cutsel_ensemble.c

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/**@file   cutsel_ensemble.c
 * @ingroup DEFPLUGINS_CUTSEL
 * @brief  ensemble cut selector
 * @author Mark Turner
 *
 * @todo separator hard limit on density is inappropriate for MINLP. Need to relax hard limit in case of all cuts dense
 * @todo penalising via parallelism is overly costly if many cuts. Hash cuts before and find appropriate groups?
 */

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

#include <assert.h>

#include "scip/scip_cutsel.h"
#include "scip/scip_cut.h"
#include "scip/scip_lp.h"
#include "scip/scip_randnumgen.h"
#include "scip/cutsel_ensemble.h"


#define CUTSEL_NAME              "ensemble"
#define CUTSEL_DESC              "weighted sum of many terms with optional filtering and penalties"
#define CUTSEL_PRIORITY           7000

#define RANDSEED                  0x5EED

#define DEFAULT_MINSCORE                0.0  /**< minimum score s.t. a cut can be selected */
#define DEFAULT_EFFICACYWEIGHT          0.75 /**< weight of normed-efficacy in score calculation */
#define DEFAULT_DIRCUTOFFDISTWEIGHT     0.0  /**< weight of normed-directed cutoff distance in score calculation */
#define DEFAULT_OBJPARALWEIGHT          0.25 /**< weight of objective parallelism in score calculation */
#define DEFAULT_INTSUPPORTWEIGHT        0.45 /**< weight of integral support in cut score calculation */
#define DEFAULT_EXPIMPROVWEIGHT         0.1  /**< weight of normed-expected improvement in cut score calculation */
#define DEFAULT_PSCOSTWEIGHT            0.75 /**< weight of normalised pseudo-costs in cut score calculation */
#define DEFAULT_NLOCKSWEIGHT            0.25 /**< weight of normalised number of locks in cut score calculation */
#define DEFAULT_MAXSPARSITYBONUS        0.5  /**< score given to a cut with complete sparsity */
#define DEFAULT_SPARSITYENDBONUS        0.2  /**< the density at which a cut no longer receives additional score */
#define DEFAULT_GOODNUMERICBONUS        0.0  /**< bonus provided for good numerics */
#define DEFAULT_MAXCOEFRATIOBONUS       10000 /**< maximum coefficient ratio of cut for which numeric bonus is given */
#define DEFAULT_PENALISELOCKS           TRUE /**< whether having less locks should be rewarded instead of more */
#define DEFAULT_PENALISEOBJPARAL        TRUE /**< whether objective parallelism should be penalised not rewarded */
#define DEFAULT_FILTERPARALCUTS         FALSE /**< should cuts be filtered so no two parallel cuts are added */
#define DEFAULT_MAXPARAL                0.95 /**< threshold for when two cuts are considered parallel to each other */
#define DEFAULT_PENALISEPARALCUTS       TRUE /**< should two parallel cuts be penalised instead of outright filtered */
#define DEFAULT_PARALPENALTY            0.25 /**< penalty for weaker of two parallel cuts if penalising parallel cuts */
#define DEFAULT_FILTERDENSECUTS         TRUE /**< should cuts over a given density threshold be filtered */
#define DEFAULT_MAXCUTDENSITY           0.425 /**< max allowed cut density if filtering dense cuts */
#define DEFAULT_MAXNONZEROROOTROUND     4.5  /**< max nonzeros per round (root). Gets multiplied by num LP cols */
#define DEFAULT_MAXNONZEROTREEROUND     9.5  /**< max nonzeros per round (tree). Gets multiplied by num LP cols */
#define DEFAULT_MAXCUTS                 200  /**< maximum number of cuts that can be considered by this cut selector */
#define DEFAULT_MAXNUMVARS              50000 /**< maximum number of variables that a problem can have while calling this cut selector */

/*
 * Data structures
 */

/** cut selector data */
struct SCIP_CutselData
{
   SCIP_RANDNUMGEN*      randnumgen;         /**< random generator for tie-breaking */
   SCIP_Real             minscore;           /**< minimum score for a cut to be added to the LP */
   SCIP_Real             objparalweight;     /**< weight of objective parallelism in cut score calculation */
   SCIP_Real             efficacyweight;     /**< weight of normed-efficacy in cut score calculation */
   SCIP_Real             dircutoffdistweight;/**< weight of normed-directed cutoff distance in cut score calculation */
   SCIP_Real             expimprovweight;    /**< weight of normed-expected improvement in cut score calculation */
   SCIP_Real             intsupportweight;   /**< weight of integral support in cut score calculation */
   SCIP_Real             pscostweight;       /**< weight of normalised pseudo-costs in cut score calculation */
   SCIP_Real             locksweight;        /**< weight of normed-number of active locks in cut score calculation */
   SCIP_Real             maxsparsitybonus;   /**< weight of maximum sparsity reward in cut score calculation */
   SCIP_Real             goodnumericsbonus;  /**< weight of good numeric bonus in cut score calculation */
   SCIP_Real             endsparsitybonus;   /**< max sparsity value for which a bonus is applied */
   SCIP_Real             maxparal;           /**< threshold for when two cuts are considered parallel to each other */
   SCIP_Real             paralpenalty;       /**< penalty for weaker of two parallel cuts if penalising parallel cuts */
   SCIP_Real             maxcutdensity;      /**< max allowed cut density if filtering dense cuts */
   SCIP_Real             maxnonzerorootround;/**< max nonzeros per round (root). Gets multiplied by num LP cols */
   SCIP_Real             maxnonzerotreeround;/**< max nonzeros per round (tree). Gets multiplied by num LP cols */
   SCIP_Bool             filterparalcuts;   /**< should cuts be filtered so no two parallel cuts are added */
   SCIP_Bool             penaliseparalcuts;  /**< should two parallel cuts be penalised instead of outright filtered */
   SCIP_Bool             filterdensecuts;    /**< should cuts over a given density threshold be filtered */
   SCIP_Bool             penaliselocks;      /**< whether the number of locks should be penalised instead of rewarded */
   SCIP_Bool             penaliseobjparal;   /**< whether objective parallelism should be penalised */
   int                   maxcoefratiobonus;  /**< maximum coefficient ratio for which numeric bonus is applied */
   int                   maxcuts;            /**< maximum number of cuts that can be considered by this cut selector */
   int                   maxnumvars;         /**< maximum number of variables that a problem can have while calling this cut selector */
};


/*
 * Local methods
 */

/** returns the maximum score of cuts; if scores is not NULL, then stores the individual score of each cut in scores */
static
SCIP_RETCODE scoring(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_ROW**            cuts,               /**< array with cuts to score */
   SCIP_CUTSELDATA*      cutseldata,         /**< cut selector data */
   SCIP_Real*            scores,             /**< array to store the score of cuts or NULL */
   SCIP_Bool             root,               /**< whether we are at the root node or not */
   int                   ncuts               /**< number of cuts in cuts array */
   )
{
   SCIP_Real* effs;
   SCIP_Real* dcds;
   SCIP_Real* exps;
   SCIP_Real* cutdensities;
   SCIP_Real* cutlocks;
   SCIP_Real* pscosts;
   SCIP_SOL* sol;
   SCIP_Real maxdcd = 0.0;
   SCIP_Real maxeff = 0.0;
   SCIP_Real maxexp = 0.0;
   SCIP_Real maxpscost = 0.0;
   SCIP_Real maxlocks = 0.0;
   SCIP_Real ncols;

   /* Get the solution that we use for directed cutoff distance calculations. Get the number of columns too */
   sol = SCIPgetBestSol(scip);
   ncols = SCIPgetNLPCols(scip);

   /* Initialise all array information that we're going to use for scoring */
   SCIP_CALL(SCIPallocBufferArray(scip, &effs, ncuts));
   SCIP_CALL(SCIPallocBufferArray(scip, &dcds, ncuts));
   SCIP_CALL(SCIPallocBufferArray(scip, &exps, ncuts));
   SCIP_CALL(SCIPallocBufferArray(scip, &cutdensities, ncuts));
   SCIP_CALL(SCIPallocBufferArray(scip, &cutlocks, ncuts));
   SCIP_CALL(SCIPallocBufferArray(scip, &pscosts, ncuts));

   /* Populate the number of cut locks, the pseudo-cost scores, and the cut densities */
   for (int i = 0; i < ncuts; ++i )
   {
      SCIP_COL** cols;
      SCIP_Real* cutvals;
      SCIP_Real sqrcutnorm;
      SCIP_Real ncutcols;
      SCIP_Real cutalpha;

      cols = SCIProwGetCols(cuts[i]);
      cutvals = SCIProwGetVals(cuts[i]);
      sqrcutnorm = MAX(SCIPsumepsilon(scip), SQR(SCIProwGetNorm(cuts[i]))); /*lint !e666*/
      cutalpha = -SCIPgetRowFeasibility(scip, cuts[i]) / sqrcutnorm;
      ncutcols = SCIProwGetNNonz(cuts[i]);
      cutdensities[i] = ncutcols / ncols;
      cutlocks[i] = 0;
      pscosts[i] = 0;

      for ( int j = 0; j < (int) ncutcols; ++j )
      {
         SCIP_VAR* colvar;
         SCIP_Real colval;
         SCIP_Real l1dist;

         colval = SCIPcolGetPrimsol(cols[j]);
         colvar = SCIPcolGetVar(cols[j]);
         /* Get the number of active locks feature in the cut */
         if( ! SCIPisInfinity(scip, SCIProwGetRhs(cuts[i])) && cutvals[j] > 0.0 )
            cutlocks[i] += SCIPvarGetNLocksUp(colvar);
         if( ! SCIPisInfinity(scip, -SCIProwGetLhs(cuts[i])) && cutvals[j] < 0.0 )
            cutlocks[i] += SCIPvarGetNLocksUp(colvar);
         if( ! SCIPisInfinity(scip, SCIProwGetRhs(cuts[i])) && cutvals[j] < 0.0 )
            cutlocks[i] += SCIPvarGetNLocksDown(colvar);
         if( ! SCIPisInfinity(scip, -SCIProwGetLhs(cuts[i])) && cutvals[j] > 0.0 )
            cutlocks[i] += SCIPvarGetNLocksDown(colvar);

         /* Get the L1 distance from the projection onto the cut and the LP solution in the variable direction */
         l1dist = ABS(colval - (cutalpha * cutvals[j]));
         pscosts[i] += SCIPgetVarPseudocostScore(scip, colvar, colval) * l1dist;
      }
      cutlocks[i] = cutlocks[i] / ncutcols; /*lint !e414*/

      if( cutlocks[i] > maxlocks )
         maxlocks = cutlocks[i];

      if( pscosts[i] > maxpscost )
         maxpscost = pscosts[i];
   }
   
   /* account for the case where maxlocks or maxpscost is 0 */
   maxpscost = MAX(maxpscost, SCIPepsilon(scip)); /*lint !e666*/
   maxlocks = MAX(maxlocks, 1);

   for ( int i = 0; i < ncuts; i++ )
   {
      cutlocks[i] = cutlocks[i] / maxlocks; /*lint !e414*/
      /* if locks are penalized, we complement the corresponding score */
      if( cutseldata->penaliselocks )
         cutlocks[i] = 1 - cutlocks[i];
      pscosts[i] = pscosts[i] / maxpscost; /*lint !e414*/
   }

   /* Get the arrays / maximums of directed cutoff distance, efficacy, and expected improvement values. */
   if ( sol != NULL && root )
   {
      for ( int i = 0; i < ncuts; i++ )
      {
         dcds[i] = SCIPgetCutLPSolCutoffDistance(scip, sol, cuts[i]);
         maxdcd = MAX(maxdcd, dcds[i]);
      }
   }

   for ( int i = 0; i < ncuts; ++i )
   {
      effs[i] = SCIPgetCutEfficacy(scip, NULL, cuts[i]);
      exps[i] = effs[i] * SCIPgetRowObjParallelism(scip, cuts[i]);
      maxeff = MAX(maxeff, effs[i]);
      maxexp = MAX(maxexp, exps[i]);
   }

   /* Now score the cuts */
   for ( int i = 0; i < ncuts; ++i )
   {
      SCIP_Real score;
      SCIP_Real scaleddcd;
      SCIP_Real scaledeff;
      SCIP_Real scaledexp;
      SCIP_Real objparallelism;
      SCIP_Real intsupport;
      SCIP_Real density;
      SCIP_Real dynamism;
      SCIP_Real mincutval;
      SCIP_Real maxcutval;
      SCIP_Real pscost;
      SCIP_Real cutlock;

      /* Get the integer support */
      intsupport = SCIPgetRowNumIntCols(scip, cuts[i]) / (SCIP_Real) SCIProwGetNNonz(cuts[i]);
      intsupport *= cutseldata->intsupportweight;

      /* Get the objective parallelism and orthogonality */
      if( ! cutseldata->penaliseobjparal )
         objparallelism = cutseldata->objparalweight * SCIPgetRowObjParallelism(scip, cuts[i]);
      else
         objparallelism = cutseldata->objparalweight * (1 - SCIPgetRowObjParallelism(scip, cuts[i]));

      /* Get the density score */
      density = (cutseldata->maxsparsitybonus / cutseldata->endsparsitybonus) * -1 * cutdensities[i];
      density += cutseldata->maxsparsitybonus;
      density = MAX(density, 0.0);

      /* Get the normalised pseudo-cost and number of locks score */
      if( root )
         pscost = 0.0;
      else
         pscost = cutseldata->pscostweight * pscosts[i];
      cutlock = cutseldata->locksweight * cutlocks[i];

      /* Get the dynamism (good numerics) score */
      maxcutval = SCIPgetRowMaxCoef(scip, cuts[i]);
      mincutval = SCIPgetRowMinCoef(scip, cuts[i]);
      mincutval = mincutval > 0.0 ? mincutval : 1.0;
      dynamism = cutseldata->maxcoefratiobonus >= maxcutval / mincutval ? cutseldata->goodnumericsbonus : 0.0;

      /* Get the dcd / eff / exp score */
      if ( sol != NULL && root )
      {
         if ( SCIPisSumLE(scip, dcds[i], 0.0))
            scaleddcd = 0.0;
         else
            scaleddcd = cutseldata->dircutoffdistweight * SQR(LOG1P(dcds[i]) / LOG1P(maxdcd)); /*lint !e666*/
      }
      else
      {
         scaleddcd = 0.0;
      }

      if ( SCIPisSumLE(scip, exps[i], 0.0))
         scaledexp = 0.0;
      else
         scaledexp = cutseldata->expimprovweight * SQR(LOG1P(exps[i]) / LOG1P(maxexp)); /*lint !e666*/

      if ( SCIPisSumLE(scip, effs[i], 0.0))
      {
         scaledeff = 0.0;
      }
      else
      {
         if ( sol != NULL && root )
            scaledeff = cutseldata->efficacyweight * SQR(LOG1P(effs[i]) / LOG1P(maxeff)); /*lint !e666*/
         else
            scaledeff = (cutseldata->efficacyweight + cutseldata->dircutoffdistweight) * SQR(LOG1P(effs[i]) / LOG1P(maxeff)); /*lint !e666*/
      }

      /* Combine all scores and introduce some minor randomness */
      score = scaledeff + scaleddcd + scaledexp + objparallelism + intsupport + density + dynamism + pscost + cutlock;

      score += SCIPrandomGetReal(cutseldata->randnumgen, 0.0, 1e-6);

      scores[i] = score;
   }

   SCIPfreeBufferArray(scip, &effs);
   SCIPfreeBufferArray(scip, &dcds);
   SCIPfreeBufferArray(scip, &exps);
   SCIPfreeBufferArray(scip, &cutdensities);
   SCIPfreeBufferArray(scip, &cutlocks);
   SCIPfreeBufferArray(scip, &pscosts);

   return SCIP_OKAY;
}


/** move the cut with the highest score to the first position in the array; there must be at least one cut */
static
void selectBestCut(
   SCIP_ROW**            cuts,               /**< array with cuts to perform selection algorithm */
   SCIP_Real*            scores,             /**< array with scores of cuts to perform selection algorithm */
   int                   ncuts               /**< number of cuts in given array */
   )
{
   int bestpos;
   SCIP_Real bestscore;

   assert(ncuts > 0);
   assert(cuts != NULL);
   assert(scores != NULL);

   bestscore = scores[0];
   bestpos = 0;

   for( int i = 1; i < ncuts; ++i )
   {
      if( scores[i] > bestscore )
      {
         bestpos = i;
         bestscore = scores[i];
      }
   }

   SCIPswapPointers((void**) &cuts[bestpos], (void**) &cuts[0]);
   SCIPswapReals(&scores[bestpos], &scores[0]);
}

/** filters the given array of cuts to enforce a maximum parallelism constraint
 *  w.r.t the given cut; moves filtered cuts to the end of the array and returns number of selected cuts */
static
int filterWithParallelism(
   SCIP_ROW*             cut,                /**< cut to filter orthogonality with */
   SCIP_ROW**            cuts,               /**< array with cuts to perform selection algorithm */
   SCIP_Real*            scores,             /**< array with scores of cuts to perform selection algorithm */
   int                   ncuts,              /**< number of cuts in given array */
   SCIP_Real             maxparallel         /**< maximal parallelism for all cuts that are not good */
   )
{
   assert( cut != NULL );
   assert( ncuts == 0 || cuts != NULL );
   assert( ncuts == 0 || scores != NULL );

   for( int i = ncuts - 1; i >= 0; --i )
   {
      SCIP_Real thisparallel;

      thisparallel = SCIProwGetParallelism(cut, cuts[i], 'e');

      if( thisparallel > maxparallel )
      {
         --ncuts;
         SCIPswapPointers((void**) &cuts[i], (void**) &cuts[ncuts]);
         SCIPswapReals(&scores[i], &scores[ncuts]);
      }
   }

   return ncuts;
}

/** penalises any cut too parallel to cut by reducing the parallel cut's score. */
static
int penaliseWithParallelism(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_ROW*             cut,                /**< cut to filter orthogonality with */
   SCIP_ROW**            cuts,               /**< array with cuts to perform selection algorithm */
   SCIP_Real*            scores,             /**< array with scores of cuts to perform selection algorithm */
   int                   ncuts,              /**< number of cuts in given array */
   SCIP_Real             maxparallel,        /**< maximal parallelism for all cuts that are not good */
   SCIP_Real             paralpenalty        /**< penalty for weaker of two parallel cuts if penalising parallel cuts */
   )
{
   assert( cut != NULL );
   assert( ncuts == 0 || cuts != NULL );
   assert( ncuts == 0 || scores != NULL );

   for( int i = ncuts - 1; i >= 0; --i )
   {
      SCIP_Real thisparallel;

      thisparallel = SCIProwGetParallelism(cut, cuts[i], 'e');

      /* Filter cuts that are absolutely parallel still. Otherwise penalise if closely parallel */
      if( thisparallel > 1 - SCIPsumepsilon(scip) )
      {
         --ncuts;
         SCIPswapPointers((void**) &cuts[i], (void**) &cuts[ncuts]);
         SCIPswapReals(&scores[i], &scores[ncuts]);
      }
      else if( thisparallel > maxparallel )
      {
         scores[i] -= paralpenalty;
      }
   }

   return ncuts;
}

/** filters the given array of cuts to enforce a maximum density constraint,
 *  Moves filtered cuts to the end of the array and returns number of selected cuts */
static
int filterWithDensity(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_ROW**            cuts,               /**< array with cuts to perform selection algorithm */
   SCIP_Real             maxdensity,         /**< maximum density s.t. a cut is not filtered */
   int                   ncuts               /**< number of cuts in given array */
   )
{
   SCIP_Real ncols;

   assert( ncuts == 0 || cuts != NULL );

   ncols = SCIPgetNLPCols(scip);

   for( int i = ncuts - 1; i >= 0; --i )
   {
      SCIP_Real nvals;

      nvals = SCIProwGetNNonz(cuts[i]);

      if( maxdensity < nvals / ncols )
      {
         --ncuts;
         SCIPswapPointers((void**) &cuts[i], (void**) &cuts[ncuts]);
      }
   }

   return ncuts;
}


/*
 * Callback methods of cut selector
 */


/** copy method for cut selector plugin (called when SCIP copies plugins) */
static
SCIP_DECL_CUTSELCOPY(cutselCopyEnsemble)
{  /*lint --e{715}*/
   assert(scip != NULL);
   assert(cutsel != NULL);
   assert(strcmp(SCIPcutselGetName(cutsel), CUTSEL_NAME) == 0);

   /* call inclusion method of cut selector */
   SCIP_CALL( SCIPincludeCutselEnsemble(scip) );

   return SCIP_OKAY;
}

/** destructor of cut selector to free user data (called when SCIP is exiting) */
/**! [SnippetCutselFreeEnsemble] */
static
SCIP_DECL_CUTSELFREE(cutselFreeEnsemble)
{  /*lint --e{715}*/
   SCIP_CUTSELDATA* cutseldata;

   cutseldata = SCIPcutselGetData(cutsel);

   SCIPfreeBlockMemory(scip, &cutseldata);

   SCIPcutselSetData(cutsel, NULL);

   return SCIP_OKAY;
}
/**! [SnippetCutselFreeEnsemble] */

/** initialization method of cut selector (called after problem was transformed) */
static
SCIP_DECL_CUTSELINIT(cutselInitEnsemble)
{  /*lint --e{715}*/
   SCIP_CUTSELDATA* cutseldata;

   cutseldata = SCIPcutselGetData(cutsel);
   assert(cutseldata != NULL);

   SCIP_CALL( SCIPcreateRandom(scip, &(cutseldata)->randnumgen, RANDSEED, TRUE) );

   return SCIP_OKAY;
}

/** deinitialization method of cut selector (called before transformed problem is freed) */
static
SCIP_DECL_CUTSELEXIT(cutselExitEnsemble)
{  /*lint --e{715}*/
   SCIP_CUTSELDATA* cutseldata;

   cutseldata = SCIPcutselGetData(cutsel);
   assert(cutseldata != NULL);
   assert(cutseldata->randnumgen != NULL);

   SCIPfreeRandom(scip, &cutseldata->randnumgen);

   return SCIP_OKAY;
}

/** cut selection method of cut selector */
static
SCIP_DECL_CUTSELSELECT(cutselSelectEnsemble)
{  /*lint --e{715}*/
   SCIP_CUTSELDATA* cutseldata;

   assert(cutsel != NULL);
   assert(result != NULL);

   cutseldata = SCIPcutselGetData(cutsel);
   assert(cutseldata != NULL);
   
   if( ncuts > cutseldata->maxcuts || SCIPgetNVars(scip) > cutseldata->maxnumvars )
   {
      *result = SCIP_DIDNOTFIND;
      return SCIP_OKAY;
   }
   
   *result = SCIP_SUCCESS;

   SCIP_CALL( SCIPselectCutsEnsemble(scip, cuts, forcedcuts, cutseldata, root, ncuts, nforcedcuts,
      maxnselectedcuts, nselectedcuts) );

   return SCIP_OKAY;
}


/*
 * cut selector specific interface methods
 */

/** creates the ensemble cut selector and includes it in SCIP */
SCIP_RETCODE SCIPincludeCutselEnsemble(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   SCIP_CUTSELDATA* cutseldata;
   SCIP_CUTSEL* cutsel;

   /* create ensemble cut selector data */
   SCIP_CALL( SCIPallocBlockMemory(scip, &cutseldata) );
   BMSclearMemory(cutseldata);

   SCIP_CALL( SCIPincludeCutselBasic(scip, &cutsel, CUTSEL_NAME, CUTSEL_DESC, CUTSEL_PRIORITY, cutselSelectEnsemble,
                                     cutseldata) );

   assert(cutsel != NULL);

   /* set non fundamental callbacks via setter functions */
   SCIP_CALL( SCIPsetCutselCopy(scip, cutsel, cutselCopyEnsemble) );

   SCIP_CALL( SCIPsetCutselFree(scip, cutsel, cutselFreeEnsemble) );
   SCIP_CALL( SCIPsetCutselInit(scip, cutsel, cutselInitEnsemble) );
   SCIP_CALL( SCIPsetCutselExit(scip, cutsel, cutselExitEnsemble) );

   /* add ensemble cut selector parameters */
   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/efficacyweight", "weight of normed-efficacy in cut "
         "score calculation", &cutseldata->efficacyweight, FALSE, DEFAULT_EFFICACYWEIGHT, 0.0, SCIP_INVALID/10.0, NULL,
         NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/dircutoffdistweight", "weight of normed-directed "
         "cutoff distance in cut score calculation", &cutseldata->dircutoffdistweight, FALSE,
         DEFAULT_DIRCUTOFFDISTWEIGHT, 0.0, SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/objparalweight", "weight of objective parallelism "
         "in cut score calculation", &cutseldata->objparalweight, FALSE, DEFAULT_OBJPARALWEIGHT, 0.0, SCIP_INVALID/10.0,
         NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/intsupportweight", "weight of integral support in "
         "cut score calculation", &cutseldata->intsupportweight, FALSE, DEFAULT_INTSUPPORTWEIGHT, 0.0,
         SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/expimprovweight", "weight of normed-expected obj "
         "improvement in cut score calculation", &cutseldata->expimprovweight, FALSE, DEFAULT_EXPIMPROVWEIGHT, 0.0,
         SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/minscore", "minimum score s.t. a cut can be added",
         &cutseldata->minscore, FALSE, DEFAULT_MINSCORE, -SCIP_INVALID/10.0, SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/pscostweight", "weight of normed-pseudo-costs in "
         "cut score calculation", &cutseldata->pscostweight, FALSE, DEFAULT_PSCOSTWEIGHT, 0.0, SCIP_INVALID/10.0, NULL,
         NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/locksweight", "weight of normed-num-locks in cut "
         "score calculation", &cutseldata->locksweight, FALSE, DEFAULT_NLOCKSWEIGHT, 0.0, SCIP_INVALID/10.0, NULL,
         NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/maxsparsitybonus", "weight of maximum sparsity "
         "reward in cut score calculation", &cutseldata->maxsparsitybonus, FALSE, DEFAULT_MAXSPARSITYBONUS, 0.0,
         SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/goodnumericsbonus", "weight of good numerics bonus "
         "(ratio of coefficients) in cut score calculation", &cutseldata->goodnumericsbonus, FALSE,
         DEFAULT_GOODNUMERICBONUS, 0.0, SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/endsparsitybonus", "max sparsity value for which a "
         "bonus is applied in cut score calculation", &cutseldata->endsparsitybonus, FALSE, DEFAULT_SPARSITYENDBONUS,
         0.0, SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/maxparal", "threshold for when two cuts are "
         "considered parallel to each other", &cutseldata->maxparal, FALSE, DEFAULT_MAXPARAL, 0.0, 1.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/paralpenalty", "penalty for weaker of two parallel "
         "cuts if penalising parallel cuts", &cutseldata->paralpenalty, TRUE, DEFAULT_PARALPENALTY, 0.0,
         SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/maxcutdensity", "max allowed cut density if "
         "filtering dense cuts", &cutseldata->maxcutdensity, TRUE, DEFAULT_MAXCUTDENSITY, 0.0, 1.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/maxnonzerorootround", "max non-zeros per round "
         "applied cuts (root). multiple num LP cols.", &cutseldata->maxnonzerorootround, FALSE,
         DEFAULT_MAXNONZEROROOTROUND, 0.0, SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddRealParam(scip, "cutselection/" CUTSEL_NAME "/maxnonzerotreeround", "max non-zeros per round "
         "applied cuts (tree). multiple num LP cols.", &cutseldata->maxnonzerotreeround, FALSE,
         DEFAULT_MAXNONZEROTREEROUND, 0.0, SCIP_INVALID/10.0, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "cutselection/" CUTSEL_NAME "/filterparalcuts", "should cuts be filtered so no "
         "two parallel cuts are added", &cutseldata->filterparalcuts, FALSE, DEFAULT_FILTERPARALCUTS, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "cutselection/" CUTSEL_NAME "/penaliseparalcuts", "should two parallel cuts be "
         "penalised instead of outright filtered", &cutseldata->penaliseparalcuts, TRUE, DEFAULT_PENALISEPARALCUTS,
         NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "cutselection/" CUTSEL_NAME "/filterdensecuts", "should cuts over a given density "
         "threshold be filtered", &cutseldata->filterdensecuts, TRUE, DEFAULT_FILTERDENSECUTS, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "cutselection/" CUTSEL_NAME "/penaliselocks", "should the number of locks be "
         "penalised instead of rewarded", &cutseldata->penaliselocks, TRUE, DEFAULT_PENALISELOCKS, NULL, NULL) );

   SCIP_CALL( SCIPaddBoolParam(scip, "cutselection/" CUTSEL_NAME "/penaliseobjparal", "should objective parallelism "
         "be penalised instead of rewarded", &cutseldata->penaliseobjparal, TRUE, DEFAULT_PENALISEOBJPARAL, NULL, NULL)
         );

   SCIP_CALL( SCIPaddIntParam(scip, "cutselection/" CUTSEL_NAME "/maxcoefratiobonus", "max coefficient ratio for "
         "which numeric bonus is applied.", &cutseldata->maxcoefratiobonus, TRUE, DEFAULT_MAXCOEFRATIOBONUS, 1, 1000000,
         NULL, NULL) );

   SCIP_CALL( SCIPaddIntParam(scip, "cutselection/" CUTSEL_NAME "/maxcuts", "max number of cuts such that cut "
         "selector is applied.", &cutseldata->maxcuts, TRUE, DEFAULT_MAXCUTS, 1, 1000000, NULL, NULL) );

   SCIP_CALL( SCIPaddIntParam(scip, "cutselection/" CUTSEL_NAME "/maxnumvars", "max number of variables such that cut "
         "selector is applied.", &cutseldata->maxnumvars, TRUE, DEFAULT_MAXNUMVARS, 1, 1000000, NULL, NULL) );

   return SCIP_OKAY;
}

/** perform a cut selection algorithm for the given array of cuts
 *
 *  This is the selection method of the ensemble cut selector. It uses a weighted sum of normalised efficacy,
 *  normalised directed cutoff distance, normalised expected improvements, objective parallelism,
 *  integer support, sparsity, dynamism, pseudo-costs, and variable locks.
 *  In addition to the weighted sum score, there are optionally parallelism-based filtering and penalties,
 *  and density filtering.
 *  There are also additional budget constraints on the number of cuts that should be added.
 *  The input cuts array gets re-sorted such that the selected cuts come first and the remaining ones are the end.
 */
SCIP_RETCODE SCIPselectCutsEnsemble(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_ROW**            cuts,               /**< array with cuts to perform selection algorithm */
   SCIP_ROW**            forcedcuts,         /**< array with forced cuts */
   SCIP_CUTSELDATA*      cutseldata,         /**< cut selector data */
   SCIP_Bool             root,               /**< whether we are at the root node or not */
   int                   ncuts,              /**< number of cuts in cuts array */
   int                   nforcedcuts,        /**< number of forced cuts */
   int                   maxselectedcuts,    /**< maximal number of cuts from cuts array to select */
   int*                  nselectedcuts       /**< pointer to return number of selected cuts from cuts array */
   )
{
   SCIP_Real* scores;
   SCIP_Real* origscoresptr;
   SCIP_Real nonzerobudget;
   SCIP_Real budgettaken = 0.0;
   SCIP_Real ncols;

   assert(cuts != NULL && ncuts > 0);
   assert(forcedcuts != NULL || nforcedcuts == 0);
   assert(nselectedcuts != NULL);

   *nselectedcuts = 0;
   ncols = SCIPgetNLPCols(scip);

   /* filter dense cuts */
   if( cutseldata->filterdensecuts )
   {
      ncuts = filterWithDensity(scip, cuts, cutseldata->maxcutdensity, ncuts);
      if( ncuts == 0 )
         return SCIP_OKAY;
   }

   /* Initialise the score array */
   SCIP_CALL( SCIPallocBufferArray(scip, &scores, ncuts) );
   origscoresptr = scores;

   /* compute scores of cuts */
   SCIP_CALL( scoring(scip, cuts, cutseldata, scores, root, ncuts) );

   /* perform cut selection algorithm for the cuts */

   /* forced cuts are going to be selected so use them to filter cuts */
   for( int i = 0; i < nforcedcuts && ncuts > 0; ++i )
   {
      if( cutseldata->filterparalcuts )
         ncuts = filterWithParallelism(forcedcuts[i], cuts, scores, ncuts, cutseldata->maxparal);
      else if( cutseldata->penaliseparalcuts )
         ncuts = penaliseWithParallelism(scip, forcedcuts[i], cuts, scores, ncuts, cutseldata->maxparal, cutseldata->paralpenalty);
   }

   /* Get the budget depending on if we are the root or not */
   nonzerobudget = root ? cutseldata->maxnonzerorootround : cutseldata->maxnonzerotreeround;

   /* now greedily select the remaining cuts */
   while( ncuts > 0 )
   {
      SCIP_ROW* selectedcut;

      selectBestCut(cuts, scores, ncuts);
      selectedcut = cuts[0];

      /* if the best cut of the remaining cuts is considered bad, we discard it and all remaining cuts */
      if( scores[0] < cutseldata->minscore )
         break;

      ++(*nselectedcuts);

      /* if the maximal number of cuts was selected, we can stop here */
      if( *nselectedcuts == maxselectedcuts )
         break;

      /* increase the non-zero budget counter of added cuts */
      budgettaken += SCIProwGetNNonz(cuts[0]) / ncols;

      /* move the pointers to the next position and filter the remaining cuts to enforce the maximum parallelism constraint */
      ++cuts;
      ++scores;
      --ncuts;

      if( cutseldata->filterparalcuts && ncuts > 0)
         ncuts = filterWithParallelism(selectedcut, cuts, scores, ncuts, cutseldata->maxparal);
      else if( cutseldata->penaliseparalcuts && ncuts > 0 )
         ncuts = penaliseWithParallelism(scip, selectedcut, cuts, scores, ncuts, cutseldata->maxparal, cutseldata->paralpenalty);

      /* Filter out all remaining cuts that would go over the non-zero budget threshold */
      if( nonzerobudget - budgettaken < 1 && ncuts > 0 )
         ncuts = filterWithDensity(scip, cuts, nonzerobudget - budgettaken, ncuts);
   }

   SCIPfreeBufferArray(scip, &origscoresptr);

   return SCIP_OKAY;
}