heur_rec.c

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the program and library             */
/*         SCIP --- Solving Constraint Integer Programs                      */
/*                                                                           */
/*    Copyright (C) 2002-2019 Konrad-Zuse-Zentrum                            */
/*                            fuer Informationstechnik Berlin                */
/*                                                                           */
/*  SCIP is distributed under the terms of the ZIB Academic License.         */
/*                                                                           */
/*  You should have received a copy of the ZIB Academic License              */
/*  along with SCIP; see the file COPYING. If not visit scip.zib.de.         */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/**@file   heur_rec.c
 * @brief  Primal recombination heuristic for Steiner problems
 * @author Daniel Rehfeldt
 *
 * This file implements a recombination heuristic for Steiner problems, see
 * "SCIP-Jack - A solver for STP and variants with parallelization extensions" (2017) by
 * Gamrath, Koch, Maher, Rehfeldt and Shinano
 *
 * A list of all interface methods can be found in heur_rec.h
 *
 */

/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/

#include <assert.h>
#include <string.h>
#include <stdio.h>
#include "scip/scip.h"
#include "scip/scipdefplugins.h"
#include "scip/cons_linear.h"
#include "heur_rec.h"
#include "heur_prune.h"
#include "heur_slackprune.h"
#include "heur_local.h"
#include "grph.h"
#include "heur_tm.h"
#include "cons_stp.h"
#include "scip/pub_misc.h"
#include "probdata_stp.h"
#include "math.h"

#define HEUR_NAME             "rec"
#define HEUR_DESC             "recombination heuristic for Steiner problems"
#define HEUR_DISPCHAR         'R'
#define HEUR_PRIORITY         100
#define HEUR_FREQ             1
#define HEUR_FREQOFS          0
#define HEUR_MAXDEPTH         -1
#define HEUR_TIMING           (SCIP_HEURTIMING_DURINGLPLOOP | SCIP_HEURTIMING_AFTERLPLOOP | SCIP_HEURTIMING_AFTERNODE)
#define HEUR_USESSUBSCIP      FALSE           /**< does the heuristic use a secondary SCIP instance?                                 */

#define DEFAULT_MAXFREQREC     FALSE         /**< executions of the rec heuristic at maximum frequency?                             */
#define DEFAULT_MAXNSOLS       15            /**< default maximum number of (good) solutions be regarded in the subproblem          */
#define DEFAULT_NUSEDSOLS      4             /**< number of solutions that will be taken into account                               */
#define DEFAULT_RANDSEED       1984          /**< random seed                                                                       */
#define DEFAULT_NTMRUNS        100           /**< number of runs in TM heuristic                                                    */
#define DEFAULT_NWAITINGSOLS   4             /**< max number of new solutions to be available before executing the heuristic again  */

#define BOUND_MAXNTERMINALS 1000
#define BOUND_MAXNEDGES     20000
#define RUNS_RESTRICTED     3
#define RUNS_NORMAL         10
#define CYCLES_PER_RUN      3
#define REC_MAX_FAILS       4
#define REC_MIN_NSOLS       4
#define REC_ADDEDGE_FACTOR 1.0

#define COST_MAX_POLY_x0 500
#define COST_MIN_POLY_x0 100

#ifdef WITH_UG
extern
int getUgRank(void);
#endif


/*
 * Data structures
 */

/** primal heuristic data */
struct SCIP_HeurData
{
   int                   lastsolindex;
   int                   bestsolindex;       /**< best solution during the previous run                             */
   int                   maxnsols;           /**< maximum number of (good) solutions be regarded in the subproblem  */
   SCIP_Longint          ncalls;             /**< number of calls                                                   */
   SCIP_Longint          nlastsols;          /**< number of solutions during the last run                           */
   int                   ntmruns;            /**< number of runs in TM heuristic                                    */
   int                   nusedsols;          /**< number of solutions that will be taken into account               */
   int                   nselectedsols;      /**< number of solutions actually selected                             */
   int                   nwaitingsols;       /**< number of new solutions before executing the heuristic again      */
   int                   nfailures;          /**< number of failures since last successful call                     */
   unsigned int          randseed;           /**< seed value for random number generator                            */
   SCIP_RANDNUMGEN*      randnumgen;         /**< random number generator                                           */
   SCIP_Bool             maxfreq;            /**< should the heuristic be called at maximum frequency?              */
};


/*
 * Local methods
 */

/** information method for a parameter change of random seed */
static
SCIP_DECL_PARAMCHGD(paramChgdRandomseed)
{  /*lint --e{715}*/
   SCIP_HEURDATA* heurdata;
   int newrandseed;

   newrandseed = SCIPparamGetInt(param);

   heurdata = (SCIP_HEURDATA*)SCIPparamGetData(param);
   assert(heurdata != NULL);

   heurdata->randseed = (int) newrandseed;

   return SCIP_OKAY;
}


/** edge cost multiplier */
static
int edgecostmultiplier(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_HEURDATA*        heurdata,           /**< SCIP data structure */
   SCIP_Real             avg                 /**< number of solutions containing this edge */
   )
{
   SCIP_Real normed;
   int maxpolyx0;
   int minpolyx0;

   int upper;
   int lower;
   int factor;

   /* if STP, then avg >= 2.0 */
   assert(SCIPisGE(scip, avg, 1.0));
   assert(heurdata->nusedsols  >= 2);

   maxpolyx0 = COST_MAX_POLY_x0 * (heurdata->nusedsols - 1);
   minpolyx0 = COST_MIN_POLY_x0 * (heurdata->nusedsols - 1);

   /* norm to [0,1] (STP) or [-1,1] and evaluate polynomials */
   normed = (avg - 2.0) / ((double) heurdata->nusedsols - 1.0);
   upper = (int) (maxpolyx0 - 2 * maxpolyx0 * normed + maxpolyx0 * (normed * normed));
   lower = (int) (minpolyx0 - 2 * minpolyx0 * normed + minpolyx0 * (normed * normed));

   assert(SCIPisGE(scip, normed, -1.0) && SCIPisLE(scip, normed, 1.0));

   lower = MAX(0, lower);
   upper = MAX(0, upper);

   factor = SCIPrandomGetInt(heurdata->randnumgen, lower, upper);
   factor++;

   assert(factor <= COST_MAX_POLY_x0 * 3 + 1 || avg <= 2.0);
   assert(factor >= 1);

   return factor;
}

/** select solutions to be merged */
static
SCIP_RETCODE selectdiffsols(
   SCIP*                 scip,               /**< SCIP data structure */
   const STPSOLPOOL*     pool,               /**< solution pool or NULL */
   const GRAPH*          graph,              /**< graph data structure */
   SCIP_HEURDATA*        heurdata,           /**< SCIP data structure */
   SCIP_VAR**            vars,               /**< problem variables */
   const int*            incumbentedges,     /**< edges of solution to be used as recombination root */
   int*                  incumbentindex,     /**< index of ancestor of incumbent solution */
   int*                  selection,          /**< selected solutions */
   SCIP_Bool*            success             /**< could at least two solutions be selected? */
   )
{
   SCIP_SOL** sols = NULL;
   STPSOL** poolsols = NULL;
   int* perm;
   int* soledgestmp;
   STP_Bool* solselected;
   STP_Bool* soledges;
   int pos;
   int nsols;
   int maxnsols = heurdata->maxnsols;
   int nselectedsols = 0;
   const int nedges = graph->edges;
   const int nusedsols = heurdata->nusedsols;
   const SCIP_Bool usestppool = (pool != NULL);

   assert(selection != NULL);
   assert(graph != NULL);

   if( !usestppool )
   {
      assert(vars != NULL);

      /* get solution data */
      sols = SCIPgetSols(scip);
      nsols = SCIPgetNSols(scip);
   }
   else
   {
      poolsols = pool->sols;
      nsols = pool->size;
      assert(nsols > 1);
   }

   assert(nusedsols > 1);
   assert(nsols >= nusedsols);

   /* allocate memory */
   SCIP_CALL( SCIPallocBufferArray(scip, &solselected, nsols) );
   SCIP_CALL( SCIPallocBufferArray(scip, &perm, nsols) );
   SCIP_CALL( SCIPallocBufferArray(scip, &soledges, nedges / 2) );
   SCIP_CALL( SCIPallocBufferArray(scip, &soledgestmp, nedges / 2) );

   for( int i = 0; i < nsols; i++ )
   {
      perm[i] = i;
      solselected[i] = FALSE;
   }

   if( usestppool )
   {
      for( pos = 0; pos < nsols; pos++ )
         if( *incumbentindex == poolsols[pos]->index )
            break;
   }
   else
   {
      for( pos = 0; pos < nsols; pos++ )
         if( *incumbentindex == SCIPsolGetIndex(sols[pos]) )
            break;
   }
   assert(pos < nsols);
   solselected[pos] = TRUE;
   selection[nselectedsols++] = pos;

   for( int e = 0; e < nedges; e += 2 )
      soledges[e / 2] = (incumbentedges[e] == CONNECT
                      || incumbentedges[e + 1] == CONNECT);

   maxnsols = MIN(nsols, maxnsols);

   if( !usestppool )
   {
      int sqrtnallsols = (int) sqrt((double) nsols);

      if( sqrtnallsols >= REC_MIN_NSOLS && sqrtnallsols < maxnsols )
         maxnsols = sqrtnallsols;
   }

   SCIPrandomPermuteIntArray(heurdata->randnumgen, perm, 0, maxnsols);

   for( int i = 0; i < nsols; i++ )
   {
      if( solselected[perm[i]] == FALSE )
      {
         int eqnedges = 0;
         int diffnedges = 0;
         const int k = perm[i];
         SCIP_SOL* solk = NULL;
         const int* solKedges = NULL;

         if( usestppool )
            solKedges = poolsols[k]->soledges;
         else
            solk = sols[k];

         for( int e = 0; e < nedges; e += 2 )
         {
            SCIP_Bool hit;

            if( usestppool )
               hit = (solKedges[e] == CONNECT || solKedges[e + 1] == CONNECT);
            else
               hit = SCIPisEQ(scip, SCIPgetSolVal(scip, solk, vars[e]), 1.0)
                  || SCIPisEQ(scip, SCIPgetSolVal(scip, solk, vars[e + 1]), 1.0);

            if( hit )
            {
               if( soledges[e / 2] == FALSE )
                  soledgestmp[diffnedges++] = e / 2;
               else
               {
                  const int tail = graph->tail[e];
                  const int head = graph->head[e];

                  /* no dummy edge? */
                  if( !(Is_term(graph->term[tail]) && Is_term(graph->term[head])) )
                     eqnedges++;
               }
            }
         }

         /* enough similarities and differences with new solution? */
         if( diffnedges > 5 && eqnedges > 0  )
         {
            SCIPdebugMessage("REC: different edges: %d same edges: %d \n", diffnedges, eqnedges);
            selection[nselectedsols++] = k;
            solselected[k] = TRUE;
            *success = TRUE;

            for( int j = 0; j < diffnedges; j++ )
               soledges[soledgestmp[j]] = TRUE;

            if( nselectedsols >= nusedsols )
               break;
         }
      }
   }

   assert(nselectedsols <= nusedsols);

   heurdata->nselectedsols = nselectedsols;

   SCIPdebugMessage("REC: selected %d sols \n", nselectedsols);

   /* free memory */
   SCIPfreeBufferArray(scip, &soledgestmp);
   SCIPfreeBufferArray(scip, &soledges);
   SCIPfreeBufferArray(scip, &perm);
   SCIPfreeBufferArray(scip, &solselected);

   return SCIP_OKAY;
}

/** select solutions to be merged */
static
SCIP_RETCODE selectsols(
   SCIP*                 scip,               /**< SCIP data structure */
   const STPSOLPOOL*     pool,               /**< solution pool or NULL */
   SCIP_HEURDATA*        heurdata,           /**< SCIP data structure */
   int*                  incumbentindex,     /**< index of ancestor of incumbent solution */
   int*                  selection,          /**< selected solutions */
   SCIP_Bool             randomize           /**< select solutions randomly? */
   )
{
   SCIP_SOL** sols = NULL;                          /* array of all solutions found so far         */
   STPSOL** poolsols = NULL;
   int* perm;
   STP_Bool* solselected;
   int i;
   int nsols;                                /* number of all available solutions        */
   int maxnsols;
   int nusedsols;                            /* number of solutions to use in rec           */
   int nselectedsols;

   const SCIP_Bool usestppool = (pool != NULL);
   assert(selection != NULL);

   if( usestppool )
   {
      poolsols = pool->sols;
      nsols = pool->size;
      assert(nsols > 1);
   }
   else
   {
      /* get solution data */
      sols = SCIPgetSols(scip);
      nsols = SCIPgetNSols(scip);
   }

   maxnsols = heurdata->maxnsols;
   nusedsols = heurdata->nusedsols;
   assert(nusedsols <= nsols);
   nselectedsols = 0;

   assert(nusedsols > 1);
   assert(nsols >= nusedsols);

   /* allocate memory */
   SCIP_CALL( SCIPallocBufferArray(scip, &solselected, nsols) );
   SCIP_CALL( SCIPallocBufferArray(scip, &perm, nsols) );

   for( i = 0; i < nsols; i++ )
   {
      perm[i] = i;
      solselected[i] = FALSE;
   }

   if( usestppool )
   {
      for( i = 0; i < nsols; i++ )
         if( *incumbentindex == poolsols[i]->index )
            break;
   }
   else
   {
      for( i = 0; i < nsols; i++ )
         if( *incumbentindex == SCIPsolGetIndex(sols[i]) )
            break;
   }

   assert(i < nsols);
   solselected[i] = TRUE;
   selection[nselectedsols++] = i;

   if( !randomize )
   {
      const int end = SCIPrandomGetInt(heurdata->randnumgen, 1, nusedsols - 1);
      int shift = SCIPrandomGetInt(heurdata->randnumgen, end, 2 * nusedsols - 1);

      if( shift > nsols )
         shift = nsols;

      SCIPrandomPermuteIntArray(heurdata->randnumgen, perm, 0, shift);

      for( i = 0; i < end; i++ )
      {
         if( solselected[perm[i]] == FALSE )
         {
            selection[nselectedsols++] = perm[i];
            solselected[perm[i]] = TRUE;
         }
      }
   }

   maxnsols = MIN(nsols, maxnsols);

   if( !usestppool )
   {
      int sqrtnallsols = (int) sqrt(nsols);

      if( sqrtnallsols >= REC_MIN_NSOLS && sqrtnallsols < maxnsols )
         maxnsols = sqrtnallsols;
   }

   SCIPdebugMessage("maxnsols in REC %d \n", maxnsols);

   if( nselectedsols < nusedsols )
   {
      SCIPrandomPermuteIntArray(heurdata->randnumgen, perm, 0, maxnsols);
      for( i = 0; i < maxnsols; i++ )
      {
         if( solselected[perm[i]] == FALSE )
         {
            selection[nselectedsols++] = perm[i];
            if( nselectedsols >= nusedsols )
               break;
         }
      }
   }

   assert(nselectedsols <= nusedsols);

   SCIPdebugMessage("REC: selected %d sols \n", nselectedsols);

   heurdata->nselectedsols = nselectedsols;
   SCIPfreeBufferArray(scip, &perm);
   SCIPfreeBufferArray(scip, &solselected);

   return SCIP_OKAY;
}

/** merge selected solutions to a new graph */
static
SCIP_RETCODE buildsolgraph(
   SCIP*                 scip,               /**< SCIP data structure */
   const STPSOLPOOL*     pool,               /**< solution pool or NULL */
   SCIP_HEURDATA*        heurdata,           /**< SCIP data structure */
   const GRAPH*          graph,              /**< graph structure */
   GRAPH**               solgraph,           /**< pointer to store new graph */
   const int*            incumbentedges,     /**< edges of solution to be used as recombination root */
   int*                  incumbentindex,     /**< index of ancestor of incumbent solution */
   int**                 edgeancestor,       /**< ancestor to edge edge */
   int**                 edgeweight,         /**< for each edge: number of solution that contain this edge */
   SCIP_Bool*            success,            /**< new graph constructed? */
   SCIP_Bool             randomize,          /**< select solution randomly? */
   SCIP_Bool             addedges            /**< add additional edges between solution vertices? */
   )
{
   GRAPH* newgraph = NULL;
   SCIP_SOL** sols = NULL;
   STPSOL** poolsols = NULL;
   SCIP_VAR** vars = NULL;
   int* solselection;
   const SCIP_Bool pcmw = (graph->stp_type == STP_PCSPG || graph->stp_type == STP_MWCSP
                        || graph->stp_type == STP_RPCSPG || graph->stp_type == STP_RMWCSP );
   const SCIP_Bool usestppool = (pool != NULL);

   assert(scip != NULL);
   assert(graph != NULL);

   if( !usestppool )
   {
      sols = SCIPgetSols(scip);
      vars = SCIPprobdataGetEdgeVars(scip);
      assert(vars != NULL);
      assert(sols != NULL);
   }
   else
   {
      poolsols = pool->sols;
   }

   *success = TRUE;
   *edgeweight = NULL;
   *edgeancestor = NULL;

   /* allocate memory */
   SCIP_CALL( SCIPallocBufferArray(scip, &solselection, heurdata->nusedsols) );

   /* select solutions to be merged */
   if( pcmw || graph->stp_type == STP_DCSTP )
      SCIP_CALL( selectdiffsols(scip, pool, graph, heurdata, vars, incumbentedges, incumbentindex, solselection, success) );
   else
      SCIP_CALL( selectsols(scip, pool, heurdata, incumbentindex, solselection, randomize) );

   if( *success )
   {
      int* dnodemap;
      STP_Bool* solnode;               /* marks nodes contained in at least one solution */
      STP_Bool* soledge;               /* marks edges contained in at least one solution */
      int j;
      int nsoledges = 0;
      int nsolnodes = 0;
      const int nedges = graph->edges;
      const int nnodes = graph->knots;
      const int selectedsols = heurdata->nselectedsols;

      SCIPdebugMessage("REC: successfully selected new solutions \n");

      assert(selectedsols > 0);

      SCIP_CALL( SCIPallocBufferArray(scip, &solnode, nnodes) );
      SCIP_CALL( SCIPallocBufferArray(scip, &dnodemap, nnodes) );
      SCIP_CALL( SCIPallocBufferArray(scip, &soledge, nedges / 2) );

      for( int i = 0; i < nnodes; i++ )
      {
         solnode[i] = FALSE;
         dnodemap[i] = UNKNOWN;
      }

      /* count and mark selected nodes and edges */
      for( int i = 0; i < nedges; i += 2 )
      {
         const int ihalf = i / 2;
         soledge[ihalf] = FALSE;

         if( graph->oeat[i] == EAT_FREE )
            continue;

         for( j = 0; j < selectedsols; j++ )
         {
            SCIP_Bool hit;

            if( j == 0 )
            {
               hit = (incumbentedges[i] == CONNECT
                   || incumbentedges[i + 1] == CONNECT);
            }
            else if( usestppool )
               hit = (poolsols[solselection[j]]->soledges[i] == CONNECT
                   || poolsols[solselection[j]]->soledges[i + 1] == CONNECT);
            else
               hit = (SCIPisEQ(scip, SCIPgetSolVal(scip, sols[solselection[j]], vars[i]), 1.0)
                   || SCIPisEQ(scip, SCIPgetSolVal(scip, sols[solselection[j]], vars[i + 1]), 1.0));

            if( hit )
            {
               nsoledges++;
               soledge[ihalf] = TRUE;
               if( !solnode[graph->tail[i]] )
               {
                  solnode[graph->tail[i]] = TRUE;
                  nsolnodes++;
               }
               if( !solnode[graph->head[i]] )
               {
                  solnode[graph->head[i]] = TRUE;
                  nsolnodes++;
               }
               break;
            }
         }
      }
      if( pcmw ) /* todo this probably won't work for RMWCSP */
      {
         const int oldroot = graph->source;
         for( int i = graph->outbeg[oldroot]; i != EAT_LAST; i = graph->oeat[i] )
         {
            if( Is_gterm(graph->term[graph->head[i]]) )
            {
               const int ihalf = i / 2;
               const int head = graph->head[i];
               if( soledge[ihalf] == FALSE )
               {
                  nsoledges++;
                  soledge[ihalf] = TRUE;
                  if( !solnode[head] && SCIPisEQ(scip, graph->cost[flipedge(i)], FARAWAY) )
                  {
                     solnode[head] = TRUE;
                     nsolnodes++;
                  }
                  assert(solnode[graph->head[i]]);
               }

               if( Is_pterm(graph->term[head]) )
               {
                  int e2;
                  for( e2 = graph->outbeg[head]; e2 != EAT_LAST; e2 = graph->oeat[e2] )
                     if( Is_term(graph->term[graph->head[e2]]) && graph->head[e2] != oldroot )
                        break;

                  assert(e2 != EAT_LAST);

                  if( soledge[e2 / 2] == FALSE )
                  {
                     nsoledges++;
                     soledge[e2 / 2] = TRUE;
                  }
               }
               else
               {
                  int e2;
                  assert(Is_term(graph->term[head]));
                  for( e2 = graph->outbeg[head]; e2 != EAT_LAST; e2 = graph->oeat[e2] )
                     if( Is_pterm(graph->term[graph->head[e2]]) && graph->head[e2] != oldroot )
                        break;

                  assert(e2 != EAT_LAST);

                  if( soledge[e2 / 2] == FALSE )
                  {
                     nsoledges++;
                     soledge[e2 / 2] = TRUE;
                  }
               }
            }
         }
      }

      /* add additional edges? */
      if( addedges )
      {
         int naddedges = 0;

         for( int e = 0; e < nedges && naddedges <= (int)(REC_ADDEDGE_FACTOR * nsoledges); e += 2 )
         {
            int tail;
            int head;

            if( soledge[e / 2] )
               continue;
            // todo if fixed to zero, continue?
            if( graph->oeat[e] == EAT_FREE )
               continue;

            tail = graph->tail[e];
            head = graph->head[e];

            if( solnode[tail] && solnode[head] )
            {
               soledge[e / 2] = TRUE;
               naddedges++;
            }
         }
         SCIPdebugMessage("additional edges %d (orig: %d )\n", naddedges, nsoledges);

         nsoledges += naddedges;
      }

      if( graph->stp_type == STP_GSTP )
      {
         for( int k = 0; k < nnodes; k++ )
         {
            if( Is_term(graph->term[k]) )
            {
               assert(solnode[k]);
               for( int i = graph->outbeg[k]; i != EAT_LAST; i = graph->oeat[i] )
               {
                  if( solnode[graph->head[i]] && !soledge[i / 2] )
                  {
                     soledge[i / 2] = TRUE;
                     nsoledges++;
                  }
               }
            }
         }
      }

      /* initialize new graph */
      SCIP_CALL( graph_init(scip, &newgraph, nsolnodes, 2 * nsoledges, 1) );

      if( graph->stp_type == STP_RSMT || graph->stp_type == STP_OARSMT || graph->stp_type == STP_GSTP )
         newgraph->stp_type = STP_SPG;
      else
         newgraph->stp_type = graph->stp_type;

      if( pcmw )
      {
         SCIP_CALL( graph_pc_init(scip, newgraph, nsolnodes, nsolnodes) );
      }

      newgraph->hoplimit = graph->hoplimit;
      j = 0;
      for( int i = 0; i < nnodes; i++ )
      {
         if( solnode[i] )
         {
            if( pcmw )
            {
               if( (!Is_term(graph->term[i])) )
                  newgraph->prize[j] = graph->prize[i];
               else
                  newgraph->prize[j] = 0.0;
            }

            graph_knot_add(newgraph, graph->term[i]);
            dnodemap[i] = j++;
         }
      }

      if( pcmw )
      {
         newgraph->extended = TRUE;
         newgraph->norgmodelknots = newgraph->knots - newgraph->terms;
      }

      SCIPdebugMessage("REC: sol graph with nodes: %d, edges: %d, terminals: %d  \n", nsolnodes, 2 * nsoledges, newgraph->terms);

      /* set root */
      newgraph->source = dnodemap[graph->source];
      if( newgraph->stp_type == STP_RPCSPG || newgraph->stp_type == STP_RMWCSP )
         newgraph->prize[newgraph->source] = FARAWAY;

      assert(newgraph->source >= 0);

      /* copy max degrees*/
      if( graph->stp_type == STP_DCSTP )
      {
         SCIP_CALL( SCIPallocMemoryArray(scip, &(newgraph->maxdeg), nsolnodes) );
         for( int i = 0; i < nnodes; i++ )
            if( solnode[i] )
               newgraph->maxdeg[dnodemap[i]] = graph->maxdeg[i];
      }
      /* allocate memory */
      SCIP_CALL( SCIPallocMemoryArray(scip, edgeancestor, 2 * nsoledges) );
      SCIP_CALL( SCIPallocMemoryArray(scip, edgeweight, 2 * nsoledges) );

      for( int i = 0; i < 2 * nsoledges; i++ )
         (*edgeweight)[i] = 1;

      /* store original ID of each new edge (i.e. edge in the merged graph) */
      j = 0;
      assert(selectedsols == heurdata->nselectedsols);
      for( int i = 0; i < nedges; i += 2 )
      {
         if( soledge[i / 2] )
         {
            const int orgtail = graph->tail[i];
            const int orghead = graph->head[i];

            (*edgeancestor)[j++] = i;
            (*edgeancestor)[j++] = i + 1;

            if( pcmw )
            {
               assert(newgraph->term2edge != NULL);
               graph_pc_updateTerm2edge(newgraph, graph, dnodemap[orgtail], dnodemap[orghead], orgtail, orghead);
            }

            graph_edge_add(scip, newgraph, dnodemap[orgtail], dnodemap[orghead], graph->cost[i], graph->cost[i + 1]);

            /* (*edgeweight)[e]: number of solutions containing edge e */
            for( int k = 0; k < selectedsols; k++ )
            {
               SCIP_Bool hit;

               if( k == 0 )
               {
                  hit = (incumbentedges[i] == CONNECT
                      || incumbentedges[i + 1] == CONNECT);
               }
               else if( usestppool )
                  hit = (poolsols[solselection[k]]->soledges[i] == CONNECT
                      || poolsols[solselection[k]]->soledges[i + 1] == CONNECT);
               else
                  hit = (SCIPisEQ(scip, SCIPgetSolVal(scip, sols[solselection[k]], vars[i]), 1.0)
                      || SCIPisEQ(scip, SCIPgetSolVal(scip, sols[solselection[k]], vars[i + 1]), 1.0));

               /* is edge i or reversed edge in current solution? */
               if( hit )
               {
                  (*edgeweight)[j - 2]++;
                  (*edgeweight)[j - 1]++;
               }
            }
         }
      }

      assert(j == 2 * nsoledges);
      SCIPfreeBufferArray(scip, &soledge);
      SCIPfreeBufferArray(scip, &dnodemap);
      SCIPfreeBufferArray(scip, &solnode);
   }

   SCIPfreeBufferArray(scip, &solselection);
   assert(graph_valid(newgraph));
   *solgraph = newgraph;

   return SCIP_OKAY;
}

static
void marksolverts(
   GRAPH* g,
   IDX* curr,
   int* unodemap,
   STP_Bool* stvertex
   )
{
   while( curr != NULL )
   {
      int i = curr->index;

      stvertex[unodemap[ g->orghead[i] ]] = TRUE;
      stvertex[unodemap[ g->orgtail[i] ]] = TRUE;

      curr = curr->parent;
   }
}

static
SCIP_Bool isInPool(
   const int*            soledges,           /**< edge array of solution to be checked */
   const STPSOLPOOL*     pool                /**< the pool */
)
{
   STPSOL** poolsols = pool->sols;
   const int poolsize = pool->size;
   const int nedges = pool->nedges;

   for( int i = 0; i < poolsize; i++ )
   {
      int j;
      const int* pooledges = poolsols[i]->soledges;
      assert(pooledges != NULL);

      for( j = 0; j < nedges; j++ )
         if( pooledges[j] != soledges[j] )
            break;

      /* pooledges == soledges? */
      if( j == nedges )
      {
         SCIPdebugMessage("Pool: solution is already contained \n");
         return TRUE;
      }
   }
   return FALSE;
}

/*
 * primal heuristic specific interface methods
 */


/** get solution from index */
STPSOL* SCIPStpHeurRecSolfromIdx(
   STPSOLPOOL*           pool,               /**< the pool */
   const int             soindex             /**< the index */
      )
{
   int i;
   int size;

   assert(pool != NULL);
   assert(soindex >= 0 && soindex <= pool->maxindex);

   size = pool->size;

   for( i = 0; i < size; i++ )
      if( pool->sols[i]->index == soindex )
         break;

   if( i == size )
      return NULL;
   else
      return pool->sols[i];
}

/** initializes STPSOL pool */
SCIP_RETCODE SCIPStpHeurRecInitPool(
   SCIP*                 scip,               /**< SCIP data structure */
   STPSOLPOOL**          pool,               /**< the pool */
   const int             nedges,             /**< number of edges of solutions to be stored in the pool */
   const int             maxsize             /**< capacity of pool */
   )
{
   STPSOLPOOL* dpool;

   assert(pool != NULL);
   assert(nedges > 0);
   assert(maxsize > 0);

   SCIP_CALL( SCIPallocBlockMemory(scip, pool) );

   dpool = *pool;
   SCIP_CALL( SCIPallocMemoryArray(scip, &(dpool->sols), maxsize) );

   for( int i = 0; i < maxsize; i++ )
      dpool->sols[i] = NULL;

   dpool->size = 0;
   dpool->nedges = nedges;
   dpool->maxsize = maxsize;
   dpool->maxindex = -1;

   return SCIP_OKAY;
}


/** frees STPSOL pool */
void SCIPStpHeurRecFreePool(
   SCIP*                 scip,               /**< SCIP data structure */
   STPSOLPOOL**          pool                /**< the pool */
   )
{
   STPSOLPOOL* dpool = *pool;
   const int poolsize = dpool->size;

   assert(pool != NULL);
   assert(dpool != NULL);
   assert(poolsize == dpool->maxsize || dpool->sols[poolsize] == NULL);

   for( int i = poolsize - 1; i >= 0; i-- )
   {
      STPSOL* sol = dpool->sols[i];

      assert(sol != NULL);

      SCIPfreeMemoryArray(scip, &(sol->soledges));
      SCIPfreeBlockMemory(scip, &sol);
   }

   SCIPfreeMemoryArray(scip, &(dpool->sols));
   SCIPfreeBlockMemory(scip, pool);
}


/** tries to add STPSOL to pool */
SCIP_RETCODE SCIPStpHeurRecAddToPool(
   SCIP*                 scip,               /**< SCIP data structure */
   const SCIP_Real       obj,                /**< objective of solution to be added */
   const int*            soledges,           /**< edge array of solution to be added */
   STPSOLPOOL*           pool,               /**< the pool */
   SCIP_Bool*            success             /**< has solution been added? */
   )
{
   STPSOL** poolsols = pool->sols;
   STPSOL* sol;
   int i;
   int poolsize = pool->size;
   const int nedges = pool->nedges;
   const int poolmaxsize = pool->maxsize;

   assert(scip != NULL);
   assert(pool != NULL);
   assert(poolsols != NULL);
   assert(poolsize >= 0);
   assert(poolmaxsize >= 0);
   assert(poolsize <= poolmaxsize);

   *success = FALSE;

   /* is solution in pool? */
   if( isInPool(soledges, pool) )
      return SCIP_OKAY;

   SCIPdebugMessage("Pool: add to pool (current size: %d, max: %d) \n", poolsize, poolmaxsize);

   /* enlarge pool if possible */
   if( poolsize < poolmaxsize )
   {
      SCIPdebugMessage("Pool: alloc memory at position %d \n", poolsize);

      SCIP_CALL( SCIPallocBlockMemory(scip, &(poolsols[poolsize])) );
      SCIP_CALL( SCIPallocMemoryArray(scip, &(poolsols[poolsize]->soledges), nedges) );

      poolsize++;
      pool->size++;
   }
   /* pool is full; new solution worse than worst solution in pool? */
   else if( SCIPisGT(scip, obj, poolsols[poolsize - 1]->obj) )
   {
      return SCIP_OKAY;
   }

   /* overwrite last element of pool (either empty or inferior to current solution) */
   sol = poolsols[poolsize - 1];
   assert(sol != NULL);
   sol->obj = obj;
   sol->index = ++(pool->maxindex);
   BMScopyMemoryArray(sol->soledges, soledges, nedges);

   /* shift solution up */
   for( i = poolsize - 1; i >= 1; i-- )
   {
      if( SCIPisGT(scip, obj, poolsols[i - 1]->obj) )
         break;

      poolsols[i] = poolsols[i - 1];
   }

   poolsols[i] = sol;
   SCIPdebugMessage("Pool: put new solution to position %d \n", i);
   *success = TRUE;

   return SCIP_OKAY;
}



/** runs STP recombination heuristic */
SCIP_RETCODE SCIPStpHeurRecRun(
   SCIP*                 scip,               /**< SCIP data structure */
   STPSOLPOOL*           pool,               /**< STP solution pool or NULL */
   SCIP_HEUR*            heur,               /**< heuristic or NULL */
   SCIP_HEURDATA*        heurdata,           /**< heuristic data or NULL */
   const GRAPH*          graph,              /**< graph data */
   SCIP_VAR**            vars,               /**< variables or NULL */
   int*                  newsolindex,        /**< index of new solution */
   int                   runs,               /**< number of runs */
   int                   nsols,              /**< number of solutions in pool (SCIP or STP) */
   SCIP_Bool             restrictheur,       /**< use restricted version of heur? */
   SCIP_Bool*            solfound            /**< new solution found? */
)
{
   int* newsoledges;
   int* incumbentedges;
   SCIP_Real incumentobj;
   SCIP_Real hopfactor = 0.1;

   const STP_Bool usestppool = (pool != NULL);
   const int nnodes = graph->knots;
   const int nedges = graph->edges;
   const int probtype = graph->stp_type;
   const SCIP_Bool pcmw = (probtype == STP_PCSPG || probtype == STP_MWCSP || probtype == STP_RPCSPG || probtype == STP_RMWCSP );
   STP_Bool* stnodes;

   assert(runs >= 0);
   assert(graph != NULL);
   assert(scip != NULL);
   assert(*newsolindex >= 0);

   SCIPdebugMessage("REC: start \n");

   *solfound = FALSE;

   SCIP_CALL( SCIPallocBufferArray(scip, &newsoledges, nedges) );
   SCIP_CALL( SCIPallocBufferArray(scip, &incumbentedges, nedges) );
   SCIP_CALL( SCIPallocBufferArray(scip, &stnodes, nnodes) );

   /*
    * initialize incumbent solution
    */

   if( usestppool )
   {
      int i;
      STPSOL** poolsols = pool->sols;

      assert(pool->nedges == nedges);

      for( i = 0; i < nsols; i++ )
         if( *newsolindex == poolsols[i]->index )
            break;
      assert(i < nsols);

      BMScopyMemoryArray(incumbentedges, poolsols[i]->soledges, nedges);
   }
   else
   {
      SCIP_SOL* newsol;
      SCIP_SOL** sols = SCIPgetSols(scip);
      int i;

      assert(sols != NULL);

      for( i = 0; i < nsols; i++ )
         if( *newsolindex == SCIPsolGetIndex(sols[i]) )
            break;
      assert(i < nsols);

      newsol = sols[i];

      for( int e = 0; e < nedges; e++ )
         if( SCIPisEQ(scip, SCIPgetSolVal(scip, newsol, vars[e]), 1.0) )
            incumbentedges[e] = CONNECT;
         else
            incumbentedges[e] = UNKNOWN;
   }

   /* get objective value of incumbent */
   incumentobj = graph_sol_getObj(graph->cost, incumbentedges, 0.0, nedges);

   SCIPdebugMessage("REC: incumbent obj: %f \n", incumentobj);

   if( heur == NULL )
   {
      heur = SCIPfindHeur(scip, "rec");
      assert(heur != NULL);
      heurdata = SCIPheurGetData(heur);
      assert(heurdata != NULL);
   }

   /* main loop (for recombination) */
   for( int v = 0, failcount = 0; v < CYCLES_PER_RUN * runs && !SCIPisStopped(scip); v++ )
   {
      GRAPH* solgraph;
      IDX* curr;
      int* edgeweight;
      int* edgeancestor;
      SCIP_Real pobj;
      SCIP_Bool success;
      SCIP_Bool randomize;
      int randn;

      if( SCIPrandomGetInt(heurdata->randnumgen, 0, 1) == 1 )
         randomize = TRUE;
      else
         randomize = FALSE;

      if( restrictheur )
         randn = SCIPrandomGetInt(heurdata->randnumgen, 0, 3);
      else
         randn = SCIPrandomGetInt(heurdata->randnumgen, 0, 6);

      if( (randn <= 2) || (nsols < 3) )
         heurdata->nusedsols = 2;
      else if( (randn <= 4) || (nsols < 4) )
         heurdata->nusedsols = 3;
      else
         heurdata->nusedsols = 4;

      SCIPdebugMessage("REC: merge %d solutions \n", heurdata->nusedsols);

      /* build a new graph, consisting of several solutions */
      SCIP_CALL( buildsolgraph(scip, pool, heurdata, graph, &solgraph, incumbentedges, newsolindex,
            &edgeancestor, &edgeweight, &success, randomize, TRUE) );

      /* valid graph built? */
      if( success )
      {
         IDX** ancestors;
         GRAPH* psolgraph;
         STP_Bool* solnodes = NULL;
         int* soledges = NULL;
         SCIP_HEURDATA* tmheurdata;
         int nsoledges;

         SCIPdebugMessage("REC: solution successfully built \n");

         assert(SCIPfindHeur(scip, "TM") != NULL);
         tmheurdata = SCIPheurGetData(SCIPfindHeur(scip, "TM"));

         assert(graph_valid(solgraph));

         /* reduce new graph */
         if( probtype == STP_RPCSPG || probtype == STP_DHCSTP || probtype == STP_DCSTP
             || probtype == STP_NWSPG || probtype == STP_SAP || probtype == STP_RMWCSP )
            SCIP_CALL( reduce(scip, &solgraph, &pobj, 0, 5, FALSE) );
         else
            SCIP_CALL( reduce(scip, &solgraph, &pobj, 2, 5, FALSE) );

         SCIP_CALL( graph_pack(scip, solgraph, &psolgraph, FALSE) );

         solgraph = psolgraph;
         ancestors = solgraph->ancestors;
         nsoledges = solgraph->edges;

         /* if graph reduction solved the whole problem, solgraph has only one node */
         if( solgraph->terms > 1 )
         {
            SCIP_Real* cost;
            SCIP_Real* costrev;
            SCIP_Real* orgprize = NULL;
            SCIP_Real* nodepriority;
            SCIP_Real maxcost;
            int best_start;
            const int nsolnodes = solgraph->knots;

            SCIPdebugMessage("REC: graph not completely reduced, nodes: %d, edges: %d, terminals: %d \n", solgraph->knots, nsoledges, solgraph->terms);

            /* allocate memory */
            SCIP_CALL( SCIPallocBufferArray(scip, &soledges, nsoledges) );
            SCIP_CALL( SCIPallocBufferArray(scip, &cost, nsoledges) );
            SCIP_CALL( SCIPallocBufferArray(scip, &costrev, nsoledges) );
            SCIP_CALL( SCIPallocBufferArray(scip, &nodepriority, nsolnodes) );

            if( pcmw )
               SCIP_CALL( SCIPallocBufferArray(scip, &orgprize, nsolnodes) );

            for( int i = 0; i < nsolnodes; i++ )
               nodepriority[i] = 0.0;

            /*
             * 1. modify edge costs
             */

            /* copy edge costs */
            BMScopyMemoryArray(cost, solgraph->cost, nsoledges);

            maxcost = 0.0;
            for( int e = 0; e < nsoledges; e++ )
            {
               SCIP_Real avg = 0.0;
               int i = 0;
               SCIP_Bool fixed = FALSE;

               curr = ancestors[e];

               if( curr != NULL )
               {
                  while( curr != NULL )
                  {
                     i++;
                     avg += edgeweight[curr->index];
                     if( !usestppool && SCIPvarGetUbGlobal(vars[edgeancestor[curr->index]] ) < 0.5 )
                        fixed = TRUE;

                     curr = curr->parent;
                  }
                  avg = avg / (double) i;
                  assert(avg >= 1);
               }
               /* is an ancestor edge fixed? */
               if( fixed )
               {
                  cost[e] = BLOCKED;

                  nodepriority[solgraph->head[e]] /= 2.0;
                  nodepriority[solgraph->tail[e]] /= 2.0;
               }

               nodepriority[solgraph->head[e]] += avg - 1.0;
               nodepriority[solgraph->tail[e]] += avg - 1.0;

               cost[e] *= edgecostmultiplier(scip, heurdata, avg);

               if( probtype == STP_DHCSTP && SCIPisLT(scip, cost[e], BLOCKED) && SCIPisGT(scip, cost[e], maxcost) )
                  maxcost = cost[e];
            }

            /* adapted prizes */
            if( pcmw )
            {
               const int solgraphroot = solgraph->source;
               SCIP_Real* const prize = solgraph->prize;

               assert(prize != NULL);
               assert(orgprize != NULL);
               assert(solgraph->extended);

#ifndef NDEBUG
               graph_pc_2org(solgraph);
               assert(graph_pc_term2edgeConsistent(solgraph));
               graph_pc_2trans(solgraph);
#endif

               for( int k = 0; k < nsolnodes; k++ )
               {
                  if( Is_pterm(solgraph->term[k]) && k != solgraphroot )
                  {
                     int e;
                     const int term = solgraph->head[solgraph->term2edge[k]];
                     orgprize[k] = prize[k];

                     assert(term >= 0);
                     assert(Is_term(solgraph->term[term]));

                     for( e = solgraph->inpbeg[term]; e != EAT_LAST; e = solgraph->ieat[e] )
                        if( solgraph->tail[e] == solgraphroot )
                           break;

                     assert(e != EAT_LAST);

                     prize[k] = cost[e];
                     assert(solgraph->cost[e] > 0);
                  }
               }
            }

            for( int e = 0; e < nsoledges; e++ )
            {
               costrev[e] = cost[flipedge(e)];
               soledges[e] = UNKNOWN;
            }

            /* initialize shortest path algorithm */
            SCIP_CALL( graph_path_init(scip, solgraph) );

            /*
             *  2. compute solution
             */

            // todo: run prune heuristic with changed weights!

            /* run TM heuristic */
            SCIP_CALL( SCIPStpHeurTMRun(scip, tmheurdata, solgraph, NULL, &best_start, soledges, heurdata->ntmruns,
                  solgraph->source, cost, costrev, &hopfactor, nodepriority, maxcost, &success, FALSE) );

            assert(SCIPisStopped(scip) || success);
            assert(SCIPisStopped(scip) || graph_sol_valid(scip, solgraph, soledges));

            /* reset vertex weights */
            if( pcmw )
            {
               SCIP_Real* const prize = solgraph->prize;

               assert(orgprize != NULL);

               for( int k = 0; k < nsolnodes; k++ )
                  if( Is_pterm(solgraph->term[k]) && k != solgraph->source )
                     prize[k] = orgprize[k];

               SCIPfreeBufferArray(scip, &orgprize);
            }

            assert(graph_valid(solgraph));

            /* run local heuristic (with original costs) */
            if( !SCIPisStopped(scip) && probtype != STP_DHCSTP && probtype != STP_DCSTP
                  && probtype != STP_SAP && probtype != STP_NWSPG && probtype != STP_RMWCSP )
            {
               SCIP_CALL( SCIPStpHeurLocalRun(scip, solgraph, solgraph->cost, soledges) );
               assert(graph_sol_valid(scip, solgraph, soledges));
            }

            graph_path_exit(scip, solgraph);

            SCIPfreeBufferArray(scip, &nodepriority);
            SCIPfreeBufferArray(scip, &costrev);
            SCIPfreeBufferArray(scip, &cost);
         } /* graph->terms > 1 */

         for( int i = 0; i < nedges; i++ )
            newsoledges[i] = UNKNOWN;

         for( int i = 0; i < nnodes; i++ )
            stnodes[i] = FALSE;

         if( pcmw )
         {
            SCIP_CALL( SCIPallocBufferArray(scip, &solnodes, solgraph->orgknots) );

            for( int i = 0; i < solgraph->orgknots; i++ )
               solnodes[i] = FALSE;
         }

         /*
          *  retransform solution found by heuristic
          */

         if( solgraph->terms > 1 )
         {
            assert(soledges != NULL);
            for( int e = 0; e < nsoledges; e++ )
            {
               if( soledges[e] == CONNECT )
               {
                  /* iterate through list of ancestors */
                  if( probtype != STP_DCSTP )
                  {
                     curr = ancestors[e];

                     while( curr != NULL )
                     {
                        int i = edgeancestor[curr->index];

                        stnodes[graph->head[i]] = TRUE;
                        stnodes[graph->tail[i]] = TRUE;

                        if( pcmw )
                        {
                           assert(solgraph->orghead[curr->index] < solgraph->orgknots);
                           assert(solgraph->orgtail[curr->index] < solgraph->orgknots);

                           solnodes[solgraph->orghead[curr->index]] = TRUE;
                           solnodes[solgraph->orgtail[curr->index]] = TRUE;
                        }

                        curr = curr->parent;
                     }
                  }
                  else
                  {
                     curr = ancestors[e];
                     while( curr != NULL )
                     {
                        int i = edgeancestor[curr->index];
                        newsoledges[i] = CONNECT;

                        curr = curr->parent;
                     }
                  }
               }
            }
         } /* if( solgraph->terms > 1 ) */

         /* retransform edges fixed during graph reduction */
         if( probtype != STP_DCSTP )
         {
            curr = solgraph->fixedges;

            while( curr != NULL )
            {
               const int i = edgeancestor[curr->index];

               stnodes[graph->head[i]] = TRUE;
               stnodes[graph->tail[i]] = TRUE;
               if( pcmw )
               {
                  assert(solgraph->orghead[curr->index] < solgraph->orgknots);
                  assert(solgraph->orgtail[curr->index] < solgraph->orgknots);

                  solnodes[solgraph->orghead[curr->index]] = TRUE;
                  solnodes[solgraph->orgtail[curr->index]] = TRUE;
               }

               curr = curr->parent;
            }
         }
         else
         {
            curr = solgraph->fixedges;
            while( curr != NULL )
            {
               const int i = edgeancestor[curr->index];
               newsoledges[i] = CONNECT;
            }
         }

         if( pcmw )
         {
            STP_Bool* pcancestoredges;
            SCIP_CALL( SCIPallocBufferArray(scip, &pcancestoredges, solgraph->orgedges) );

            for( int k = 0; k < solgraph->orgedges; k++ )
               pcancestoredges[k] = FALSE;

            SCIP_CALL( graph_sol_markPcancestors(scip, solgraph->pcancestors, solgraph->orgtail, solgraph->orghead, solgraph->orgknots,
                  solnodes, pcancestoredges, NULL, NULL, NULL ) );

            for( int k = 0; k < solgraph->orgedges; k++ )
               if( pcancestoredges[k] )
               {
                  const int i = edgeancestor[k];
                  stnodes[graph->tail[i]] = TRUE;
                  stnodes[graph->head[i]] = TRUE;
               }

            SCIPfreeBufferArray(scip, &pcancestoredges);
            SCIPfreeBufferArray(scip, &solnodes);
         }

         SCIPfreeMemoryArray(scip, &edgeancestor);

         graph_free(scip, &solgraph, TRUE);

         /* prune solution (in the original graph) */
         if( pcmw )
            SCIP_CALL( SCIPStpHeurTMPrunePc(scip, graph, graph->cost, newsoledges, stnodes) );
         else if( probtype == STP_DCSTP )
            SCIP_CALL( SCIPStpHeurTMBuildTreeDc(scip, graph, newsoledges, stnodes) );
         else
            SCIP_CALL( SCIPStpHeurTMPrune(scip, graph, graph->cost, 0, newsoledges, stnodes) );

         assert(graph_sol_valid(scip, graph, newsoledges));
         pobj = graph_sol_getObj(graph->cost, newsoledges, 0.0, nedges);

         SCIPdebugMessage("REC: new obj: %f \n", pobj);

         /* improved incumbent solution? */
         if( !SCIPisStopped(scip) && SCIPisLT(scip, pobj, incumentobj) )
         {
            SCIPdebugMessage("...is better! \n");
            incumentobj = pobj;
            *solfound = TRUE;
            BMScopyMemoryArray(incumbentedges, newsoledges, nedges);
         }
         else
         {
            failcount++;
         }

         SCIPfreeBufferArrayNull(scip, &soledges);
      }
      else
      {
         failcount++;
      }

      SCIPfreeMemoryArray(scip, &edgeweight);

      /* too many fails? */
      if( failcount >= REC_MAX_FAILS )
      {
         SCIPdebugMessage("REC: too many fails, exit! \n");
         break;
      }
   }

   SCIPfreeBufferArray(scip, &stnodes);

   /* improving solution found? */
   if( *solfound )
   {
      /*
       * store best solution in pool
       */

      SCIPdebugMessage("REC: better solution found ...  ");

      if( usestppool )
      {
         const int maxindex = pool->maxindex;
         SCIP_CALL( SCIPStpHeurRecAddToPool(scip, incumentobj, incumbentedges, pool, solfound) );

         if( *solfound )
         {
            assert(pool->maxindex == maxindex + 1);
            *newsolindex = maxindex + 1;
            SCIPdebugMessage("and added! \n");
         }
         else
         {
            *newsolindex = -1;
         }
      }
      else
      {
         SCIP_SOL* sol = NULL;
         SCIP_Real* nval = NULL;

         SCIP_CALL( SCIPallocBufferArray(scip, &nval, nedges) );

         for( int e = 0; e < nedges; e++ )
         {
            if( newsoledges[e] == CONNECT )
               nval[e] = 1.0;
            else
               nval[e] = 0.0;
         }

         SCIP_CALL( SCIPprobdataAddNewSol(scip, nval, sol, heur, solfound) );

         if( *solfound )
         {
            SCIP_SOL** sols = SCIPgetSols(scip);
            int idx = -1;

            SCIPdebugMessage("and added! \n");

            nsols = SCIPgetNSols(scip);

            assert(nsols > 0);

            for( int i = 1; i < nsols; i++ )
               if( SCIPsolGetIndex(sols[i]) > idx )
                  idx = SCIPsolGetIndex(sols[i]);

            assert(idx >= 0);

            *newsolindex = idx;
         }
         SCIPfreeBufferArray(scip, &nval);

      }
   }
   else
   {
      *newsolindex = -1;
   }

   SCIPfreeBufferArray(scip, &incumbentedges);
   SCIPfreeBufferArray(scip, &newsoledges);


   return SCIP_OKAY;
}

/** heuristic to exclude vertices or edges from a given solution (and inserting other edges) to improve objective */
SCIP_RETCODE SCIPStpHeurRecExclude(
   SCIP*                 scip,               /**< SCIP data structure */
   const GRAPH*          graph,              /**< graph structure */
   const int*            result,             /**< edge solution array (UNKNOWN/CONNECT) */
   int*                  newresult,          /**< new edge solution array (UNKNOWN/CONNECT) */
   int*                  dnodemap,           /**< node array for internal use */
   STP_Bool*             stvertex,           /**< node array for internally marking solution vertices */
   SCIP_Bool*            success             /**< solution improved? */
   )
{
   SCIP_HEURDATA* tmheurdata;
   GRAPH* newgraph;
   int* unodemap;
   STP_Bool* solnodes;
   SCIP_Real dummy;
   int j;
   int nsolterms;
   int nsoledges;
   int nsolnodes;
   int best_start;
   const int root = graph->source;
   const int nedges = graph->edges;
   const int nnodes = graph->knots;

   assert(scip != NULL);
   assert(graph != NULL);
   assert(result != NULL);
   assert(stvertex != NULL);
   assert(success != NULL);
   assert(dnodemap != NULL);
   assert(newresult != NULL);

   *success = FALSE;
   assert(graph->stp_type == STP_MWCSP);
   assert(graph_valid(graph));

   /* killed solution edge? */
   for( int e = 0; e < nedges; e++ )
      if( result[e] == CONNECT && graph->oeat[e] == EAT_FREE )
         return SCIP_OKAY;

   /*** 1. step: for solution S and original graph (V,E) initialize new graph (V[S], (V[S] X V[S]) \cup E) ***/

   BMSclearMemoryArray(stvertex, nnodes);

   nsolnodes = 1;
   nsolterms = 0;
   stvertex[root] = 1;

   /* mark nodes in solution */
   for( int e = 0; e < nedges; e++ )
   {
      if( result[e] == CONNECT )
      {
         int tail = graph->tail[e];
         int head = graph->head[e];

         if( tail == root )
         {
            /* there might be only one node */
            if( Is_pterm(graph->term[head]) )
            {
               stvertex[head] = 1;
               nsolterms++;
               nsolnodes++;
            }

            continue;
         }

         assert(!stvertex[head] );
         stvertex[head] = 1;

         if( Is_pterm(graph->term[head]) )
            nsolterms++;
         nsolnodes++;
      }
   }

   assert(nsolterms > 0);

   nsoledges = 0;

   /* count edges of new graph */
   for( int i = 0; i < nedges; i += 2 )
      if( stvertex[graph->tail[i]] && stvertex[graph->head[i]] && graph->oeat[i] != EAT_FREE  )
         nsoledges++;

   nsoledges *= 2;

   /* create new graph */
   SCIP_CALL( graph_init(scip, &newgraph, nsolnodes, nsoledges, 1) );

   newgraph->stp_type = graph->stp_type;
   newgraph->extended = TRUE;

   SCIP_CALL( SCIPallocBufferArray(scip, &unodemap, nsolnodes) );
   SCIP_CALL( graph_pc_init(scip, newgraph, nsolnodes, nsolnodes) );

   j = 0;
   for( int i = 0; i < nnodes; i++ )
   {
      if( stvertex[i] )
      {
         if( (!Is_term(graph->term[i])) )
            newgraph->prize[j] = graph->prize[i];
         else
            newgraph->prize[j] = 0.0;

         graph_knot_add(newgraph, graph->term[i]);
         unodemap[j] = i;
         dnodemap[i] = j++;
      }
      else
      {
         dnodemap[i] = -1;
      }
   }

   assert(j == nsolnodes);

   /* set root */
   newgraph->source = dnodemap[root];
   assert(newgraph->source >= 0 && newgraph->source < nsolnodes);

   /* add edges */
   for( int i = 0; i < nedges; i += 2 )
      if( stvertex[graph->tail[i]] && stvertex[graph->head[i]] && graph->oeat[i] != EAT_FREE )
      {
         const int tail = graph->tail[i];
         const int head = graph->head[i];
         const int dtail = dnodemap[tail];
         const int dhead = dnodemap[head];

         graph_pc_updateTerm2edge(newgraph, graph, dtail, dhead, tail, head);
         graph_edge_add(scip, newgraph, dtail, dhead, graph->cost[i], graph->cost[i + 1]);
      }

   assert(newgraph->edges == nsoledges);


   /*** step 2: presolve ***/

   newgraph->norgmodelknots = nsolnodes;

   dummy = 0.0;
   SCIP_CALL( reduce(scip, &newgraph, &dummy, 1, 5, FALSE) );


   /*** step 3: compute solution on new graph ***/


   /* get TM heuristic data */
   assert(SCIPfindHeur(scip, "TM") != NULL);
   tmheurdata = SCIPheurGetData(SCIPfindHeur(scip, "TM"));

   SCIP_CALL( graph_path_init(scip, newgraph) );

   /* compute Steiner tree to obtain upper bound */
   best_start = newgraph->source;
   SCIP_CALL( SCIPStpHeurTMRun(scip, tmheurdata, newgraph, NULL, &best_start, newresult, MIN(50, nsolterms), newgraph->source, newgraph->cost,
         newgraph->cost, &dummy, NULL, 0.0, success, FALSE) );

   graph_path_exit(scip, newgraph);

   assert(*success);
   assert(graph_sol_valid(scip, newgraph, newresult));


   /*** step 4: retransform solution to original graph ***/


   BMSclearMemoryArray(stvertex, nnodes);

   for( int e = 0; e < nsoledges; e++ )
      if( newresult[e] == CONNECT )
         marksolverts(newgraph, newgraph->ancestors[e], unodemap, stvertex);

   /* retransform edges fixed during graph reduction */
   marksolverts(newgraph, newgraph->fixedges, unodemap, stvertex);

   for( int k = 0; k < nsolnodes; k++ )
      if( stvertex[unodemap[k]] )
         marksolverts(newgraph, newgraph->pcancestors[k], unodemap, stvertex);

   SCIP_CALL(SCIPallocBufferArray(scip, &solnodes, nsolnodes));

   for( int k = 0; k < nsolnodes; k++ )
      solnodes[k] = FALSE;

   for( int k = 0; k < nnodes; k++ )
      if( stvertex[k] )
      {
         assert(dnodemap[k] < nsolnodes);
         solnodes[dnodemap[k]] = TRUE;
      }

   SCIP_CALL( graph_sol_markPcancestors(scip, newgraph->pcancestors, newgraph->orgtail, newgraph->orghead, nsolnodes, solnodes, NULL, NULL, NULL, NULL ) );

   for( int k = 0; k < nsolnodes; k++ )
      if( solnodes[k] )
         stvertex[unodemap[k]] = TRUE;

   SCIPfreeBufferArray(scip, &solnodes);

   for( int e = 0; e < nedges; e++ )
      newresult[e] = UNKNOWN;

   SCIP_CALL( SCIPStpHeurTMPrunePc(scip, graph, graph->cost, newresult, stvertex) );

   /* solution better than original one?  */

   if( SCIPisLT(scip, graph_sol_getObj(graph->cost, newresult, 0.0, nedges),
         graph_sol_getObj(graph->cost, result, 0.0, nedges)) )
   {
      *success = TRUE;
      SCIPdebugMessage("success %f < %f \n", graph_sol_getObj(graph->cost, newresult, 0.0, nedges), graph_sol_getObj(graph->cost, result, 0.0, nedges));
   }
   else
   {
      SCIPdebugMessage("no improvements %f >= %f \n", graph_sol_getObj(graph->cost, newresult, 0.0, nedges), graph_sol_getObj(graph->cost, result, 0.0, nedges));
      *success = FALSE;
   }

   assert(graph_sol_valid(scip, graph, newresult));

   if( !graph_sol_valid(scip, graph, newresult) )
      *success = FALSE;

   SCIPfreeBufferArray(scip, &unodemap);
   graph_free(scip, &newgraph, TRUE);

   return SCIP_OKAY;
}




/*
 * Callback methods of primal heuristic
 */

/** deinitialization method of primal heuristic (called before transformed problem is freed) */
static
SCIP_DECL_HEUREXIT(heurExitRec)
{
   SCIP_HEURDATA* heurdata;

   heurdata = SCIPheurGetData(heur);
   assert(heurdata != NULL);

   SCIPheurSetData(heur, heurdata);

   return SCIP_OKAY;
}

/** copy method for primal heuristic plugins (called when SCIP copies plugins) */
static
SCIP_DECL_HEURCOPY(heurCopyRec)
{  /*lint --e{715}*/
   assert(scip != NULL);
   assert(heur != NULL);
   assert(strcmp(SCIPheurGetName(heur), HEUR_NAME) == 0);

   /* call inclusion method of primal heuristic */
   SCIP_CALL( SCIPStpIncludeHeurRec(scip) );

   return SCIP_OKAY;
}

/** destructor of primal heuristic to free user data (called when SCIP is exiting) */
static
SCIP_DECL_HEURFREE(heurFreeRec)
{  /*lint --e{715}*/
   SCIP_HEURDATA* heurdata;

   assert(heur != NULL);
   assert(scip != NULL);

   /* get heuristic data */
   heurdata = SCIPheurGetData(heur);
   assert(heurdata != NULL);

   /* free random number generator */
   SCIPfreeRandom(scip, &heurdata->randnumgen);

   /* free heuristic data */
   SCIPfreeMemory(scip, &heurdata);
   SCIPheurSetData(heur, NULL);

   return SCIP_OKAY;
}

/** initialization method of primal heuristic (called after problem was transformed) */
static
SCIP_DECL_HEURINIT(heurInitRec)
{  /*lint --e{715}*/

   assert(heur != NULL);
   assert(scip != NULL);

   return SCIP_OKAY;
}

/** solving process initialization method of primal heuristic (called when branch and bound process is about to begin) */
static
SCIP_DECL_HEURINITSOL(heurInitsolRec)
{  /*lint --e{715}*/
   SCIP_HEURDATA* heurdata;

   assert(heur != NULL);
   assert(scip != NULL);

   heurdata = SCIPheurGetData(heur);
   assert(heurdata != NULL);

   /* initialize data */
   heurdata->nselectedsols = 0;
   heurdata->nusedsols = DEFAULT_NUSEDSOLS;
   heurdata->randseed = DEFAULT_RANDSEED;
   heurdata->nselectedsols = 0;
   heurdata->ncalls = 0;
   heurdata->nlastsols = 0;
   heurdata->lastsolindex = -1;
   heurdata->bestsolindex = -1;
   heurdata->nfailures = 0;


   return SCIP_OKAY;
}

/** solving process deinitialization method of primal heuristic (called before branch and bound process data is freed) */
static
SCIP_DECL_HEUREXITSOL(heurExitsolRec)
{  /*lint --e{715}*/

   return SCIP_OKAY;
}

/** execution method of primal heuristic */
static
SCIP_DECL_HEUREXEC(heurExecRec)
{  /*lint --e{715}*/
   SCIP_HEURDATA* heurdata;
   SCIP_PROBDATA* probdata;
   SCIP_VAR** vars;
   SCIP_SOL** sols;
   GRAPH* graph;
   SCIP_Longint nallsols;
   SCIP_Bool pcmw;
   SCIP_Bool solfound;
   SCIP_Bool restrictheur;

   int runs;
   int nsols;
   int solindex;
   int probtype;
   int newsolindex;
   int nreadysols;
   int bestsolindex;

   assert(heur != NULL);
   assert(scip != NULL);
   assert(strcmp(SCIPheurGetName(heur), HEUR_NAME) == 0);
   assert(result != NULL);

   /* get heuristic data */
   heurdata = SCIPheurGetData(heur);
   assert(heurdata != NULL);

   /* get problem data */
   probdata = SCIPgetProbData(scip);
   assert(probdata != NULL);

   /* get graph */
   graph = SCIPprobdataGetGraph(probdata);
   assert(graph != NULL);

   probtype = graph->stp_type;
   *result = SCIP_DIDNOTRUN;

   if( probtype == STP_RMWCSP )
      return SCIP_OKAY;

   SCIPdebugMessage("REC: checking ... \n");

   pcmw = (probtype == STP_PCSPG || probtype == STP_MWCSP || probtype == STP_RPCSPG || probtype == STP_RMWCSP);
   nallsols = SCIPgetNSolsFound(scip);
   nreadysols = SCIPgetNSols(scip);

   /* only call heuristic if sufficiently many solutions are available */
   if( nreadysols < DEFAULT_NUSEDSOLS )
      return SCIP_OKAY;

   if( probtype == STP_DCSTP )
      return SCIP_OKAY;

   /* suspend heuristic? */
   if( pcmw || probtype == STP_DHCSTP || probtype == STP_DCSTP )
   {
      int i;
      if( heurdata->ncalls == 0 )
         i = 0;
      else if( heurdata->maxfreq )
         i = 1;
      else if( probtype == STP_RPCSPG || probtype == STP_DCSTP )
         i = MIN(2 * heurdata->nwaitingsols, 2 * heurdata->nfailures);
      else
         i = MIN(heurdata->nwaitingsols, heurdata->nfailures);

      if( nallsols <= heurdata->nlastsols + i )
         return SCIP_OKAY;
   }
   else
   {
      int i;
      if( heurdata->maxfreq )
         i = 1;
      else
         i = MIN(heurdata->nwaitingsols, heurdata->nfailures);

      if( nallsols <= heurdata->nlastsols + i && heurdata->bestsolindex == SCIPsolGetIndex(SCIPgetBestSol(scip)) )
         return SCIP_OKAY;
   }

   /* get edge variables */
   vars = SCIPprobdataGetVars(scip);
   assert(vars != NULL);
   assert(vars[0] != NULL);

   heurdata->ncalls++;

   restrictheur = (graph->terms > BOUND_MAXNTERMINALS && graph->edges > BOUND_MAXNEDGES);

   if( restrictheur )
      runs = RUNS_RESTRICTED;
   else
      runs = RUNS_NORMAL;

   if( runs > nreadysols )
      runs = nreadysols;

   assert(runs > 0);

   sols = SCIPgetSols(scip);
   assert(sols != NULL);

   bestsolindex = SCIPsolGetIndex(SCIPgetBestSol(scip));

   /* first run or exotic variant? */
   if( heurdata->lastsolindex == -1 || probtype == STP_DHCSTP || probtype == STP_DCSTP )
      newsolindex = bestsolindex;
   else
   {
      /* get best new solution */

      SCIP_Real minobj = FARAWAY;
      const int lastindex = heurdata->lastsolindex;

      newsolindex = -1;
      assert(lastindex >= 0);

      for( int i = 0; i < nreadysols; i++ )
      {
         const int currindex = SCIPsolGetIndex(sols[i]);
         if( currindex > lastindex && SCIPisLT(scip, SCIPgetSolOrigObj(scip, sols[i]), minobj) )
         {
            newsolindex = currindex;
            minobj = SCIPgetSolOrigObj(scip, sols[i]);
            SCIPdebugMessage("REC: better start solution, obj: %f \n", minobj);
         }
      }
      if( newsolindex == -1 )
      {
         SCIPdebugMessage("REC: random start solution\n");
         newsolindex = SCIPsolGetIndex(sols[SCIPrandomGetInt(heurdata->randnumgen, 0, nreadysols)]);
      }
   }

   /* run the actual heuristic */
   SCIP_CALL( SCIPStpHeurRecRun(scip, NULL, heur, heurdata, graph, vars, &newsolindex, runs, nreadysols, restrictheur, &solfound) );

   /* save latest solution index */
   solindex = 0;
   nsols = SCIPgetNSols(scip);
   assert(nsols > 0);
   sols = SCIPgetSols(scip);

   for( int i = 1; i < nsols; i++ )
      if( SCIPsolGetIndex(sols[i]) > SCIPsolGetIndex(sols[solindex]) )
         solindex = i;

   if( solfound )
      *result = SCIP_FOUNDSOL;

   if( SCIPsolGetIndex(SCIPgetBestSol(scip)) == bestsolindex )
      heurdata->nfailures++;
   else
      heurdata->nfailures = 0;

   heurdata->lastsolindex = SCIPsolGetIndex(sols[solindex]);
   heurdata->bestsolindex = SCIPsolGetIndex(SCIPgetBestSol(scip));
   heurdata->nlastsols = SCIPgetNSolsFound(scip);

   return SCIP_OKAY;
}


/** creates the rec primal heuristic and includes it in SCIP */
SCIP_RETCODE SCIPStpIncludeHeurRec(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   SCIP_HEURDATA* heurdata;
   SCIP_HEUR* heur;

   /* create Rec primal heuristic data */
   SCIP_CALL( SCIPallocMemory(scip, &heurdata) );

   /* 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, heurExecRec, heurdata) );

   assert(heur != NULL);

   /* set non-NULL pointers to callback methods */
   SCIP_CALL( SCIPsetHeurCopy(scip, heur, heurCopyRec) );
   SCIP_CALL( SCIPsetHeurFree(scip, heur, heurFreeRec) );
   SCIP_CALL( SCIPsetHeurInit(scip, heur, heurInitRec) );
   SCIP_CALL( SCIPsetHeurExit(scip, heur, heurExitRec) );
   SCIP_CALL( SCIPsetHeurInitsol(scip, heur, heurInitsolRec) );
   SCIP_CALL( SCIPsetHeurExitsol(scip, heur, heurExitsolRec) );

   /* add rec primal heuristic parameters */
   SCIP_CALL( SCIPaddIntParam(scip, "heuristics/"HEUR_NAME"/nwaitingsols",
         "number of solution findings to be in abeyance",
         &heurdata->nwaitingsols, FALSE, DEFAULT_NWAITINGSOLS, 1, INT_MAX, NULL, NULL) );

   SCIP_CALL( SCIPaddIntParam(scip, "heuristics/"HEUR_NAME"/randseed",
         "random seed for heuristic",
         NULL, FALSE, DEFAULT_RANDSEED, 1, INT_MAX, paramChgdRandomseed, (SCIP_PARAMDATA*)heurdata) );

   SCIP_CALL( SCIPaddIntParam(scip, "heuristics/"HEUR_NAME"/maxnsols",
         "max size of solution pool for heuristic",
         &heurdata->maxnsols, FALSE, DEFAULT_MAXNSOLS, 5, INT_MAX, NULL, NULL) );

   SCIP_CALL( SCIPaddIntParam(scip, "heuristics/"HEUR_NAME"/ntmruns",
         "number of runs in TM",
         &heurdata->ntmruns, FALSE, DEFAULT_NTMRUNS, 1, INT_MAX, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "heuristics/"HEUR_NAME"/maxfreq",
         "should the heuristic be executed at maximum frequeny?",
         &heurdata->maxfreq, FALSE, DEFAULT_MAXFREQREC, NULL, NULL) );

   heurdata->nusedsols = DEFAULT_NUSEDSOLS;
   heurdata->randseed = DEFAULT_RANDSEED;

#ifdef WITH_UG
   heurdata->randseed += getUgRank();
#endif

   /* create random number generator */
   SCIP_CALL( SCIPcreateRandom(scip, &heurdata->randnumgen, heurdata->randseed, TRUE) );

   return SCIP_OKAY;
}