parameter p is not zero, it must specify the reference number

 *  of some active subproblem, in which case the routine returns the

 *  reference number of the next active subproblem. However, if there is

 *  no next active subproblem in the list, zero is returned.

 *

 *  All subproblems in the active list are ordered chronologically, i.e.

 *  subproblem A precedes subproblem B if A was created before B. */

 int glp_ios_next_node(glp_tree *tree, int p)

 {     IOSNPD *node;

       if (p == 0)

       {  /* obtain pointer to the first active subproblem */

          node = tree->head;

       }

       else

       {  /* obtain pointer to the specified subproblem */

          if (!(1 <= p && p <= tree->nslots))

 err:        xerror("glp_ios_next_node: p = %d; invalid subproblem refer"

                "ence number\n", p);

          node = tree->slot[p].node;

          if (node == NULL) goto err;

          /* the specified subproblem must be active */

          if (node->count != 0)

             xerror("glp_ios_next_node: p = %d; subproblem not in the ac"

                "tive list\n", p);

          /* obtain pointer to the next active subproblem */

          node = node->next;

       }

       /* return the reference number */

       return node == NULL ? 0 : node->p;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_prev_node - determine previous active subproblem

 *

 *  SYNOPSIS

 *

 *  int glp_ios_prev_node(glp_tree *tree, int p);

 *

 *  RETURNS

 *

 *  If the parameter p is zero, the routine glp_ios_prev_node returns

 *  the reference number of the last active subproblem. However, if the

 *  tree is empty, zero is returned.

 *

 *  If the parameter p is not zero, it must specify the reference number

 *  of some active subproblem, in which case the routine returns the

 *  reference number of the previous active subproblem. However, if there

 *  is no previous active subproblem in the list, zero is returned.

 *

 *  All subproblems in the active list are ordered chronologically, i.e.

 *  subproblem A precedes subproblem B if A was created before B. */

 int glp_ios_prev_node(glp_tree *tree, int p)

 {     IOSNPD *node;

       if (p == 0)

       {  /* obtain pointer to the last active subproblem */

          node = tree->tail;

       }

       else

       {  /* obtain pointer to the specified subproblem */

          if (!(1 <= p && p <= tree->nslots))

 err:        xerror("glp_ios_prev_node: p = %d; invalid subproblem refer"

                "ence number\n", p);

          node = tree->slot[p].node;

          if (node == NULL) goto err;

          /* the specified subproblem must be active */

          if (node->count != 0)

             xerror("glp_ios_prev_node: p = %d; subproblem not in the ac"

                "tive list\n", p);

          /* obtain pointer to the previous active subproblem */

          node = node->prev;

       }

       /* return the reference number */

       return node == NULL ? 0 : node->p;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_up_node - determine parent subproblem

 *

 *  SYNOPSIS

 *

 *  int glp_ios_up_node(glp_tree *tree, int p);

 *

 *  RETURNS

 *

 *  The parameter p must specify the reference number of some (active or

 *  inactive) subproblem, in which case the routine iet_get_up_node

 *  returns the reference number of its parent subproblem. However, if

 *  the specified subproblem is the root of the tree and, therefore, has

 *  no parent, the routine returns zero. */

 int glp_ios_up_node(glp_tree *tree, int p)

 {     IOSNPD *node;

       /* obtain pointer to the specified subproblem */

       if (!(1 <= p && p <= tree->nslots))

 err:     xerror("glp_ios_up_node: p = %d; invalid subproblem reference "

             "number\n", p);

       node = tree->slot[p].node;

       if (node == NULL) goto err;

       /* obtain pointer to the parent subproblem */

       node = node->up;

       /* return the reference number */

       return node == NULL ? 0 : node->p;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_node_level - determine subproblem level

 *

 *  SYNOPSIS

 *

 *  int glp_ios_node_level(glp_tree *tree, int p);

 *

 *  RETURNS

 *

 *  The routine glp_ios_node_level returns the level of the subproblem,

 *  whose reference number is p, in the branch-and-bound tree. (The root

 *  subproblem has level 0, and the level of any other subproblem is the

 *  level of its parent plus one.) */

 int glp_ios_node_level(glp_tree *tree, int p)

 {     IOSNPD *node;

       /* obtain pointer to the specified subproblem */

       if (!(1 <= p && p <= tree->nslots))

 err:     xerror("glp_ios_node_level: p = %d; invalid subproblem referen"

             "ce number\n", p);

       node = tree->slot[p].node;

       if (node == NULL) goto err;

       /* return the node level */

       return node->level;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_node_bound - determine subproblem local bound

 *

 *  SYNOPSIS

 *

 *  double glp_ios_node_bound(glp_tree *tree, int p);

 *

 *  RETURNS

 *

 *  The routine glp_ios_node_bound returns the local bound for (active or

 *  inactive) subproblem, whose reference number is p.

 *

 *  COMMENTS

 *

 *  The local bound for subproblem p is an lower (minimization) or upper

 *  (maximization) bound for integer optimal solution to this subproblem

 *  (not to the original problem). This bound is local in the sense that

 *  only subproblems in the subtree rooted at node p cannot have better

 *  integer feasible solutions.

 *

 *  On creating a subproblem (due to the branching step) its local bound

 *  is inherited from its parent and then may get only stronger (never

 *  weaker). For the root subproblem its local bound is initially set to

 *  -DBL_MAX (minimization) or +DBL_MAX (maximization) and then improved

 *  as the root LP relaxation has been solved.

 *

 *  Note that the local bound is not necessarily the optimal objective

 *  value to corresponding LP relaxation; it may be stronger. */

 double glp_ios_node_bound(glp_tree *tree, int p)

 {     IOSNPD *node;

       /* obtain pointer to the specified subproblem */

       if (!(1 <= p && p <= tree->nslots))

 err:     xerror("glp_ios_node_bound: p = %d; invalid subproblem referen"

             "ce number\n", p);

       node = tree->slot[p].node;

       if (node == NULL) goto err;

       /* return the node local bound */

       return node->bound;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_best_node - find active subproblem with best local bound

 *

 *  SYNOPSIS

 *

 *  int glp_ios_best_node(glp_tree *tree);

 *

 *  RETURNS

 *

 *  The routine glp_ios_best_node returns the reference number of the

 *  active subproblem, whose local bound is best (i.e. smallest in case

 *  of minimization or largest in case of maximization). However, if the

 *  tree is empty, the routine returns zero.

 *

 *  COMMENTS

 *

 *  The best local bound is an lower (minimization) or upper

 *  (maximization) bound for integer optimal solution to the original

 *  MIP problem. */

 int glp_ios_best_node(glp_tree *tree)

 {     return

          ios_best_node(tree);

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_mip_gap - compute relative MIP gap

 *

 *  SYNOPSIS

 *

 *  double glp_ios_mip_gap(glp_tree *tree);

 *

 *  DESCRIPTION

 *

 *  The routine glp_ios_mip_gap computes the relative MIP gap with the

 *  following formula:

 *

 *     gap = |best_mip - best_bnd| / (|best_mip| + DBL_EPSILON),

 *

 *  where best_mip is the best integer feasible solution found so far,

 *  best_bnd is the best (global) bound. If no integer feasible solution

 *  has been found yet, gap is set to DBL_MAX.

 *

 *  RETURNS

 *

 *  The routine glp_ios_mip_gap returns the relative MIP gap. */

 double glp_ios_mip_gap(glp_tree *tree)

 {     return

          ios_relative_gap(tree);

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_node_data - access subproblem application-specific data

 *

 *  SYNOPSIS

 *

 *  void *glp_ios_node_data(glp_tree *tree, int p);

 *

 *  DESCRIPTION

 *

 *  The routine glp_ios_node_data allows the application accessing a

 *  memory block allocated for the subproblem (which may be active or

 *  inactive), whose reference number is p.

 *

 *  The size of the block is defined by the control parameter cb_size

 *  passed to the routine glp_intopt. The block is initialized by binary

 *  zeros on creating corresponding subproblem, and its contents is kept

 *  until the subproblem will be removed from the tree.

 *

 *  The application may use these memory blocks to store specific data

 *  for each subproblem.

 *

 *  RETURNS

 *

 *  The routine glp_ios_node_data returns a pointer to the memory block

 *  for the specified subproblem. Note that if cb_size = 0, the routine

 *  returns a null pointer. */

 void *glp_ios_node_data(glp_tree *tree, int p)

 {     IOSNPD *node;

       /* obtain pointer to the specified subproblem */

       if (!(1 <= p && p <= tree->nslots))

 err:     xerror("glp_ios_node_level: p = %d; invalid subproblem referen"

             "ce number\n", p);

       node = tree->slot[p].node;

       if (node == NULL) goto err;

       /* return pointer to the application-specific data */

       return node->data;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_row_attr - retrieve additional row attributes

 *

 *  SYNOPSIS

 *

 *  void glp_ios_row_attr(glp_tree *tree, int i, glp_attr *attr);

 *

 *  DESCRIPTION

 *

 *  The routine glp_ios_row_attr retrieves additional attributes of row

 *  i and stores them in the structure glp_attr. */

 void glp_ios_row_attr(glp_tree *tree, int i, glp_attr *attr)

 {     GLPROW *row;

       if (!(1 <= i && i <= tree->mip->m))

          xerror("glp_ios_row_attr: i = %d; row number out of range\n",

             i);

       row = tree->mip->row[i];

       attr->level = row->level;

       attr->origin = row->origin;

       attr->klass = row->klass;

       return;

 }

 /**********************************************************************/

 int glp_ios_pool_size(glp_tree *tree)

 {     /* determine current size of the cut pool */

       if (tree->reason != GLP_ICUTGEN)

          xerror("glp_ios_pool_size: operation not allowed\n");

       xassert(tree->local != NULL);

       return tree->local->size;

 }

 /**********************************************************************/

 int glp_ios_add_row(glp_tree *tree,

       const char *name, int klass, int flags, int len, const int ind[],

       const double val[], int type, double rhs)

 {     /* add row (constraint) to the cut pool */

       int num;

       if (tree->reason != GLP_ICUTGEN)

          xerror("glp_ios_add_row: operation not allowed\n");

       xassert(tree->local != NULL);

       num = ios_add_row(tree, tree->local, name, klass, flags, len,

          ind, val, type, rhs);

       return num;

 }

 /**********************************************************************/

 void glp_ios_del_row(glp_tree *tree, int i)

 {     /* remove row (constraint) from the cut pool */

       if (tree->reason != GLP_ICUTGEN)

          xerror("glp_ios_del_row: operation not allowed\n");

       ios_del_row(tree, tree->local, i);

       return;

 }

 /**********************************************************************/

 void glp_ios_clear_pool(glp_tree *tree)

 {     /* remove all rows (constraints) from the cut pool */

       if (tree->reason != GLP_ICUTGEN)

          xerror("glp_ios_clear_pool: operation not allowed\n");

       ios_clear_pool(tree, tree->local);

       return;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_can_branch - check if can branch upon specified variable

 *

 *  SYNOPSIS

 *

 *  int glp_ios_can_branch(glp_tree *tree, int j);

 *

 *  RETURNS

 *

 *  If j-th variable (column) can be used to branch upon, the routine

 *  glp_ios_can_branch returns non-zero, otherwise zero. */

 int glp_ios_can_branch(glp_tree *tree, int j)

 {     if (!(1 <= j && j <= tree->mip->n))

          xerror("glp_ios_can_branch: j = %d; column number out of range"

             "\n", j);

       return tree->non_int[j];

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_branch_upon - choose variable to branch upon

 *

 *  SYNOPSIS

 *

 *  void glp_ios_branch_upon(glp_tree *tree, int j, int sel);

 *

 *  DESCRIPTION

 *

 *  The routine glp_ios_branch_upon can be called from the user-defined

 *  callback routine in response to the reason GLP_IBRANCH to choose a

 *  branching variable, whose ordinal number is j. Should note that only

 *  variables, for which the routine glp_ios_can_branch returns non-zero,

 *  can be used to branch upon.

 *

 *  The parameter sel is a flag that indicates which branch (subproblem)

 *  should be selected next to continue the search:

 *

 *  GLP_DN_BRNCH - select down-branch;

 *  GLP_UP_BRNCH - select up-branch;

 *  GLP_NO_BRNCH - use general selection technique. */

 void glp_ios_branch_upon(glp_tree *tree, int j, int sel)

 {     if (!(1 <= j && j <= tree->mip->n))

          xerror("glp_ios_branch_upon: j = %d; column number out of rang"

             "e\n", j);

       if (!(sel == GLP_DN_BRNCH || sel == GLP_UP_BRNCH ||

             sel == GLP_NO_BRNCH))

          xerror("glp_ios_branch_upon: sel = %d: invalid branch selectio"

             "n flag\n", sel);

       if (!(tree->non_int[j]))

          xerror("glp_ios_branch_upon: j = %d; variable cannot be used t"

             "o branch upon\n", j);

       if (tree->br_var != 0)

          xerror("glp_ios_branch_upon: branching variable already chosen"

             "\n");

       tree->br_var = j;

       tree->br_sel = sel;

       return;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_select_node - select subproblem to continue the search

 *

 *  SYNOPSIS

 *

 *  void glp_ios_select_node(glp_tree *tree, int p);

 *

 *  DESCRIPTION

 *

 *  The routine glp_ios_select_node can be called from the user-defined

 *  callback routine in response to the reason GLP_ISELECT to select an

 *  active subproblem, whose reference number is p. The search will be

 *  continued from the subproblem selected. */

 void glp_ios_select_node(glp_tree *tree, int p)

 {     IOSNPD *node;

       /* obtain pointer to the specified subproblem */

       if (!(1 <= p && p <= tree->nslots))

 err:     xerror("glp_ios_select_node: p = %d; invalid subproblem refere"

             "nce number\n", p);

       node = tree->slot[p].node;

       if (node == NULL) goto err;

       /* the specified subproblem must be active */

       if (node->count != 0)

          xerror("glp_ios_select_node: p = %d; subproblem not in the act"

             "ive list\n", p);

       /* no subproblem must be selected yet */

       if (tree->next_p != 0)

          xerror("glp_ios_select_node: subproblem already selected\n");

       /* select the specified subproblem to continue the search */

       tree->next_p = p;

       return;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_heur_sol - provide solution found by heuristic

 *

 *  SYNOPSIS

 *

 *  int glp_ios_heur_sol(glp_tree *tree, const double x[]);

 *

 *  DESCRIPTION

 *

 *  The routine glp_ios_heur_sol can be called from the user-defined

 *  callback routine in response to the reason GLP_IHEUR to provide an

 *  integer feasible solution found by a primal heuristic.

 *

 *  Primal values of *all* variables (columns) found by the heuristic

 *  should be placed in locations x[1], ..., x[n], where n is the number

 *  of columns in the original problem object. Note that the routine

 *  glp_ios_heur_sol *does not* check primal feasibility of the solution

 *  provided.

 *

 *  Using the solution passed in the array x the routine computes value

 *  of the objective function. If the objective value is better than the

 *  best known integer feasible solution, the routine computes values of

 *  auxiliary variables (rows) and stores all solution components in the

 *  problem object.

 *

 *  RETURNS

 *

 *  If the provided solution is accepted, the routine glp_ios_heur_sol

 *  returns zero. Otherwise, if the provided solution is rejected, the

 *  routine returns non-zero. */

 int glp_ios_heur_sol(glp_tree *tree, const double x[])

 {     glp_prob *mip = tree->mip;

       int m = tree->orig_m;

       int n = tree->n;

       int i, j;

       double obj;

       xassert(mip->m >= m);

       xassert(mip->n == n);

       /* check values of integer variables and compute value of the

          objective function */

       obj = mip->c0;

       for (j = 1; j <= n; j++)

       {  GLPCOL *col = mip->col[j];

          if (col->kind == GLP_IV)

          {  /* provided value must be integral */

             if (x[j] != floor(x[j])) return 1;

          }

          obj += col->coef * x[j];

       }

       /* check if the provided solution is better than the best known

          integer feasible solution */

       if (mip->mip_stat == GLP_FEAS)

       {  switch (mip->dir)

          {  case GLP_MIN:

                if (obj >= tree->mip->mip_obj) return 1;

                break;

             case GLP_MAX:

                if (obj <= tree->mip->mip_obj) return 1;

                break;

             default:

                xassert(mip != mip);

          }

       }

       /* it is better; store it in the problem object */

       if (tree->parm->msg_lev >= GLP_MSG_ON)

          xprintf("Solution found by heuristic: %.12g\n", obj);

       mip->mip_stat = GLP_FEAS;

       mip->mip_obj = obj;

       for (j = 1; j <= n; j++)

          mip->col[j]->mipx = x[j];

       for (i = 1; i <= m; i++)

       {  GLPROW *row = mip->row[i];

          GLPAIJ *aij;

          row->mipx = 0.0;

          for (aij = row->ptr; aij != NULL; aij = aij->r_next)

             row->mipx += aij->val * aij->col->mipx;

       }

       return 0;

 }

 /***********************************************************************

 *  NAME

 *

 *  glp_ios_terminate - terminate the solution process.

 *

 *  SYNOPSIS

 *

 *  void glp_ios_terminate(glp_tree *tree);

 *

 *  DESCRIPTION

 *

 *  The routine glp_ios_terminate sets a flag indicating that the MIP

 *  solver should prematurely terminate the search. */

 void glp_ios_terminate(glp_tree *tree)

 {     if (tree->parm->msg_lev >= GLP_MSG_DBG)

          xprintf("The search is prematurely terminated due to applicati"

             "on request\n");

       tree->stop = 1;

       return;

 }

 /* eof */