branch_cloud.c

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the program and library             */
/*         SCIP --- Solving Constraint Integer Programs                      */
/*                                                                           */
/*    Copyright (C) 2002-2020 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 scipopt.org.         */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/**@file   branch_cloud.c
 * @ingroup DEFPLUGINS_BRANCH
 * @brief  cloud branching rule
 * @author Timo Berthold
 * @author Domenico Salvagnin
 *
 * Branching rule based on muliple optimal solutions to the current LP relaxation. See@n
 * Cloud Branching@n
 * Timo Berthold and Domenico Salvagnin@n
 * Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR 2013, LNCS 7874@n
 * Preliminary version available as <a href="http://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/1730">ZIB-Report 13-01</a>.
 */

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

#include "blockmemshell/memory.h"
#include "scip/branch_allfullstrong.h"
#include "scip/branch_cloud.h"
#include "scip/branch_fullstrong.h"
#include "scip/pub_branch.h"
#include "scip/pub_lp.h"
#include "scip/pub_message.h"
#include "scip/pub_tree.h"
#include "scip/pub_var.h"
#include "scip/scip_branch.h"
#include "scip/scip_general.h"
#include "scip/scip_lp.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_numerics.h"
#include "scip/scip_param.h"
#include "scip/scip_prob.h"
#include "scip/scip_sol.h"
#include "scip/scip_solvingstats.h"
#include "scip/scip_timing.h"
#include "scip/scip_tree.h"
#include "scip/scip_var.h"
#include <string.h>


#define BRANCHRULE_NAME            "cloud"
#define BRANCHRULE_DESC            "branching rule that considers several alternative LP optima"
#define BRANCHRULE_PRIORITY        0
#define BRANCHRULE_MAXDEPTH        -1
#define BRANCHRULE_MAXBOUNDDIST    1.0

#define DEFAULT_USECLOUD           TRUE      /**< should a cloud of points be used? */
#define DEFAULT_USEUNION           FALSE     /**< should the union of candidates be used? */
#define DEFAULT_MAXPOINTS          -1        /**< maximum number of points for the cloud (-1 means no limit) */
#define DEFAULT_MINSUCCESSRATE     0.0       /**< minimum success rate for the cloud */
#define DEFAULT_MINSUCCESSUNION    0.0       /**< minimum success rate for the union */
#define DEFAULT_MAXDEPTHUNION      65000     /**< maximum depth for the union */
#define DEFAULT_ONLYF2             FALSE     /**< should only F2 be used? */

/*
 * Data structures
 */

/** branching rule data */
struct SCIP_BranchruleData
{
   int                   lastcand;           /**< last evaluated candidate of last branching rule execution */
   SCIP_Bool             usecloud;           /**< should a cloud of points be used? */
   SCIP_Bool             useunion;           /**< should the union of candidates be used? */
   SCIP_Bool             onlyF2;             /**< should only F2 be used? */
   int                   maxpoints;          /**< maximum number of points for the cloud (-1 means no limit) */
   SCIP_Real             minsuccessrate;     /**< minimum success rate for the cloud */
   SCIP_Real             minsuccessunion;    /**< minimum success rate for the union */
   SCIP_CLOCK*           cloudclock;         /**< clock for cloud diving */
   SCIP_Bool*            skipdown;           /**< should down branch be skiped? */
   SCIP_Bool*            skipup;             /**< should up branch be skiped? */
   int                   ntried;             /**< number of times the cloud was tried */
   int                   ntriedunions;       /**< number of times the cloud was tried */
   int                   nuseful;            /**< number of times the cloud was useful (at least one LP skipped) */
   int                   nusefulunions;      /**< number of times the union was useful (took candidate from new list) */
   int                   ncloudpoints;       /**< sum of cloud points taken over all nodes with at least two poitns in cloud */
   int                   nsavedlps;          /**< sum of saved LPs taken over all nodes with at least two points in cloud */
   int                   maxdepthunion;      /**< maximum depth for the union */
   int                   skipsize;           /**< size of skipdown and skipup array */
};

/*
 * Callback methods of branching rule
 */

/** destructor of branching rule to free user data (called when SCIP is exiting) */
static
SCIP_DECL_BRANCHFREE(branchFreeCloud)
{  /*lint --e{715}*/
   SCIP_BRANCHRULEDATA* branchruledata;

   /* free branching rule data */
   branchruledata = SCIPbranchruleGetData(branchrule);

   if( branchruledata->cloudclock != NULL)
   {
      SCIPstatistic(
         int ntried;
         int nuseful;
         int ncloudpoints;
         int nsavedlps;

         ntried = branchruledata->ntried;
         nuseful = branchruledata->nuseful;
         ncloudpoints = branchruledata->ncloudpoints;
         nsavedlps = branchruledata->nsavedlps;

         SCIPstatisticMessage("time spent diving in cloud branching: %g\n", SCIPgetClockTime(scip, branchruledata->cloudclock));
         SCIPstatisticMessage("cloud branching tried: %6d      found cloud: %6d \n", ntried, nuseful);
         SCIPstatisticMessage("cloud used points: %6d      saved LPs: %6d \n", ncloudpoints, nsavedlps);
         SCIPstatisticMessage("cloud success rates useful/tried: %8.6g points/useful: %8.6g  saved/useful: %8.6g \n",
            ntried == 0 ? -1 : (SCIP_Real)nuseful / ntried,  nuseful == 0 ? -1 : (SCIP_Real)ncloudpoints / nuseful, nuseful == 0 ? -1 :  (SCIP_Real)nsavedlps / nuseful);
      )

      SCIP_CALL( SCIPfreeClock(scip, &(branchruledata->cloudclock)) );
   }

   SCIPfreeBlockMemoryArrayNull(scip, &branchruledata->skipdown, branchruledata->skipsize);
   SCIPfreeBlockMemoryArrayNull(scip, &branchruledata->skipup, branchruledata->skipsize);

   SCIPfreeBlockMemory(scip, &branchruledata);
   SCIPbranchruleSetData(branchrule, NULL);

   return SCIP_OKAY;
}


/** initialization method of branching rule (called after problem was transformed) */
static
SCIP_DECL_BRANCHINIT(branchInitCloud)
{  /*lint --e{715}*/
   SCIP_BRANCHRULEDATA* branchruledata;

   /* initialize branching rule data */
   branchruledata = SCIPbranchruleGetData(branchrule);
   branchruledata->lastcand = 0;
   branchruledata->nuseful = 0;
   branchruledata->nusefulunions = 0;
   branchruledata->ntried = 0;
   branchruledata->ntriedunions = 0;
   branchruledata->ncloudpoints = 0;
   branchruledata->nsavedlps = 0;

   if( branchruledata->cloudclock != NULL)
   {
      SCIP_CALL( SCIPresetClock(scip, branchruledata->cloudclock) );
   }

   return SCIP_OKAY;
}

/** branching execution method for fractional LP solutions */
static
SCIP_DECL_BRANCHEXECLP(branchExeclpCloud)
{  /*lint --e{715}*/
   SCIP_BRANCHRULEDATA* branchruledata;

   SCIP_VAR** lpcands;
   SCIP_VAR** lpcandscopy;

   SCIP_VAR** vars;
   SCIP_ROW** lprows;
   SCIP_Real* lpcandsfrac;
   SCIP_Real* lpcandssol;
   SCIP_Real* lpcandsfraccopy;
   SCIP_Real* lpcandssolcopy;
   SCIP_Real* lpcandsmin;
   SCIP_Real* lpcandsmax;
   SCIP_Real* newlpcandsmin;
   SCIP_Real* newlpcandsmax;

   SCIP_Real bestdown;
   SCIP_Real bestup;
   SCIP_Real bestscore;
   SCIP_Real provedbound;

   SCIP_Bool bestdownvalid;
   SCIP_Bool bestupvalid;
   SCIP_Bool newpoint;
   SCIP_Bool lperror;

   int nlpcands;
   int npriolpcands;
   int nvars;
   int bestcand;
   int nlprows;
   int i;
   int counter;
   int ncomplete;
   int ndiscvars;

   assert(branchrule != NULL);
   assert(strcmp(SCIPbranchruleGetName(branchrule), BRANCHRULE_NAME) == 0);
   assert(scip != NULL);
   assert(result != NULL);

   if( !SCIPisLPSolBasic(scip) )
      return SCIP_OKAY;

   SCIPdebugMsg(scip, "Execlp method of " BRANCHRULE_NAME " branching\n");

   /* get problem variables and LP row data */
   SCIP_CALL( SCIPgetVarsData(scip, &vars, &nvars, NULL, NULL, NULL, NULL) );
   ndiscvars = SCIPgetNBinVars(scip)+SCIPgetNIntVars(scip);
   nlprows = SCIPgetNLPRows(scip);
   lprows = SCIPgetLPRows(scip);

   /* get branching candidates */
   SCIP_CALL( SCIPgetLPBranchCands(scip, &lpcands, &lpcandssol, &lpcandsfrac, &nlpcands, &npriolpcands, NULL) );
   nlpcands = SCIPgetNLPBranchCands(scip);
   assert(nlpcands > 0);

   /* get branching rule data */
   branchruledata = SCIPbranchruleGetData(branchrule);
   assert(branchruledata != NULL);

   /* allocate skipping arrays on first call */
   if( branchruledata->skipdown == NULL )
   {
      assert(branchruledata->skipup == NULL);

      branchruledata->skipsize = nvars;
      SCIP_CALL( SCIPallocBlockMemoryArray(scip, &branchruledata->skipdown, branchruledata->skipsize) );
      SCIP_CALL( SCIPallocBlockMemoryArray(scip, &branchruledata->skipup, branchruledata->skipsize) );
   }

   /* reset skipping arrays to zero */
   BMSclearMemoryArray(branchruledata->skipdown, branchruledata->skipsize);
   BMSclearMemoryArray(branchruledata->skipup, branchruledata->skipsize);

   /* allocate required data structures */
   SCIP_CALL( SCIPallocBufferArray(scip, &lpcandsmin, nlpcands) );
   SCIP_CALL( SCIPallocBufferArray(scip, &lpcandsmax, nlpcands) );
   SCIP_CALL( SCIPallocBufferArray(scip, &lpcandscopy, nlpcands) );
   SCIP_CALL( SCIPallocBufferArray(scip, &lpcandsfraccopy, nlpcands) );
   SCIP_CALL( SCIPallocBufferArray(scip, &lpcandssolcopy, nlpcands) );
   newlpcandsmin = NULL;
   newlpcandsmax = NULL;
   if( branchruledata->useunion && SCIPgetDepth(scip) < branchruledata->maxdepthunion && !branchruledata->onlyF2)
   {
      SCIP_CALL( SCIPallocBufferArray(scip, &newlpcandsmin, ndiscvars) );
      SCIP_CALL( SCIPallocBufferArray(scip, &newlpcandsmax, ndiscvars) );
   }
   BMScopyMemoryArray(lpcandsmin, lpcandssol, nlpcands);
   BMScopyMemoryArray(lpcandsmax, lpcandssol, nlpcands);
   BMScopyMemoryArray(lpcandssolcopy, lpcandssol, nlpcands);
   BMScopyMemoryArray(lpcandsfraccopy, lpcandsfrac, nlpcands);
   BMScopyMemoryArray(lpcandscopy, lpcands, nlpcands);

   SCIP_CALL( SCIPstartClock(scip, branchruledata->cloudclock) );
   branchruledata->ntried++;

   /* start diving to calculate the solution cloud */
   SCIP_CALL( SCIPstartDive(scip) );

   /* fix variables with nonzero reduced costs to reduce LP to the optimal face */
   for( i = 0; i < nvars; ++i )
   {
      SCIP_Real solval;
      solval = SCIPgetSolVal(scip, NULL, vars[i]);

      if( !SCIPisFeasZero(scip, SCIPgetVarRedcost(scip, vars[i])) )
      {
         SCIP_CALL( SCIPchgVarLbDive(scip, vars[i], solval) );
         SCIP_CALL( SCIPchgVarUbDive(scip, vars[i], solval) );
      }
      else if( SCIPvarGetType(vars[i]) == SCIP_VARTYPE_INTEGER && !SCIPisIntegral(scip, solval) )
      {
         SCIP_CALL( SCIPchgVarLbDive(scip, vars[i], SCIPfloor(scip, solval)) );
         SCIP_CALL( SCIPchgVarUbDive(scip, vars[i], SCIPceil(scip, solval)) );
      }

      SCIP_CALL( SCIPchgVarObjDive(scip, vars[i], 0.0) );
   }

   /* fix LP rows with nonzero dual solution to reduce LP to the optimal face */
   for( i = 0; i < nlprows; ++i )
   {
      SCIP_Real dualsol;
      dualsol = SCIProwGetDualsol(lprows[i]);
      if( !SCIPisZero(scip, dualsol) )
      {
         if( dualsol > 0 && SCIPisFeasEQ(scip, SCIProwGetLhs(lprows[i]), SCIPgetRowActivity(scip,lprows[i])) )
         {
            SCIP_CALL( SCIPchgRowRhsDive(scip, lprows[i], SCIProwGetLhs(lprows[i])) );
         }
         else if( dualsol < 0 && SCIPisFeasEQ(scip, SCIProwGetRhs(lprows[i]), SCIPgetRowActivity(scip,lprows[i])) )
         {
            SCIP_CALL( SCIPchgRowLhsDive(scip, lprows[i], SCIProwGetRhs(lprows[i])) );
         }
      }
   }

   newpoint = TRUE;
   counter = 0;

   if( branchruledata->useunion && !branchruledata->onlyF2 && SCIPgetDepth(scip) < branchruledata->maxdepthunion )
   {
      /* update cloud intervals for candidates that have been integral in original LP, but have been fractional in previous cloud points */
      for( i = 0; i < ndiscvars; ++i)
      {
         SCIP_Real solval;
         solval = SCIPgetSolVal(scip, NULL, vars[i]);

         assert(newlpcandsmin != NULL);
         assert(newlpcandsmax != NULL);

         newlpcandsmin[i] = solval;
         newlpcandsmax[i] = solval;
      }
   }

   /* loop that generates new cloud point */
   while( newpoint && branchruledata->usecloud )
   {
#ifdef NDEBUG
      SCIP_RETCODE retcode;
#endif

      /* apply feasibility pump objective function to fractional variables */
      for( i = 0; i < nlpcands; ++i )
      {
         SCIP_Real frac;
         frac = SCIPfrac(scip, SCIPgetSolVal(scip, NULL, lpcandscopy[i]));

         if( !SCIPisZero(scip, frac) && !SCIPisIntegral(scip, lpcandsmin[i]) && !SCIPisIntegral(scip, lpcandsmax[i]) )
         {
            if( frac < 0.5 )
            {
               SCIP_CALL( SCIPchgVarObjDive(scip, vars[i], 1.0) );
            }
            else
            {
               SCIP_CALL( SCIPchgVarObjDive(scip, vars[i], -1.0) );
            }
         }
      }

      /* Errors in the LP solver should not kill the overall solving process, if the LP is just needed for a heuristic.
       * Hence in optimized mode, the return code is caught and a warning is printed, only in debug mode, SCIP will stop.
       */
#ifdef NDEBUG
      retcode = SCIPsolveDiveLP(scip, -1, &lperror, NULL);
      if( retcode != SCIP_OKAY )
      {
         SCIPwarningMessage(scip, "Error while solving LP in " BRANCHRULE_NAME "; LP solve terminated with code <%d>\n",retcode);
      }
#else
      SCIP_CALL( SCIPsolveDiveLP(scip, -1, &lperror, NULL) );
#endif

      if( lperror || SCIPgetLPSolstat(scip) != SCIP_LPSOLSTAT_OPTIMAL )
         break;

      /* check if a solution has been found */
      if( SCIPgetNLPBranchCands(scip) == 0 )
      {
         SCIP_Bool success;
         SCIP_SOL* sol;

         /* create solution from diving LP */
         SCIP_CALL( SCIPcreateSol(scip, &sol, NULL) );
         SCIP_CALL( SCIPlinkLPSol(scip, sol) );
         SCIPdebugMsg(scip, "cloud branching found primal solution: obj=%g\n", SCIPgetSolOrigObj(scip, sol));

         /* try to add solution to SCIP */
         SCIP_CALL( SCIPtrySolFree(scip, &sol, FALSE, FALSE, FALSE, FALSE, FALSE, &success) );

         /* check, if solution was feasible and good enough */
         if( success )
         {
            SCIPdebugMsg(scip, " -> solution was feasible and good enough\n");
            SCIP_CALL( SCIPendDive(scip) );
            *result = SCIP_CUTOFF;
            goto TERMINATE;
         }
      }

      /* update cloud intervals for candidates that have been fractional in original LP */
      newpoint = FALSE;
      for( i = 0; i < nlpcands; ++i)
      {
         SCIP_Real solval;
         solval = SCIPgetSolVal(scip, NULL, lpcandscopy[i]);

         if( SCIPisFeasIntegral(scip,solval) && !SCIPisFeasIntegral(scip, lpcandsmin[i]) && !SCIPisFeasIntegral(scip, lpcandsmax[i]) )
            newpoint = TRUE;

         lpcandsmin[i] = MIN(lpcandsmin[i], solval);
         lpcandsmax[i] = MAX(lpcandsmax[i], solval);
      }

      if( branchruledata->useunion && !branchruledata->onlyF2 && SCIPgetDepth(scip) < branchruledata->maxdepthunion )
      {
         /* update cloud intervals for candidates that have been integral in original LP, but have been fractional in previous cloud points */
         for( i = 0; i < ndiscvars; ++i)
         {
            SCIP_Real solval;
            solval = SCIPgetSolVal(scip, NULL, vars[i]);

            assert(newlpcandsmin != NULL);
            assert(newlpcandsmax != NULL);

            newlpcandsmin[i] = MIN(newlpcandsmin[i], solval);
            newlpcandsmax[i] = MAX(newlpcandsmax[i], solval);
         }
      }

      if( newpoint )
         counter++;

      if( branchruledata->maxpoints != -1 && counter >= branchruledata->maxpoints )
         break;
   }

   SCIPdebugMsg(scip, "considered %d additional points in the cloud\n",counter);

   /* terminate the diving */
   SCIP_CALL( SCIPendDive(scip) );

   SCIP_CALL( SCIPstopClock(scip, branchruledata->cloudclock) );
   ncomplete = nlpcands;

   if( counter > 0 )
   {
      branchruledata->ncloudpoints += (counter+1);
      branchruledata->nuseful++;

      counter = 0;

      /* sort all variables for which both bounds are fractional to the front */
      for( i = 0; i < nlpcands; ++i)
      {
         if( !SCIPisFeasIntegral(scip, lpcandsmin[i]) && !SCIPisFeasIntegral(scip, lpcandsmax[i]) )
         {
            assert(counter <= i);
            lpcandscopy[counter] = lpcandscopy[i];
            lpcandssolcopy[counter] = lpcandssolcopy[i];
            lpcandsfraccopy[counter] = lpcandsfraccopy[i];
            counter++;
         }
      }

      /* should only be in that if condition when at least one bound could be made integral */
      assert(nlpcands - counter > 0);

      ncomplete = counter;

      /* filter all variables for which exactly one interval bound is fractional */
      for( i = 0; i < nlpcands && !branchruledata->onlyF2; ++i)
      {
         if( SCIPisFeasIntegral(scip, lpcandsmin[i]) != SCIPisFeasIntegral(scip, lpcandsmax[i]) )
         {
            assert(counter < nlpcands);
            lpcandscopy[counter] = lpcandscopy[i];
            lpcandssolcopy[counter] = lpcandssolcopy[i];
            lpcandsfraccopy[counter] = lpcandsfraccopy[i];

            if( SCIPisFeasIntegral(scip, lpcandsmin[i]) )
               branchruledata->skipdown[counter] = TRUE;
            if( SCIPisFeasIntegral(scip, lpcandsmax[i]) )
               branchruledata->skipup[counter] = TRUE;
            assert(branchruledata->skipdown[counter] != branchruledata->skipup[counter]);

            counter++;
         }
      }

      SCIPdebugMsg(scip, "can fully skip %d/%d strong branching candidates\n", nlpcands - counter, nlpcands);
      SCIPdebugMsg(scip, "can half  skip %d/%d strong branching candidates\n", counter - ncomplete, nlpcands);
   }
   else
      counter = nlpcands;

   /* if cloud sampling was not successful enough, disable it */
   if( branchruledata->usecloud &&
      branchruledata->ntried > 100 &&
      (SCIP_Real)branchruledata->nuseful / branchruledata->ntried < branchruledata->minsuccessrate )
   {
      SCIPdebugMsg(scip, "Disabling cloud branching (not effective)\n");
      branchruledata->usecloud = FALSE;
   }

   if( branchruledata->onlyF2 )
      counter = MAX(counter,1);

   /* the second counter should maybe be replaced at some point */
   SCIP_CALL( SCIPselectVarStrongBranching(scip, lpcandscopy, lpcandssolcopy, lpcandsfraccopy, branchruledata->skipdown,
         branchruledata->skipup, counter, counter, ncomplete, &branchruledata->lastcand, 0, FALSE, FALSE,
         &bestcand, &bestdown, &bestup, &bestscore, &bestdownvalid, &bestupvalid, &provedbound, result) );

   if( branchruledata->lastcand <= ncomplete )
   {
      SCIPdebugMsg(scip, "saved %d of %d LPs\n", 2*(nlpcands - ncomplete), 2*nlpcands);
      branchruledata->nsavedlps += 2*(nlpcands - ncomplete);
   }
   else
   {
      SCIPdebugMsg(scip, "saved %d of %d LPs\n", 2*(nlpcands - counter)+counter - ncomplete, 2*nlpcands);
      branchruledata->nsavedlps += 2*(nlpcands - counter)+counter - ncomplete;
   }

   /* perform the branching */
   if( *result != SCIP_CUTOFF && *result != SCIP_REDUCEDDOM && *result != SCIP_CONSADDED && counter > 0 )
   {
      SCIP_NODE* downchild;
      SCIP_NODE* upchild;
      SCIP_VAR* var;
      SCIP_Bool allcolsinlp;
      SCIP_Bool exactsolve;
      SCIP_Bool newselected;

      assert(*result == SCIP_DIDNOTRUN);
      assert(0 <= bestcand && bestcand < nlpcands);
      assert(SCIPisLT(scip, provedbound, SCIPgetCutoffbound(scip)));

      var = lpcandscopy[bestcand];
      newselected = FALSE;

      /* if there are new candidates variables, also try them */
      if( branchruledata->useunion && !branchruledata->onlyF2 && SCIPgetDepth(scip) < branchruledata->maxdepthunion && branchruledata->lastcand > ncomplete )
      {
         SCIP_VAR** newlpcands;

         counter = 0;
         /* reset skipping arrays to zero */
         BMSclearMemoryArray(branchruledata->skipdown, branchruledata->skipsize);
         BMSclearMemoryArray(branchruledata->skipup, branchruledata->skipsize);

         SCIP_CALL( SCIPallocBufferArray(scip, &newlpcands, ndiscvars) );

         /* get new LP candidates with one fractional bound */
         for( i = 0; i < ndiscvars; ++i)
         {
            if( !SCIPisFeasIntegral(scip, SCIPgetSolVal(scip, NULL, vars[i])) )
               continue;

            assert(newlpcandsmin != NULL);
            assert(newlpcandsmax != NULL);

            if( SCIPisFeasIntegral(scip, newlpcandsmin[i]) != SCIPisFeasIntegral(scip, newlpcandsmax[i]) )
            {
               newlpcands[counter] = vars[i];

               if( SCIPisFeasIntegral(scip, newlpcandsmin[i]) )
                  branchruledata->skipdown[counter] = TRUE;
               if( SCIPisFeasIntegral(scip, newlpcandsmax[i]) )
                  branchruledata->skipup[counter] = TRUE;
               assert(branchruledata->skipdown[counter] != branchruledata->skipup[counter]);

               counter++;
            }
         }

         /* when there are new candidates, also try these */
         if( counter > 0 )
         {
            SCIP_Real newdown;
            SCIP_Real newup;
            SCIP_Real newscore;
            int newcand;
            SCIP_Bool newdownvalid;
            SCIP_Bool newupvalid;
            SCIP_Real newbound;

            branchruledata->ntriedunions++;
            newscore = -SCIPinfinity(scip);
            SCIP_CALL( SCIPselectVarPseudoStrongBranching(scip, newlpcands, branchruledata->skipdown, branchruledata->skipup, counter, counter,
                  &newcand, &newdown, &newup, &newscore, &newdownvalid, &newupvalid, &newbound, result) );

            if( *result == SCIP_CUTOFF || *result == SCIP_REDUCEDDOM || *result == SCIP_CONSADDED  )
            {
               SCIPfreeBufferArray(scip, &newlpcands);
               goto TERMINATE;
            }

            if( newscore > bestscore )
            {
               bestcand = newcand;
               var = newlpcands[newcand];
               bestdown = newdown;
               bestup = newup;
               bestdownvalid = newdownvalid;
               bestupvalid = newupvalid;
               bestscore = newscore;
               newselected = TRUE;
               branchruledata->nusefulunions++;
            }
         }
         /* free temporary array for new union candidates */
         SCIPfreeBufferArray(scip, &newlpcands);
      }

      /* perform the branching */
      if( !newselected )
      {
         SCIPdebugMsg(scip, " -> %d candidates, selected candidate %d: variable <%s> (solval=%g, down=%g, up=%g, score=%g)\n",
            counter, bestcand, SCIPvarGetName(var), lpcandssolcopy[bestcand], bestdown, bestup, bestscore);
      }
      else
      {
         SCIPdebugMsg(scip, " -> selected from %d new candidates,  candidate %d: variable <%s> (down=%g, up=%g, score=%g)\n",
            counter, bestcand, SCIPvarGetName(var), bestdown, bestup, bestscore);
      }

      assert(!SCIPisFeasIntegral(scip, SCIPvarGetSol(lpcands[bestcand], TRUE)));

      SCIP_CALL( SCIPbranchVar(scip, var, &downchild, NULL, &upchild) );
      assert(downchild != NULL);
      assert(upchild != NULL);

      /* check, if we want to solve the problem exactly, meaning that strong branching information is not useful
       * for cutting off sub problems and improving lower bounds of children
       */
      exactsolve = SCIPisExactSolve(scip);

      /* check, if all existing columns are in LP, and thus the strong branching results give lower bounds */
      allcolsinlp = SCIPallColsInLP(scip);

      /* update the lower bounds in the children */
      if( allcolsinlp && !exactsolve )
      {
         SCIP_CALL( SCIPupdateNodeLowerbound(scip, downchild, bestdownvalid ? MAX(bestdown, provedbound) : provedbound) );
         SCIP_CALL( SCIPupdateNodeLowerbound(scip, upchild, bestupvalid ? MAX(bestup, provedbound) : provedbound) );
      }
      SCIPdebugMsg(scip, " -> down child's lowerbound: %g\n", SCIPnodeGetLowerbound(downchild));
      SCIPdebugMsg(scip, " -> up child's lowerbound: %g\n", SCIPnodeGetLowerbound(upchild));

      *result = SCIP_BRANCHED;
   }

 TERMINATE:
   if( branchruledata->useunion && !branchruledata->onlyF2 && SCIPgetDepth(scip) < branchruledata->maxdepthunion )
   {
      SCIPfreeBufferArray(scip, &newlpcandsmax);
      SCIPfreeBufferArray(scip, &newlpcandsmin);
   }
   SCIPfreeBufferArray(scip, &lpcandscopy);
   SCIPfreeBufferArray(scip, &lpcandssolcopy);
   SCIPfreeBufferArray(scip, &lpcandsfraccopy);
   SCIPfreeBufferArray(scip, &lpcandsmax);
   SCIPfreeBufferArray(scip, &lpcandsmin);

   /* if union usage was not successful enough, disable it */
   if( branchruledata->useunion &&
      branchruledata->ntriedunions > 10 &&
      (SCIP_Real)branchruledata->nusefulunions / branchruledata->ntriedunions < branchruledata->minsuccessunion )
   {
      SCIPdebugMsg(scip, "Disabling union usage (not effective)\n");
      branchruledata->useunion = FALSE;
   }

   return SCIP_OKAY;  /*lint !e438*/
}

/*
 * branching rule specific interface methods
 */

/** creates the cloud branching rule and includes it in SCIP */
SCIP_RETCODE SCIPincludeBranchruleCloud(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   SCIP_BRANCHRULEDATA* branchruledata;
   SCIP_BRANCHRULE* branchrule;

   /* create cloud branching rule data */
   SCIP_CALL( SCIPallocBlockMemory(scip, &branchruledata) );
   branchruledata->lastcand = 0;
   branchruledata->skipsize = 0;
   branchruledata->skipup = NULL;
   branchruledata->skipdown = NULL;
   SCIP_CALL( SCIPcreateClock(scip, &(branchruledata->cloudclock)) );

   /* include branching rule */
   branchrule = NULL;
   SCIP_CALL( SCIPincludeBranchruleBasic(scip, &branchrule, BRANCHRULE_NAME, BRANCHRULE_DESC, BRANCHRULE_PRIORITY,
         BRANCHRULE_MAXDEPTH, BRANCHRULE_MAXBOUNDDIST, branchruledata) );
   assert(branchrule != NULL);

   /* set non-fundamental callbacks via setter functions */
   SCIP_CALL( SCIPsetBranchruleFree(scip, branchrule, branchFreeCloud) );
   SCIP_CALL( SCIPsetBranchruleInit(scip, branchrule, branchInitCloud) );
   SCIP_CALL( SCIPsetBranchruleExecLp(scip, branchrule, branchExeclpCloud) );

   /* add cloud branching rule parameters */
   SCIP_CALL( SCIPaddBoolParam(scip,
         "branching/" BRANCHRULE_NAME "/usecloud",
         "should a cloud of points be used?",
         &branchruledata->usecloud, FALSE, DEFAULT_USECLOUD, NULL, NULL) );
   SCIP_CALL( SCIPaddBoolParam(scip,
         "branching/" BRANCHRULE_NAME "/onlyF2",
         "should only F2 be used?",
         &branchruledata->onlyF2, FALSE, DEFAULT_ONLYF2, NULL, NULL) );
   SCIP_CALL( SCIPaddBoolParam(scip,
         "branching/" BRANCHRULE_NAME "/useunion",
         "should the union of candidates be used?",
         &branchruledata->useunion, FALSE, DEFAULT_USEUNION, NULL, NULL) );
   SCIP_CALL( SCIPaddIntParam(scip,
         "branching/" BRANCHRULE_NAME "/maxpoints",
         "maximum number of points for the cloud (-1 means no limit)",
         &branchruledata->maxpoints, FALSE, DEFAULT_MAXPOINTS, -1, INT_MAX, NULL, NULL) );
   SCIP_CALL( SCIPaddRealParam(scip,
         "branching/" BRANCHRULE_NAME "/minsuccessrate",
         "minimum success rate for the cloud",
         &branchruledata->minsuccessrate, FALSE, DEFAULT_MINSUCCESSRATE, 0.0, 1.0, NULL, NULL) );
   SCIP_CALL( SCIPaddRealParam(scip,
         "branching/" BRANCHRULE_NAME "/minsuccessunion",
         "minimum success rate for the union",
         &branchruledata->minsuccessunion, FALSE, DEFAULT_MINSUCCESSUNION, 0.0, 1.0, NULL, NULL) );
   SCIP_CALL( SCIPaddIntParam(scip,
         "branching/" BRANCHRULE_NAME "/maxdepthunion",
         "maximum depth for the union",
         &branchruledata->maxdepthunion, FALSE, DEFAULT_MAXDEPTHUNION, 0, 65000, NULL, NULL) );

   return SCIP_OKAY;
}