branch_pscost.c

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the program and library             */
/*         SCIP --- Solving Constraint Integer Programs                      */
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/*  Copyright (c) 2002-2025 Zuse Institute Berlin (ZIB)                      */
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/**@file   branch_pscost.c
 * @ingroup DEFPLUGINS_BRANCH
 * @brief  pseudo costs branching rule
 * @author Tobias Achterberg
 * @author Stefan Vigerske
 * @author Krunal Patel
 */
 
/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
 
#include "blockmemshell/memory.h"
#include "scip/branch_pscost.h"
#include "scip/pub_branch.h"
#include "scip/pub_message.h"
#include "scip/pub_misc.h"
#include "scip/pub_misc_sort.h"
#include "scip/pub_tree.h"
#include "scip/pub_var.h"
#include "scip/scip_branch.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_numerics.h"
#include "scip/scip_param.h"
#include "scip/scip_randnumgen.h"
#include "scip/scip_sol.h"
#include "scip/scip_tree.h"
#include "scip/scip_var.h"
#include <string.h>
 
#define BRANCHRULE_NAME          "pscost"
#define BRANCHRULE_DESC          "branching on pseudo cost values"
#define BRANCHRULE_PRIORITY      2000
#define BRANCHRULE_MAXDEPTH      -1
#define BRANCHRULE_MAXBOUNDDIST  1.0
 
#define BRANCHRULE_STRATEGIES          "dsuv" /**< possible pseudo cost multiplication strategies for branching on external candidates */
#define BRANCHRULE_STRATEGY_DEFAULT       'u' /**< default pseudo cost multiplication strategy */
#define BRANCHRULE_SCOREMINWEIGHT_DEFAULT 0.8 /**< default weight for minimum of scores of a branching candidate */
#define BRANCHRULE_SCOREMAXWEIGHT_DEFAULT 1.3 /**< default weight for maximum of scores of a branching candidate */
#define BRANCHRULE_SCORESUMWEIGHT_DEFAULT 0.1 /**< default weight for sum of scores of a branching candidate */
#define BRANCHRULE_NCHILDREN_DEFAULT        2 /**< default number of children in n-ary branching */
#define BRANCHRULE_NARYMAXDEPTH_DEFAULT    -1 /**< default maximal depth where to do n-ary branching */
#define BRANCHRULE_NARYMINWIDTH_DEFAULT 0.001 /**< default minimal domain width in children when doing n-ary branching */
#define BRANCHRULE_NARYWIDTHFAC_DEFAULT   2.0 /**< default factor of domain width in n-ary branching */
#define BRANCHRULE_RANDSEED_DEFAULT        47 /**< initial random seed */
#define BRANCHRULE_DISCOUNTFACTOR        0.2 /**< default discount factor for discounted pseudo costs */
 
 
#define WEIGHTEDSCORING(data, min, max, sum) \
   ((data)->scoreminweight * (min) + (data)->scoremaxweight * (max) + (data)->scoresumweight * (sum))
 
/** branching rule data */
struct SCIP_BranchruleData
{
   SCIP_RANDNUMGEN*      randnumgen;         /**< random number generator */
 
   char                  strategy;           /**< strategy for computing score of external candidates */
   SCIP_Real             scoreminweight;     /**< weight for minimum of scores of a branching candidate */
   SCIP_Real             scoremaxweight;     /**< weight for maximum of scores of a branching candidate */
   SCIP_Real             scoresumweight;     /**< weight for sum of scores of a branching candidate */
 
   char                  updatestrategy;     /**< strategy used to update pseudo costs of continuous variables */
 
   int                   nchildren;          /**< targeted number of children in n-ary branching */
   int                   narymaxdepth;       /**< maximal depth where to do n-ary branching, -1 to turn off */
   SCIP_Real             naryminwidth;       /**< minimal domain width in children when doing n-ary branching, relative to global bounds */
   SCIP_Real             narywidthfactor;    /**< factor of domain width in n-ary branching */
   SCIP_Real             discountfactor;     /**< discount factor for discounted pseudo costs.*/
};
 
/*
 * Local methods
 */
 
/** checks if a given branching candidate is better than a previous one and updates the best branching candidate accordingly */
static
SCIP_RETCODE updateBestCandidate(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_BRANCHRULEDATA*  branchruledata,     /**< branching rule data */
   SCIP_VAR**            bestvar,            /**< best branching candidate */
   SCIP_Real*            bestbrpoint,        /**< branching point for best branching candidate */
   SCIP_Real*            bestscore,          /**< score of best branching candidate */
   SCIP_Real*            bestrndscore,       /**< random score of the best branching candidate */
   SCIP_VAR*             cand,               /**< branching candidate to consider */
   SCIP_Real             candscoremin,       /**< minimal score of branching candidate */
   SCIP_Real             candscoremax,       /**< maximal score of branching candidate */
   SCIP_Real             candscoresum,       /**< sum of scores of branching candidate */
   SCIP_Real             candrndscore,       /**< random score of branching candidate */
   SCIP_Real             candsol             /**< proposed branching point of branching candidate */
   )
{
   SCIP_Real candbrpoint;
   SCIP_Real branchscore;
 
   SCIP_Real deltaminus;
   SCIP_Real deltaplus;
 
   SCIP_Real pscostdown;
   SCIP_Real pscostup;
 
   SCIP_VARTYPE besttype;
   SCIP_VARTYPE candtype;
 
   char strategy;
 
   assert(scip != NULL);
   assert(branchruledata != NULL);
   assert(bestvar != NULL);
   assert(bestbrpoint != NULL);
   assert(bestscore != NULL);
   assert(cand != NULL);
 
   /* a branching variable candidate should either be an active problem variable or a multi-aggregated variable */
   assert(SCIPvarIsActive(SCIPvarGetProbvar(cand)) ||
      SCIPvarGetStatus(SCIPvarGetProbvar(cand)) == SCIP_VARSTATUS_MULTAGGR);
 
   if( SCIPvarGetStatus(SCIPvarGetProbvar(cand)) == SCIP_VARSTATUS_MULTAGGR )
   {
      /* for a multi-aggregated variable, we call updateBestCandidate function recursively with all variables in the multi-aggregation */
      SCIP_VAR** multvars;
      int nmultvars;
      int i;
      SCIP_Bool success;
      SCIP_Real multvarlb;
      SCIP_Real multvarub;
 
      cand = SCIPvarGetProbvar(cand);
      multvars = SCIPvarGetMultaggrVars(cand);
      nmultvars = SCIPvarGetMultaggrNVars(cand);
 
      /* if we have a candidate branching point, then first register only aggregation variables
       * for which we can compute a corresponding branching point too (see also comments below)
       * if this fails, then register all (unfixed) aggregation variables, thereby forgetting about candsol
       */
      success = FALSE;
      if( candsol != SCIP_INVALID ) /*lint !e777*/
      {
         SCIP_Real* multscalars;
         SCIP_Real minact;
         SCIP_Real maxact;
         SCIP_Real aggrvarsol;
         SCIP_Real aggrvarsol1;
         SCIP_Real aggrvarsol2;
 
         multscalars = SCIPvarGetMultaggrScalars(cand);
 
         /* for computing the branching point, we need the current bounds of the multi-aggregated variable */
         minact = SCIPcomputeVarLbLocal(scip, cand);
         maxact = SCIPcomputeVarUbLocal(scip, cand);
 
         for( i = 0; i < nmultvars; ++i )
         {
            /* skip fixed variables */
            multvarlb = SCIPcomputeVarLbLocal(scip, multvars[i]);
            multvarub = SCIPcomputeVarUbLocal(scip, multvars[i]);
            if( SCIPisEQ(scip, multvarlb, multvarub) )
               continue;
 
            assert(multscalars != NULL);
            assert(multscalars[i] != 0.0);
 
            /* we cannot ensure that both the upper bound in the left node and the lower bound in the right node
             * will be candsol by a clever choice for the branching point of multvars[i],
             * but we can try to ensure that at least one of them will be at candsol
             */
            if( multscalars[i] > 0.0 )
            {
               /*    cand >= candsol
                * if multvars[i] >= (candsol - (maxact - multscalars[i] * ub(multvars[i]))) / multscalars[i]
                *                 = (candsol - maxact) / multscalars[i] + ub(multvars[i])
                */
               aggrvarsol1 = (candsol - maxact) / multscalars[i] + multvarub;
 
               /*     cand <= candsol
                * if multvars[i] <= (candsol - (minact - multscalar[i] * lb(multvars[i]))) / multscalars[i]
                *                 = (candsol - minact) / multscalars[i] + lb(multvars[i])
                */
               aggrvarsol2 = (candsol - minact) / multscalars[i] + multvarlb;
            }
            else
            {
               /*    cand >= candsol
                * if multvars[i] <= (candsol - (maxact - multscalars[i] * lb(multvars[i]))) / multscalars[i]
                *                 = (candsol - maxact) / multscalars[i] + lb(multvars[i])
                */
               aggrvarsol2 = (candsol - maxact) / multscalars[i] + multvarlb;
 
               /*    cand <= candsol
                * if multvars[i] >= (candsol - (minact - multscalar[i] * ub(multvars[i]))) / multscalars[i]
                *                 = (candsol - minact) / multscalars[i] + ub(multvars[i])
                */
               aggrvarsol1 = (candsol - minact) / multscalars[i] + multvarub;
            }
 
            /* by the above choice, aggrvarsol1 <= ub(multvars[i]) and aggrvarsol2 >= lb(multvars[i])
             * if aggrvarsol1 <= lb(multvars[i]) or aggrvarsol2 >= ub(multvars[i]), then choose the other one
             * if both are out of bounds, then give up
             * if both are inside bounds, then choose the one closer to 0.0 (someone has better idea???)
             */
            if( SCIPisFeasLE(scip, aggrvarsol1, multvarlb) )
            {
               if( SCIPisFeasGE(scip, aggrvarsol2, multvarub) )
                  continue;
               else
                  aggrvarsol = aggrvarsol2;
            }
            else
            {
               if( SCIPisFeasGE(scip, aggrvarsol2, multvarub) )
                  aggrvarsol = aggrvarsol1;
               else
                  aggrvarsol = REALABS(aggrvarsol1) < REALABS(aggrvarsol2) ? aggrvarsol1 : aggrvarsol2;
            }
            success = TRUE;
 
            SCIP_CALL( updateBestCandidate(scip, branchruledata, bestvar, bestbrpoint, bestscore, bestrndscore,
                  multvars[i], candscoremin, candscoremax, candscoresum, candrndscore, aggrvarsol) );
         }
      }
 
      if( !success )
         for( i = 0; i < nmultvars; ++i )
         {
            /* skip fixed variables */
            multvarlb = SCIPcomputeVarLbLocal(scip, multvars[i]);
            multvarub = SCIPcomputeVarUbLocal(scip, multvars[i]);
            if( SCIPisEQ(scip, multvarlb, multvarub) )
               continue;
 
            SCIP_CALL( updateBestCandidate(scip, branchruledata, bestvar, bestbrpoint, bestscore, bestrndscore,
               multvars[i], candscoremin, candscoremax, candscoresum, candrndscore, SCIP_INVALID) );
         }
 
      assert(*bestvar != NULL); /* if all variables were fixed, something is strange */
 
      return SCIP_OKAY;
   }
 
   /* select branching point for this variable */
   candbrpoint = SCIPgetBranchingPoint(scip, cand, candsol);
   assert(candbrpoint >= SCIPvarGetLbLocal(cand));
   assert(candbrpoint <= SCIPvarGetUbLocal(cand));
 
   /* we cannot branch on a huge value for a discrete variable, because we simply cannot enumerate such huge integer values in floating point
    * arithmetics
    */
   if( SCIPvarIsIntegral(cand) && (SCIPisHugeValue(scip, candbrpoint) || SCIPisHugeValue(scip, -candbrpoint)) )
      return SCIP_OKAY;
 
   assert(!SCIPvarIsIntegral(cand) || !SCIPisIntegral(scip, candbrpoint));
 
   if( !SCIPvarIsIntegral(cand) )
      strategy = (branchruledata->strategy == 'u' ? branchruledata->updatestrategy : branchruledata->strategy);
   else
      strategy = (branchruledata->strategy == 'u' ? 'l' : branchruledata->strategy);
 
   switch( strategy )
   {
   case 'l':
      if( SCIPisInfinity(scip,  SCIPgetSolVal(scip, NULL, cand)) || SCIPgetSolVal(scip, NULL, cand) <= SCIPadjustedVarUb(scip, cand, candbrpoint) )
         deltaminus = 0.0;
      else
         deltaminus = SCIPgetSolVal(scip, NULL, cand) - SCIPadjustedVarUb(scip, cand, candbrpoint);
      if( SCIPisInfinity(scip, -SCIPgetSolVal(scip, NULL, cand)) || SCIPgetSolVal(scip, NULL, cand) >= SCIPadjustedVarLb(scip, cand, candbrpoint) )
         deltaplus = 0.0;
      else
         deltaplus = SCIPadjustedVarLb(scip, cand, candbrpoint) - SCIPgetSolVal(scip, NULL, cand);
      break;
 
   case 'd':
      if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(cand)) )
         deltaminus = SCIPisInfinity(scip, candscoremax) ? SCIPinfinity(scip) : WEIGHTEDSCORING(branchruledata, candscoremin, candscoremax, candscoresum);
      else
         deltaminus = SCIPadjustedVarUb(scip, cand, candbrpoint) - SCIPvarGetLbLocal(cand);
 
      if( SCIPisInfinity(scip,  SCIPvarGetUbLocal(cand)) )
         deltaplus = SCIPisInfinity(scip, candscoremax) ? SCIPinfinity(scip) : WEIGHTEDSCORING(branchruledata, candscoremin, candscoremax, candscoresum);
      else
         deltaplus = SCIPvarGetUbLocal(cand) - SCIPadjustedVarLb(scip, cand, candbrpoint);
      break;
 
   case 's':
      if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(cand)) )
         deltaplus = SCIPisInfinity(scip, candscoremax) ? SCIPinfinity(scip) : WEIGHTEDSCORING(branchruledata, candscoremin, candscoremax, candscoresum);
      else
         deltaplus = SCIPadjustedVarUb(scip, cand, candbrpoint) - SCIPvarGetLbLocal(cand);
 
      if( SCIPisInfinity(scip,  SCIPvarGetUbLocal(cand)) )
         deltaminus = SCIPisInfinity(scip, candscoremax) ? SCIPinfinity(scip) : WEIGHTEDSCORING(branchruledata, candscoremin, candscoremax, candscoresum);
      else
         deltaminus = SCIPvarGetUbLocal(cand) - SCIPadjustedVarLb(scip, cand, candbrpoint);
      break;
 
   case 'v':
      deltaplus = SCIPisInfinity(scip, candscoremax) ? SCIPinfinity(scip) : WEIGHTEDSCORING(branchruledata, candscoremin, candscoremax, candscoresum);
      deltaminus = deltaplus;
      break;
 
   default :
      SCIPerrorMessage("branching strategy %c unknown\n", strategy);
      SCIPABORT();
      return SCIP_INVALIDDATA;  /*lint !e527*/
   }
 
   if( SCIPisInfinity(scip, deltaminus) || SCIPisInfinity(scip, deltaplus) )
   {
      branchscore = SCIPinfinity(scip);
   }
   else
   {
      pscostdown  = SCIPgetVarPseudocostVal(scip, cand, -deltaminus);
      pscostup    = SCIPgetVarPseudocostVal(scip, cand,  deltaplus);
      branchscore = SCIPgetBranchScore(scip, cand, pscostdown, pscostup);
      assert(!SCIPisNegative(scip, branchscore));
   }
   SCIPdebugMsg(scip, "branching score variable <%s>[%g,%g] = %g; wscore = %g; type=%d bestbrscore=%g\n",
      SCIPvarGetName(cand), SCIPvarGetLbLocal(cand), SCIPvarGetUbLocal(cand), branchscore, WEIGHTEDSCORING(branchruledata, candscoremin, candscoremax, candscoresum),
      SCIPvarGetType(cand), *bestscore);
 
   if( SCIPisInfinity(scip, branchscore) )
      branchscore = 0.9*SCIPinfinity(scip);
 
   if( SCIPisSumGT(scip, branchscore, *bestscore) )
   {
      (*bestscore)    = branchscore;
      (*bestrndscore) = candrndscore;
      (*bestvar)      = cand;
      (*bestbrpoint)  = candbrpoint;
      return SCIP_OKAY;
   }
 
   /* if score of candidate is worse than bestscore, stay with best candidate */
   if( !SCIPisSumEQ(scip, branchscore, *bestscore) )
      return SCIP_OKAY;
 
   if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(*bestvar)) && SCIPisInfinity(scip, SCIPvarGetUbLocal(*bestvar)) )
   {
      /* best candidate is unbounded -> we prefer to branch on it */
      if( SCIPisInfinity(scip, -SCIPvarGetLbLocal(cand)) && SCIPisInfinity(scip, SCIPvarGetUbLocal(cand)) &&
          SCIPrandomGetReal(branchruledata->randnumgen, 0.0, 1.0) <= 0.5
        )
      {
         /* but if the new candidate is also unbounded (thus as good as best candidate),
          * then switch to the candidate with 50% probability to reduce performance variability
          */
         (*bestscore)    = branchscore;
         (*bestrndscore) = candrndscore;
         (*bestvar)      = cand;
         (*bestbrpoint)  = candbrpoint;
      }
 
      return SCIP_OKAY;
   }
 
   /* best candidate has a finite lower or upper bound -> consider taking the other candidate */
 
   if( (SCIPisInfinity(scip, -SCIPvarGetLbLocal(cand))     || SCIPisInfinity(scip, SCIPvarGetUbLocal(cand))) &&
       (SCIPisInfinity(scip, -SCIPvarGetLbLocal(*bestvar)) || SCIPisInfinity(scip, SCIPvarGetUbLocal(*bestvar))) )
   {
      /* both candidates are unbounded, but one side may be finite (for bestcand we know there is one)
       * take the candidate with the larger bound on the bounded side (hope that this avoids branching on always the same variable)
       * this will also prefer unbounded variables over bounded ones
       */
      if( SCIPvarGetUbLocal(cand) > SCIPvarGetUbLocal(*bestvar) || SCIPvarGetLbLocal(cand) < SCIPvarGetLbLocal(*bestvar) )
      {
         /* cand is better than bestvar */
         (*bestscore)    = branchscore;
         (*bestrndscore) = candrndscore;
         (*bestvar)      = cand;
         (*bestbrpoint)  = candbrpoint;
         return SCIP_OKAY;
      }
 
      if( SCIPvarGetUbLocal(*bestvar) > SCIPvarGetUbLocal(cand) || SCIPvarGetLbLocal(*bestvar) < SCIPvarGetLbLocal(cand) )
      {
         /* bestvar is better than cand */
         return SCIP_OKAY;
      }
 
      /* both are equally good */
   }
 
   /* @TODO: handle implied integrality like in relpscost */
   besttype = SCIPvarIsImpliedIntegral(*bestvar) ? SCIP_DEPRECATED_VARTYPE_IMPLINT : SCIPvarGetType(*bestvar);
   candtype = SCIPvarIsImpliedIntegral(cand) ? SCIP_DEPRECATED_VARTYPE_IMPLINT : SCIPvarGetType(cand);
 
   if( besttype == candtype )
   {
      /* if both have the same type, take the one with larger relative diameter */
      if( SCIPrelDiff(SCIPvarGetUbLocal(*bestvar), SCIPvarGetLbLocal(*bestvar)) < SCIPrelDiff(SCIPvarGetUbLocal(cand), SCIPvarGetLbLocal(cand)) )
      {
         /* cand has larger diameter than bestvar*/
         (*bestscore)    = branchscore;
         (*bestrndscore) = candrndscore;
         (*bestvar)      = cand;
         (*bestbrpoint)  = candbrpoint;
         return SCIP_OKAY;
      }
 
      if( SCIPrelDiff(SCIPvarGetUbLocal(*bestvar), SCIPvarGetLbLocal(*bestvar)) > SCIPrelDiff(SCIPvarGetUbLocal(cand), SCIPvarGetLbLocal(cand)) )
      {
         /* bestvar has larger diameter than cand */
         return SCIP_OKAY;
      }
   }
 
   /* take the one with better type ("more discrete") */
   if( besttype > candtype )
   {
      /* cand is more discrete than bestvar */
      (*bestscore)    = branchscore;
      (*bestrndscore) = candrndscore;
      (*bestvar)      = cand;
      (*bestbrpoint)  = candbrpoint;
      return SCIP_OKAY;
   }
   if( besttype < candtype )
   {
      /* bestvar is more discrete than cand */
      return SCIP_OKAY;
   }
 
   /* cand seems to be as good as the currently best one (bestvar); use the random score as a final tie-breaker */
   if( candrndscore >= (*bestrndscore) )
   {
      (*bestscore)    = branchscore;
      (*bestrndscore) = candrndscore;
      (*bestvar)      = cand;
      (*bestbrpoint)  = candbrpoint;
   }
 
   return SCIP_OKAY;
}
 
/** selects the branching variable from given candidate array */
static
SCIP_RETCODE selectBranchVar(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_BRANCHRULE*      branchrule,         /**< branching rule */
   SCIP_VAR**            cands,              /**< array of branching candidates */
   SCIP_Real*            candssol,           /**< array of candidate solution values */
   SCIP_Real*            candsscore,         /**< array of candidate scores */
   int                   ncands,             /**< the number of candidates */
   SCIP_VAR**            brvar,              /**< pointer to store the selected branching candidate or NULL if none */
   SCIP_Real*            brpoint             /**< pointer to store branching point of selected branching variable */
   )
{ /*lint --e{850}*/
   SCIP_BRANCHRULEDATA* branchruledata;
 
   SCIP_VAR* cand;
   SCIP_Real candsol;
 
   SCIP_Real bestbranchscore;
   SCIP_Real bestrndscore;
 
   SCIP_Real scoremin;
   SCIP_Real scoresum;
   SCIP_Real scoremax;
 
   SCIP_VAR** candssorted;
   int* candsorigidx;
 
   int i;
   int j;
 
   assert(brvar   != NULL);
   assert(brpoint != NULL);
 
   (*brvar)   = NULL;
   (*brpoint) = SCIP_INVALID;
 
   if( ncands == 0 )
      return SCIP_OKAY;
 
   branchruledata = SCIPbranchruleGetData(branchrule);
   assert(branchruledata != NULL);
 
   /* sort branching candidates (in a copy), such that same variables are on consecutive positions */
   SCIP_CALL( SCIPduplicateBufferArray(scip, &candssorted, cands, ncands) );
   SCIP_CALL( SCIPallocBufferArray(scip, &candsorigidx, ncands) );
   for( i = 0; i < ncands; ++i )
      candsorigidx[i] = i;
 
   SCIPsortPtrInt((void**)candssorted, candsorigidx, SCIPvarComp, ncands);
 
   bestbranchscore = -1.0;
   bestrndscore = -1.0;
 
   for( i = 0; i < ncands; ++i )
   {
      cand = candssorted[i];
 
      /* there should be no fixed branching candidates */
      assert(!SCIPisEQ(scip, SCIPvarGetLbLocal(cand), SCIPvarGetUbLocal(cand)));
 
      /* compute min, sum, and max of all registered scores for this variables
       * set candsol to a valid value, if someone registered one */
      scoremin = candsscore[candsorigidx[i]];
      scoresum = scoremin;
      scoremax = scoremin;
      candsol  = candssol[candsorigidx[i]];
      for( j = i+1 ; j < ncands && SCIPvarCompare(candssorted[j], cand) == 0; ++j )
      {
         assert(candsscore[candsorigidx[j]] >= 0.0);
         scoresum += candsscore[candsorigidx[j]];
         if( candsscore[candsorigidx[j]] < scoremin )
            scoremin = candsscore[candsorigidx[j]];
         else if( candsscore[candsorigidx[j]] > scoremax )
            scoremax = candsscore[candsorigidx[j]];
 
         /* @todo if there are two valid externcandssol available for the same variable, should we take the one closer to the middle of the domain? */
         if( SCIPisInfinity(scip, REALABS(candsol)) )
            candsol = candssol[candsorigidx[j]];
      }
      /* set i to last occurrence of cand in candssorted (instead of first one as before), so in next round we look at another variable */
      i = j-1;
      assert(candssorted[i] == cand);
 
      /* check if new candidate is better than previous candidate (if any) */
      SCIP_CALL( updateBestCandidate(scip, branchruledata, brvar, brpoint, &bestbranchscore, &bestrndscore, cand,
            scoremin, scoremax, scoresum, SCIPrandomGetReal(branchruledata->randnumgen, 0.0, 1.0), candsol) );
   }
 
   /* there were candidates, but no variable was selected; this can only happen if the branching points are huge values
    * for all non-continuous variables on which we cannot branch
    * @todo delay the node?
    */
   if( (*brvar) == NULL )
   {
      SCIPerrorMessage("no branching could be created: all external candidates have huge bounds\n");
      return SCIP_BRANCHERROR; /*lint !e527*/
   }
 
   /* free buffer arrays */
   SCIPfreeBufferArray(scip, &candsorigidx);
   SCIPfreeBufferArray(scip, &candssorted);
 
   return SCIP_OKAY;
}
 
/*
 * Callback methods
 */
 
/** copy method for branchrule plugins (called when SCIP copies plugins) */
static
SCIP_DECL_BRANCHCOPY(branchCopyPscost)
{  /*lint --e{715}*/
   assert(scip != NULL);
   assert(branchrule != NULL);
   assert(strcmp(SCIPbranchruleGetName(branchrule), BRANCHRULE_NAME) == 0);
 
   /* call inclusion method of branchrule */
   SCIP_CALL( SCIPincludeBranchrulePscost(scip) );
 
   return SCIP_OKAY;
}
 
/** destructor of branching rule to free user data (called when SCIP is exiting) */
static
SCIP_DECL_BRANCHFREE(branchFreePscost)
{  /*lint --e{715}*/
   SCIP_BRANCHRULEDATA* branchruledata;
 
   /* get branching rule data */
   branchruledata = SCIPbranchruleGetData(branchrule);
   assert(branchruledata != NULL);
 
   /* free random number generator */
   SCIPfreeRandom(scip, &branchruledata->randnumgen);
 
   /* free branching rule data */
   SCIPfreeBlockMemory(scip, &branchruledata);
   SCIPbranchruleSetData(branchrule, NULL);
 
   return SCIP_OKAY;
}
 
/** initialization method of branching rule (called after problem was transformed) */
static
SCIP_DECL_BRANCHINIT(branchInitPscost)
{  /*lint --e{715}*/
   SCIP_BRANCHRULEDATA* branchruledata;
 
   /* initialize branching rule data */
   branchruledata = SCIPbranchruleGetData(branchrule);
   assert(branchruledata != NULL);
 
   SCIPsetRandomSeed(scip, branchruledata->randnumgen, BRANCHRULE_RANDSEED_DEFAULT);
 
   return SCIP_OKAY;
}
 
/** branching execution method for fractional LP solutions */
static
SCIP_DECL_BRANCHEXECLP(branchExeclpPscost)
{  /*lint --e{715}*/
   SCIP_BRANCHRULEDATA* branchruledata;
   SCIP_VAR** lpcands;
   SCIP_Real* lpcandssol;
   SCIP_Real bestscore;
   SCIP_Real bestrootdiff;
   int nlpcands;
   int bestcand;
   int c;
 
   assert(branchrule != NULL);
   assert(strcmp(SCIPbranchruleGetName(branchrule), BRANCHRULE_NAME) == 0);
   assert(scip != NULL);
   assert(result != NULL);
 
   branchruledata = SCIPbranchruleGetData(branchrule);
   assert(branchruledata != NULL);
 
   SCIPdebugMsg(scip, "Execlp method of pscost branching\n");
 
   /* get branching candidates */
   SCIP_CALL( SCIPgetLPBranchCands(scip, &lpcands, &lpcandssol, NULL, NULL, &nlpcands, NULL) );
   assert(nlpcands > 0);
 
   bestcand = -1;
   bestscore = -SCIPinfinity(scip);
   bestrootdiff = 0.0;
   for( c = 0; c < nlpcands; ++c )
   {
      SCIP_Real score;
      SCIP_Real rootsolval;
      SCIP_Real rootdiff;
 
      score = SCIPgetVarDPseudocostScore(scip, lpcands[c], lpcandssol[c], branchruledata->discountfactor);
      rootsolval = SCIPvarGetRootSol(lpcands[c]);
      rootdiff = REALABS(lpcandssol[c] - rootsolval);
      if( SCIPisSumGT(scip, score, bestscore) || (SCIPisSumEQ(scip, score, bestscore) && rootdiff > bestrootdiff) )
      {
         bestcand = c;
         bestscore = score;
         bestrootdiff = rootdiff;
      }
   }
   assert(0 <= bestcand && bestcand < nlpcands);
   assert(!SCIPisFeasIntegral(scip, lpcandssol[bestcand]));
   assert(!SCIPisFeasIntegral(scip, SCIPvarGetSol(lpcands[bestcand], TRUE)));
 
   /* perform the branching */
   SCIPdebugMsg(scip, " -> %d cands, selected cand %d: variable <%s> (solval=%g, score=%g)\n",
      nlpcands, bestcand, SCIPvarGetName(lpcands[bestcand]), lpcandssol[bestcand], bestscore);
 
   /* perform the branching */
   SCIP_CALL( SCIPbranchVar(scip, lpcands[bestcand], NULL, NULL, NULL) );
   *result = SCIP_BRANCHED;
 
   return SCIP_OKAY;
}
 
 
/** branching execution method for external candidates
 *
 * @todo extend discounted pseudocosts for non-linear problems
 */
static
SCIP_DECL_BRANCHEXECEXT(branchExecextPscost)
{  /*lint --e{715}*/
   SCIP_BRANCHRULEDATA* branchruledata;
   SCIP_VAR** externcands;
   SCIP_Real* externcandssol;
   SCIP_Real* externcandsscore;
   int nprioexterncands;
   SCIP_VAR* brvar;
   SCIP_Real brpoint;
   int nchildren;
 
   assert(branchrule != NULL);
   assert(strcmp(SCIPbranchruleGetName(branchrule), BRANCHRULE_NAME) == 0);
   assert(scip != NULL);
   assert(result != NULL);
 
   branchruledata = SCIPbranchruleGetData(branchrule);
   assert(branchruledata != NULL);
 
   SCIPdebugMsg(scip, "Execext method of pscost branching\n");
 
   /* get branching candidates */
   SCIP_CALL( SCIPgetExternBranchCands(scip, &externcands, &externcandssol, &externcandsscore, NULL, &nprioexterncands, NULL, NULL, NULL) );
   assert(nprioexterncands > 0);
 
   /* get current update strategy for pseudo costs, if our multiplier rule is 'u' */
   if( branchruledata->strategy == 'u' )
   {
      SCIP_CALL( SCIPgetCharParam(scip, "branching/lpgainnormalize", &branchruledata->updatestrategy) );
   }
 
   /* select branching variable */
   SCIP_CALL( selectBranchVar(scip, branchrule, externcands, externcandssol, externcandsscore, nprioexterncands, &brvar, &brpoint) );
 
   if( brvar == NULL )
   {
      /* can happen if all candidates were non-continous variables with huge bounds */
      *result = SCIP_DIDNOTFIND;
      return SCIP_OKAY;
   }
 
   assert(SCIPvarIsActive(SCIPvarGetProbvar(brvar)));
 
   SCIPdebugMsg(scip, "branching on variable <%s>: new intervals: [%g, %g] and [%g, %g]\n",
      SCIPvarGetName(brvar), SCIPvarGetLbLocal(brvar), SCIPadjustedVarUb(scip, brvar, brpoint), SCIPadjustedVarLb(scip, brvar, brpoint), SCIPvarGetUbLocal(brvar));
 
   if( branchruledata->nchildren > 2 && SCIPnodeGetDepth(SCIPgetCurrentNode(scip)) <= branchruledata->narymaxdepth )
   {
      /* do n-ary branching */
      SCIP_Real minwidth;
 
      minwidth = 0.0;
      if( !SCIPisInfinity(scip, -SCIPvarGetLbGlobal(brvar)) && !SCIPisInfinity(scip, SCIPvarGetUbGlobal(brvar)) )
         minwidth = branchruledata->naryminwidth * (SCIPvarGetUbGlobal(brvar) - SCIPvarGetLbGlobal(brvar));
 
      SCIP_CALL( SCIPbranchVarValNary(scip, brvar, brpoint, branchruledata->nchildren, minwidth, branchruledata->narywidthfactor, &nchildren) );
   }
   else
   {
      /* do binary branching */
      SCIP_CALL( SCIPbranchVarValNary(scip, brvar, brpoint, 2, 0.0, 1.0, &nchildren) );
   }
 
   if( nchildren > 1 )
   {
      *result = SCIP_BRANCHED;
   }
   else
   {
      /* if there are no children, then variable should have been fixed by SCIPbranchVarVal */
      assert(SCIPisEQ(scip, SCIPvarGetLbLocal(brvar), SCIPvarGetUbLocal(brvar)));
      *result = SCIP_REDUCEDDOM;
   }
 
   return SCIP_OKAY;
}
 
 
/*
 * branching specific interface methods
 */
 
/** creates the pseudo cost branching rule and includes it in SCIP */
SCIP_RETCODE SCIPincludeBranchrulePscost(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   SCIP_BRANCHRULEDATA* branchruledata;
   SCIP_BRANCHRULE* branchrule;
 
   /* create pscost branching rule data */
   SCIP_CALL( SCIPallocBlockMemory(scip, &branchruledata) );
 
   /* include allfullstrong branching rule */
   SCIP_CALL( SCIPincludeBranchruleBasic(scip, &branchrule, BRANCHRULE_NAME, BRANCHRULE_DESC, BRANCHRULE_PRIORITY,
         BRANCHRULE_MAXDEPTH, BRANCHRULE_MAXBOUNDDIST, branchruledata) );
 
   assert(branchrule != NULL);
   /* create a random number generator */
   SCIP_CALL( SCIPcreateRandom(scip, &branchruledata->randnumgen,
         BRANCHRULE_RANDSEED_DEFAULT, TRUE) );
 
   /* set non-fundamental callbacks via specific setter functions*/
   SCIP_CALL( SCIPsetBranchruleCopy(scip, branchrule, branchCopyPscost) );
   SCIP_CALL( SCIPsetBranchruleFree(scip, branchrule, branchFreePscost) );
   SCIP_CALL( SCIPsetBranchruleInit(scip, branchrule, branchInitPscost) );
   SCIP_CALL( SCIPsetBranchruleExecLp(scip, branchrule, branchExeclpPscost) );
   SCIP_CALL( SCIPsetBranchruleExecExt(scip, branchrule, branchExecextPscost) );
 
   SCIP_CALL( SCIPaddCharParam(scip, "branching/" BRANCHRULE_NAME "/strategy",
         "strategy for utilizing pseudo-costs of external branching candidates (multiply as in pseudo costs 'u'pdate rule, or by 'd'omain reduction, or by domain reduction of 's'ibling, or by 'v'ariable score)",
         &branchruledata->strategy, FALSE, BRANCHRULE_STRATEGY_DEFAULT, BRANCHRULE_STRATEGIES, NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "branching/" BRANCHRULE_NAME "/minscoreweight",
         "weight for minimum of scores of a branching candidate when building weighted sum of min/max/sum of scores",
         &branchruledata->scoreminweight, TRUE, BRANCHRULE_SCOREMINWEIGHT_DEFAULT, -SCIPinfinity(scip), SCIPinfinity(scip), NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "branching/" BRANCHRULE_NAME "/maxscoreweight",
         "weight for maximum of scores of a branching candidate when building weighted sum of min/max/sum of scores",
         &branchruledata->scoremaxweight, TRUE, BRANCHRULE_SCOREMAXWEIGHT_DEFAULT, -SCIPinfinity(scip), SCIPinfinity(scip), NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "branching/" BRANCHRULE_NAME "/sumscoreweight",
         "weight for sum of scores of a branching candidate when building weighted sum of min/max/sum of scores",
         &branchruledata->scoresumweight, TRUE, BRANCHRULE_SCORESUMWEIGHT_DEFAULT, -SCIPinfinity(scip), SCIPinfinity(scip), NULL, NULL) );
 
   SCIP_CALL( SCIPaddIntParam(scip, "branching/" BRANCHRULE_NAME "/nchildren",
         "number of children to create in n-ary branching",
         &branchruledata->nchildren, FALSE, BRANCHRULE_NCHILDREN_DEFAULT, 2, INT_MAX, NULL, NULL) );
 
   SCIP_CALL( SCIPaddIntParam(scip, "branching/" BRANCHRULE_NAME "/narymaxdepth",
         "maximal depth where to do n-ary branching, -1 to turn off",
         &branchruledata->narymaxdepth, FALSE, BRANCHRULE_NARYMAXDEPTH_DEFAULT, -1, INT_MAX, NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "branching/" BRANCHRULE_NAME "/naryminwidth",
         "minimal domain width in children when doing n-ary branching, relative to global bounds",
         &branchruledata->naryminwidth, FALSE, BRANCHRULE_NARYMINWIDTH_DEFAULT, 0.0, 1.0, NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "branching/" BRANCHRULE_NAME "/narywidthfactor",
         "factor of domain width in n-ary branching when creating nodes with increasing distance from branching value",
         &branchruledata->narywidthfactor, FALSE, BRANCHRULE_NARYWIDTHFAC_DEFAULT, 1.0, SCIP_REAL_MAX, NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip, "branching/" BRANCHRULE_NAME "/discountfactor",
         "discount factor for ancestral pseudo costs (0.0: disable discounted pseudo costs)",
         &branchruledata->discountfactor, FALSE, BRANCHRULE_DISCOUNTFACTOR, 0.0, 1.0, NULL, NULL) );
 
   return SCIP_OKAY;
}
 
/** selects a branching variable, due to pseudo cost, from the given candidate array and returns this variable together
 *  with a branching point */
SCIP_RETCODE SCIPselectBranchVarPscost(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_VAR**            branchcands,        /**< branching candidates */
   SCIP_Real*            branchcandssol,     /**< solution value for the branching candidates */
   SCIP_Real*            branchcandsscore,   /**< array of candidate scores */
   int                   nbranchcands,       /**< number of branching candidates */
   SCIP_VAR**            var,                /**< pointer to store the variable to branch on, or NULL if none */
   SCIP_Real*            brpoint             /**< pointer to store the branching point for the branching variable, will be fractional for a discrete variable */
   )
{
   SCIP_BRANCHRULE* branchrule;
 
   assert(scip != NULL);
 
   /* find branching rule */
   branchrule = SCIPfindBranchrule(scip, BRANCHRULE_NAME);
   assert(branchrule != NULL);
 
   /* select branching variable */
   SCIP_CALL( selectBranchVar(scip, branchrule, branchcands, branchcandssol, branchcandsscore, nbranchcands, var, brpoint) );
 
   return SCIP_OKAY;
}