コード例 #1
0
ファイル: heur_objpscostdiving.c プロジェクト: hhexiy/scip
/** execution method of primal heuristic */
static
SCIP_DECL_HEUREXEC(heurExecObjpscostdiving) /*lint --e{715}*/
{  /*lint --e{715}*/
   SCIP_HEURDATA* heurdata;
   SCIP_LPSOLSTAT lpsolstat;
   SCIP_VAR* var;
   SCIP_VAR** lpcands;
   SCIP_Real* lpcandssol;
   SCIP_Real* lpcandsfrac;
   SCIP_Real primsol;
   SCIP_Real frac;
   SCIP_Real pscostquot;
   SCIP_Real bestpscostquot;
   SCIP_Real oldobj;
   SCIP_Real newobj;
   SCIP_Real objscale;
   SCIP_Bool bestcandmayrounddown;
   SCIP_Bool bestcandmayroundup;
   SCIP_Bool bestcandroundup;
   SCIP_Bool mayrounddown;
   SCIP_Bool mayroundup;
   SCIP_Bool roundup;
   SCIP_Bool lperror;
   SCIP_Longint ncalls;
   SCIP_Longint nsolsfound;
   SCIP_Longint nlpiterations;
   SCIP_Longint maxnlpiterations;
   int* roundings;
   int nvars;
   int varidx;
   int nlpcands;
   int startnlpcands;
   int depth;
   int maxdepth;
   int maxdivedepth;
   int divedepth;
   int bestcand;
   int c;

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

   *result = SCIP_DELAYED;

   /* do not call heuristic of node was already detected to be infeasible */
   if( nodeinfeasible )
      return SCIP_OKAY;

   /* only call heuristic, if an optimal LP solution is at hand */
   if( SCIPgetLPSolstat(scip) != SCIP_LPSOLSTAT_OPTIMAL )
      return SCIP_OKAY;

   /* only call heuristic, if the LP objective value is smaller than the cutoff bound */
   if( SCIPisGE(scip, SCIPgetLPObjval(scip), SCIPgetCutoffbound(scip)) )
      return SCIP_OKAY;

   /* only call heuristic, if the LP solution is basic (which allows fast resolve in diving) */
   if( !SCIPisLPSolBasic(scip) )
      return SCIP_OKAY;

   /* don't dive two times at the same node */
   if( SCIPgetLastDivenode(scip) == SCIPgetNNodes(scip) && SCIPgetDepth(scip) > 0 )
      return SCIP_OKAY;

   *result = SCIP_DIDNOTRUN;

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

   /* only apply heuristic, if only a few solutions have been found */
   if( heurdata->maxsols >= 0 && SCIPgetNSolsFound(scip) >= heurdata->maxsols )
      return SCIP_OKAY;

   /* only try to dive, if we are in the correct part of the tree, given by minreldepth and maxreldepth */
   depth = SCIPgetDepth(scip);
   maxdepth = SCIPgetMaxDepth(scip);
   maxdepth = MAX(maxdepth, 30);
   if( depth < heurdata->minreldepth*maxdepth || depth > heurdata->maxreldepth*maxdepth )
      return SCIP_OKAY;

   /* calculate the maximal number of LP iterations until heuristic is aborted */
   nlpiterations = SCIPgetNNodeLPIterations(scip);
   ncalls = SCIPheurGetNCalls(heur);
   nsolsfound = 10*SCIPheurGetNBestSolsFound(heur) + heurdata->nsuccess;
   maxnlpiterations = (SCIP_Longint)((1.0 + 10.0*(nsolsfound+1.0)/(ncalls+1.0)) * heurdata->maxlpiterquot * nlpiterations);
   maxnlpiterations += heurdata->maxlpiterofs;

   /* don't try to dive, if we took too many LP iterations during diving */
   if( heurdata->nlpiterations >= maxnlpiterations )
      return SCIP_OKAY;

   /* allow at least a certain number of LP iterations in this dive */
   maxnlpiterations = MAX(maxnlpiterations, heurdata->nlpiterations + MINLPITER);

   /* get fractional variables that should be integral */
   SCIP_CALL( SCIPgetLPBranchCands(scip, &lpcands, &lpcandssol, &lpcandsfrac, &nlpcands, NULL, NULL) );

   /* don't try to dive, if there are no fractional variables */
   if( nlpcands == 0 )
      return SCIP_OKAY;

   /* calculate the maximal diving depth */
   nvars = SCIPgetNBinVars(scip) + SCIPgetNIntVars(scip);
   if( SCIPgetNSolsFound(scip) == 0 )
      maxdivedepth = (int)(heurdata->depthfacnosol * nvars);
   else
      maxdivedepth = (int)(heurdata->depthfac * nvars);
   maxdivedepth = MIN(maxdivedepth, 10*maxdepth);


   *result = SCIP_DIDNOTFIND;

   /* get temporary memory for remembering the current soft roundings */
   SCIP_CALL( SCIPallocBufferArray(scip, &roundings, nvars) );
   BMSclearMemoryArray(roundings, nvars);

   /* start diving */
   SCIP_CALL( SCIPstartDive(scip) );

   SCIPdebugMessage("(node %"SCIP_LONGINT_FORMAT") executing objpscostdiving heuristic: depth=%d, %d fractionals, dualbound=%g, maxnlpiterations=%"SCIP_LONGINT_FORMAT", maxdivedepth=%d\n",
      SCIPgetNNodes(scip), SCIPgetDepth(scip), nlpcands, SCIPgetDualbound(scip), maxnlpiterations, maxdivedepth);

   /* dive as long we are in the given diving depth and iteration limits and fractional variables exist, but
    * - if the last objective change was in a direction, that corresponds to a feasible rounding, we continue in any case
    * - if possible, we dive at least with the depth 10
    * - if the number of fractional variables decreased at least with 1 variable per 2 dive depths, we continue diving
    */
   lperror = FALSE;
   lpsolstat = SCIP_LPSOLSTAT_OPTIMAL;
   divedepth = 0;
   bestcandmayrounddown = FALSE;
   bestcandmayroundup = FALSE;
   startnlpcands = nlpcands;
   while( !lperror && lpsolstat == SCIP_LPSOLSTAT_OPTIMAL && nlpcands > 0
      && (divedepth < 10
         || nlpcands <= startnlpcands - divedepth/2
         || (divedepth < maxdivedepth && nlpcands <= startnlpcands - divedepth/10
            && heurdata->nlpiterations < maxnlpiterations)) && !SCIPisStopped(scip) )
   {
      SCIP_RETCODE retcode;

      divedepth++;

      /* choose variable for objective change:
       * - prefer variables that may not be rounded without destroying LP feasibility:
       *   - of these variables, change objective value of variable with largest rel. difference of pseudo cost values
       * - if all remaining fractional variables may be rounded without destroying LP feasibility:
       *   - change objective value of variable with largest rel. difference of pseudo cost values
       */
      bestcand = -1;
      bestpscostquot = -1.0;
      bestcandmayrounddown = TRUE;
      bestcandmayroundup = TRUE;
      bestcandroundup = FALSE;
      for( c = 0; c < nlpcands; ++c )
      {
         var = lpcands[c];
         mayrounddown = SCIPvarMayRoundDown(var);
         mayroundup = SCIPvarMayRoundUp(var);
         primsol = lpcandssol[c];
         frac = lpcandsfrac[c];
         if( mayrounddown || mayroundup )
         {
            /* the candidate may be rounded: choose this candidate only, if the best candidate may also be rounded */
            if( bestcandmayrounddown || bestcandmayroundup )
            {
               /* choose rounding direction:
                * - if variable may be rounded in both directions, round corresponding to the pseudo cost values
                * - otherwise, round in the infeasible direction, because feasible direction is tried by rounding
                *   the current fractional solution
                */
               roundup = FALSE;
               if( mayrounddown && mayroundup )
                  calcPscostQuot(scip, var, primsol, frac, 0, &pscostquot, &roundup);
               else if( mayrounddown )
                  calcPscostQuot(scip, var, primsol, frac, +1, &pscostquot, &roundup);
               else
                  calcPscostQuot(scip, var, primsol, frac, -1, &pscostquot, &roundup);

               /* prefer variables, that have already been soft rounded but failed to get integral */
               varidx = SCIPvarGetProbindex(var);
               assert(0 <= varidx && varidx < nvars);
               if( roundings[varidx] != 0 )
                  pscostquot *= 1000.0;

               /* check, if candidate is new best candidate */
               if( pscostquot > bestpscostquot )
               {
                  bestcand = c;
                  bestpscostquot = pscostquot;
                  bestcandmayrounddown = mayrounddown;
                  bestcandmayroundup = mayroundup;
                  bestcandroundup = roundup;
               }
            }
         }
         else
         {
            /* the candidate may not be rounded: calculate pseudo cost quotient and preferred direction */
            calcPscostQuot(scip, var, primsol, frac, 0, &pscostquot, &roundup);

            /* prefer variables, that have already been soft rounded but failed to get integral */
            varidx = SCIPvarGetProbindex(var);
            assert(0 <= varidx && varidx < nvars);
            if( roundings[varidx] != 0 )
               pscostquot *= 1000.0;

            /* check, if candidate is new best candidate: prefer unroundable candidates in any case */
            if( bestcandmayrounddown || bestcandmayroundup || pscostquot > bestpscostquot )
            {
               bestcand = c;
               bestpscostquot = pscostquot;
               bestcandmayrounddown = FALSE;
               bestcandmayroundup = FALSE;
               bestcandroundup = roundup;
            }
         }
      }
      assert(bestcand != -1);

      /* if all candidates are roundable, try to round the solution */
      if( bestcandmayrounddown || bestcandmayroundup )
      {
         SCIP_Bool success;

         /* create solution from diving LP and try to round it */
         SCIP_CALL( SCIPlinkLPSol(scip, heurdata->sol) );
         SCIP_CALL( SCIProundSol(scip, heurdata->sol, &success) );

         if( success )
         {
            SCIPdebugMessage("objpscostdiving found roundable primal solution: obj=%g\n",
               SCIPgetSolOrigObj(scip, heurdata->sol));

            /* try to add solution to SCIP */
            SCIP_CALL( SCIPtrySol(scip, heurdata->sol, FALSE, FALSE, FALSE, FALSE, &success) );

            /* check, if solution was feasible and good enough */
            if( success )
            {
               SCIPdebugMessage(" -> solution was feasible and good enough\n");
               *result = SCIP_FOUNDSOL;
            }
         }
      }

      var = lpcands[bestcand];

      /* check, if the best candidate was already subject to soft rounding */
      varidx = SCIPvarGetProbindex(var);
      assert(0 <= varidx && varidx < nvars);
      if( roundings[varidx] == +1 )
      {
         /* variable was already soft rounded upwards: hard round it downwards */
         SCIP_CALL( SCIPchgVarUbDive(scip, var, SCIPfeasFloor(scip, lpcandssol[bestcand])) );
         SCIPdebugMessage("  dive %d/%d: var <%s>, round=%u/%u, sol=%g, was already soft rounded upwards -> bounds=[%g,%g]\n",
            divedepth, maxdivedepth, SCIPvarGetName(var), bestcandmayrounddown, bestcandmayroundup,
            lpcandssol[bestcand], SCIPgetVarLbDive(scip, var), SCIPgetVarUbDive(scip, var));
      }
      else if( roundings[varidx] == -1 )
      {
         /* variable was already soft rounded downwards: hard round it upwards */
         SCIP_CALL( SCIPchgVarLbDive(scip, var, SCIPfeasCeil(scip, lpcandssol[bestcand])) );
         SCIPdebugMessage("  dive %d/%d: var <%s>, round=%u/%u, sol=%g, was already soft rounded downwards -> bounds=[%g,%g]\n",
            divedepth, maxdivedepth, SCIPvarGetName(var), bestcandmayrounddown, bestcandmayroundup,
            lpcandssol[bestcand], SCIPgetVarLbDive(scip, var), SCIPgetVarUbDive(scip, var));
      }
      else
      {
         assert(roundings[varidx] == 0);

         /* apply soft rounding of best candidate via a change in the objective value */
         objscale = divedepth * 1000.0;
         oldobj = SCIPgetVarObjDive(scip, var);
         if( bestcandroundup )
         {
            /* soft round variable up: make objective value (more) negative */
            if( oldobj < 0.0 )
               newobj = objscale * oldobj;
            else
               newobj = -objscale * oldobj;
            newobj = MIN(newobj, -objscale);

            /* remember, that this variable was soft rounded upwards */
            roundings[varidx] = +1;
         }
         else
         {
            /* soft round variable down: make objective value (more) positive */
            if( oldobj > 0.0 )
               newobj = objscale * oldobj;
            else
               newobj = -objscale * oldobj;
            newobj = MAX(newobj, objscale);

            /* remember, that this variable was soft rounded downwards */
            roundings[varidx] = -1;
         }
         SCIP_CALL( SCIPchgVarObjDive(scip, var, newobj) );
         SCIPdebugMessage("  dive %d/%d, LP iter %"SCIP_LONGINT_FORMAT"/%"SCIP_LONGINT_FORMAT": var <%s>, round=%u/%u, sol=%g, bounds=[%g,%g], obj=%g, newobj=%g\n",
            divedepth, maxdivedepth, heurdata->nlpiterations, maxnlpiterations,
            SCIPvarGetName(var), bestcandmayrounddown, bestcandmayroundup,
            lpcandssol[bestcand], SCIPgetVarLbDive(scip, var), SCIPgetVarUbDive(scip, var), oldobj, newobj);
      }

      /* resolve the diving LP */
      nlpiterations = SCIPgetNLPIterations(scip);
      retcode =  SCIPsolveDiveLP(scip, MAX((int)(maxnlpiterations - heurdata->nlpiterations), MINLPITER), &lperror, NULL);
      lpsolstat = SCIPgetLPSolstat(scip);

      /* 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.
       */
      if( retcode != SCIP_OKAY )
      {
#ifndef NDEBUG
         if( lpsolstat != SCIP_LPSOLSTAT_UNBOUNDEDRAY )
         {
            SCIP_CALL( retcode );
         }
#endif
         SCIPwarningMessage(scip, "Error while solving LP in Objpscostdiving heuristic; LP solve terminated with code <%d>\n", retcode);
         SCIPwarningMessage(scip, "This does not affect the remaining solution procedure --> continue\n");
      }

      if( lperror )
         break;

      /* update iteration count */
      heurdata->nlpiterations += SCIPgetNLPIterations(scip) - nlpiterations;

      /* get LP solution status  and fractional variables, that should be integral */
      if( lpsolstat == SCIP_LPSOLSTAT_OPTIMAL )
      {
         /* get new fractional variables */
         SCIP_CALL( SCIPgetLPBranchCands(scip, &lpcands, &lpcandssol, &lpcandsfrac, &nlpcands, NULL, NULL) );
      }
      SCIPdebugMessage("   -> lpsolstat=%d, nfrac=%d\n", lpsolstat, nlpcands);
   }

   /* check if a solution has been found */
   if( nlpcands == 0 && !lperror && lpsolstat == SCIP_LPSOLSTAT_OPTIMAL )
   {
      SCIP_Bool success;

      /* create solution from diving LP */
      SCIP_CALL( SCIPlinkLPSol(scip, heurdata->sol) );
      SCIPdebugMessage("objpscostdiving found primal solution: obj=%g\n", SCIPgetSolOrigObj(scip, heurdata->sol));

      /* try to add solution to SCIP */
      SCIP_CALL( SCIPtrySol(scip, heurdata->sol, FALSE, FALSE, FALSE, FALSE, &success) );

      /* check, if solution was feasible and good enough */
      if( success )
      {
         SCIPdebugMessage(" -> solution was feasible and good enough\n");
         *result = SCIP_FOUNDSOL;
      }
   }

   /* end diving */
   SCIP_CALL( SCIPendDive(scip) );

   if( *result == SCIP_FOUNDSOL )
      heurdata->nsuccess++;

   /* free temporary memory for remembering the current soft roundings */
   SCIPfreeBufferArray(scip, &roundings);

   SCIPdebugMessage("objpscostdiving heuristic finished\n");

   return SCIP_OKAY;
}
コード例 #2
0
/** execution method of primal heuristic */
static
SCIP_DECL_HEUREXEC(heurExecRootsoldiving) /*lint --e{715}*/
{  /*lint --e{715}*/
   SCIP_HEURDATA* heurdata;
   SCIP_VAR** vars;
   SCIP_Real* rootsol;
   SCIP_Real* objchgvals;
   int* softroundings;
   int* intvalrounds;
   int nvars;
   int nbinvars;
   int nintvars;
   int nlpcands;
   SCIP_LPSOLSTAT lpsolstat;
   SCIP_Real absstartobjval;
   SCIP_Real objstep;
   SCIP_Real alpha;
   SCIP_Real oldobj;
   SCIP_Real newobj;
   SCIP_Bool lperror;
   SCIP_Bool lpsolchanged;
   SCIP_Longint nsolsfound;
   SCIP_Longint ncalls;
   SCIP_Longint nlpiterations;
   SCIP_Longint maxnlpiterations;
   int depth;
   int maxdepth;
   int maxdivedepth;
   int divedepth;
   int startnlpcands;
   int ncycles;
   int i;

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

   *result = SCIP_DELAYED;

   /* only call heuristic, if an optimal LP solution is at hand */
   if( SCIPgetLPSolstat(scip) != SCIP_LPSOLSTAT_OPTIMAL )
      return SCIP_OKAY;

   /* only call heuristic, if the LP solution is basic (which allows fast resolve in diving) */
   if( !SCIPisLPSolBasic(scip) )
      return SCIP_OKAY;

   /* don't dive two times at the same node */
   if( SCIPgetLastDivenode(scip) == SCIPgetNNodes(scip) && SCIPgetDepth(scip) > 0 )
      return SCIP_OKAY;

   *result = SCIP_DIDNOTRUN;

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

   /* only apply heuristic, if only a few solutions have been found */
   if( heurdata->maxsols >= 0 && SCIPgetNSolsFound(scip) >= heurdata->maxsols )
      return SCIP_OKAY;

   /* only try to dive, if we are in the correct part of the tree, given by minreldepth and maxreldepth */
   depth = SCIPgetDepth(scip);
   maxdepth = SCIPgetMaxDepth(scip);
   maxdepth = MAX(maxdepth, 30);
   if( depth < heurdata->minreldepth*maxdepth || depth > heurdata->maxreldepth*maxdepth )
      return SCIP_OKAY;

   /* calculate the maximal number of LP iterations until heuristic is aborted */
   nlpiterations = SCIPgetNNodeLPIterations(scip);
   ncalls = SCIPheurGetNCalls(heur);
   nsolsfound = 10*SCIPheurGetNBestSolsFound(heur) + heurdata->nsuccess;
   maxnlpiterations = (SCIP_Longint)((1.0 + 10.0*(nsolsfound+1.0)/(ncalls+1.0)) * heurdata->maxlpiterquot * nlpiterations);
   maxnlpiterations += heurdata->maxlpiterofs;

   /* don't try to dive, if we took too many LP iterations during diving */
   if( heurdata->nlpiterations >= maxnlpiterations )
      return SCIP_OKAY;

   /* allow at least a certain number of LP iterations in this dive */
   maxnlpiterations = MAX(maxnlpiterations, heurdata->nlpiterations + MINLPITER);

   /* get number of fractional variables, that should be integral */
   nlpcands = SCIPgetNLPBranchCands(scip);

   /* don't try to dive, if there are no fractional variables */
   if( nlpcands == 0 )
      return SCIP_OKAY;

   /* calculate the maximal diving depth */
   nvars = SCIPgetNBinVars(scip) + SCIPgetNIntVars(scip);
   if( SCIPgetNSolsFound(scip) == 0 )
      maxdivedepth = (int)(heurdata->depthfacnosol * nvars);
   else
      maxdivedepth = (int)(heurdata->depthfac * nvars);
   maxdivedepth = MAX(maxdivedepth, 10);

   *result = SCIP_DIDNOTFIND;

   /* get all variables of LP */
   SCIP_CALL( SCIPgetVarsData(scip, &vars, &nvars, &nbinvars, &nintvars, NULL, NULL) );

   /* get root solution value of all binary and integer variables */
   SCIP_CALL( SCIPallocBufferArray(scip, &rootsol, nbinvars + nintvars) );
   for( i = 0; i < nbinvars + nintvars; i++ )
      rootsol[i] = SCIPvarGetRootSol(vars[i]);

   /* get current LP objective value, and calculate length of a single step in an objective coefficient */
   absstartobjval = SCIPgetLPObjval(scip);
   absstartobjval = ABS(absstartobjval);
   absstartobjval = MAX(absstartobjval, 1.0);
   objstep = absstartobjval / 10.0;

   /* initialize array storing the preferred soft rounding directions and counting the integral value rounds */
   SCIP_CALL( SCIPallocBufferArray(scip, &softroundings, nbinvars + nintvars) );
   BMSclearMemoryArray(softroundings, nbinvars + nintvars);
   SCIP_CALL( SCIPallocBufferArray(scip, &intvalrounds, nbinvars + nintvars) );
   BMSclearMemoryArray(intvalrounds, nbinvars + nintvars);

   /* allocate temporary memory for buffering objective changes */
   SCIP_CALL( SCIPallocBufferArray(scip, &objchgvals, nbinvars + nintvars) );

   /* start diving */
   SCIP_CALL( SCIPstartDive(scip) );

   SCIPdebugMessage("(node %"SCIP_LONGINT_FORMAT") executing rootsoldiving heuristic: depth=%d, %d fractionals, dualbound=%g, maxnlpiterations=%"SCIP_LONGINT_FORMAT", maxdivedepth=%d, LPobj=%g, objstep=%g\n",
      SCIPgetNNodes(scip), SCIPgetDepth(scip), nlpcands, SCIPgetDualbound(scip), maxnlpiterations, maxdivedepth,
      SCIPgetLPObjval(scip), objstep);

   lperror = FALSE;
   divedepth = 0;
   lpsolstat = SCIP_LPSOLSTAT_OPTIMAL;
   alpha = heurdata->alpha;
   ncycles = 0;
   lpsolchanged = TRUE;
   startnlpcands = nlpcands;
   while( !lperror && lpsolstat == SCIP_LPSOLSTAT_OPTIMAL && nlpcands > 0 && ncycles < 10
      && (divedepth < 10
         || nlpcands <= startnlpcands - divedepth/2
         || (divedepth < maxdivedepth && heurdata->nlpiterations < maxnlpiterations))
      && !SCIPisStopped(scip) )
   {
      SCIP_Bool success;
      int hardroundingidx;
      int hardroundingdir;
      SCIP_Real hardroundingoldbd;
      SCIP_Real hardroundingnewbd;
      SCIP_Bool boundschanged;

      SCIP_RETCODE retcode;

      /* create solution from diving LP and try to round it */
      SCIP_CALL( SCIPlinkLPSol(scip, heurdata->sol) );
      SCIP_CALL( SCIProundSol(scip, heurdata->sol, &success) );

      if( success )
      {
         SCIPdebugMessage("rootsoldiving found roundable primal solution: obj=%g\n", SCIPgetSolOrigObj(scip, heurdata->sol));

         /* try to add solution to SCIP */
         SCIP_CALL( SCIPtrySol(scip, heurdata->sol, FALSE, FALSE, FALSE, FALSE, &success) );

         /* check, if solution was feasible and good enough */
         if( success )
         {
            SCIPdebugMessage(" -> solution was feasible and good enough\n");
            *result = SCIP_FOUNDSOL;
         }
      }

      divedepth++;
      hardroundingidx = -1;
      hardroundingdir = 0;
      hardroundingoldbd = 0.0;
      hardroundingnewbd = 0.0;
      boundschanged = FALSE;

      SCIPdebugMessage("dive %d/%d, LP iter %"SCIP_LONGINT_FORMAT"/%"SCIP_LONGINT_FORMAT":\n", divedepth, maxdivedepth, heurdata->nlpiterations, maxnlpiterations);

      /* round solution x* from diving LP:
       *   - x~_j = down(x*_j)    if x*_j is integer or binary variable and x*_j <= root solution_j
       *   - x~_j = up(x*_j)      if x*_j is integer or binary variable and x*_j  > root solution_j
       *   - x~_j = x*_j          if x*_j is continuous variable
       * change objective function in diving LP:
       *   - if x*_j is integral, or j is a continuous variable, set obj'_j = alpha * obj_j
       *   - otherwise, set obj'_j = alpha * obj_j + sign(x*_j - x~_j)
       */
      for( i = 0; i < nbinvars + nintvars; i++ )
      {
         SCIP_VAR* var;
         SCIP_Real solval;

         var = vars[i];
         oldobj = SCIPgetVarObjDive(scip, var);
         newobj = oldobj;

         solval =  SCIPvarGetLPSol(var);
         if( SCIPisFeasIntegral(scip, solval) )
         {
            /* if the variable became integral after a soft rounding, count the rounds; after a while, fix it to its
             * current integral value;
             * otherwise, fade out the objective value
             */
            if( softroundings[i] != 0 && lpsolchanged )
            {
               intvalrounds[i]++;
               if( intvalrounds[i] == 5 && SCIPgetVarLbDive(scip, var) < SCIPgetVarUbDive(scip, var) - 0.5 )
               {
                  /* use exact integral value, if the variable is only integral within numerical tolerances */
                  solval = SCIPfloor(scip, solval+0.5);
                  SCIPdebugMessage(" -> fixing <%s> = %g\n", SCIPvarGetName(var), solval);
                  SCIP_CALL( SCIPchgVarLbDive(scip, var, solval) );
                  SCIP_CALL( SCIPchgVarUbDive(scip, var, solval) );
                  boundschanged = TRUE;
               }
            }
            else
               newobj = alpha * oldobj;
         }
         else if( solval <= rootsol[i] )
         {
            /* if the variable was soft rounded most of the time downwards, round it downwards by changing the bounds;
             * otherwise, apply soft rounding by changing the objective value
             */
            softroundings[i]--;
            if( softroundings[i] <= -10 && hardroundingidx == -1 )
            {
               SCIPdebugMessage(" -> hard rounding <%s>[%g] <= %g\n",
                  SCIPvarGetName(var), solval, SCIPfeasFloor(scip, solval));
               hardroundingidx = i;
               hardroundingdir = -1;
               hardroundingoldbd = SCIPgetVarUbDive(scip, var);
               hardroundingnewbd = SCIPfeasFloor(scip, solval);
               SCIP_CALL( SCIPchgVarUbDive(scip, var, hardroundingnewbd) );
               boundschanged = TRUE;
            }
            else
               newobj = alpha * oldobj + objstep;
         }
         else
         {
            /* if the variable was soft rounded most of the time upwards, round it upwards by changing the bounds;
             * otherwise, apply soft rounding by changing the objective value
             */
            softroundings[i]++;
            if( softroundings[i] >= +10 && hardroundingidx == -1 )
            {
               SCIPdebugMessage(" -> hard rounding <%s>[%g] >= %g\n",
                  SCIPvarGetName(var), solval, SCIPfeasCeil(scip, solval));
               hardroundingidx = i;
               hardroundingdir = +1;
               hardroundingoldbd = SCIPgetVarLbDive(scip, var);
               hardroundingnewbd = SCIPfeasCeil(scip, solval);
               SCIP_CALL( SCIPchgVarLbDive(scip, var, hardroundingnewbd) );
               boundschanged = TRUE;
            }
            else
               newobj = alpha * oldobj - objstep;
         }

         /* remember the objective change */
         objchgvals[i] = newobj;
      }

      /* apply objective changes if there was no bound change */
      if( !boundschanged )
      {
         /* apply cached changes on integer variables */
         for( i = 0; i < nbinvars + nintvars; ++i )
         {
            SCIP_VAR* var;

            var = vars[i];
            SCIPdebugMessage(" -> i=%d  var <%s>, solval=%g, rootsol=%g, oldobj=%g, newobj=%g\n",
               i, SCIPvarGetName(var), SCIPvarGetLPSol(var), rootsol[i], SCIPgetVarObjDive(scip, var), objchgvals[i]);

            SCIP_CALL( SCIPchgVarObjDive(scip, var, objchgvals[i]) );
         }

         /* fade out the objective values of the continuous variables */
         for( i = nbinvars + nintvars; i < nvars; i++ )
         {
            SCIP_VAR* var;

            var = vars[i];
            oldobj = SCIPgetVarObjDive(scip, var);
            newobj = alpha * oldobj;

            SCIPdebugMessage(" -> i=%d  var <%s>, solval=%g, oldobj=%g, newobj=%g\n",
               i, SCIPvarGetName(var), SCIPvarGetLPSol(var), oldobj, newobj);

            SCIP_CALL( SCIPchgVarObjDive(scip, var, newobj) );
         }
      }

   SOLVEAGAIN:
      /* resolve the diving LP */
      nlpiterations = SCIPgetNLPIterations(scip);

      retcode = SCIPsolveDiveLP(scip,  MAX((int)(maxnlpiterations - heurdata->nlpiterations), MINLPITER), &lperror);
      lpsolstat = SCIPgetLPSolstat(scip);

      /* 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.
       */
      if( retcode != SCIP_OKAY )
      {
#ifndef NDEBUG
         if( lpsolstat != SCIP_LPSOLSTAT_UNBOUNDEDRAY )
         {
            SCIP_CALL( retcode );
         }
#endif
         SCIPwarningMessage(scip, "Error while solving LP in Rootsoldiving heuristic; LP solve terminated with code <%d>\n", retcode);
         SCIPwarningMessage(scip, "This does not affect the remaining solution procedure --> continue\n");
      }

      if( lperror )
         break;

      /* update iteration count */
      heurdata->nlpiterations += SCIPgetNLPIterations(scip) - nlpiterations;

      /* if no LP iterations were performed, we stayed at the same solution -> count this cycling */
      lpsolchanged = (SCIPgetNLPIterations(scip) != nlpiterations);
      if( lpsolchanged )
         ncycles = 0;
      else if( !boundschanged ) /* do not count if integral variables have been fixed */
         ncycles++;

      /* get LP solution status and number of fractional variables, that should be integral */
      if( lpsolstat == SCIP_LPSOLSTAT_INFEASIBLE && hardroundingidx != -1 )
      {
         SCIP_VAR* var;

         var = vars[hardroundingidx];

         /* round the hard rounded variable to the opposite direction and resolve the LP */
         if( hardroundingdir == -1 )
         {
            SCIPdebugMessage(" -> opposite hard rounding <%s> >= %g\n", SCIPvarGetName(var), hardroundingnewbd + 1.0);
            SCIP_CALL( SCIPchgVarUbDive(scip, var, hardroundingoldbd) );
            SCIP_CALL( SCIPchgVarLbDive(scip, var, hardroundingnewbd + 1.0) );
         }
         else
         {
            SCIPdebugMessage(" -> opposite hard rounding <%s> <= %g\n", SCIPvarGetName(var), hardroundingnewbd - 1.0);
            SCIP_CALL( SCIPchgVarLbDive(scip, var, hardroundingoldbd) );
            SCIP_CALL( SCIPchgVarUbDive(scip, var, hardroundingnewbd - 1.0) );
         }
         hardroundingidx = -1;
         goto SOLVEAGAIN;
      }
      if( lpsolstat == SCIP_LPSOLSTAT_OPTIMAL )
         nlpcands = SCIPgetNLPBranchCands(scip);
      SCIPdebugMessage("   -> lpsolstat=%d, nfrac=%d\n", lpsolstat, nlpcands);
   }

   SCIPdebugMessage("---> diving finished: lpsolstat = %d, depth %d/%d, LP iter %"SCIP_LONGINT_FORMAT"/%"SCIP_LONGINT_FORMAT"\n",
      lpsolstat, divedepth, maxdivedepth, heurdata->nlpiterations, maxnlpiterations);

   /* check if a solution has been found */
   if( nlpcands == 0 && !lperror && lpsolstat == SCIP_LPSOLSTAT_OPTIMAL )
   {
      SCIP_Bool success;

      /* create solution from diving LP */
      SCIP_CALL( SCIPlinkLPSol(scip, heurdata->sol) );
      SCIPdebugMessage("rootsoldiving found primal solution: obj=%g\n", SCIPgetSolOrigObj(scip, heurdata->sol));

      /* try to add solution to SCIP */
      SCIP_CALL( SCIPtrySol(scip, heurdata->sol, FALSE, FALSE, FALSE, FALSE, &success) );

      /* check, if solution was feasible and good enough */
      if( success )
      {
         SCIPdebugMessage(" -> solution was feasible and good enough\n");
         *result = SCIP_FOUNDSOL;
      }
   }

   /* end diving */
   SCIP_CALL( SCIPendDive(scip) );

   if( *result == SCIP_FOUNDSOL )
      heurdata->nsuccess++;

   /* free temporary memory */
   SCIPfreeBufferArray(scip, &objchgvals);
   SCIPfreeBufferArray(scip, &intvalrounds);
   SCIPfreeBufferArray(scip, &softroundings);
   SCIPfreeBufferArray(scip, &rootsol);

   SCIPdebugMessage("rootsoldiving heuristic finished\n");

   return SCIP_OKAY;
}