benderscut_int.c

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/*         SCIP --- Solving Constraint Integer Programs                      */
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/**@file   benderscut_int.c
 * @ingroup OTHER_CFILES
 * @brief  Generates a Laporte and Louveaux Benders' decomposition integer cut
 * @author Stephen J. Maher
 */
 
/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
 
#include "scip/benderscut_int.h"
#include "scip/cons_linear.h"
#include "scip/pub_benderscut.h"
#include "scip/pub_benders.h"
#include "scip/pub_lp.h"
#include "scip/pub_message.h"
#include "scip/pub_misc.h"
#include "scip/pub_paramset.h"
#include "scip/pub_var.h"
#include "scip/scip_benders.h"
#include "scip/scip_cons.h"
#include "scip/scip_cut.h"
#include "scip/scip_general.h"
#include "scip/scip_lp.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_numerics.h"
#include "scip/scip_param.h"
#include "scip/scip_prob.h"
#include "scip/scip_sol.h"
#include "scip/type_message.h"
#include <string.h>
 
#define BENDERSCUT_NAME             "integer"
#define BENDERSCUT_DESC             "Laporte and Louveaux Benders' decomposition integer cut"
#define BENDERSCUT_PRIORITY         0
#define BENDERSCUT_LPCUT        FALSE
 
#define SCIP_DEFAULT_ADDCUTS             FALSE  /** Should cuts be generated, instead of constraints */
#define SCIP_DEFAULT_CUTCONSTANT          -10000.0
 
/*
 * Data structures
 */
 
/** Benders' decomposition cuts data */
struct SCIP_BenderscutData
{
   SCIP_BENDERS*         benders;            /**< the Benders' decomposition data structure */
   SCIP_Real             cutconstant;        /**< the constant for computing the integer cuts */
   SCIP_Real*            subprobconstant;    /**< the constant for each subproblem used for computing the integer cuts */
   SCIP_Bool             addcuts;            /**< should cuts be generated instead of constraints */
   SCIP_Bool*            firstcut;           /**< flag to indicate that the first cut needs to be generated. */
   int                   nsubproblems;       /**< the number of subproblems for the Benders' decomposition */
   SCIP_Bool             subprobsvalid;      /**< is it valid to apply integer cuts for this problem */
   SCIP_Bool             created;            /**< has the Benders cut data been created */
};
 
/** method to call, when the priority of a Benders' decomposition was changed */
static
SCIP_DECL_PARAMCHGD(paramChgdBenderscutintConstant)
{  /*lint --e{715}*/
   SCIP_BENDERSCUTDATA* benderscutdata;
   int i;
 
   benderscutdata = (SCIP_BENDERSCUTDATA*)SCIPparamGetData(param);
   assert(benderscutdata != NULL);
 
   for( i = 0; i < benderscutdata->nsubproblems; i++ )
      benderscutdata->subprobconstant[i] = benderscutdata->cutconstant;
 
   return SCIP_OKAY;
}
 
 
/** creates the Benders' decomposition cut data */
static
SCIP_RETCODE createBenderscutData(
   SCIP*                 scip,               /**< the SCIP data structure */
   SCIP_BENDERSCUTDATA*  benderscutdata      /**< the Benders' cut data */
   )
{
   int nmastervars;
   int nmasterbinvars;
   int i;
 
   assert(scip != NULL);
   assert(benderscutdata != NULL);
 
   benderscutdata->nsubproblems = SCIPbendersGetNSubproblems(benderscutdata->benders);
   benderscutdata->subprobsvalid = TRUE;
 
   /* allocating the memory for the subproblem constants */
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &benderscutdata->subprobconstant, benderscutdata->nsubproblems) );
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &benderscutdata->firstcut, benderscutdata->nsubproblems) );
 
   for( i = 0; i < benderscutdata->nsubproblems; i++ )
   {
      benderscutdata->subprobconstant[i] = benderscutdata->cutconstant;
      benderscutdata->firstcut[i] = TRUE;
 
      /* it is only possible to generate the no-good cut for subproblems that only include binary master variables */
      SCIPbendersGetSubproblemMasterVarsData(benderscutdata->benders, i, NULL, &nmastervars, &nmasterbinvars, NULL);
 
      if( nmastervars != nmasterbinvars )
      {
         benderscutdata->subprobsvalid = FALSE;
      }
   }
 
   benderscutdata->created = TRUE;
 
   return SCIP_OKAY;
}
 
/*
 * Local methods
 */
 
/** updates the cut constant for the given subproblem based upon the global bounds of the associated auxiliary variable */
static
void updateSubproblemCutConstant(
   SCIP*                 masterprob,         /**< the SCIP instance of the master problem */
   SCIP_BENDERS*         benders,            /**< the benders' decomposition structure */
   SCIP_BENDERSCUTDATA*  benderscutdata,     /**< the Benders' decomposition cut data */
   int                   probnumber          /**< the index for the subproblem */
   )
{
   SCIP_VAR* auxiliaryvar;
 
   assert(masterprob != NULL);
   assert(benders != NULL);
   assert(benderscutdata != NULL);
 
   auxiliaryvar = SCIPbendersGetAuxiliaryVar(benders, probnumber);
 
   /* checking if the subproblem lower bound has been updated. If it is has changed, then firstcut is set to TRUE.
    * Otherwise, the constant remains the same.
    */
   if( SCIPisGT(masterprob, SCIPbendersGetSubproblemLowerbound(benders, probnumber),
         benderscutdata->subprobconstant[probnumber]) )
   {
      benderscutdata->subprobconstant[probnumber] = SCIPbendersGetSubproblemLowerbound(benders, probnumber);
      benderscutdata->firstcut[probnumber] = TRUE;
   }
 
   /* updating the cut constant if the auxiliary variable global lower bound is greater than the current constant */
   if( SCIPisGT(masterprob, SCIPvarGetLbGlobal(auxiliaryvar), benderscutdata->subprobconstant[probnumber]) )
      benderscutdata->subprobconstant[probnumber] = SCIPvarGetLbGlobal(auxiliaryvar);
}
 
/** computes a standard Benders' optimality cut from the dual solutions of the LP */
static
SCIP_RETCODE computeStandardIntegerOptCut(
   SCIP*                 masterprob,         /**< the SCIP instance of the master problem */
   SCIP_BENDERS*         benders,            /**< the benders' decomposition structure */
   SCIP_SOL*             sol,                /**< primal CIP solution */
   SCIP_CONS*            cons,               /**< the constraint for the generated cut, can be NULL */
   SCIP_ROW*             row,                /**< the row for the generated cut, can be NULL */
   SCIP_Real             cutconstant,        /**< the constant value in the integer optimality cut */
   int                   probnumber,         /**< the number of the pricing problem */
   SCIP_Bool             addcut,             /**< indicates whether a cut is created instead of a constraint */
   SCIP_Bool*            success             /**< was the cut generation successful? */
   )
{
   SCIP_VAR** vars;
   int nvars;
   SCIP_Real subprobobj;   /* the objective function value of the subproblem */
   SCIP_Real lhs;          /* the left hand side of the cut */
   int i;
   SCIPdebug( SCIP* subproblem; )
 
#ifndef NDEBUG
   SCIP_Real verifyobj = 0;
#endif
 
   assert(masterprob != NULL);
   assert(benders != NULL);
   assert(cons != NULL || addcut);
   assert(row != NULL || !addcut);
 
   (*success) = FALSE;
 
   /* getting the best solution from the subproblem */
 
   subprobobj = SCIPbendersGetSubproblemObjval(benders, probnumber);
 
   SCIPdebug( subproblem = SCIPbendersSubproblem(benders, probnumber); )
   SCIPdebug( SCIPdebugMsg(masterprob, "Subproblem %d - Objective Value: Stored - %g Orig Obj - %g Cut constant - %g\n",
      probnumber, SCIPbendersGetSubproblemObjval(benders, probnumber), SCIPgetSolOrigObj(subproblem, SCIPgetBestSol(subproblem))*(int)SCIPgetObjsense(subproblem),
      cutconstant); )
 
   nvars = SCIPgetNVars(masterprob);
   vars = SCIPgetVars(masterprob);
 
   /* adding the subproblem objective function value to the lhs */
   if( addcut )
      lhs = SCIProwGetLhs(row);
   else
      lhs = SCIPgetLhsLinear(masterprob, cons);
 
   /* looping over all master problem variables to update the coefficients in the computed cut. */
   for( i = 0; i < nvars; i++ )
   {
      SCIP_VAR* subprobvar;
      SCIP_Real coef;
 
      SCIP_CALL( SCIPgetBendersSubproblemVar(masterprob, benders, vars[i], &subprobvar, probnumber) );
 
      /* if there is a corresponding subproblem variable, then the variable will not be NULL. */
      if( subprobvar != NULL )
      {
         /* if the variable is on its upper bound, then the subproblem objective value is added to the cut */
         if( SCIPisFeasEQ(masterprob, SCIPgetSolVal(masterprob, sol, vars[i]), 1.0) )
         {
            coef = -(subprobobj - cutconstant);
            lhs -= (subprobobj - cutconstant);
         }
         else
            coef = (subprobobj - cutconstant);
 
         /* adding the variable to the cut. The coefficient is the subproblem objective value */
         if( addcut )
         {
            SCIP_CALL( SCIPaddVarToRow(masterprob, row, vars[i], coef) );
         }
         else
         {
            SCIP_CALL( SCIPaddCoefLinear(masterprob, cons, vars[i], coef) );
         }
      }
   }
 
   lhs += subprobobj;
 
   /* if the bound becomes infinite, then the cut generation terminates. */
   if( SCIPisInfinity(masterprob, lhs) || SCIPisInfinity(masterprob, -lhs) )
   {
      (*success) = FALSE;
      SCIPdebugMsg(masterprob, "Infinite bound when generating integer optimality cut.\n");
      return SCIP_OKAY;
   }
 
   /* Update the lhs of the cut */
   if( addcut )
   {
      SCIP_CALL( SCIPchgRowLhs(masterprob, row, lhs) );
   }
   else
   {
      SCIP_CALL( SCIPchgLhsLinear(masterprob, cons, lhs) );
   }
 
#ifndef NDEBUG
   if( addcut )
      lhs = SCIProwGetLhs(row);
   else
      lhs = SCIPgetLhsLinear(masterprob, cons);
   verifyobj += lhs;
 
   if( addcut )
      verifyobj -= SCIPgetRowSolActivity(masterprob, row, sol);
   else
      verifyobj -= SCIPgetActivityLinear(masterprob, cons, sol);
#endif
 
   assert(SCIPisFeasEQ(masterprob, verifyobj, subprobobj));
 
   (*success) = TRUE;
 
   return SCIP_OKAY;
}
 
 
/** adds the auxiliary variable to the generated cut. If this is the first optimality cut for the subproblem, then the
 *  auxiliary variable is first created and added to the master problem.
 */
static
SCIP_RETCODE addAuxiliaryVariableToCut(
   SCIP*                 masterprob,         /**< the SCIP instance of the master problem */
   SCIP_BENDERS*         benders,            /**< the benders' decomposition structure */
   SCIP_CONS*            cons,               /**< the constraint for the generated cut, can be NULL */
   SCIP_ROW*             row,                /**< the row for the generated cut, can be NULL */
   int                   probnumber,         /**< the number of the pricing problem */
   SCIP_Bool             addcut              /**< indicates whether a cut is created instead of a constraint */
   )
{
   SCIP_VAR* auxiliaryvar;
 
   assert(masterprob != NULL);
   assert(benders != NULL);
   assert(cons != NULL || addcut);
   assert(row != NULL || !addcut);
 
   auxiliaryvar = SCIPbendersGetAuxiliaryVar(benders, probnumber);
 
   /* adding the auxiliary variable to the generated cut */
   if( addcut )
   {
      SCIP_CALL( SCIPaddVarToRow(masterprob, row, auxiliaryvar, 1.0) );
   }
   else
   {
      SCIP_CALL( SCIPaddCoefLinear(masterprob, cons, auxiliaryvar, 1.0) );
   }
 
   return SCIP_OKAY;
}
 
 
/** generates and applies Benders' cuts */
static
SCIP_RETCODE generateAndApplyBendersIntegerCuts(
   SCIP*                 masterprob,         /**< the SCIP instance of the master problem */
   SCIP_BENDERS*         benders,            /**< the benders' decomposition */
   SCIP_BENDERSCUT*      benderscut,         /**< the benders' decomposition cut method */
   SCIP_SOL*             sol,                /**< primal CIP solution */
   int                   probnumber,         /**< the number of the pricing problem */
   SCIP_BENDERSENFOTYPE  type,               /**< the enforcement type calling this function */
   SCIP_RESULT*          result,             /**< the result from solving the subproblems */
   SCIP_Bool             initcons            /**< is this function called to generate the initial constraint */
   )
{
   SCIP_BENDERSCUTDATA* benderscutdata;
   SCIP_CONSHDLR* consbenders;
   SCIP_CONS* cons;
   SCIP_ROW* row;
   char cutname[SCIP_MAXSTRLEN];
   SCIP_Bool optimal;
   SCIP_Bool addcut;
   SCIP_Bool success;
 
   assert(masterprob != NULL);
   assert(benders != NULL);
   assert(benderscut != NULL);
   assert(result != NULL);
 
   row = NULL;
   cons = NULL;
 
   success = FALSE;
 
   /* retrieving the Benders' cut data */
   benderscutdata = SCIPbenderscutGetData(benderscut);
 
   /* if the cuts are generated prior to the solving stage, then rows can not be generated. So constraints must be added
    * to the master problem.
    */
   if( SCIPgetStage(masterprob) < SCIP_STAGE_INITSOLVE )
      addcut = FALSE;
   else
      addcut = benderscutdata->addcuts;
 
   /* retrieving the Benders' decomposition constraint handler */
   consbenders = SCIPfindConshdlr(masterprob, "benders");
 
   /* checking the optimality of the original problem with a comparison between the auxiliary variable and the
    * objective value of the subproblem
    */
   optimal = FALSE;
   SCIP_CALL( SCIPcheckBendersSubproblemOptimality(masterprob, benders, sol, probnumber, &optimal) );
 
   if( optimal )
   {
      (*result) = SCIP_FEASIBLE;
      SCIPdebugMsg(masterprob, "No <%s> cut added. Current Master Problem Obj: %g\n", BENDERSCUT_NAME,
         SCIPgetSolOrigObj(masterprob, NULL)*(int)SCIPgetObjsense(masterprob));
      return SCIP_OKAY;
   }
 
   /* checking whether the subproblem constant is less than the auxiliary variable global lower bound */
   updateSubproblemCutConstant(masterprob, benders, benderscutdata, probnumber);
 
   /* if no integer cuts have been previously generated and the bound on the auxiliary variable is -infinity,
    * then an initial lower bounding cut is added
    */
   if( benderscutdata->firstcut[probnumber]
      && SCIPisInfinity(masterprob, -SCIPvarGetLbGlobal(SCIPbendersGetAuxiliaryVar(benders, probnumber))) )
   {
      benderscutdata->firstcut[probnumber] = FALSE;
      SCIP_CALL( generateAndApplyBendersIntegerCuts(masterprob, benders, benderscut, sol, probnumber, type, result,
            TRUE) );
   }
 
   /* setting the name of the generated cut */
   (void) SCIPsnprintf(cutname, SCIP_MAXSTRLEN, "integeroptcut_%d_%" SCIP_LONGINT_FORMAT, probnumber,
      SCIPbenderscutGetNFound(benderscut) );
 
   /* creating an empty row or constraint for the Benders' cut */
   if( addcut )
   {
      SCIP_CALL( SCIPcreateEmptyRowConshdlr(masterprob, &row, consbenders, cutname, 0.0, SCIPinfinity(masterprob), FALSE,
            FALSE, TRUE) );
   }
   else
   {
      SCIP_CALL( SCIPcreateConsBasicLinear(masterprob, &cons, cutname, 0, NULL, NULL, 0.0, SCIPinfinity(masterprob)) );
      SCIP_CALL( SCIPsetConsDynamic(masterprob, cons, TRUE) );
      SCIP_CALL( SCIPsetConsRemovable(masterprob, cons, TRUE) );
   }
 
   if( initcons )
   {
      SCIP_Real lhs;
 
      /* adding the subproblem objective function value to the lhs */
      if( addcut )
         lhs = SCIProwGetLhs(row);
      else
         lhs = SCIPgetLhsLinear(masterprob, cons);
 
      lhs += benderscutdata->subprobconstant[probnumber];
 
      /* if the bound becomes infinite, then the cut generation terminates. */
      if( SCIPisInfinity(masterprob, lhs) || SCIPisInfinity(masterprob, -lhs) )
      {
         success = FALSE;
         SCIPdebugMsg(masterprob, "Infinite bound when generating integer optimality cut.\n");
      }
 
      /* Update the lhs of the cut */
      if( addcut )
      {
         SCIP_CALL( SCIPchgRowLhs(masterprob, row, lhs) );
      }
      else
      {
         SCIP_CALL( SCIPchgLhsLinear(masterprob, cons, lhs) );
      }
   }
   else
   {
      /* computing the coefficients of the optimality cut */
      SCIP_CALL( computeStandardIntegerOptCut(masterprob, benders, sol, cons, row,
            benderscutdata->subprobconstant[probnumber], probnumber, addcut, &success) );
   }
 
   /* if success is FALSE, then there was an error in generating the integer optimality cut. No cut will be added to
    * the master problem. Otherwise, the constraint is added to the master problem.
    */
   if( !success )
   {
      (*result) = SCIP_DIDNOTFIND;
      SCIPdebugMsg(masterprob, "Error in generating Benders' integer optimality cut for problem %d.\n", probnumber);
   }
   else
   {
      /* adding the auxiliary variable to the optimality cut */
      SCIP_CALL( addAuxiliaryVariableToCut(masterprob, benders, cons, row, probnumber, addcut) );
 
      /* adding the constraint to the master problem */
      if( addcut )
      {
         SCIP_Bool infeasible;
 
         if( type == SCIP_BENDERSENFOTYPE_LP || type == SCIP_BENDERSENFOTYPE_RELAX )
         {
            SCIP_CALL( SCIPaddRow(masterprob, row, FALSE, &infeasible) );
            assert(!infeasible);
         }
         else
         {
            assert(type == SCIP_BENDERSENFOTYPE_CHECK || type == SCIP_BENDERSENFOTYPE_PSEUDO);
            SCIP_CALL( SCIPaddPoolCut(masterprob, row) );
         }
 
#ifdef SCIP_DEBUG
         SCIP_CALL( SCIPprintRow(masterprob, row, NULL) );
         SCIPinfoMessage(masterprob, NULL, ";\n");
#endif
 
         (*result) = SCIP_SEPARATED;
      }
      else
      {
         SCIP_CALL( SCIPaddCons(masterprob, cons) );
 
         SCIPdebugPrintCons(masterprob, cons, NULL);
 
         (*result) = SCIP_CONSADDED;
      }
   }
 
   if( addcut )
   {
      /* release the row */
      SCIP_CALL( SCIPreleaseRow(masterprob, &row) );
   }
   else
   {
      /* release the constraint */
      SCIP_CALL( SCIPreleaseCons(masterprob, &cons) );
   }
 
   return SCIP_OKAY;
}
 
/*
 * Callback methods of Benders' decomposition cuts
 */
 
/** destructor of Benders' decomposition cuts to free user data (called when SCIP is exiting) */
static
SCIP_DECL_BENDERSCUTFREE(benderscutFreeInt)
{  /*lint --e{715}*/
   SCIP_BENDERSCUTDATA* benderscutdata;
 
   assert( benderscut != NULL );
   assert( strcmp(SCIPbenderscutGetName(benderscut), BENDERSCUT_NAME) == 0 );
 
   /* free Benders' cut data */
   benderscutdata = SCIPbenderscutGetData(benderscut);
   assert( benderscutdata != NULL );
 
   SCIPfreeBlockMemory(scip, &benderscutdata);
 
   SCIPbenderscutSetData(benderscut, NULL);
 
   return SCIP_OKAY;
}
 
 
/** deinitialization method of Benders' decomposition cuts (called before transformed problem is freed) */
static
SCIP_DECL_BENDERSCUTEXIT(benderscutExitInt)
{  /*lint --e{715}*/
   SCIP_BENDERSCUTDATA* benderscutdata;
 
   assert( benderscut != NULL );
   assert( strcmp(SCIPbenderscutGetName(benderscut), BENDERSCUT_NAME) == 0 );
 
   /* free Benders' cut data */
   benderscutdata = SCIPbenderscutGetData(benderscut);
   assert( benderscutdata != NULL );
 
   if( benderscutdata->firstcut != NULL )
      SCIPfreeBlockMemoryArray(scip, &benderscutdata->firstcut, benderscutdata->nsubproblems);
 
   if( benderscutdata->subprobconstant != NULL)
      SCIPfreeBlockMemoryArray(scip, &benderscutdata->subprobconstant, benderscutdata->nsubproblems);
 
   return SCIP_OKAY;
}
 
/** execution method of Benders' decomposition cuts */
static
SCIP_DECL_BENDERSCUTEXEC(benderscutExecInt)
{  /*lint --e{715}*/
   SCIP* subproblem;
   SCIP_BENDERSCUTDATA* benderscutdata;
 
   assert(scip != NULL);
   assert(benders != NULL);
   assert(benderscut != NULL);
   assert(result != NULL);
 
   subproblem = SCIPbendersSubproblem(benders, probnumber);
 
   if( subproblem == NULL )
   {
      SCIPdebugMsg(scip, "The subproblem %d is set to NULL. The <%s> Benders' decomposition cut can not be executed.\n",
         probnumber, BENDERSCUT_NAME);
 
      (*result) = SCIP_DIDNOTRUN;
      return SCIP_OKAY;
   }
 
   /* retrieving the Benders' cut data */
   benderscutdata = SCIPbenderscutGetData(benderscut);
   assert(benderscutdata != NULL);
 
   /* if the Benders' cut data has not been created, then it is created now */
   if( !benderscutdata->created )
   {
      SCIP_CALL( createBenderscutData(scip, benderscutdata) );
   }
 
   /* it is only possible to generate the Laporte and Louveaux cuts when the linking variables are all binary */
   if( !benderscutdata->subprobsvalid )
   {
      SCIPwarningMessage(scip, "The integer optimality cuts have been disabled because some linking variables are not binary.\n"
         "Since there is at least one non-convex subproblem, i.e. not LP or convex NLP, the problem will be solved heuristically.\n");
 
      SCIPbenderscutSetEnabled(benderscut, FALSE);
 
      return SCIP_OKAY;
   }
 
   /* the integer subproblem could terminate early if the auxiliary variable value is much greater than the optimal
    * solution. As such, it is only necessary to generate a cut if the subproblem is OPTIMAL */
   if( SCIPgetStatus(subproblem) == SCIP_STATUS_OPTIMAL )
   {
      /* generating a cut for a given subproblem */
      SCIP_CALL( generateAndApplyBendersIntegerCuts(scip, benders, benderscut, sol, probnumber, type, result, FALSE) );
   }
 
   return SCIP_OKAY;
}
 
 
/*
 * Benders' decomposition cuts specific interface methods
 */
 
/** creates the int Benders' decomposition cuts and includes it in SCIP */
SCIP_RETCODE SCIPincludeBenderscutInt(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_BENDERS*         benders             /**< Benders' decomposition */
   )
{
   SCIP_BENDERSCUTDATA* benderscutdata;
   SCIP_BENDERSCUT* benderscut;
   char paramname[SCIP_MAXSTRLEN];
 
   assert(benders != NULL);
 
   /* create int Benders' decomposition cuts data */
   SCIP_CALL( SCIPallocBlockMemory(scip, &benderscutdata) );
   BMSclearMemory(benderscutdata);
   benderscutdata->benders = benders;
 
   benderscut = NULL;
 
   /* include Benders' decomposition cuts */
   SCIP_CALL( SCIPincludeBenderscutBasic(scip, benders, &benderscut, BENDERSCUT_NAME, BENDERSCUT_DESC,
         BENDERSCUT_PRIORITY, BENDERSCUT_LPCUT, benderscutExecInt, benderscutdata) );
 
   assert(benderscut != NULL);
 
   /* set non fundamental callbacks via setter functions */
   SCIP_CALL( SCIPsetBenderscutFree(scip, benderscut, benderscutFreeInt) );
   SCIP_CALL( SCIPsetBenderscutExit(scip, benderscut, benderscutExitInt) );
 
   /* add int Benders' decomposition cuts parameters */
   (void) SCIPsnprintf(paramname, SCIP_MAXSTRLEN, "benders/%s/benderscut/%s/cutsconstant",
      SCIPbendersGetName(benders), BENDERSCUT_NAME);
   SCIP_CALL( SCIPaddRealParam(scip, paramname,
         "the constant term of the integer Benders' cuts.",
         &benderscutdata->cutconstant, FALSE, SCIP_DEFAULT_CUTCONSTANT, -SCIPinfinity(scip), SCIPinfinity(scip),
         paramChgdBenderscutintConstant, (SCIP_PARAMDATA*)benderscutdata) );
 
   (void) SCIPsnprintf(paramname, SCIP_MAXSTRLEN, "benders/%s/benderscut/%s/addcuts",
      SCIPbendersGetName(benders), BENDERSCUT_NAME);
   SCIP_CALL( SCIPaddBoolParam(scip, paramname,
         "should cuts be generated and added to the cutpool instead of global constraints directly added to the problem.",
         &benderscutdata->addcuts, FALSE, SCIP_DEFAULT_ADDCUTS, NULL, NULL) );
 
   return SCIP_OKAY;
}