heur_dks.c

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the program and library             */
/*         SCIP --- Solving Constraint Integer Programs                      */
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/*  Copyright (c) 2002-2026 Zuse Institute Berlin (ZIB)                      */
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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
 
/**@file   heur_dks.c
 * @ingroup DEFPLUGINS_HEUR
 * @brief  dks primal heuristic
 * @author Adrian Göß
 * @author Dieter Weninger
 *
 * Primal heuristic based on ideas published in the paper
 * "Exploiting user-supplied Decompositions inside Heuristics" by Katrin Halbig, Adrian Göß and Dieter Weninger.
 */
 
/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+--*/
 
#include "scip/pub_lp.h"
#include "blockmemshell/memory.h"
#include "scip/cons_linear.h"
#include "scip/debug.h"
#include "scip/heuristics.h"
#include "scip/pub_cons.h"
#include "scip/pub_event.h"
#include "scip/pub_fileio.h"
#include "scip/pub_tree.h"
#include "scip/pub_heur.h"
#include "scip/pub_message.h"
#include "scip/pub_misc.h"
#include "scip/pub_misc_select.h"
#include "scip/pub_sol.h"
#include "scip/pub_var.h"
#include "scip/scipdefplugins.h"
#include "scip/scip_branch.h"
#include "scip/scip_cons.h"
#include "scip/scip_copy.h"
#include "scip/scip_dcmp.h"
#include "scip/scip_event.h"
#include "scip/scip_general.h"
#include "scip/scip_heur.h"
#include "scip/scip_lp.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_nodesel.h"
#include "scip/scip_numerics.h"
#include "scip/scip_param.h"
#include "scip/scip_prob.h"
#include "scip/scip_randnumgen.h"
#include "scip/scip_sol.h"
#include "scip/scip_solve.h"
#include "scip/scip_solvingstats.h"
#include "scip/scip_table.h"
#include "scip/scip_timing.h"
#include "scip/scip_tree.h"
#include "scip/scip_var.h"
#include "scip/sol.h"
#include "scip/heur_dks.h"
 
 
#define HEUR_NAME             "dks"
#define HEUR_DESC             "decomposition kernel search"
#define HEUR_DISPCHAR         'D'
#define HEUR_PRIORITY         -1102500
#define HEUR_FREQ             -1
#define HEUR_FREQOFS          0
#define HEUR_MAXDEPTH         0
#define HEUR_TIMING           SCIP_HEURTIMING_AFTERLPNODE
#define HEUR_USESSUBSCIP      TRUE           /**< does the heuristic use a secondary SCIP instance? */
 
#define DEFAULT_MAXBUCKS         20          /**< default value for the number of buckets to investigate */
#define DEFAULT_KERNELSIZEFACTOR 2.0         /**< default value for the maximal growing of the kernel size */
#define DEFAULT_ADDUSECONSS      TRUE        /**< default value to add a use constraint */
#define DEFAULT_LINKBUCKSIZE     TRUE        /**< default value to respect kernel linking vars for the bucket size */
#define DEFAULT_TRANSLBKERNEL    TRUE        /**< default value to respect the diff of var lb in trans and orig prob */
#define DEFAULT_LESSLOCKSKERNEL  FALSE       /**< default value to respect <= 1 up- & downlock in kernel construction */
#define DEFAULT_USETRANSPROB     TRUE        /**< default value to use the original or transformed problem **/
#define DEFAULT_BUCKMAXGAP       0.01        /**< default value for the maximal mip gap of a bucket */
#define DEFAULT_MAXLINKSCORE     1.0         /**< default value for the maximal linking score of an instance */
#define DEFAULT_MAXBUCKFRAC      0.10        /**< default value to respect buckets with <= this share of bin/int vars */
#define DEFAULT_MAXNODES         5000LL      /**< default node limit of the heuristic */
#define DEFAULT_USETWOLEVEL      TRUE        /**< default value to use a two level structure for the buckets */
#define DEFAULT_USEDECOMP        TRUE        /**< default value to use the decomp if given */
#define DEFAULT_USEBESTSOL       TRUE        /**< default value to use the best existing solution or the lp solution */
#define DEFAULT_REDCOSTSORT      TRUE        /**< default value to sort the non kernel vars before bucket split */
#define DEFAULT_PRIMALONLY       FALSE       /**< default value to kill dks after the first primal solution is found */
#define DEFAULT_REDCOSTLOGSORT   TRUE        /**< default value to sort non kernel vars logarithmically by redcost */
#define DEFAULT_OBJCUTOFF        TRUE        /**< default value to add an objective cutoff */
#define DEFAULT_RUNBINPROBSONLY  FALSE       /**< default value to run only for bin or bin + int only problems */
 
/*
 * Data structures
 */
 
/** data related to one bucket list, details see below **/
typedef struct Bucketlist BUCKETLIST;
 
/** data related to one bucket **/
typedef struct Bucket
{
   BUCKETLIST*           bucketlist;         /**< the bucketlist the bucket belongs to */
   SCIP*                 subscip;            /**< scip structure to solve smaller MIPs later */
   int                   number;             /**< component number */
   SCIP_VAR**            contbucketvars;     /**< continuous variables for this bucket */
   SCIP_VAR**            bucketvars;         /**< variables of this bucket, just binary if 2-level bucket */
   SCIP_VAR**            intbucketvars;      /**< just integer variables if 2-level bucket */
   int                   ncontbucketvars;    /**< amount of continuous variables in this bucket */
   int                   nbucketvars;        /**< amount of variables in this bucket */
   int                   nintbucketvars;     /**< amount of integer variables in a 2-level bucket */
   SCIP_Bool             twolevel;           /**< is the current bucket a 2-level one */
   SCIP_VAR**            sub2scip;           /**< mapping the variables to the original ones */
   SCIP_VAR**            scip2sub;           /**< mapping original variables to subscip ones */
} BUCKET;
 
/** data related to one whole list of buckets **/
struct Bucketlist
{
   SCIP*                 scip;               /**< scip instance this bucketlist belongs to */
   BUCKET*               buckets;            /**< buckets in this bucketlist */
   int                   nbuckets;           /**< amount of buckets in this bucketlist */
};
 
/** primal heuristic data */
struct SCIP_HeurData
{
   int                   maxbucks;           /**< maximum amount of buckets that are investigated */
   SCIP_Real             kernelsizefactor;   /**< factor with which initial kernel can grow max */
   SCIP_Bool             addUseConss;        /**< add a constraint that ensures a use of the bucket variables or not */
   SCIP_Bool             linkbucksize;       /**< respect the kernel linking variables for the initial bucket size */
   SCIP_Bool             translbkernel;      /**< respect the variable's lb in transprob at kernel construction */
   SCIP_Bool             lesslockskernel;    /**< respect variables with <= 1 up & downlock at kernel construction */
   SCIP_Bool             usetransprob;       /**< use the transformed problem instead of the original one */
   SCIP_Real             buckmaxgap;         /**< set an upper bound for the maximum mip gap of each bucket */
   SCIP_Real             maxlinkscore;       /**< set an upper bound for the linking score to get solved by dks */
   SCIP_Real             maxbuckfrac;        /**< maximal share of int/bin variables for a bucket to be computed */
   SCIP_Longint          maxnodes;           /**< maximum number of nodes to regard in all subproblems */
   SCIP_Bool             usetwolevel;        /**< use two level structure for the buckets if possible */
   SCIP_Bool             usedecomp;          /**< use decomp if given */
   SCIP_Bool             usebestsol;         /**< use best solution or alt. LP sol */
   SCIP_Bool             redcostsort;        /**< sort the non kernel variables by reduced costs */
   SCIP_Bool             primalonly;         /**< terminate after the first found primal solution */
   SCIP_Bool             redcostlogsort;     /**< flag indicating logarithmically sorted reduced costs at bucket init */
   SCIP_Bool             objcutoff;          /**< add an objective cutoff for the current best sol */
   int                   ncalls;             /**< amount of calls of the heuristic */
   SCIP_Bool             runbinprobsonly;    /**< flag indicating if executing only on bin/int problems  */
   SCIP_Bool             uselesscall;        /**< flag indicating if DKS has been called once & not found a solution */
};
 
 
/*
 * Local methods
 */
 
/** calculate the linking score of a given decomposition */
static
SCIP_RETCODE getLinkingScoreAndBlocklabels(
   int*                  blocklabels,        /**< int array to store the different block labels */
   int*                  varlabels,          /**< array of variable labels */
   int*                  conslabels,         /**< array of constraint labels */
   SCIP_Real*            linkscore,          /**< linking score to return */
   int*                  nblocklabels,       /**< number of block labels to return */
   int                   nblocks,            /**< number of blocks */
   int                   nvars,              /**< number of variables */
   int                   nconss              /**< number of constraints */
   )
{
   int v;
   int b;
 
   int nlinkscoreconss = 0;                  /* number of linking conss for calculation */
   int nlinkscorevars = 0;                   /* number of linking vars for calculation */
 
   assert(nblocklabels != NULL);
 
   *nblocklabels = 0;                        /* number of distinct block labels */
 
   for( v = 0; v < nvars; v++ )
   {
      assert(varlabels != NULL);
 
      /* counting of linking variables */
      if( varlabels[v] == SCIP_DECOMP_LINKVAR )
         nlinkscorevars++;
      /* fill an array for the existing distinct block labels that are not linking variables */
      else if( *nblocklabels < nblocks && blocklabels != NULL )
      {
         SCIP_Bool newlabel = TRUE;  /* indication of finding a new label */
 
         /* check the current label for novelty */
         for( b = 0; b < *nblocklabels; b++ )
         {
            if( blocklabels[b] == varlabels[v] )
            {
               newlabel = FALSE;
               break;
            }
         }
 
         /* add unseen labels */
         if( newlabel )
            blocklabels[(*nblocklabels)++] = varlabels[v];
      }
   }
 
   /* counting of linking constraints */
   for( v = 0; v < nconss; v++ )
   {
      assert(conslabels != NULL);
      if( conslabels[v] == SCIP_DECOMP_LINKCONS )
         nlinkscoreconss++;
   }
 
   /* linking score calculation */
   *linkscore = ( (SCIP_Real)nlinkscorevars*(SCIP_Real)nconss + (SCIP_Real)nlinkscoreconss*(SCIP_Real)nvars -
      (SCIP_Real)nlinkscorevars*(SCIP_Real)nlinkscoreconss ) / ((SCIP_Real)nconss*(SCIP_Real)nvars);
 
   return SCIP_OKAY;
}
 
/** count of potential kernel variables for one level or two level structure */
static
SCIP_RETCODE countKernelVariables(
   SCIP*                 scip,               /**< main SCIP data structure */
   SCIP_VAR**            vars,               /**< array of variables */
   SCIP_SOL*             bestcurrsol,        /**< best current solution */
   SCIP_HASHMAP*         lbvarmap,           /**< original lower bound of transformed variables */
   SCIP_Bool             twolevel,           /**< usage of one or two level structure */
   SCIP_Bool             usebestsol,         /**< usage of best or lp solution */
   SCIP_Bool             usetransprob,       /**< usage of transformed or original problem */
   SCIP_Bool             usetranslb,         /**< usage of transformed lb in comparison to original lb */
   int*                  bw_ncontkernelvars, /**< blockwise number of continuous kernel variables */
   int*                  bw_ncontnonkernelvars, /**< blockwise number of continuous non-kernel variables */
   int*                  bw_nkernelvars,     /**< blockwise number of (binary) kernel variables */
   int*                  bw_nnonkernelvars,  /**< blockwise number of (binary) non-kernel variables */
   int*                  bw_nintkernelvars,  /**< blockwise number of integer kernel variables */
   int*                  bw_nintnonkernelvars, /**< blockwise number of integer non-kernel variables */
   int*                  ncontkernelvars,    /**< number of continuous kernel variables */
   int*                  ncontnonkernelvars, /**< number of continuous non-kernel variables */
   int*                  nkernelvars,        /**< number of (binary) kernel variables */
   int*                  nnonkernelvars,     /**< number of (binary) non-kernel variables */
   int*                  nintkernelvars,     /**< number of integer kernel variables */
   int*                  nintnonkernelvars,  /**< number of integer non-kernel variables */
   int*                  block2index,        /**< mapping of block labels to block index */
   int*                  varlabels,          /**< array of variable labels */
   int                   blklbl_offset,      /**< optional offset for the blocklabels, if it exists a block 0 */
   int                   nvars               /**< number of variables */
   )
{
   SCIP_Real lpval;      /* variable value in LP solution */
   SCIP_Real lb;
   SCIP_Real lborig;
   int i;
   int block;
 
   assert(bw_ncontkernelvars != NULL);
   assert(bw_ncontnonkernelvars != NULL);
   assert(bw_nkernelvars != NULL);
   assert(bw_nnonkernelvars != NULL);
 
   assert(ncontkernelvars != NULL);
   assert(ncontnonkernelvars != NULL);
   assert(nkernelvars != NULL);
   assert(nnonkernelvars != NULL);
 
   /* count all possible kernel variables dependent on their type blockwise and overall */
   for( i = 0; i < nvars; i++ )
   {
      /* calculate the variable's LP solution value, the lower bound in the transformed and original problem */
      lpval = usebestsol ? SCIPgetSolVal(scip, bestcurrsol, vars[i]) : SCIPvarGetLPSol(vars[i]);
      lb = SCIPvarGetLbLocal(vars[i]);
      lborig = usetransprob ? SCIPhashmapGetImageReal(lbvarmap, vars[i]) : SCIPvarGetLbOriginal(vars[i]);
 
      /* definition of the variable's block (SCIP_DECOMP_LINKVAR = -1, but is stored as 0) */
      block = block2index[MAX(varlabels[i] + blklbl_offset, 0)];
 
      switch( SCIPvarGetType(vars[i]) )
      {
      /* compare binaries only to the lower bound of 0.0 and count as kernel or non-kernel variable */
      case SCIP_VARTYPE_BINARY:
         if( !SCIPisEQ(scip, lpval, 0.0) )
         {
            (*nkernelvars)++;
            bw_nkernelvars[block]++;
         }
         else
         {
            (*nnonkernelvars)++;
            bw_nnonkernelvars[block]++;
         }
         break;
 
      /* LP value > lb -> count integer as kernel variable else not */
      /* count separatly if binaries and integers are present */
      case SCIP_VARTYPE_INTEGER:
         if(  (!SCIPisEQ(scip, lpval, 0.0) && !SCIPisEQ(scip, lpval, lb))
            || (usetranslb && SCIPisGT(scip, lb, lborig)) )
         {
            if( twolevel )
            {
               if( nintkernelvars != NULL )
                  (*nintkernelvars)++;
               if( bw_nintkernelvars != NULL )
                  bw_nintkernelvars[block]++;
            }
            else
            {
               (*nkernelvars)++;
               bw_nkernelvars[block]++;
            }
         }
         else
         {
            if( twolevel )
            {
               if( nintnonkernelvars != NULL )
                  (*nintnonkernelvars)++;
               if( bw_nintnonkernelvars != NULL )
                  bw_nintnonkernelvars[block]++;
            }
            else
            {
               (*nnonkernelvars)++;
               bw_nnonkernelvars[block]++;
            }
         }
         break;
 
      /* LP value > lower bound -> potential kernel variable else not for continuous vars */
      case SCIP_VARTYPE_CONTINUOUS:
      default:
         if(  (!SCIPisEQ(scip, lpval, 0.0) && !SCIPisEQ(scip, lpval, lb) )
            || (usetranslb && SCIPisGT(scip, lb, lborig)) )
         {
            (*ncontkernelvars)++;
            bw_ncontkernelvars[block]++;
         }
         else
         {
            (*ncontnonkernelvars)++;
            bw_ncontnonkernelvars[block]++;
         }
         break;
      } /*lint !e788*/
   }
 
   return SCIP_OKAY;
}
 
/** fill the blockwise kernels with the respective variables */
static
SCIP_RETCODE fillKernels(
   SCIP*                 scip,               /**< main SCIP data structure */
   SCIP_VAR**            vars,               /**< array of variables */
   SCIP_VAR**            binintvars,         /**< array of binary and integer variables */
   SCIP_VAR***           bw_contkernelvars,  /**< blockwise array of continuous kernel variables */
   SCIP_VAR***           bw_contnonkernelvars,     /**< blockwise array of continuous non-kernel variables */
   SCIP_VAR***           bw_kernelvars,      /**< blockwise array of (binary) kernel variables */
   SCIP_VAR***           bw_nonkernelvars,   /**< blockwise array of (binary) non-kernel variables */
   SCIP_VAR***           bw_intkernelvars,   /**< blockwise array of integer kernel variables */
   SCIP_VAR***           bw_intnonkernelvars,   /**< blockwise array of integer non-kernel variables */
   SCIP_SOL*             bestcurrsol,        /**< best current solution */
   SCIP_HASHMAP*         lbvarmap,           /**< original lower bound of transformed variables */
   SCIP_Bool             twolevel,           /**< usage of one or two level structure */
   SCIP_Bool             usebestsol,         /**< usage of best or lp solution */
   SCIP_Bool             usetransprob,       /**< usage of transformed or original problem */
   SCIP_Bool             usetranslb,         /**< usage of transformed lb in comparison to original lb */
   int*                  bw_contkernelcount, /**< blockwise counter of continuous kernel variables */
   int*                  bw_contnonkernelcount,    /**< blockwise counter of continuous non-kernel variables */
   int*                  bw_kernelcount,     /**< blockwise counter of (binary) kernel variables */
   int*                  bw_nonkernelcount,  /**< blockwise counter of (binary) non-kernel variables */
   int*                  bw_intkernelcount,  /**< blockwise counter of integer kernel variables */
   int*                  bw_intnonkernelcount,     /**< blockwise counter of integer non-kernel variables */
   int*                  bw_ncontkernelvars, /**< blockwise number of continuous kernel variables */
   int*                  bw_ncontnonkernelvars, /**< blockwise number of continuous non-kernel variables */
   int*                  bw_nkernelvars,     /**< blockwise number of (binary) kernel variables */
   int*                  bw_nnonkernelvars,  /**< blockwise number of (binary) non-kernel variables */
   int*                  bw_nintkernelvars,  /**< blockwise number of integer kernel variables */
   int*                  bw_nintnonkernelvars, /**< blockwise number of integer non-kernel variables */
   int*                  block2index,        /**< mapping of block labels to block index */
   int*                  varlabels,          /**< array of variable labels */
   int                   blklbl_offset,      /**< optional offset for the blocklabels, if it exists a block 0 */
   int                   nvars,              /**< number of variables */
   int                   nbinintvars         /**< number of binary and integer variables */
   )
{
   SCIP_Real lpval;      /* variable value in LP solution */
   SCIP_Real lb;
   SCIP_Real lborig;
   int i;                /* variable counter */
   int j = 0;            /* integer and binary variable counter */
   int m;                /* temporary integer variable index */
   int n;                /* temporary (binary) variable index */
   int l;                /* temporary continuous variable index */
   int block_index;
 
   assert(bw_contkernelvars != NULL);
   assert(bw_contnonkernelvars != NULL);
   assert(bw_kernelvars != NULL);
   assert(bw_nonkernelvars != NULL);
   assert(bw_contkernelcount != NULL);
   assert(bw_contnonkernelcount  != NULL);
   assert(bw_kernelcount != NULL);
   assert(bw_nonkernelcount != NULL);
 
   /* assign all variables dependent on their type blockwise to a kernel or a non-kernel */
   for( i = 0; i < nvars; i++ )
   {
      /* calculate the variable's LP solution value, the lower bound in the transformed and original problem */
      lpval = usebestsol ? SCIPgetSolVal(scip, bestcurrsol, vars[i]) : SCIPvarGetLPSol(vars[i]);
      lb = SCIPvarGetLbLocal(vars[i]);
      lborig = usetransprob ? SCIPhashmapGetImageReal(lbvarmap, vars[i]) : SCIPvarGetLbOriginal(vars[i]);
 
      /* definition of the variable's block index (SCIP_DECOMP_LINKVAR = -1, but is stored as 0 in block2index) */
      block_index = block2index[MAX(varlabels[i] + blklbl_offset, 0)];
 
      switch( SCIPvarGetType(vars[i]) )
      {
      /* compare binaries only to the lower bound of 0.0 and add to kernel or non-kernel variables */
      case SCIP_VARTYPE_BINARY:
         /* adding the variable to the binary and integer variable array */
         assert(j < nbinintvars);
         binintvars[j++] = vars[i];
 
         if( !SCIPisEQ(scip, lpval, 0.0) )
         {
            n = bw_kernelcount[block_index];
            assert(bw_nnonkernelvars != NULL);
            assert(n < bw_nkernelvars[block_index] + bw_nnonkernelvars[block_index]);
            bw_kernelvars[block_index][n] = vars[i];
            bw_kernelcount[block_index]++;
         }
         else
         {
            n = bw_nonkernelcount[block_index];
            assert(bw_nnonkernelvars != NULL);
            assert(n < bw_nkernelvars[block_index] + bw_nnonkernelvars[block_index]);
            bw_nonkernelvars[block_index][n] = vars[i];
            bw_nonkernelcount[block_index]++;
         }
         break;
 
      /* LP value > lb -> integer kernel variable else non-kernel variable */
      /* count separatly if binaries and integers are present */
      case SCIP_VARTYPE_INTEGER:
         /* adding the variable to the binary and integer variable array */
         assert(j < nbinintvars);
         binintvars[j++] = vars[i];
 
         if(  (!SCIPisEQ(scip, lpval, 0.0) && !SCIPisEQ(scip, lpval, lb))
            || (usetranslb && SCIPisGT(scip, lb, lborig)) )
         {
            if( twolevel )
            {
               if( bw_intkernelcount != NULL )
               {
                  m = bw_intkernelcount[block_index];
                  assert(bw_nintnonkernelvars != NULL);
                  assert(bw_nintkernelvars != NULL);
                  assert(m < bw_nintkernelvars[block_index] + bw_nintnonkernelvars[block_index]);
                  if( bw_intkernelvars != NULL )
                     bw_intkernelvars[block_index][m] = vars[i];
                  bw_intkernelcount[block_index]++;
               }
            }
            else
            {
               m = bw_kernelcount[block_index];
               assert(bw_nnonkernelvars != NULL);
               assert(m < bw_nkernelvars[block_index] + bw_nnonkernelvars[block_index]);
               bw_kernelvars[block_index][m] = vars[i];
               bw_kernelcount[block_index]++;
            }
         }
         else
         {
            if( twolevel )
            {
               if( bw_intnonkernelcount != NULL )
               {
                  m = bw_intnonkernelcount[block_index];
                  assert(bw_nintnonkernelvars != NULL);
                  assert(bw_nintkernelvars != NULL);
                  assert(m < bw_nintkernelvars[block_index] + bw_nintnonkernelvars[block_index]);
                  if( bw_intnonkernelvars != NULL )
                     bw_intnonkernelvars[block_index][m] = vars[i];
                  bw_intnonkernelcount[block_index]++;
               }
            }
            else
            {
               m = bw_nonkernelcount[block_index];
               assert(bw_nnonkernelvars != NULL);
               assert(m < bw_nkernelvars[block_index] + bw_nnonkernelvars[block_index]);
               bw_nonkernelvars[block_index][m] = vars[i];
               bw_nonkernelcount[block_index]++;
            }
         }
         break;
 
      /* LP value > lower bound -> continuous kernel variable else non-kernel variable */
      case SCIP_VARTYPE_CONTINUOUS:
      default:
         if( (!SCIPisEQ(scip, lpval, 0.0) && !SCIPisEQ(scip, lpval, lb) )
            || (usetranslb && SCIPisGT(scip, lb, lborig)) )
         {
            l = bw_contkernelcount[block_index];
            assert(bw_ncontnonkernelvars != NULL);
            assert(l < bw_ncontkernelvars[block_index] + bw_ncontnonkernelvars[block_index]);
            bw_contkernelvars[block_index][l] = vars[i];
            bw_contkernelcount[block_index]++;
         }
         else
         {
            l = bw_contnonkernelcount[block_index];
            assert(bw_ncontnonkernelvars != NULL);
            assert(l < bw_ncontkernelvars[block_index] + bw_ncontnonkernelvars[block_index]);
            bw_contnonkernelvars[block_index][l] = vars[i];
            bw_contnonkernelcount[block_index]++;
         }
         break;
      } /*lint !e788*/
   }
 
   return SCIP_OKAY;
}
 
/** calculation of reduced costs and non-decreasing sorting **/
static
SCIP_RETCODE reducedCostSort(
   SCIP*                 scip,               /**< main SCIP data structure */
   SCIP_VAR***           bw_contnonkernelvars, /**< array pointer of continuous, non-kernel variables */
   SCIP_VAR***           bw_nonkernelvars,   /**< array pointer of (binary,) non-kernel variables */
   SCIP_VAR***           bw_intnonkernelvars,  /**< array pointer of integer, non-kernel variables */
   SCIP_Real***          bw_cont_redcost,    /**< array pointer with reduced costs for continuous variables */
   SCIP_Real***          bw_redcost,         /**< array pointer with reduced costs for (binary) variables */
   SCIP_Real***          bw_int_redcost,     /**< array pointer with reduced costs for integer variables */
   int*                  bw_ncontnonkernelvars, /**< blockwise number of continuous, non-kernel variables */
   int*                  bw_nnonkernelvars,  /**< blockwise number of (binary,) non-kernel variables */
   int*                  bw_nintnonkernelvars, /**< blockwise number of integer, non-kernel variables */
   SCIP_Bool             twolevel,           /**< usage of one or two level structure */
   int                   nblocks             /**< number of blocks */
   )
{
   int b;                /* block counter */
   int i;                /* variable counter */
 
   SCIP_CALL( SCIPallocBufferArray(scip, bw_cont_redcost, nblocks + 1) );
   SCIP_CALL( SCIPallocBufferArray(scip, bw_redcost, nblocks + 1) );
   if( twolevel )
      SCIP_CALL( SCIPallocBufferArray(scip, bw_int_redcost, nblocks + 1) );
 
   /* blockwise and type-wise extraction of reduced costs and sorting in non-decreasing order */
   for( b = 0; b < nblocks + 1; b++ )
   {
      SCIP_CALL( SCIPallocBufferArray(scip, &((*bw_cont_redcost)[b]), bw_ncontnonkernelvars[b]) );
      SCIP_CALL( SCIPallocBufferArray(scip, &((*bw_redcost)[b]), bw_nnonkernelvars[b]) );
 
      for( i = 0; i < bw_ncontnonkernelvars[b]; i++ )
      {
         (*bw_cont_redcost)[b][i] = SCIPgetVarRedcost(scip, bw_contnonkernelvars[b][i]);
         /* if a var is not in LP (SCIP_INVALID), we assign a reduced cost of zero & thus the var to an early bucket */
         if( (*bw_cont_redcost)[b][i] == SCIP_INVALID ) /*lint !e777*/
            (*bw_cont_redcost)[b][i] = 0.0;
      }
 
      for( i = 0; i < bw_nnonkernelvars[b]; i++ )
      {
         (*bw_redcost)[b][i] = SCIPgetVarRedcost(scip, bw_nonkernelvars[b][i]);
         /* if a var is not in LP (SCIP_INVALID), we assign a reduced cost of zero & thus the var to an early bucket */
         if( (*bw_redcost)[b][i] == SCIP_INVALID ) /*lint !e777*/
            (*bw_redcost)[b][i] = 0.0;
      }
 
      SCIPsortRealPtr((*bw_cont_redcost)[b], (void**)bw_contnonkernelvars[b], bw_ncontnonkernelvars[b]);
      SCIPsortRealPtr((*bw_redcost)[b], (void**)bw_nonkernelvars[b], bw_nnonkernelvars[b]);
 
      if( twolevel )
      {
         SCIP_CALL( SCIPallocBufferArray(scip, &((*bw_int_redcost)[b]), bw_nintnonkernelvars[b]) );
 
         for( i = 0; i < bw_nintnonkernelvars[b]; i++ )
         {
            (*bw_int_redcost)[b][i] = SCIPgetVarRedcost(scip, bw_intnonkernelvars[b][i]);
            /* if a var is not in LP (SCIP_INVALID), we assign a red cost of zero & thus the var to an early bucket */
            if( (*bw_int_redcost)[b][i] == SCIP_INVALID ) /*lint !e777*/
               (*bw_int_redcost)[b][i] = 0.0;
         }
 
         SCIPsortRealPtr((*bw_int_redcost)[b], (void**)bw_intnonkernelvars[b], bw_nintnonkernelvars[b]);
      }
   }
 
   return SCIP_OKAY;
}
 
/** free memory of reduced cost arrays */
static
SCIP_RETCODE freeRedcostArrays(
   SCIP*                 scip,               /**< main SCIP data structure */
   SCIP_Real***          bw_cont_redcost,    /**< array pointer with reduced costs for continuous variables */
   SCIP_Real***          bw_redcost,         /**< array pointer with reduced costs for (binary) variables */
   SCIP_Real***          bw_int_redcost,     /**< array pointer with reduced costs for integer variables */
   int                   nblocks             /**< number of blocks */
   )
{
   int b;
 
   /* type-wise and blockwise freeing of reduced cost arrays */
   if( *bw_cont_redcost != NULL )
   {
      for( b = 0; b < nblocks + 1; b++ )
      {
         if( (*bw_cont_redcost)[b] != NULL )
            SCIPfreeBufferArray(scip, &((*bw_cont_redcost)[b]));
      }
 
      SCIPfreeBufferArray(scip, bw_cont_redcost);
   }
 
   if( *bw_redcost != NULL )
   {
      for( b = 0; b < nblocks + 1; b++ )
      {
         if( (*bw_redcost)[b] != NULL )
            SCIPfreeBufferArray(scip, &((*bw_redcost)[b]));
      }
 
      SCIPfreeBufferArray(scip, bw_redcost);
   }
 
   if( *bw_int_redcost != NULL )
   {
      for( b = 0; b < nblocks + 1; b++ )
      {
         if( (*bw_int_redcost)[b] != NULL )
            SCIPfreeBufferArray(scip, &((*bw_int_redcost)[b]));
      }
 
      SCIPfreeBufferArray(scip, bw_int_redcost);
   }
 
   return SCIP_OKAY;
}
 
/** determines affiliation to a redcost (logsorted) bucket, avoiding inf to inf comparison */
static
SCIP_Bool isInCurrentLogBucket(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Real             base,               /**< the nbuckets-th-root of the shifted max red costs in current bucket */
   SCIP_Real             redcost,            /**< the reduced cost of the current variable */
   SCIP_Real             redcostmin,         /**< the minimal reduced cost of the current block for shifting */
   int                   currentindex,       /**< current iteration index */
   int                   nbuckets            /**< number of buckets */
   )
{
   /* compute the reduced cost bounds for the current interval for logarithmic sorting */
   SCIP_Real redcostlb = pow(base, (double)(currentindex - 1));
   SCIP_Real redcostub = pow(base, (double)currentindex);
 
   /* shift the current reduced cost for determining the membership to the current interval */
   SCIP_Real shifted_redcost = redcost - redcostmin + 1.0;
 
   /* check whether the current reduced cost is in (min, max] */
   SCIP_Bool greatermincost = SCIPisGT(scip, shifted_redcost, redcostlb);
   SCIP_Bool lessequalmaxcost = SCIPisLE(scip, shifted_redcost, redcostub);
 
   assert(base >= 1);
   assert(!SCIPisInfinity(scip, base));
 
   /* respecting the edge cases, return the result */
   if( currentindex == 1 )
      /* there is no minimal reduced cost to respect */
      return lessequalmaxcost;
   else if ( currentindex == nbuckets )
      /* there is no maximal reduced cost to respect */
      return greatermincost;
   else
      /* both interval bounds must be respected */
      return greatermincost && lessequalmaxcost;
}
 
/** fill bucket with its variables */
static
SCIP_RETCODE fillBuckets(
   SCIP*                 scip,               /**< main SCIP data structure */
   BUCKETLIST**          bucketlist,         /**< array pointer of buckets to fill */
   SCIP_VAR***           bw_contnonkernelvars,     /**< array of continuous, non-kernel variables */
   SCIP_VAR***           bw_nonkernelvars,   /**< array of (binary,) non-kernel variables */
   SCIP_VAR***           bw_intnonkernelvars,   /**< array of integer, non-kernel variables */
   int*                  bw_ncontnonkernelvars,    /**< blockwise number of continuous, non-kernel variables */
   int*                  bw_nnonkernelvars,  /**< blockwise number of (binary,) non-kernel variables */
   int*                  bw_nintnonkernelvars,     /**< blockwise number of integer, non-kernel variables */
   SCIP_Real**           bw_cont_redcost,    /**< blockwise reduced costs of continuous, non-kernel variables */
   SCIP_Real**           bw_redcost,         /**< blockwise reduced costs of (binary,) non-kernel variables */
   SCIP_Real**           bw_int_redcost,     /**< blockwise reduced costs of integer, non-kernel variables */
   SCIP_Bool             twolevel,           /**< usage of one or two level structure */
   SCIP_Bool             redcostlogsort,     /**< filling the buckets by logarithmically reduced cost sort */
   int                   nbuckets,           /**< number of buckets */
   int                   nblocks             /**< number of blocks */
   )
{
   BUCKET* bucket;                           /* temporary bucket */
   int contbucklength;                       /* temporary length of the continuous bucket */
   int bucklength;                           /* temporary length of the (binary) bucket */
   int intbucklength;                        /* temporary length of the integer bucket */
   int fromcontvars;                         /* temporary start index for the variables of a continuous bucket */
   int tocontvars;                           /* temporary end index for the variables of a continuous bucket */
   int fromvars;                             /* temporary start index for the variables of a (binary) bucket */
   int tovars;                               /* temporary end index for the variables of a (binary) bucket */
   int fromintvars;                          /* temporary start index for the variables of a integer bucket */
   int tointvars;                            /* temporary end index for the variables of a integer bucket */
   int k;                                    /* bucket counter */
   int b;                                    /* block counter */
   int l;                                    /* variable counter */
   int j;                                    /* temporary continuous variable counter */
   int n;                                    /* temporary (binary) variable counter */
   int m;                                    /* temporary integer variable counter */
   SCIP_Real* contbases = NULL;              /* blockwise the nbuckets-th-root of the max reduced costs of cont vars */
   SCIP_Real* bases = NULL;                  /* blockwise the nbuckets-th-root of the max reduced costs of (bin) vars */
   SCIP_Real* intbases = NULL;               /* blockwise the nbuckets-th-root of the max reduced costs of int vars */
 
   assert(nbuckets > 0);
 
   /* when sorting logarithmically by reduced costs, get maximum per block and its shifted nbuckets-th-root */
   if( redcostlogsort )
   {
      SCIP_Real tmp_max;
      SCIP_Real tmp_min;
 
      SCIP_CALL( SCIPallocBufferArray(scip, &contbases, nblocks + 1) );
      SCIP_CALL( SCIPallocBufferArray(scip, &bases, nblocks + 1) );
      if( twolevel )
         SCIP_CALL( SCIPallocBufferArray(scip, &intbases, nblocks + 1) );
 
      for( b = 0; b < nblocks + 1; b++ )
      {
         if( bw_ncontnonkernelvars[b] > 0 )
         {
            /* reduced costs are not supposed to be +inf or -inf */
            tmp_max = bw_cont_redcost[b][bw_ncontnonkernelvars[b] - 1];
            tmp_min = bw_cont_redcost[b][0];
            assert(!(SCIPisInfinity(scip, tmp_max) || SCIPisInfinity(scip, -tmp_max)));
            assert(!(SCIPisInfinity(scip, tmp_min) || SCIPisInfinity(scip, -tmp_min)));
 
            /* compute the nbuckets-th root of (redcostmax - redcostmin + 1.0) from the sorted(!) bw_cont_redcost[b] */
            contbases[b] = (SCIP_Real) pow(tmp_max - tmp_min + 1.0, 1.0/nbuckets);
         }
         else
            /* save -1.0 as placeholder */
            contbases[b] = -1.0;
 
         if( bw_nnonkernelvars[b] > 0 )
         {
            /* reduced costs are not supposed to be +inf or -inf */
            tmp_max = bw_redcost[b][bw_nnonkernelvars[b] - 1];
            tmp_min = bw_redcost[b][0];
            assert(!(SCIPisInfinity(scip, tmp_max) || SCIPisInfinity(scip, -tmp_max)));
            assert(!(SCIPisInfinity(scip, tmp_min) || SCIPisInfinity(scip, -tmp_min)));
 
            /* compute the nbuckets-th root of (redcostmax - redcostmin + 1.0) from the sorted(!) bw_cont_redcost[b] */
            bases[b] = (SCIP_Real) pow(tmp_max - tmp_min + 1.0, 1.0/nbuckets);
         }
         else
            /* save -1.0 as placeholder */
            bases[b] = -1.0;
 
         if( twolevel )
         {
            if( bw_nintnonkernelvars[b] > 0 )
            {
               /* reduced costs are not supposed to be +inf or -inf */
               tmp_max = bw_int_redcost[b][bw_nintnonkernelvars[b] - 1];
               tmp_min = bw_int_redcost[b][0];
               assert(!(SCIPisInfinity(scip, tmp_max) || SCIPisInfinity(scip, -tmp_max)));
               assert(!(SCIPisInfinity(scip, tmp_min) || SCIPisInfinity(scip, -tmp_min)));
 
               intbases[b] = (SCIP_Real) pow(tmp_max - tmp_min + 1.0, 1.0/nbuckets);
            }
            else
               /* save -1.0 as placeholder */
               intbases[b] = -1.0;
         }
      }
   }
 
   /* iteration over all buckets to fill, k = 0 is empty bucket by definition */
   for( k = 1; k < nbuckets + 1; k++ )
   {
      bucket = &(*bucketlist)->buckets[k];
 
      contbucklength = 0;
      bucklength = 0;
      intbucklength = 0;
 
      /* calculate the length of the variable arrays for the current bucket typewise */
      for( b = 0; b < nblocks + 1; b++ )
      {
         if( redcostlogsort )
         {
            /* calculation of the variable array length for each type */
            for( l = 0; l < bw_ncontnonkernelvars[b]; l++ )
            {
               if( isInCurrentLogBucket(scip, contbases[b], bw_cont_redcost[b][l], bw_cont_redcost[b][0], k, nbuckets) )
                  contbucklength++;
            }
 
            for( l = 0; l < bw_nnonkernelvars[b]; l++ )
            {
               if( isInCurrentLogBucket(scip, bases[b], bw_redcost[b][l], bw_redcost[b][0], k, nbuckets) )
                  bucklength++;
            }
 
            if( twolevel )
            {
               for( l = 0; l < bw_nintnonkernelvars[b]; l++ )
               {
                  if( isInCurrentLogBucket(scip, intbases[b], bw_int_redcost[b][l], bw_int_redcost[b][0], k, nbuckets) )
                     intbucklength++;
               }
            }
         }
         else
         {
            /* initialize the start/end indices to split the non-kernel vars typewise and compute the bucket length */
            fromcontvars = (int)SCIPceil(scip, (bw_ncontnonkernelvars[b] / (SCIP_Real)nbuckets) * (k - 1) );
            tocontvars = (int)SCIPceil(scip, (bw_ncontnonkernelvars[b] / (SCIP_Real)nbuckets) * k );
            fromvars = (int)SCIPceil(scip, (bw_nnonkernelvars[b] / (SCIP_Real)nbuckets) * (k - 1) );
            tovars = (int)SCIPceil(scip, (bw_nnonkernelvars[b] / (SCIP_Real)nbuckets) * k );
 
            contbucklength += tocontvars - fromcontvars;
            bucklength += tovars - fromvars;
 
            if( twolevel )
            {
               fromintvars = (int)SCIPceil(scip, (bw_nintnonkernelvars[b] / (SCIP_Real)nbuckets) * (k - 1) );
               tointvars = (int)SCIPceil(scip, (bw_nintnonkernelvars[b] / (SCIP_Real)nbuckets) * k );
 
               intbucklength += tointvars - fromintvars;
            }
         }
      }
 
      /* initialize all buffer arrays for the continuous, binary/integer and (if necessary) integer bucket variables */
      SCIP_CALL( SCIPallocBufferArray(scip, &(bucket->contbucketvars), contbucklength) );
      bucket->ncontbucketvars = contbucklength;
      SCIP_CALL( SCIPallocBufferArray(scip, &(bucket->bucketvars), bucklength) );
      bucket->nbucketvars = bucklength;
      if( twolevel )
      {
         SCIP_CALL( SCIPallocBufferArray(scip, &(bucket->intbucketvars), intbucklength) );
         bucket->nintbucketvars = intbucklength;
      }
 
      /* fill the initialized arrays with the respective variables */
      j = 0;
      n = 0;
      m = 0;
      for( b = 0; b < nblocks + 1; b++ )
      {
         if( redcostlogsort )
         {
            /* assignment of the variables to the respective bucket variable arrays for each type */
            for( l = 0; l < bw_ncontnonkernelvars[b]; l++ )
            {
               if( isInCurrentLogBucket(scip, contbases[b], bw_cont_redcost[b][l], bw_cont_redcost[b][0], k, nbuckets) )
                  bucket->contbucketvars[j++] = bw_contnonkernelvars[b][l];
            }
 
            for( l = 0; l < bw_nnonkernelvars[b]; l++ )
            {
               if( isInCurrentLogBucket(scip, bases[b], bw_redcost[b][l], bw_redcost[b][0], k, nbuckets) )
                  bucket->bucketvars[n++] = bw_nonkernelvars[b][l];
            }
 
            if( twolevel )
            {
               for( l = 0; l < bw_nintnonkernelvars[b]; l++ )
               {
                  if( isInCurrentLogBucket(scip, intbases[b], bw_int_redcost[b][l], bw_int_redcost[b][0], k, nbuckets) )
                     bucket->intbucketvars[m++] = bw_intnonkernelvars[b][l];
               }
            }
         }
         else
         {
            /* calculate again the necessary start and end indices to split the non-kernel variables typewise */
            fromcontvars = (int)SCIPceil(scip, (bw_ncontnonkernelvars[b] / (SCIP_Real)nbuckets) * (k - 1) );
            tocontvars = (int)SCIPceil(scip, (bw_ncontnonkernelvars[b] / (SCIP_Real)nbuckets) * k );
            fromvars = (int)SCIPceil(scip, (bw_nnonkernelvars[b] / (SCIP_Real)nbuckets) * (k - 1) );
            tovars = (int)SCIPceil(scip, (bw_nnonkernelvars[b] / (SCIP_Real)nbuckets) * k );
 
            /* fill the variable arrays */
            for( l = 0; l < tocontvars - fromcontvars; l++ )
               bucket->contbucketvars[j++] = bw_contnonkernelvars[b][fromcontvars + l];
            for( l = 0; l < tovars - fromvars; l++ )
               bucket->bucketvars[n++] = bw_nonkernelvars[b][fromvars + l];
 
            /* apply the procedure above for the integer variables if necessary */
            if( twolevel )
            {
               fromintvars = (int)SCIPceil(scip, (bw_nintnonkernelvars[b] / (SCIP_Real)nbuckets) * (k - 1) );
               tointvars = (int)SCIPceil(scip, (bw_nintnonkernelvars[b] / (SCIP_Real)nbuckets) * k );
 
               for( l = 0; l < tointvars - fromintvars; l++ )
                  bucket->intbucketvars[m++] = bw_intnonkernelvars[b][fromintvars + l];
            }
         }
      }
 
      assert(j == contbucklength);
      assert(n == bucklength);
      if( twolevel )
         assert(m == intbucklength);
   }
 
   if( redcostlogsort )
   {
      SCIPfreeBufferArray(scip, &contbases);
      SCIPfreeBufferArray(scip, &bases);
      if( twolevel )
         SCIPfreeBufferArray(scip, &intbases);
   }
 
   return SCIP_OKAY;
}
 
/** release memory of bucket arrays */
static
SCIP_RETCODE freeBucketArrays(
   SCIP*                 scip,               /**< main SCIP data structure */
   BUCKET*               bucket,             /**< bucket to free the arrays from */
   SCIP_Bool             twolevel            /**< usage of one or two level structure */
   )
{
   if( bucket->contbucketvars != NULL )
      SCIPfreeBufferArray(scip, &bucket->contbucketvars);
   if( bucket->bucketvars != NULL )
      SCIPfreeBufferArray(scip, &bucket->bucketvars);
   if( twolevel && bucket->intbucketvars != NULL )
      SCIPfreeBufferArray(scip, &bucket->intbucketvars);
 
   return SCIP_OKAY;
}
 
/** initialize a bucket */
static
SCIP_RETCODE initBucket(
   BUCKETLIST*           bucketlist          /**< bucketlist structure where the bucket belongs to */
   )
{
   BUCKET* bucket;
 
   assert(bucketlist != NULL);
   assert(bucketlist->scip != NULL);
 
   bucket = &bucketlist->buckets[bucketlist->nbuckets];
 
   bucket->bucketlist = bucketlist;
   bucket->subscip = NULL;
   bucket->contbucketvars = NULL;
   bucket->bucketvars = NULL;
   bucket->intbucketvars = NULL;
   bucket->ncontbucketvars = 0;
   bucket->nbucketvars = 0;
   bucket->nintbucketvars = 0;
   bucket->number = bucketlist->nbuckets;
   bucket->twolevel = FALSE;
   bucket->scip2sub = NULL;
   bucket->sub2scip = NULL;
 
   ++bucketlist->nbuckets;
 
   return SCIP_OKAY;
}
 
/** free bucket structure */
static
SCIP_RETCODE freeBucket(
   SCIP*                 scip,               /**< SCIP data structure */
   BUCKET*               bucket              /**< bucket structure to free */
   )
{
   assert(scip != NULL);
   assert(bucket != NULL);
 
   assert(bucket->subscip != NULL);
 
   /* free variable mappings subscip -> scip and scip -> subscip */
   SCIPfreeBufferArrayNull(scip, &bucket->scip2sub);
   SCIPfreeBufferArrayNull(scip, &bucket->sub2scip);
 
   SCIP_CALL( SCIPfree(&bucket->subscip) );
   bucket->subscip = NULL;
 
   return SCIP_OKAY;
}
 
/** initialize the bucketlist */
static
SCIP_RETCODE initBucketlist(
   SCIP*                 scip,               /**< SCIP data structure */
   BUCKETLIST**          bucketlist,         /**< pointer to bucketlist */
   int                   nbuckets            /**< number of buckets */
   )
{
   char name[SCIP_MAXSTRLEN];
 
   assert(scip != NULL);
   assert(bucketlist != NULL);
 
   SCIP_CALL( SCIPallocBlockMemory(scip, bucketlist) );
   assert(*bucketlist != NULL);
 
   (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "%s", SCIPgetProbName(scip));
 
   SCIPdebugMessage("initialized problem %s\n", name);
 
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &(*bucketlist)->buckets, nbuckets) );
 
   (*bucketlist)->scip = scip;
   (*bucketlist)->nbuckets = 0;
 
   return SCIP_OKAY;
}
 
/** free bucketlist structure */
static
SCIP_RETCODE freeBucketlist(
   BUCKETLIST**          bucketlist,         /**< pointer to bucketlist to free */
   int                   nbuckets            /**< number of buckets to free */
   )
{
   SCIP* scip;
 
   assert(bucketlist != NULL);
   assert(*bucketlist != NULL);
 
   scip = (*bucketlist)->scip;
   assert(scip != NULL);
 
   if( (*bucketlist)->buckets != NULL )
      SCIPfreeBlockMemoryArray(scip, &(*bucketlist)->buckets, nbuckets);
 
   SCIPfreeBlockMemory(scip, bucketlist);
   *bucketlist = NULL;
 
   return SCIP_OKAY;
}
 
/** creates the subscip for each bucket */
static
SCIP_RETCODE bucketCreateSubscip(
   BUCKET*               bucket,             /**< the bucket to create the subscip for */
   SCIP_Bool             usetransprob,       /**< indicating whether the transformed or the original problem is used */
   SCIP_Bool*            success             /**< pointer to store if the creation process was successfull */
   )
{
   BUCKETLIST* bucketlist;
   SCIP* scip;
   SCIP_VAR**  vars;
   SCIP_VAR**  subvars;
   SCIP_VAR*   var;
   SCIP_VAR*   subvar;
   SCIP_HASHMAP* varsmap;
   SCIP_HASHMAP* consmap;
   char probname[SCIP_MAXSTRLEN];
   int i;
   int nvars;
   int nsubvars;
 
   SCIP_CONS** conss;
   SCIP_CONS*  newcons;
 
   assert(bucket != NULL);
   assert(success != NULL);
 
   bucketlist = bucket->bucketlist;
   assert(bucketlist != NULL);
 
   scip = bucketlist->scip;
   assert(scip != NULL);
 
   /* start new creation process */
   SCIP_CALL( SCIPgetVarsData(scip, &vars, &nvars, NULL, NULL, NULL, NULL) );
 
   /* initializing the subproblem */
   SCIP_CALL( SCIPcreate(&bucket->subscip) );
 
   /* create variable hash mapping scip -> subscip */
   SCIP_CALL( SCIPhashmapCreate(&varsmap, SCIPblkmem(scip), nvars) );
 
   (*success) = TRUE;
 
#ifdef SCIP_DEBUG /* we print statistics later, so we need to copy statistics tables */
   SCIP_CALL( SCIPcopyPlugins(scip, bucket->subscip,
         TRUE, FALSE, TRUE, TRUE, TRUE,
         TRUE, TRUE, TRUE, TRUE, TRUE,
         TRUE, TRUE, TRUE, FALSE, TRUE,
         TRUE, TRUE, TRUE, TRUE, TRUE, success) );
#else
   SCIP_CALL( SCIPcopyPlugins(scip, bucket->subscip,
         TRUE, FALSE, TRUE, TRUE, TRUE,
         TRUE, TRUE, TRUE, TRUE, TRUE,
         TRUE, TRUE, TRUE, FALSE, FALSE,
         TRUE, FALSE, FALSE, TRUE, TRUE, success) );
#endif
 
   /* copy parameter settings */
   SCIP_CALL( SCIPcopyParamSettings(scip, bucket->subscip) );
 
   /* adapt limit settings */
   SCIP_CALL( SCIPcopyLimits(scip, bucket->subscip) );
 
   /* create problem in subscip */
   /* get name of the original problem and add "dksbucket" + [bucketnumber] */
   (void) SCIPsnprintf(probname, SCIP_MAXSTRLEN, "%s_dksbucket%d", SCIPgetProbName(scip), bucket->number);
 
   /* from before: avoid recursive calls */
   SCIP_CALL( SCIPsetSubscipsOff(bucket->subscip, TRUE) );
 
   /* copy all variables */
   SCIP_CALL( SCIPcopyProb(scip, bucket->subscip, varsmap, NULL, FALSE, probname) );
   SCIP_CALL( SCIPcopyVars(scip, bucket->subscip, varsmap, NULL, NULL, NULL, 0, TRUE) );
 
   /* copy as many constraints as possible */
   SCIP_CALL( SCIPhashmapCreate(&consmap, SCIPblkmem(scip), SCIPgetNConss(scip)) );
 
   conss = SCIPgetConss(scip);
 
   for( i = 0; i < SCIPgetNConss(scip); ++i )
   {
      /* do not check this if we use the transformed problem */
      if( !usetransprob )
         assert(!SCIPconsIsModifiable(conss[i]));
      /* copy the constraint */
      SCIP_CALL( SCIPgetConsCopy(scip, bucket->subscip, conss[i], &newcons, SCIPconsGetHdlr(conss[i]), varsmap, consmap,
            NULL, SCIPconsIsInitial(conss[i]), SCIPconsIsSeparated(conss[i]), SCIPconsIsEnforced(conss[i]),
            SCIPconsIsChecked(conss[i]), SCIPconsIsPropagated(conss[i]), FALSE, FALSE, SCIPconsIsDynamic(conss[i]),
            SCIPconsIsRemovable(conss[i]), FALSE, FALSE, success) );
 
      /* abort if constraint was not successfully copied */
      if( !(*success) )
      {
         *success = FALSE;
         if( newcons != NULL )
         {
            SCIP_CALL( SCIPreleaseCons(bucket->subscip, &newcons) );
         }
         SCIPhashmapFree(&varsmap);
         SCIPhashmapFree(&consmap);
         return SCIP_OKAY;
      }
 
      if( newcons != NULL )
      {
         SCIP_CALL( SCIPaddCons(bucket->subscip, newcons) );
         SCIP_CALL( SCIPreleaseCons(bucket->subscip, &newcons) );
      }
   }
 
   SCIPhashmapFree(&consmap);
   if( !(*success) )
   {
      SCIPverbMessage(scip, SCIP_VERBLEVEL_FULL, NULL, "In heur_dks: failed to copy some constraints, continuing\n");
      SCIPdebugMsg(scip, "In heur_dks: failed to copy some constraints to subscip, continue anyway\n");
   }
 
   /* create arrays translating scip transformed vars to subscip original vars, and vice versa
    * capture variables in scip and subscip
    * catch global bound change events
    */
 
   SCIP_CALL( SCIPgetVarsData(bucket->subscip, &subvars, &nsubvars, NULL, NULL, NULL, NULL) );
 
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bucket->sub2scip, nsubvars) );
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bucket->scip2sub, nvars) );
 
   /* iteration over varsmap to get the original and corresponding subscip variables*/
   for( i = 0; i < SCIPhashmapGetNEntries(varsmap); i++ )
   {
      SCIP_HASHMAPENTRY* entry;
      entry = SCIPhashmapGetEntry(varsmap, i);
      if( entry != NULL )
      {
         var = (SCIP_VAR*) SCIPhashmapEntryGetOrigin(entry);
         subvar = (SCIP_VAR*) SCIPhashmapEntryGetImage(entry);
         assert(subvar != NULL);
         assert(SCIPvarGetProbindex(subvar) >= 0);
         assert(SCIPvarGetProbindex(subvar) <= nsubvars);
 
         if( SCIPvarIsActive(var) )
         {
            assert(SCIPvarGetProbindex(var) <= nvars);
            assert(bucket->scip2sub[SCIPvarGetProbindex(var)] == NULL);
            bucket->scip2sub[SCIPvarGetProbindex(var)] = subvar;
         }
         assert(bucket->sub2scip[SCIPvarGetProbindex(subvar)] == NULL);
         bucket->sub2scip[SCIPvarGetProbindex(subvar)] = var;
      }
   }
 
#ifdef SCIP_DEBUG
   for( i = 0; i < nsubvars; i++ )
   {
      subvar = SCIPgetVars(bucket->subscip)[i];
      assert(SCIPvarGetProbindex(subvar) == i);
      var = bucket->sub2scip[i];
 
      assert(SCIPisFeasEQ(scip, SCIPvarGetLbGlobal(var), SCIPvarGetLbGlobal(subvar)));
      assert(SCIPisFeasEQ(scip, SCIPvarGetUbGlobal(var), SCIPvarGetUbGlobal(subvar)));
   }
#endif
 
   SCIPhashmapFree(&varsmap);
 
   /* avoid recursive calls */
   SCIP_CALL( SCIPsetSubscipsOff(bucket->subscip, TRUE) );
 
   /* do not abort subproblem on CTRL-C */
   SCIP_CALL( SCIPsetBoolParam(bucket->subscip, "misc/catchctrlc", FALSE) );
 
   /* forbid recursive call of DKS heuristic on subproblems */
   if( SCIPisParamFixed(bucket->subscip, "heuristics/" HEUR_NAME "/freq") )
   {
      SCIPwarningMessage(scip, "unfixing param heuristics/" HEUR_NAME "/freq in DKS to avoid recursive calls\n");
      SCIP_CALL( SCIPunfixParam(bucket->subscip, "heuristics/" HEUR_NAME "/freq") );
   }
   SCIP_CALL( SCIPsetIntParam(bucket->subscip, "heuristics/" HEUR_NAME "/freq", -1) );
 
#ifdef SCIP_DEBUG
   /* for debugging, enable full output */
   SCIP_CALL( SCIPsetIntParam(bucket->subscip, "display/verblevel", 5) );
   SCIP_CALL( SCIPsetIntParam(bucket->subscip, "display/freq", 100000000) );
#else
   /* disable statistic timing inside sub SCIP and output to console */
   SCIP_CALL( SCIPsetIntParam(bucket->subscip, "display/verblevel", 0) );
   SCIP_CALL( SCIPsetBoolParam(bucket->subscip, "timing/statistictiming", FALSE) );
#endif
 
   SCIPdebugMsg(scip, "created subscip of bucket %d\n", bucket->number);
 
   return SCIP_OKAY;
}
 
/** create bucketlist and initialize buckets */
static
SCIP_RETCODE createBucketlistAndBuckets(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Bool             usetransprob,       /**< indication whether to use the transformed problem (or the original) */
   int                   nbuckets,           /**< number of buckets (without kernel only) */
   BUCKETLIST**          bucketlist,         /**< pointer to store bucketlist structure */
   SCIP_Bool*            success             /**< pointer to store if the creation process was successfull */
   )
{
   BUCKET* bucket;
   int b;
 
   bucket = NULL;
   *success = TRUE;
 
   /* init bucketlist data structure with nbucket + 1 because the initial bucket with kernel vars is included */
   SCIP_CALL( initBucketlist(scip, bucketlist, nbuckets + 1) );
   assert((*bucketlist)->buckets != NULL);
 
   /* loop over all buckets and the initial "kernel"bucket */
   for( b = 0; b < nbuckets + 1; b++ )
   {
      SCIP_CALL( initBucket(*bucketlist) );
      assert((*bucketlist)->nbuckets == b + 1);
 
      bucket = &(*bucketlist)->buckets[b];
 
      /* build subscip for bucket */
      SCIP_CALL( bucketCreateSubscip(bucket, usetransprob, success) );
 
      if( !(*success) )
         return SCIP_OKAY;
   }
   assert(nbuckets + 1 == (*bucketlist)->nbuckets);
 
   return SCIP_OKAY;
}
 
/** search variable in kernel and bucket */
static
SCIP_RETCODE searchKernelAndBucket(
   BUCKET*               bucket,             /**< bucket to be solved next */
   SCIP_VAR**            contkernelvars,     /**< continuous variables in the latest kernel */
   int                   ncontkernelvars,    /**< amount of continuous variables in the latest kernel */
   SCIP_VAR**            kernelvars,         /**< variables in the kernel */
   int                   nkernelvars,        /**< amount of variables in the kernel */
   SCIP_VAR**            intkernelvars,      /**< variables in the integer kernel, if 2-level buckets are present */
   int                   nintkernelvars,     /**< amount of variables in the integer kernel */
   SCIP_VAR*             var,                /**< variable to search for in the kernel/buckets */
   SCIP_Bool*            found               /**< is the variable present in the current bucket or the kernel? */
   )
{
   int j;
 
   *found = FALSE;
 
   /* search in the current continuous kernel for the given variable */
   if( SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS )
   {
      for( j = 0; j < ncontkernelvars; j++ )
      {
         if( contkernelvars[j] != NULL && var == contkernelvars[j] )
         {
            *found = TRUE;
            return SCIP_OKAY;
         }
      }
 
      /* search for the current variable in the continuous bucket variables */
      for( j = 0; j < bucket->ncontbucketvars; j++ )
      {
         if( var == bucket->contbucketvars[j] )
         {
            *found = TRUE;
            return SCIP_OKAY;
         }
      }
   }
 
   /* search in the current (binary) kernel for the variable */
   for( j = 0; j < nkernelvars; j++ )
   {
      if( kernelvars[j] != NULL && var == kernelvars[j] )
      {
         *found = TRUE;
         return SCIP_OKAY;
      }
   }
 
   /* if 2-level buckets are used, also search for the current variable in the integer kernel */
   for( j = 0; j < nintkernelvars; j++ )
   {
      if( intkernelvars[j] != NULL && var == intkernelvars[j] )
      {
         *found = TRUE;
         return SCIP_OKAY;
      }
   }
 
   /* search for the current variable in the (binary) bucket variables */
   for( j = 0; j < bucket->nbucketvars; j++ )
   {
      if( var == bucket->bucketvars[j] )
      {
         *found = TRUE;
         return SCIP_OKAY;
      }
   }
 
   /* if 2-level buckets are used, also search for the current variable in the integer bucket variables */
   for( j = 0; j < bucket->nintbucketvars; j++ )
   {
      if( var == bucket->intbucketvars[j] )
      {
         *found = TRUE;
         return SCIP_OKAY;
      }
   }
 
   return SCIP_OKAY;
}
 
/** adjust the kernel variables */
static
SCIP_RETCODE adjustKernelVars(
   SCIP*                 scip,               /**< current scip */
   BUCKET*               bucket,             /**< bucket that was solved last */
   SCIP_VAR***           contkernelvars,     /**< cont. kernelvars to adjust */
   int*                  ncontkernelvars,    /**< amount of cont. kernelvars */
   int                   maxcontkernelsize,  /**< maximal size of the continuous kernel */
   SCIP_VAR***           kernelvars,         /**< kernelvars to adjust */
   int*                  nkernelvars,        /**< amount of kernelvars */
   int                   maxkernelsize,      /**< maximal size of the kernel */
   SCIP_VAR***           intkernelvars,      /**< integer kernelvars to adjust */
   int*                  nintkernelvars,     /**< amount of integer kernelvars */
   int                   maxintkernelsize,   /**< maximal size of the integer kernel */
   SCIP_Bool             twolevel            /**< is a twolevel structure necessary */
   )
{
   SCIP_VAR** contkvars;                     /* temporary storage for the continuous kernel variables */
   SCIP_VAR** kvars;                         /* temporary storage for the (binary/integer) kernel variables */
   SCIP_VAR** intkvars;                      /* temporary storage for the integer kernel variables */
   SCIP_VAR *var;                            /* temporary variable */
   SCIP_Real val;                            /* variable value in solution */
   SCIP_Real lb;                             /* variable lower bound */
   SCIP_SOL* solution;                       /* solution of the current bucket */
   int nnewcontkernelvars;                   /* number of new continuous kernel variables */
   int nnewkernelvars;                       /* number of new (binary/integer) kernel variables */
   int nnewintkernelvars;                    /* number of new integer kernel variables */
   int n;                                    /* temporary variable counter */
 
   /* definition of old kernel arrays to update the actual ones live */
   contkvars = *contkernelvars;
   kvars = *kernelvars;
   intkvars = *intkernelvars;
 
   solution = SCIPgetBestSol(bucket->subscip);
 
   /* deletion of variables from the kernel */
   /* continuous kernelvariables with value equal to zero or their lb get deleted from the kernel */
   /* todo: after x tries, maybe with seperate kernelindexarray */
   nnewintkernelvars = 0;
   nnewcontkernelvars = 0;
   for( n = 0; n < *ncontkernelvars; n++ )
   {
      if( contkvars[n] == NULL )
         continue;
 
      /* get the value of the current variable and its lower bound  */
      if( SCIPvarIsActive(contkvars[n]) )
      {
         assert(SCIPvarGetProbindex(contkvars[n]) <= SCIPgetNVars(scip));
         var = bucket->scip2sub[SCIPvarGetProbindex(contkvars[n])];
 
         if( var != NULL )
            val = SCIPgetSolVal(bucket->subscip, solution, var);
         else
            continue;
      }
      else
         continue;
 
      lb = SCIPvarGetLbLocal(contkvars[n]);
 
      /* if deviating from lb and zero, re-add into current kernel vars */
      if( (!SCIPisEQ(scip, val, 0.0) && !SCIPisEQ(scip, val, lb)) )
         (*contkernelvars)[nnewcontkernelvars++] = contkvars[n];
      /* otherwise, delete it */
      else
         contkvars[n] = NULL;
   }
 
   /* dependent on #levels, check the solution value of the bin/int value to be unequal to 0 and/or its lb */
   nnewkernelvars = 0;
   for( n = 0; n < *nkernelvars; n++ )
   {
      if( kvars[n] == NULL )
         continue;
 
      /* get the value of the current kernel variable in the solution and its lower bound */
      if( SCIPvarIsActive(kvars[n]) )
      {
         assert(SCIPvarGetProbindex(kvars[n]) <= SCIPgetNVars(scip));
         var = bucket->scip2sub[SCIPvarGetProbindex(kvars[n])];
         if( var != NULL )
            val = SCIPgetSolVal(bucket->subscip, solution, var);
         else
            continue;
      }
      else
         continue;
 
      lb = SCIPvarGetLbLocal(kvars[n]);
 
      /* if two-level structure is required, the binary case occurs and only deviation to 0 has to be checked */
      if( (twolevel && !SCIPisEQ(scip, val, 0.0)) )
         (*kernelvars)[nnewkernelvars++] = kvars[n];
      /* if one-level case, the variable has to deviate from 0 and its lb */
      else if( (!twolevel && !SCIPisEQ(scip, val, 0.0) && !SCIPisEQ(scip, val, lb)) )
         (*kernelvars)[nnewkernelvars++] = kvars[n];
      /* otherwise delete the variable from its current position in the kernel */
      else
         kvars[n] = NULL;
   }
 
   /* if necessary check the relevance of pure integer variables in the current kernel */
   if( twolevel )
   {
      nnewintkernelvars = 0;
 
      for( n = 0; n < *nintkernelvars; n++ )
      {
         if( intkvars[n] == NULL )
            continue;
 
         /* get the value of the current variable in the solution and its lower bound */
         if( SCIPvarIsActive(intkvars[n]) )
         {
            assert(SCIPvarGetProbindex(intkvars[n]) <= SCIPgetNVars(scip));
            var = bucket->scip2sub[SCIPvarGetProbindex(intkvars[n])];
 
            if( var != NULL )
               val = SCIPgetSolVal(bucket->subscip, solution, var);
            else
               continue;
         }
         else
            continue;
 
         lb = SCIPvarGetLbLocal(intkvars[n]);
 
         /* if variable value is unequal to 0 and its lower bound, it is re-added into the kernel */
         if( (!SCIPisEQ(scip, val, 0.0) && !SCIPisEQ(scip, val, lb)) )
            (*intkernelvars)[nnewintkernelvars++] = intkvars[n];
         else
            intkvars[n] = NULL;
      }
   }
 
   /* addition of new variables from the bucket to the kernel */
 
   /* add continuous bucket variables with suitable values to the kernel */
   for( n = 0; n < bucket->ncontbucketvars; n++ )
   {
      if( bucket->contbucketvars[n] == NULL )
         continue;
 
      if( SCIPvarIsActive(bucket->contbucketvars[n]) )
      {
         assert(SCIPvarGetProbindex(bucket->contbucketvars[n]) <= SCIPgetNVars(scip));
         var = bucket->scip2sub[SCIPvarGetProbindex(bucket->contbucketvars[n])];
 
         if( var != NULL )
            val = SCIPgetSolVal(bucket->subscip, solution, var);
         else
            continue;
      }
      else
         continue;
 
      lb = SCIPvarGetLbLocal(bucket->contbucketvars[n]);
 
      /* if the solution value of the bucket var != zero and != its lb, add it to the cont kernel vars */
      if( !SCIPisEQ(scip, val, 0.0) && !SCIPisEQ(scip, val, lb) )
      {
         if( SCIPisGT(scip, (SCIP_Real)nnewcontkernelvars, (SCIP_Real)maxcontkernelsize) )
            break;
         else
            (*contkernelvars)[nnewcontkernelvars++] = bucket->contbucketvars[n];
      }
   }
 
   /* the size of the continuous kernel might be different -> change it */
   *ncontkernelvars = nnewcontkernelvars;
 
   /* add binary/integer bucketvariables with suitable values to the kernel */
   for( n = 0; n < bucket->nbucketvars; n++ )
   {
      if( bucket->bucketvars[n] == NULL )
         continue;
 
      if( SCIPvarIsActive(bucket->bucketvars[n]) )
      {
         assert(SCIPvarGetProbindex(bucket->bucketvars[n]) <= SCIPgetNVars(scip));
         var = bucket->scip2sub[SCIPvarGetProbindex(bucket->bucketvars[n])];
         if( var != NULL )
            val = SCIPgetSolVal(bucket->subscip, solution, var);
         else
            continue;
      }
      else
         continue;
 
      lb = SCIPvarGetLbLocal(bucket->bucketvars[n]);
 
      /* if bucket var != zero and != its lower bound (in epsilon), try adding it to the kernel vars */
      if( twolevel && !SCIPisEQ(scip, val, 0.0) )
      {
         if( SCIPisGT(scip, (SCIP_Real)nnewkernelvars, (SCIP_Real)maxkernelsize) )
            break;
         else
            (*kernelvars)[nnewkernelvars++] = bucket->bucketvars[n];
      }
      /* if one-level case, the variable has to deviate from 0 and its lb */
      else if( !twolevel && !SCIPisEQ(scip, val, 0.0) && !SCIPisEQ(scip, val, lb) )
      {
         if( SCIPisGT(scip, (SCIP_Real)nnewkernelvars, (SCIP_Real)maxkernelsize) )
            break; /* @potential todo: if kernel is "full", find a suitable variable to delete or extend kernel */
         else
            (*kernelvars)[nnewkernelvars++] = bucket->bucketvars[n];
      }
   }
 
   /* the size of the kernel might be different, so change it */
   *nkernelvars = nnewkernelvars;
 
   /* if necessary, add integer bucket variables with suitable values to the integer kernel */
   if( twolevel )
   {
      for( n = 0; n < bucket->nintbucketvars; n++ )
      {
         if( bucket->intbucketvars[n] == NULL )
            continue;
 
         if( SCIPvarIsActive(bucket->intbucketvars[n]) )
         {
            assert(SCIPvarGetProbindex(bucket->intbucketvars[n]) <= SCIPgetNVars(scip));
            var = bucket->scip2sub[SCIPvarGetProbindex(bucket->intbucketvars[n])];
            if( var != NULL )
               val = SCIPgetSolVal(bucket->subscip, solution, var);
            else
               continue;
         }
         else
            continue;
 
         lb = SCIPvarGetLbLocal(bucket->intbucketvars[n]);
 
         /* if the bucket variable's value is unequal to zero and its lb, try adding it to the integer kernel */
         if( !SCIPisEQ(scip, val, 0.0) && !SCIPisEQ(scip, val, lb) )
         {
            if( SCIPisGT(scip, (SCIP_Real)nnewintkernelvars, (SCIP_Real)maxintkernelsize) )
               break;
            else
               (*intkernelvars)[nnewintkernelvars++] = bucket->intbucketvars[n];
         }
      }
      /* if the size of the kernel is different, change it */
      *nintkernelvars = nnewintkernelvars;
   }
 
   return SCIP_OKAY;
}
 
/** add usuage constraint */
static
SCIP_RETCODE addUseConstraint(
   BUCKET*               bucket              /**< current bucket to look at */
   )
{
   SCIP_CONS* constraint;
   SCIP_VAR** subvars;
   SCIP_VAR *var;
   char consname[SCIP_MAXSTRLEN];
   SCIP_Real* coeffs;
   SCIP_Real rhs;
   SCIP_Real lb;
   int n;
   int k;
 
   /* add an array to store the binary and integer variables of the constraint to add separatly */
   SCIP_CALL( SCIPallocBufferArray(bucket->subscip, &subvars, bucket->nbucketvars + bucket->nintbucketvars) );
 
   /* add an array for the coefficients of the binary and integer variables in the constraint */
   SCIP_CALL( SCIPallocBufferArray(bucket->subscip, &coeffs, bucket->nbucketvars + bucket->nintbucketvars) );
 
   /* for all (binary/integer) variables in the current bucket add the variables to the subvars and add coeff -1 */
   k = 0;
   rhs = -1.0;
   for( n = 0; n < bucket->nbucketvars ; n++ )
   {
      if( bucket->bucketvars[n] == NULL )
         continue;
      if( SCIPvarIsActive(bucket->bucketvars[n]) )
         var = bucket->scip2sub[SCIPvarGetProbindex(bucket->bucketvars[n])];
      else
         var = NULL;
 
      if( var != NULL )
      {
         lb = SCIPvarGetLbLocal(bucket->bucketvars[n]);
 
         /* skip variables with infinite lower bound, since subtraction is not reasonable */
         /**@todo optionally take the upper bound if finite and add with coefficient +1 to bound away from the ub */
         if( SCIPisInfinity(bucket->subscip, -lb) )
            continue;
 
         subvars[k] = var;
         coeffs[k++] = -1.0; /* constraint: (sum of x_i >= 1)   iff   (-1 * sum of x_1 <= -1) */
 
         /* if the variable has a positive lower bound, it is substracted from the rhs of the constraint */
         rhs -= lb;
      }
   }
 
   for( n = 0; n < bucket->nintbucketvars; n++ )
   {
      if( bucket->intbucketvars[n] == NULL )
         continue;
      if( SCIPvarIsActive(bucket->intbucketvars[n]) )
         var = bucket->scip2sub[SCIPvarGetProbindex(bucket->intbucketvars[n])];
      else
         var = NULL;
 
      if( var != NULL )
      {
         lb = SCIPvarGetLbLocal(bucket->intbucketvars[n]);
 
         /* skip variables with infinite lower bound, since subtraction is not reasonable */
         /**@todo optionally take the upper bound if finite and add with coefficient +1 to bound away from the ub */
         if( SCIPisInfinity(bucket->subscip, -lb) )
            continue;
 
         subvars[k] = var;
         coeffs[k++] = -1.0;
 
         /* if the integer variable has a positive lower bound, it is added to the rhs of the new constraint */
         rhs -= lb;
      }
   }
 
   (void)SCIPsnprintf(consname, SCIP_MAXSTRLEN, "useconstraint_bucket_%d", bucket->number);
 
   /* add the constraint: (-1 * sum of bucket variables <= - sum of lbs - 1) s.t. at least 1 of these vars is nonzero */
   SCIP_CALL( SCIPcreateConsBasicLinear(bucket->subscip, &constraint, consname, k, subvars, coeffs, -SCIPinfinity(bucket->subscip), rhs) );
   SCIP_CALL( SCIPaddCons(bucket->subscip, constraint) );
   SCIP_CALL( SCIPreleaseCons(bucket->subscip, &constraint) );
 
   /* free the arrays */
   if( subvars != NULL )
      SCIPfreeBufferArray(bucket->subscip, &subvars);
 
   if( coeffs != NULL )
      SCIPfreeBufferArray(bucket->subscip, &coeffs);
 
   return SCIP_OKAY;
}
 
/*
 * Callback methods of primal heuristic
 */
 
/** copy method for primal heuristic plugins (called when SCIP copies plugins) */
static
SCIP_DECL_HEURCOPY(heurCopyDKS)
{  /*lint --e{715}*/
   assert(scip != NULL);
   assert(heur != NULL);
   assert(strcmp(SCIPheurGetName(heur), HEUR_NAME) == 0);
 
   /* call inclusion method of primal heuristic */
   SCIP_CALL( SCIPincludeHeurDKS(scip) );
 
   return SCIP_OKAY;
}
 
 
/** destructor of primal heuristic to free user data (called when SCIP is exiting) */
static
SCIP_DECL_HEURFREE(heurFreeDKS)
{  /*lint --e{715}*/
   SCIP_HEURDATA* heurdata;
 
   assert(heur != NULL);
   assert(scip != NULL);
 
   heurdata = SCIPheurGetData(heur);
   assert(heurdata != NULL);
 
   SCIPfreeBlockMemory(scip, &heurdata);
   SCIPheurSetData(heur, NULL);
 
   return SCIP_OKAY;
}
 
/** execution method of primal heuristic */
static
SCIP_DECL_HEUREXEC(heurExecDKS)
{  /*lint --e{715}*/
   SCIP_HEURDATA* heurdata;
   SCIP_DECOMP** alldecomps;
   SCIP_DECOMP* decomp = NULL;
   SCIP_HASHMAP* lbvarmap = NULL;            /* variable map connecting transformed vars to their original lower bd */
   SCIP_CONSHDLR* conshdlr;                  /* constraint handler to check for indicator constraints */
   SCIP_VAR*** bw_contkernelvars = NULL;
   SCIP_VAR*** bw_contnonkernelvars = NULL;
   SCIP_VAR*** bw_kernelvars = NULL;
   SCIP_VAR*** bw_nonkernelvars = NULL;
   SCIP_VAR*** bw_intkernelvars = NULL;
   SCIP_VAR*** bw_intnonkernelvars = NULL;
   SCIP_VAR** vars = NULL;
   SCIP_VAR** contkernelvars = NULL;
   SCIP_VAR** contnonkernelvars = NULL;
   SCIP_VAR** kernelvars = NULL;             /* just the bin kernel vars if problem includes bin AND int vars */
   SCIP_VAR** nonkernelvars = NULL;          /* just the bin non kernel vars if problem includes bin AND int vars */
   SCIP_VAR** intkernelvars = NULL;          /* used if problem includes binary AND integer variables */
   SCIP_VAR** intnonkernelvars = NULL;       /* used if problem includes binary AND integer variables */
   SCIP_VAR** binintvars = NULL;
   SCIP_CONS** conss = NULL;
   SCIP_CONS** bucketconss = NULL;
   SCIP_Real gapfactor;
   SCIP_Real maxcontkernelsize;
   SCIP_Real maxcontnonkernelsize;
   SCIP_Real maxkernelsize;
   SCIP_Real maxnonkernelsize;
   SCIP_Real maxintkernelsize;               /* used if problem includes binary AND integer variables */
   SCIP_Real maxintnonkernelsize;
   SCIP_Real memory;
   SCIP_Real bestlocval;
   SCIP_Real mipgap;
   SCIP_Real linkscore;
   SCIP_Real** bw_cont_redcost = NULL;
   SCIP_Real** bw_redcost = NULL;
   SCIP_Real** bw_int_redcost = NULL;
   SCIP_STATUS status;
   SCIP_Bool success;
   SCIP_Bool twolevel;                          /* clarifying if two level buckets are used */
   SCIP_Bool usebestsol;
   SCIP_SOL* bestcurrsol = NULL;
   BUCKETLIST* bucketlist = NULL;
   BUCKET* bucket;
   int* varlabels = NULL;
   int* conslabels = NULL;
   int* block2index = NULL;
   int* blocklabels = NULL;
   int* bw_ncontkernelvars = NULL;
   int* bw_ncontnonkernelvars = NULL;
   int* bw_nkernelvars = NULL;
   int* bw_nnonkernelvars = NULL;
   int* bw_nintkernelvars = NULL;
   int* bw_nintnonkernelvars = NULL;
   int* bw_contkernelcount = NULL;
   int* bw_contnonkernelcount = NULL;
   int* bw_kernelcount = NULL;
   int* bw_nonkernelcount = NULL;
   int* bw_intkernelcount = NULL;
   int* bw_intnonkernelcount = NULL;
   SCIP_Longint nodesleft;
   SCIP_Longint nnodes;
   int gapcall;
   int blklbl_offset;
   int nblocks;
   int ndecomps;
   int nvars;
   int ncontkernelvars;
   int ncontnonkernelvars;
   int nkernelvars;
   int nnonkernelvars;
   int nintkernelvars;
   int nintnonkernelvars;
   int nbinvars;
   int nintvars;
   int nbinintvars;
   int nbuckets;
   int nconss;
   int nbestbucket;
   int nusedratios;
   int nblocklabels;
   int iters;
   int b;
   int i;
   int j;
   int k;
   int l;
   int m;
   int n;
 
   assert(scip != NULL);
   assert(heur != NULL);
   assert(result != NULL);
 
   heurdata = SCIPheurGetData(heur);
   assert(heurdata != NULL);
 
   *result = SCIP_DIDNOTRUN;
 
   bestlocval = SCIPinfinity(scip);
   twolevel = FALSE;
   success = TRUE;
 
   gapfactor = 1.0;
   gapcall = 0;
   blklbl_offset = 0;
   ndecomps = 0;
   ncontkernelvars = 0;
   ncontnonkernelvars = 0;
   nkernelvars = 0;
   nnonkernelvars = 0;
   nintkernelvars = 0;
   nintnonkernelvars = 0;
   nbestbucket = -1;
   iters = 0;
   nblocklabels = 0;
 
#ifdef DKS_WRITE_PROBLEMS
   SCIP_CALL( SCIPwriteOrigProblem(scip, "orig_problem.lp", NULL, FALSE) );
   SCIP_CALL( SCIPwriteTransProblem(scip, "trans_problem.lp", NULL, FALSE) );
#endif
 
   /* exit DKS whenever indicator constraints are present as they can not handle fixed variables */
   conshdlr  = SCIPfindConshdlr(scip, "indicator");
   if( conshdlr != NULL && SCIPconshdlrGetNConss(conshdlr) > 0 )
      return SCIP_OKAY;
 
   /* exit DKS whenever there is not even an LP solution */
   if( SCIPgetLPSolstat(scip) != SCIP_LPSOLSTAT_OPTIMAL )
      return SCIP_OKAY;
 
   /* do not run heuristic if it was not successful in previous calls */
   if( heurdata->uselesscall )
      return SCIP_OKAY;
 
   heurdata->ncalls++;
 
   /* extract variables, constraints and number of constraints */
   if( heurdata->usetransprob )
   {
      SCIP_VAR* tempvar = NULL;     /* the transformed variable to each original variable */
 
      /* Extract the decompositions of the transformed problem */
      SCIPgetDecomps(scip, &alldecomps, &ndecomps, FALSE);
 
      /* get all transformed binary, integer, and continuous variables */
      vars = SCIPgetVars(scip);
      nvars = SCIPgetNVars(scip);
      nbinvars = SCIPgetNBinVars(scip) + SCIPgetNBinImplVars(scip);
      nintvars = SCIPgetNIntVars(scip) + SCIPgetNIntImplVars(scip);
 
      /* create and initialize the hashmap for the original lower bounds */
      SCIP_CALL( SCIPhashmapCreate(&lbvarmap, SCIPblkmem(scip), nvars) );
      for( i = 0; i < nvars; i++ )
      {
         SCIP_Real scalar;
         SCIP_Real constant;
         tempvar = vars[i];
 
         SCIP_CALL( SCIPvarGetOrigvarSum(&tempvar, &scalar, &constant) );
 
         if( tempvar != NULL )
            SCIP_CALL( SCIPhashmapSetImageReal(lbvarmap, vars[i], SCIPvarGetLbOriginal(tempvar)) );
      }
 
      /* initialize the constraints of the transformed problem */
      nconss = SCIPgetNConss(scip);
      conss = SCIPgetConss(scip);
   }
   else
   {
      /* extract the decompositions of the original problem */
      SCIPgetDecomps(scip, &alldecomps, &ndecomps, TRUE);
 
      /* get all original binary, integer, and continuous variables */
      vars = SCIPgetOrigVars(scip);
      nvars = SCIPgetNOrigVars(scip);
      nbinvars = SCIPgetNOrigBinVars(scip) + SCIPgetNOrigBinImplVars(scip);
      nintvars = SCIPgetNOrigIntVars(scip) + SCIPgetNOrigIntImplVars(scip);
 
      /* it is necessary to take the original constraints here, otherwise they can not be used later on */
      nconss = SCIPgetNOrigConss(scip);
      conss = SCIPgetOrigConss(scip);
   }
 
   nbinintvars = nbinvars + nintvars;
 
   if( ndecomps > 0 && heurdata->usedecomp )
   {
      /* take the first decomposition */
      decomp = alldecomps[0];
      SCIPdebugMsg(scip, "First original decomposition is selected\n");
      assert(decomp != NULL);
 
      nblocks = SCIPdecompGetNBlocks(decomp);
   }
   else
   {
      SCIPdebugMsg(scip, "No decompositions available or wanted, going ahead without decomp\n");
      ndecomps = 0;           /* set to 0 for later unnecessary ifs */
      nblocks = 0;            /* 0 means no decomp in use */
   }
 
   /* if problem has no constraints or no variables, terminate */
   if( nvars == 0 || nconss == 0 )
   {
      SCIPdebugMsg(scip, "problem has no constraints or variables\n");
      goto TERMINATE;
   }
 
   /* verify if the heuristic should be used only for problems with binary and no continuous variables */
   if( heurdata->runbinprobsonly )
   {
      if( nbinvars == 0 || nbinintvars < nvars )
      {
         SCIPdebugMsg(scip, "do not run dks if continuous variables or only integer variables are present\n");
         goto TERMINATE;
      }
   }
 
   /* estimate required memory and terminate if not enough memory is available */
   SCIP_CALL( SCIPgetRealParam(scip, "limits/memory", &memory) );
   if( (SCIPgetMemUsed(scip) + SCIPgetMemExternEstim(scip)) / 1048576.0 >= memory )
   {
      SCIPdebugMsg(scip, "The estimated memory usage is too large.\n");
      goto TERMINATE;
   }
 
   SCIP_CALL( SCIPallocBufferArray(scip, &varlabels, nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &conslabels, nconss) );
 
   if( ndecomps > 0 && heurdata->usedecomp )
   {
      /*  extract the varlabels to identify linking variables */
      SCIPdecompGetVarsLabels(decomp, vars, varlabels, nvars);
      SCIPdecompGetConsLabels(decomp, conss, conslabels, nconss);
 
      /* prepare the distinct finding of blocklabels */
      SCIP_CALL( SCIPallocBufferArray(scip, &blocklabels, nblocks) );
 
      /* check if linking score of the instance is sufficiently low to get called */
      SCIP_CALL( getLinkingScoreAndBlocklabels(blocklabels, varlabels, conslabels, &linkscore, &nblocklabels,
            nblocks, nvars, nconss) );
      if( linkscore > heurdata->maxlinkscore )
      {
         SCIPdebugMsg(scip, "decomposition has not required linking score\n");
         goto TERMINATE;
      }
 
      if( nblocklabels > 0 )
      {
         SCIPsortInt(blocklabels, nblocklabels);
 
         /* if it exists the blocklabel 0, we have to add an offset of 1 to store the linking variables at 0 */
         if( blocklabels[0] == 0 )
            blklbl_offset = 1;
 
         /* fill the mapping of blocklabels to blockindices */
         SCIP_CALL( SCIPallocClearBlockMemoryArray(scip, &block2index, blocklabels[nblocklabels - 1] + 1 + blklbl_offset) );
      }
      else
      {
         assert(nblocks == 0);
         SCIP_CALL( SCIPallocClearBlockMemoryArray(scip, &block2index, 1) );
      }
 
      block2index[0] = 0;     /* SCIP_DECOMP_LINKVAR = -1, but are saved at index 0 */
      for( b = 0; b < nblocklabels; b++ )
         block2index[blocklabels[b] + blklbl_offset] = b + 1;
   }
   else
   {
      /* initialize dummy varlabels to avoid further distinctions in the following code*/
      int v;
 
      for( v = 0; v < nvars; v++ )
         varlabels[v] = 0;
 
      /* fill the mapping of blocklabels 0 to blockindices 0; nblocks = 0 in this case */
      assert(nblocks == 0);
      SCIP_CALL( SCIPallocClearBlockMemoryArray(scip, &block2index, 1) );
      block2index[0] = 0;
   }
 
   /* if necessary store the current best solution for later use */
   usebestsol = heurdata->usebestsol;
   if( heurdata->usebestsol )
   {
      if( SCIPgetNSols(scip) > 1 )
         bestcurrsol = SCIPgetBestSol(scip);
      else
         usebestsol = FALSE;
   }
 
   /* initialize a kernel variable counter and a non kernel variable counter for each block + linking block (="+ 1") */
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_ncontkernelvars, nblocks + 1) );
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_ncontnonkernelvars, nblocks + 1) );
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_nkernelvars, nblocks + 1) );
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_nnonkernelvars, nblocks + 1) );
 
   /* if there are either integer variables or binary variables only, just consider these */
   if( nbinvars == 0 || nintvars == 0 || !heurdata->usetwolevel )
   {
      SCIP_CALL( countKernelVariables(scip, vars, bestcurrsol, lbvarmap,
            twolevel, usebestsol, heurdata->usetransprob, heurdata->translbkernel,
            bw_ncontkernelvars, bw_ncontnonkernelvars, bw_nkernelvars, bw_nnonkernelvars, NULL, NULL,
            &ncontkernelvars, &ncontnonkernelvars, &nkernelvars, &nnonkernelvars, NULL, NULL,
            block2index, varlabels, blklbl_offset, nvars) );
 
      SCIPdebugMsg(scip, "%d initial kernel variables\n", nkernelvars);
 
      /* if every variable is zero or its lower bound in the lp solution, terminate */
      if( nkernelvars == 0 )
      {
         SCIPdebugMsg(scip, "No suitable variables for dks found. Leaving heuristic. \n");
         goto TERMINATE;
      }
      else if( nkernelvars > nnonkernelvars )
         /* @possible todo: if kernel vars >> nonkernel vars or >x% of all integer/binary variables => adjust */
         SCIPdebugMsg(scip, "There are more kernel variables than not in the kernel\n");
   }
   else
   {
      SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_nintkernelvars, nblocks + 1) );
      SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_nintnonkernelvars, nblocks + 1) );
 
      /* assumption before kernel variable count: we use 2-level buckets */
      twolevel = TRUE;
 
      SCIP_CALL( countKernelVariables(scip, vars, bestcurrsol, lbvarmap,
            twolevel, usebestsol, heurdata->usetransprob, heurdata->translbkernel,
            bw_ncontkernelvars, bw_ncontnonkernelvars, bw_nkernelvars, bw_nnonkernelvars, bw_nintkernelvars,
            bw_nintnonkernelvars, &ncontkernelvars, &ncontnonkernelvars, &nkernelvars, &nnonkernelvars,
            &nintkernelvars, &nintnonkernelvars, block2index, varlabels, blklbl_offset, nvars) );
 
      SCIPdebugMsg(scip, "%d initial bin kernel vars\n%d initial int kernel vars\n", nkernelvars, nintkernelvars);
 
      if( nkernelvars == 0 )
      {
         if( nintkernelvars == 0 )
         {
            SCIPdebugMsg(scip, "No suitable variables for the construction of a kernel. Leaving heuristic. \n");
            goto TERMINATE; /* @possible todo: if continuous variables are also considered, possibly continue here */
         }
         else
         {
            /* bin vars are all zero in lp sol -> 1-level buckets with int first and bin vars in kernel afterwards */
            nkernelvars = nintkernelvars;
            nnonkernelvars += nintnonkernelvars;
            nintkernelvars = 0;
            nintnonkernelvars = 0;
 
            /* update the blockwise figures describing kernel sizes */
            for( b = 0; b < nblocks + 1; b++ )
            {
               bw_nkernelvars[b] = bw_nintkernelvars[b];
               bw_nnonkernelvars[b] += bw_nintnonkernelvars[b];
               bw_nintnonkernelvars[b] = 0;
            }
 
            twolevel = FALSE;
         }
      }
      else if( nintkernelvars == 0 )
      {
         /* int vars are all zero in lp sol -> 1-level buckets with bin first and int vars in the kernel afterwards */
         nnonkernelvars += nintnonkernelvars;
         nintnonkernelvars = 0;
 
         /* update the blockwise figures describing kernel sizes */
         for( b = 0; b < nblocks + 1; b++ )
         {
            bw_nnonkernelvars[b] += bw_nintnonkernelvars[b];
            bw_nintnonkernelvars[b] = 0;
         }
 
         twolevel = FALSE;
      }
      else if( nkernelvars > nnonkernelvars || nintkernelvars > nintnonkernelvars )
         /* @potential todo: if kernel vars >> nonkernel vars or >x% of all integer/binary variables => adjust */
         SCIPdebugMsg(scip, "There are more kernel variables than not in the kernel\n");
   }
 
   /* kernel initialization for all blocks + the linking block (= "+ 1") */
   SCIP_CALL( SCIPallocBufferArray(scip, &bw_contkernelvars, nblocks + 1) );
   SCIP_CALL( SCIPallocBufferArray(scip, &bw_contnonkernelvars, nblocks + 1) );
   SCIP_CALL( SCIPallocBufferArray(scip, &bw_kernelvars, nblocks + 1) );
   SCIP_CALL( SCIPallocBufferArray(scip, &bw_nonkernelvars, nblocks + 1) );
 
   if( twolevel )
   {
      SCIP_CALL( SCIPallocBufferArray(scip, &bw_intkernelvars, nblocks + 1 ) );
      SCIP_CALL( SCIPallocBufferArray(scip, &bw_intnonkernelvars, nblocks + 1) );
   }
 
   /* initialize kernel and non kernel variables for each block */
   for( b = 0; b < nblocks + 1; b++ )
   {
      int contblocksize = bw_ncontkernelvars[b] + bw_ncontnonkernelvars[b];
      int blocksize = bw_nkernelvars[b] + bw_nnonkernelvars[b];
 
      SCIP_CALL( SCIPallocBufferArray(scip, &(bw_contkernelvars[b]), contblocksize) );
      SCIP_CALL( SCIPallocBufferArray(scip, &(bw_contnonkernelvars[b]), contblocksize) );
      SCIP_CALL( SCIPallocBufferArray(scip, &(bw_kernelvars[b]), blocksize) );
      SCIP_CALL( SCIPallocBufferArray(scip, &(bw_nonkernelvars[b]), blocksize) );
 
      if( twolevel )
      {
         int intblocksize;
 
         assert(bw_nintkernelvars != NULL);
         assert(bw_nintnonkernelvars != NULL);
 
         intblocksize = bw_nintkernelvars[b] + bw_nintnonkernelvars[b];
 
         SCIP_CALL( SCIPallocBufferArray(scip, &(bw_intkernelvars[b]), intblocksize) );
         SCIP_CALL( SCIPallocBufferArray(scip, &(bw_intnonkernelvars[b]), intblocksize) );
      }
   }
 
   if( (int)SCIPfloor(scip, heurdata->kernelsizefactor * ncontkernelvars) < (ncontkernelvars + ncontnonkernelvars) )
      maxcontkernelsize = (int)SCIPfloor(scip, heurdata->kernelsizefactor * ncontkernelvars);
   else
      maxcontkernelsize = ncontkernelvars + ncontnonkernelvars;
 
   if( (int)SCIPfloor(scip, heurdata->kernelsizefactor * ncontnonkernelvars) < (ncontkernelvars + ncontnonkernelvars) )
      maxcontnonkernelsize = (int)SCIPfloor(scip, heurdata->kernelsizefactor * ncontnonkernelvars);
   else
      maxcontnonkernelsize = ncontkernelvars + ncontnonkernelvars;
 
   if( (int)SCIPfloor(scip, heurdata->kernelsizefactor * nkernelvars) < (nkernelvars + nnonkernelvars) )
      maxkernelsize = (int)SCIPfloor(scip, heurdata->kernelsizefactor * nkernelvars);
   else
      maxkernelsize = nkernelvars + nnonkernelvars;
 
   if( (int)SCIPfloor(scip, heurdata->kernelsizefactor * nnonkernelvars) <  (nkernelvars + nnonkernelvars) )
     maxnonkernelsize = (int)SCIPfloor(scip, heurdata->kernelsizefactor * nnonkernelvars);
   else
     maxnonkernelsize = nkernelvars + nnonkernelvars;
 
   /* initialize the kernel and non kernel variable arrays (just binary (non/)kernel variables if 2-level buckets) */
   SCIP_CALL( SCIPallocBufferArray(scip, &contkernelvars, maxcontkernelsize) );
   SCIP_CALL( SCIPallocBufferArray(scip, &contnonkernelvars, maxcontnonkernelsize) );
   SCIP_CALL( SCIPallocBufferArray(scip, &kernelvars, maxkernelsize) );
   SCIP_CALL( SCIPallocBufferArray(scip, &nonkernelvars, maxnonkernelsize) );
 
   /* include all binary AND integer variables as a separate array */
   SCIP_CALL( SCIPallocBufferArray(scip, &binintvars, nbinintvars) );
 
   /* extract (potential) init kernel vars (value > 0) and not kernel vars for all blocks + the linking one (= "+ 1") */
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_contkernelcount, nblocks + 1) );
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_contnonkernelcount, nblocks + 1) );
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_kernelcount, nblocks + 1) );
   SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_nonkernelcount, nblocks + 1) );
 
   maxintkernelsize = 0;
 
   /* 2-level buckets are necessary */
   if( twolevel )
   {
      /* additionally determine maximal integer kernel size */
      if( (int)SCIPfloor(scip, heurdata->kernelsizefactor * nintkernelvars) < (nintkernelvars + nintnonkernelvars) )
         maxintkernelsize = (int)SCIPfloor(scip, heurdata->kernelsizefactor * nintkernelvars);
      else
         maxintkernelsize = nintkernelvars + nintnonkernelvars;
 
      if( (int)SCIPfloor(scip, heurdata->kernelsizefactor * nintnonkernelvars) < (nintkernelvars + nintnonkernelvars) )
         maxintnonkernelsize = (int)SCIPfloor(scip, heurdata->kernelsizefactor * nintnonkernelvars);
      else
         maxintnonkernelsize = nintkernelvars + nintnonkernelvars;
 
      /* additionally initialize the integer kernel and the non integer kernel variable arrays */
      SCIP_CALL( SCIPallocBufferArray(scip, &intkernelvars, maxintkernelsize) );
      SCIP_CALL( SCIPallocBufferArray(scip, &intnonkernelvars, maxintnonkernelsize) );
 
      /* allocate memory for counting the pure integer variables for all blocks + the linking block (= "+ 1") */
      SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_intkernelcount, nblocks + 1) );
      SCIP_CALL( SCIPallocClearBufferArray(scip, &bw_intnonkernelcount, nblocks + 1) );
 
      /* filling of the kernels with the variables */
      SCIP_CALL( fillKernels(scip, vars, binintvars,
            bw_contkernelvars, bw_contnonkernelvars, bw_kernelvars, bw_nonkernelvars,
            bw_intkernelvars, bw_intnonkernelvars, bestcurrsol, lbvarmap, twolevel, usebestsol,
            heurdata->usetransprob, heurdata->translbkernel, bw_contkernelcount,
            bw_contnonkernelcount, bw_kernelcount, bw_nonkernelcount, bw_intkernelcount,
            bw_intnonkernelcount, bw_ncontkernelvars, bw_ncontnonkernelvars, bw_nkernelvars, bw_nnonkernelvars,
            bw_nintkernelvars, bw_nintnonkernelvars, block2index, varlabels, blklbl_offset, nvars, nbinintvars) );
   }
   else
   {
      /* filling of the kernels with the variables */
      SCIP_CALL( fillKernels(scip, vars, binintvars,
            bw_contkernelvars, bw_contnonkernelvars, bw_kernelvars, bw_nonkernelvars, NULL, NULL,
            bestcurrsol, lbvarmap, twolevel, usebestsol, heurdata->usetransprob,
            heurdata->translbkernel, bw_contkernelcount, bw_contnonkernelcount, bw_kernelcount,
            bw_nonkernelcount, NULL, NULL, bw_ncontkernelvars, bw_ncontnonkernelvars, bw_nkernelvars, bw_nnonkernelvars,
            NULL, NULL, block2index, varlabels, blklbl_offset, nvars, nbinintvars) );
   }
 
   /* sorting of bucket variables according to the reduced costs in non-decreasing order */
   if( heurdata->redcostsort || heurdata->redcostlogsort )
   {
      SCIP_CALL( reducedCostSort(scip, bw_contnonkernelvars, bw_nonkernelvars, bw_intnonkernelvars,
            &bw_cont_redcost, &bw_redcost, &bw_int_redcost, bw_ncontnonkernelvars, bw_nnonkernelvars,
            bw_nintnonkernelvars, twolevel, nblocks) );
   }
 
   /* initialization of the buckets */
   /* determine the amount of buckets needed */
   /* continuous variables are not included when calculating the number of buckets, since they are easier to handle */
   nusedratios = 0;
   if( twolevel )
   {
      SCIP_Real intratio;
      SCIP_Real binratio;
 
      nbuckets = 0;
      for( b = 0; b < nblocks + 1; b++ )
      {
          /* calculate the upper gauss bracket of the ratio of the integer (binary) kernel and non kernel variables */
         if( bw_nintnonkernelvars[b] > 0 && bw_nintkernelvars[b] > 0 )
            intratio = SCIPceil(scip, bw_nintnonkernelvars[b] / (SCIP_Real)bw_nintkernelvars[b]);
         else
            intratio = SCIPinfinity(scip);
 
         if( bw_nnonkernelvars[b] > 0 && bw_nkernelvars[b] > 0 )
            binratio = SCIPceil(scip, bw_nnonkernelvars[b] / (SCIP_Real)bw_nkernelvars[b]);
         else
            binratio = SCIPinfinity(scip);
 
         if( !SCIPisInfinity(scip, intratio) )
         {
            nbuckets += (int)intratio;
            nusedratios++;
         }
         if( !SCIPisInfinity(scip, binratio) )
         {
            nbuckets += (int)binratio;
            nusedratios++;
         }
      }
   }
   else
   {
      /* take the rounded down average bucket ratio of all blocks*/
      nbuckets = 0;
      for( b = 0; b < nblocks + 1; b++ )
      {
         if( bw_nnonkernelvars[b] > 0 && bw_nkernelvars[b] > 0 )
         {
            nbuckets += (int)SCIPceil(scip, (SCIP_Real)bw_nnonkernelvars[b] / (SCIP_Real)bw_nkernelvars[b]);
            nusedratios++;
         }
      }
   }
   /* taking the average ratio as final one for all blocks */
   if( nusedratios > 0 )
      nbuckets = (int)SCIPceil(scip, (SCIP_Real)nbuckets / (SCIP_Real)nusedratios);
   else
      nbuckets = 0;
 
   /* determine the amount of iterations over the buckets/ amount of investigated buckets */
   iters = MIN(nbuckets, heurdata->maxbucks) + 1;
 
   /* create an extra array for the bucket constraints for hashmap creation in createBucketlistAndBuckets() */
   SCIP_CALL( SCIPduplicateBufferArray(scip, &bucketconss, conss, nconss) );
 
   /* create the bucketlist and initialize as much buckets as investigated later on with a subscip for every bucket */
   SCIP_CALL( createBucketlistAndBuckets(scip, heurdata->usetransprob, iters - 1, &bucketlist, &success) );
   if( !success )
      goto TERMINATE;
 
   /* fill every bucket with its variables, nothing to do for the first ('kernel') bucket -> k = 1 */
   if( iters > 1 )
   {
      SCIP_CALL( fillBuckets(scip, &bucketlist,
            bw_contnonkernelvars, bw_nonkernelvars, bw_intnonkernelvars,
            bw_ncontnonkernelvars, bw_nnonkernelvars, bw_nintnonkernelvars,
            bw_cont_redcost, bw_redcost, bw_int_redcost,
            twolevel, heurdata->redcostlogsort, iters - 1, nblocks) );
   }
 
   /* build the kernelvariables out of each blocks kernel variables */
   j = 0;
   n = 0;
   m = 0;
   for( b = 0; b < nblocks + 1; b++ )
   {
      for( l = 0; l < bw_ncontkernelvars[b]; l++ )
         contkernelvars[j++] = bw_contkernelvars[b][l];
 
      for( l = 0; l < bw_nkernelvars[b]; l++ )
         kernelvars[n++] = bw_kernelvars[b][l];
 
      if( twolevel )
      {
         for( l = 0; l < bw_nintkernelvars[b]; l++ )
            intkernelvars[m++] = bw_intkernelvars[b][l];
      }
   }
   assert(j == ncontkernelvars);
   assert(n == nkernelvars);
   if( twolevel )
      assert(m == nintkernelvars);
 
   /* loop over all buckets, solve the small MIP defined by the bucket, adjust kernel */
   mipgap = 0.0;
   nodesleft = heurdata->maxnodes;
   nnodes = 0;
   for( k = 0; k < iters; k++ )
   {
      SCIP_Bool found;
      SCIP_Bool infeasible;
      SCIP_Bool fixed;
      SCIP_Real lb;
      SCIP_Real ub;
      SCIP_Real timeused;
      SCIP_Real totaltimelimit;
      SCIP_Real subtimelimit;
      SCIP_VAR *var;
 
      bucket = &bucketlist->buckets[k];
 
      /* do not compute the current bucket if the number of free bin/int variables exceeds some percentage */
      if( SCIPisGT(scip, (SCIP_Real)(nkernelvars + nintkernelvars + bucket->nbucketvars + bucket->nintbucketvars),
         heurdata->maxbuckfrac * nbinintvars) )
         continue;
 
      /* fix all integer and binary variables to zero that are neither in the kernel nor in the current bucket */
      for( i = 0; i < nvars ; i++ )
      {
         found = FALSE;
         infeasible = TRUE;
         fixed = FALSE;
 
         var = vars[i];
 
         if( var == NULL )
            SCIPdebugMsg(scip, "Variable is null!\n");
 
         if( SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS )
            SCIPdebugMsg(scip, "Hit a cont variable");
 
         /* search for the current variable in the kernel and in the current bucket */
         SCIP_CALL( searchKernelAndBucket(bucket, contkernelvars, ncontkernelvars, kernelvars, nkernelvars,
               intkernelvars, nintkernelvars, var, &found) );
 
         if( found == TRUE )
            continue;
 
         if( var == NULL )
            goto TERMINATE;
 
         /* variable not in kernel or bucket -> deactivate by fixing to bound or zero */
         assert(SCIPvarIsActive(var));
 
         var = bucket->scip2sub[SCIPvarGetProbindex(var)];
         if( var != NULL )
         {
            lb = SCIPvarGetLbLocal(vars[i]);
            ub = SCIPvarGetUbLocal(vars[i]);
 
            /* fix to lb if finite, else to zero if ub nonnegative, else to ub */
            if( !SCIPisInfinity(scip, -lb) )
            {
               SCIP_CALL( SCIPfixVar(bucket->subscip, var, lb, &infeasible, &fixed) );
            }
            else if( ub >= 0.0 )
            {
               SCIP_CALL( SCIPfixVar(bucket->subscip, var, 0.0, &infeasible, &fixed) );
            }
            else
            {
               SCIP_CALL( SCIPfixVar(bucket->subscip, var, ub, &infeasible, &fixed) );
            }
            assert(!infeasible);
            assert(fixed);
         }
      }
 
      /* construct a constraint that ensures the use of the bucketvariables */
      if( heurdata->addUseConss && bucket->bucketvars != NULL )
         SCIP_CALL( addUseConstraint(bucket) );
 
      /* add objective cutoff if desired */
      if( heurdata->objcutoff )
      {
         SCIP_Real cutoff = SCIPgetCutoffbound(scip);
 
         if( !SCIPisInfinity(scip, cutoff) )
            SCIP_CALL( SCIPsetObjlimit(bucket->subscip, cutoff) );
      }
 
#ifdef DKS_WRITE_PROBLEMS
      if( bucket->number < 0 )
      {
         char name[SCIP_MAXSTRLEN];
         /* write the current bucket problem */
         (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "subscip_bucket_%d.lp", bucket->number);
         SCIP_CALL( SCIPwriteOrigProblem(bucket->subscip, name, NULL, FALSE) );
      }
#endif
      /* update the time limit */
      timeused = SCIPgetTotalTime(scip);
      SCIP_CALL( SCIPgetRealParam(scip, "limits/time", &totaltimelimit) );
      subtimelimit = totaltimelimit - timeused;
      if( subtimelimit > 1.0 )
         SCIP_CALL( SCIPsetRealParam(bucket->subscip, "limits/time", subtimelimit) );
      else
         goto TERMINATE;
 
      /* update the remaining number of nodes */
      nodesleft -= nnodes;
 
      /* get the node limit which results from evenly distributing the remaining nodes */
      if( nodesleft > 0 )
      {
         SCIP_Longint nodes_evenly_dist;
         nodes_evenly_dist = (SCIP_Longint)SCIPceil(scip, ((SCIP_Real)nodesleft) / ((SCIP_Real)(iters - k)));
         if( 1LL > nodes_evenly_dist )
            nnodes = 1LL;
         else
            nnodes = nodes_evenly_dist;
      }
      else
      {
         SCIPdebugMsg(scip, "Overall node limit reached.\n");
         goto TERMINATE;
      }
 
      /* set the node limit parameter for the subscip */
      SCIP_CALL( SCIPsetLongintParam(bucket->subscip, "limits/nodes", nnodes) );
 
      /* set the mipgap parameter for the subscip */
      SCIP_CALL( SCIPsetRealParam(bucket->subscip, "limits/gap", mipgap) );
 
      /* solve the current subscip */
      SCIP_CALL_ABORT( SCIPsolve(bucket->subscip) );
      status = SCIPgetStatus(bucket->subscip);
 
      /* compute the nodes used by the subscip */
      nnodes = SCIPgetNNodes(bucket->subscip);
 
      if( bucket->number == 0 )
         *result = SCIP_DIDNOTFIND;
 
      /* if the node limit was reached, increase the mip gap */
      /* gapcall = 1 signals node limit was reached before, -1 signals gap limit, 0 means no status was reached */
      if( status == SCIP_STATUS_NODELIMIT )
      {
         if( gapcall != 0 )
            gapfactor /= 2.0;
 
         mipgap += (heurdata->buckmaxgap / iters) * gapfactor;
         gapcall = 1;
      }
      else if( status == SCIP_STATUS_GAPLIMIT )
      {
         if( gapcall != 0 )
            gapfactor /= 2.0;
 
         mipgap -= (heurdata->buckmaxgap / iters) * gapfactor;
         gapcall = -1;
      }
 
      /* check if the solution is better if one of the three cases occur:
         - solution is optimal
         - solution reached gaplimit
         - node limit is reached and there is one solution */
 
      if( status == SCIP_STATUS_OPTIMAL || status == SCIP_STATUS_GAPLIMIT ||
         (status == SCIP_STATUS_NODELIMIT && SCIPgetNSols(bucket->subscip) > 0) )
      {
         SCIP_Real val;
         SCIP_SOL* sol;
 
         sol = SCIPgetBestSol(bucket->subscip);
         val = SCIPgetSolOrigObj(bucket->subscip, sol);
 
         /* if there is no solution yet or if the value of the current solution is better than the saved solution */
         if( SCIPisInfinity(scip, bestlocval) || val <= bestlocval )
         {
            bestlocval = val;
            nbestbucket = bucket->number;
 
            if( heurdata->primalonly )
               break;
 
            /* adjust the kernel(/-variables) */
            SCIP_CALL( adjustKernelVars(scip, bucket, &contkernelvars, &ncontkernelvars, (int)maxcontkernelsize,
                  &kernelvars, &nkernelvars, (int)maxkernelsize, &intkernelvars, &nintkernelvars, (int)maxintkernelsize,
                  twolevel) );
         }
         success = FALSE;
      }
      else if( status == SCIP_STATUS_NODELIMIT )
         SCIPdebugMsg(scip, "Bucket reached node limit. No optimal solution available.\n");
      else if( status == SCIP_STATUS_INFEASIBLE )
         SCIPdebugMsg(scip, "Bucket infeasible, starting over with next one\n");
      else
      {
         SCIPdebugMsg(scip, "Bucket solving status %d is not supported\n", status);
         goto TERMINATE;
      }
 
      SCIP_CALL( SCIPfreeTransform(bucket->subscip) );
 
#ifdef DKS_KERNEL_INFO
      fclose(variable_info);
#endif
   }
 
   /* if a solution of a bucket was found, save it to the scip */
   if( nbestbucket > -1 )
   {
      SCIP_SOL* newsol;
      SCIP_SOL* bestsol;
      BUCKET* bestbucket;
 
      /* bucket with the best solution */
      bestbucket = &bucketlist->buckets[nbestbucket];
 
      /* get the best solution */
      bestsol = SCIPgetBestSol(bestbucket->subscip);
      if( bestsol == NULL )
      {
         SCIPdebugMsg(scip, "Function SCIPgetBestSol() has returned a NULL pointer\n");
         *result = SCIP_DIDNOTFIND;
         goto TERMINATE;
      }
 
      SCIPdebug( SCIP_CALL( SCIPprintSol(bestbucket->subscip, bestsol, NULL, FALSE) ) );
 
      /* extract the values of all variables in the best solution of a bucket found */
      SCIP_CALL( SCIPtranslateSubSol(scip, bestbucket->subscip, bestsol, heur, bestbucket->scip2sub, &newsol) );
 
      SCIPdebug( SCIP_CALL( SCIPprintSol(scip, newsol, NULL, FALSE) ) );
      SCIPdebugMsg(scip, "Objective value %.2f\n", SCIPgetSolOrigObj(scip, newsol));
      SCIPdebugMsg(scip, "Objective value of subscip %.2f\n", SCIPgetSolOrigObj(bestbucket->subscip, bestsol));
 
      /* check the feasibilty of the new created solution, save it if so and free it */
      SCIP_CALL( SCIPtrySolFree(scip, &newsol, FALSE, FALSE, TRUE, TRUE, TRUE, &success) );
 
      if( !success )
      {
         SCIPdebugMsg(scip, "Solution copy failed\n");
         *result = SCIP_DIDNOTFIND;
      }
      else
      {
         SCIPdebugMsg(scip, "Solution copy successfull after %f sec\n", SCIPgetSolvingTime(scip));
         *result = SCIP_FOUNDSOL;
      }
   }
   else
   {
      SCIPdebugMsg(scip, "no solution found\n");
      *result = SCIP_DIDNOTFIND;
   }
 
   /* remember if the heuristic has not provided a solution */
   if( *result != SCIP_FOUNDSOL )
      heurdata->uselesscall = TRUE;
 
TERMINATE:
   if( bucketconss != NULL )
      SCIPfreeBufferArray(scip, &bucketconss);
 
   if( bw_intnonkernelcount != NULL )
      SCIPfreeBufferArray(scip, &bw_intnonkernelcount);
 
   if( bw_intkernelcount != NULL )
      SCIPfreeBufferArray(scip, &bw_intkernelcount);
 
   if( intnonkernelvars != NULL )
      SCIPfreeBufferArray(scip, &intnonkernelvars);
 
   if( intkernelvars != NULL )
      SCIPfreeBufferArray(scip, &intkernelvars);
 
   if( bw_nonkernelcount != NULL )
      SCIPfreeBufferArray(scip, &bw_nonkernelcount);
 
   if( bw_kernelcount != NULL )
      SCIPfreeBufferArray(scip, &bw_kernelcount);
 
   if( bw_contnonkernelcount != NULL )
      SCIPfreeBufferArray(scip, &bw_contnonkernelcount);
 
   if( bw_contkernelcount != NULL )
      SCIPfreeBufferArray(scip, &bw_contkernelcount);
 
   if( binintvars != NULL )
      SCIPfreeBufferArray(scip, &binintvars);
 
   if( nonkernelvars != NULL )
      SCIPfreeBufferArray(scip, &nonkernelvars);
 
   if( kernelvars != NULL )
      SCIPfreeBufferArray(scip, &kernelvars);
 
   if( contnonkernelvars != NULL )
      SCIPfreeBufferArray(scip, &contnonkernelvars);
 
   if( contkernelvars != NULL )
      SCIPfreeBufferArray(scip, &contkernelvars);
 
   if( bw_intkernelvars != NULL )
   {
      for( b = nblocks; b >= 0; b-- )
      {
         if( bw_intnonkernelvars[b] != NULL )
            SCIPfreeBufferArray(scip, &(bw_intnonkernelvars[b]));
         if( bw_intkernelvars[b] != NULL )
            SCIPfreeBufferArray(scip, &(bw_intkernelvars[b]));
      }
   }
 
   if( bw_kernelvars != NULL )
   {
      for( b = nblocks; b >= 0; b-- )
      {
         if( bw_nonkernelvars[b] != NULL )
            SCIPfreeBufferArray(scip, &(bw_nonkernelvars[b]));
         if( bw_kernelvars[b] != NULL )
            SCIPfreeBufferArray(scip, &(bw_kernelvars[b]));
      }
   }
 
   if( bw_contkernelvars != NULL )
   {
      for( b = nblocks; b >= 0; b-- )
      {
         if( bw_contnonkernelvars[b] != NULL )
            SCIPfreeBufferArray(scip, &(bw_contnonkernelvars[b]));
         if( bw_contkernelvars[b] != NULL )
            SCIPfreeBufferArray(scip, &(bw_contkernelvars[b]));
      }
   }
 
   if( bw_intnonkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_intnonkernelvars);
 
   if( bw_intkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_intkernelvars);
 
   if( bw_nonkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_nonkernelvars);
 
   if( bw_kernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_kernelvars);
 
   if( bw_contnonkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_contnonkernelvars);
 
   if( bw_contkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_contkernelvars);
 
   if( bw_nintnonkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_nintnonkernelvars);
 
   if( bw_nintkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_nintkernelvars);
 
   if( bw_nnonkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_nnonkernelvars);
 
   if( bw_nkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_nkernelvars);
 
   if( bw_ncontnonkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_ncontnonkernelvars);
 
   if( bw_ncontkernelvars != NULL )
      SCIPfreeBufferArray(scip, &bw_ncontkernelvars);
 
   if( block2index != NULL )
   {
      if( nblocklabels > 0 )
      {
         assert(blocklabels != NULL);
         SCIPfreeBlockMemoryArray(scip, &block2index, blocklabels[nblocklabels - 1] + 1 + blklbl_offset);
      }
      else
         SCIPfreeBlockMemoryArray(scip, &block2index, 1);
   }
 
   if( blocklabels != NULL )
      SCIPfreeBufferArray(scip, &blocklabels);
 
   if( conslabels != NULL )
      SCIPfreeBufferArray(scip, &conslabels);
 
   if( varlabels != NULL )
      SCIPfreeBufferArray(scip, &varlabels);
 
   SCIP_CALL( freeRedcostArrays(scip, &bw_cont_redcost, &bw_redcost, &bw_int_redcost, nblocks) );
 
   if( lbvarmap != NULL )
      SCIPhashmapFree(&lbvarmap);
 
   if( bucketlist != NULL )
   {
      for( k = bucketlist->nbuckets - 1; k >= 1; k-- )
      {
         SCIP_CALL( freeBucket(scip, &bucketlist->buckets[k]) );
         SCIP_CALL( freeBucketArrays(scip, &bucketlist->buckets[k], twolevel) );
      }
      SCIP_CALL( freeBucket(scip, &bucketlist->buckets[0]) );
   }
 
   if( bucketlist != NULL )
   {
      SCIP_CALL( freeBucketlist(&bucketlist, iters) );
   }
 
   SCIPdebugMsg(scip, "Leave dks heuristic\n");
 
   return SCIP_OKAY;
}
 
 
/*
 * primal heuristic specific interface methods
 */
 
/** creates the DKS primal heuristic and includes it in SCIP */
SCIP_RETCODE SCIPincludeHeurDKS(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   SCIP_HEURDATA* heurdata = NULL;
   SCIP_HEUR* heur = NULL;
 
   /* create dks primal heuristic data */
   SCIP_CALL( SCIPallocBlockMemory(scip, &heurdata) );
   assert(heurdata != NULL);
   heurdata->ncalls = 0;
   heurdata->uselesscall = FALSE;
 
   /* include primal heuristic */
   SCIP_CALL( SCIPincludeHeurBasic(scip, &heur,
         HEUR_NAME, HEUR_DESC, HEUR_DISPCHAR, HEUR_PRIORITY, HEUR_FREQ, HEUR_FREQOFS,
         HEUR_MAXDEPTH, HEUR_TIMING, HEUR_USESSUBSCIP, heurExecDKS, heurdata) );
 
   assert(heur != NULL);
 
   /* set non fundamental callbacks via setter functions */
   SCIP_CALL( SCIPsetHeurCopy(scip, heur, heurCopyDKS) );
   SCIP_CALL( SCIPsetHeurFree(scip, heur, heurFreeDKS) );
 
   /* add dks primal heuristic parameters */
   SCIP_CALL( SCIPaddIntParam(scip, "heuristics/" HEUR_NAME "/maxbucks",
         "maximal number of buckets to be investigated",
         &heurdata->maxbucks, TRUE, DEFAULT_MAXBUCKS, 1, 100, NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "heuristics/" HEUR_NAME "/kernelsizefactor",
         "factor with which the initial kernel size can grow max",
         &heurdata->kernelsizefactor, TRUE, DEFAULT_KERNELSIZEFACTOR, 1.0, 10.0, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/addUseConss",
         "should a constraint be added ensuring that bucket variables are used?",
         &heurdata->addUseConss, TRUE, DEFAULT_ADDUSECONSS, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/linkbucksize",
         "should the linking variables in the kernel influence the size of the buckets?",
         &heurdata->linkbucksize, TRUE, DEFAULT_LINKBUCKSIZE, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/translbkernel",
         "should a variable with different lower bound in transformed and original problem be in the kernel?",
         &heurdata->translbkernel, TRUE, DEFAULT_TRANSLBKERNEL, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/lesslockskernel",
         "should a variable with max one uplock and one downlock be in the kernel?",
         &heurdata->lesslockskernel, TRUE, DEFAULT_LESSLOCKSKERNEL, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/usetransprob",
         "should dks use the transformed problem?",
         &heurdata->usetransprob, TRUE, DEFAULT_USETRANSPROB, NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "heuristics/" HEUR_NAME "/buckmaxgap",
         "defines the maximum mipgap a bucket can be solved to",
         &heurdata->buckmaxgap, TRUE, DEFAULT_BUCKMAXGAP, 0.0, 1.0, NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "heuristics/" HEUR_NAME "/maxlinkscore",
         "defines a bound to the linkscore of the decomp",
         &heurdata->maxlinkscore, TRUE, DEFAULT_MAXLINKSCORE, 0.0, 1.0, NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "heuristics/" HEUR_NAME "/maxbuckfrac",
         "defines a maximal share of bin/int variables for a bucket to be respected",
         &heurdata->maxbuckfrac, TRUE, DEFAULT_MAXBUCKFRAC, 0.0, 1.0, NULL, NULL) );
 
   SCIP_CALL( SCIPaddLongintParam(scip, "heuristics/" HEUR_NAME "/maxnodes",
         "maximum number of nodes to regard in all subproblems",
         &heurdata->maxnodes, TRUE, DEFAULT_MAXNODES, 0LL, SCIP_LONGINT_MAX, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/usetwolevel",
         "should a two level bucket structure be used if possible?",
         &heurdata->usetwolevel, FALSE, DEFAULT_USETWOLEVEL, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/usedecomp",
         "should a decomposition be used if given?",
         &heurdata->usedecomp, FALSE, DEFAULT_USEDECOMP, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/usebestsol",
         "should the best solution instead of the LP solution be used?",
         &heurdata->usebestsol, FALSE, DEFAULT_USEBESTSOL, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/redcostsort",
         "should the bucket variables be sorted by reduced costs in the LP solution?",
         &heurdata->redcostsort, FALSE, DEFAULT_REDCOSTSORT, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/primalonly",
         "should the heuristic terminate after the first primal solution is found?",
         &heurdata->primalonly, FALSE, DEFAULT_PRIMALONLY, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/redcostlogsort",
         "should the bucket variables be sorted logarithmically by reduced costs in the LP solution?",
         &heurdata->redcostlogsort, FALSE, DEFAULT_REDCOSTLOGSORT, NULL, NULL) ) ;
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/objcutoff",
         "should the next solution at least satisfy the old objective?",
         &heurdata->objcutoff, FALSE, DEFAULT_OBJCUTOFF, NULL, NULL) );
 
   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/" HEUR_NAME "/runbinprobsonly",
         "should the heuristic be used only for binary problems or problems with integer and binary variables?",
         &heurdata->runbinprobsonly, FALSE, DEFAULT_RUNBINPROBSONLY, NULL, NULL) );
 
   return SCIP_OKAY;
}