sepa_subtour.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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/*  Licensed under the Apache License, Version 2.0 (the "License");          */
/*  you may not use this file except in compliance with the License.         */
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/*      http://www.apache.org/licenses/LICENSE-2.0                           */
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/*  Unless required by applicable law or agreed to in writing, software      */
/*  distributed under the License is distributed on an "AS IS" BASIS,        */
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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/**@file   sepa_subtour.c
 * @brief  If there exists a transition forward along the cycle, then the state that the transition originates from can
 * be reached only after another ncluster - 1 transitions. Therefore cycles with a number of transitions smaller than
 * that can be separated.
 * @author Leon Eifler
 */
 
/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
 
#include <assert.h>
#include <string.h>
 
#include "sepa_subtour.h"
 
#include "probdata_cyc.h"
#include "scip/cons_linear.h"
#include "scip/pub_misc.h"
 
#define SEPA_NAME              "subtour"
#define SEPA_DESC              "separator that elininates subtours of length smaller than |NCluster|"
#define SEPA_PRIORITY              1000
#define SEPA_FREQ                     5
#define SEPA_MAXBOUNDDIST           0.0
#define SEPA_USESSUBSCIP          FALSE /**< does the separator use a secondary SCIP instance? */
#define SEPA_DELAY                FALSE /**< should separation method be delayed, if other separators found cuts? */
#define MAXCUTS                    2000
#define MAXROUNDS                    15
 
#ifdef SCIP_DEBUG
/** Print a cycle to the command line. For debugging purposes */
static
void printCycle(
   SCIP*                 scip,               /**< SCIP data structure */
   int*                  cycle,              /**< The cycle to be printed */
   int                   cyclelength,        /**< The length of the cycle */
   int                   nstates             /**< The number of states */
   )
{
   int i;
 
   SCIPinfoMessage(scip, NULL, "cycle_l%d_c: %d", cyclelength, cycle[0]);
   for( i = 0; i < cyclelength; ++i )
   {
      SCIPinfoMessage(scip, NULL, " -> %d", cycle[i+1]);
   }
   SCIPinfoMessage(scip, NULL, "\n");
}
#endif
 
/** get distance of longest path between two states with exactly n arcs from the matrix */
static
SCIP_Real getDist(
   SCIP_Real***          adjacencymatrix,    /**< the adjacency-matrices of all paths with 1,...,|Clutster| arcs */
   int                   n,                  /**< length */
   int                   state1,             /**< starting state */
   int                   state2              /**< end state */
   )
{
   assert(adjacencymatrix[n] != NULL);
   assert(adjacencymatrix[n][state1] != NULL);
 
   return adjacencymatrix[n][state1][state2];
}
 
/** After finding a violation, construct and add all violated subtour cuts to scip */
static
SCIP_RETCODE addSubtourCuts(
   SCIP*                 scip,               /**< SCIP data structure. */
   SCIP_SEPA*            sepa,               /**< the subtour separator */
   SCIP_Real***          adjacencymatrix,    /**< the adjacency-matrices of all paths with 1,...,|Clutster| arcs */
   SCIP_DIGRAPH*         adjacencygraph,     /**< the directed edge-graph */
   int**                 iscontracted,       /**< information of intermediate contraction-nodes for contracted arcs */
   int                   cyclelength,        /**< the length of the subtours to add */
   SCIP_RESULT*          result,             /**< pointer to store the result of separation */
   int*                  ncuts               /**< pointer to store number of cuts */
   )
{
   SCIP_VAR**** edgevars;
   char cutname[SCIP_MAXSTRLEN];
   SCIP_ROW* cut;
   int** subtours;
   int*  insubtour;
   int* successors;
   int nsuccessors;
   int nstates;
   int currentnode;
   int successor;
   int intermediate;
   int anchor;
   int ncontractions;
   int liftabley;
   int liftablez;
   int greater;
   int smaller;
   int c;
   int k;
   int l;
   SCIP_Bool isduplicate;
 
   edgevars = SCIPcycGetEdgevars(scip);
   nstates = SCIPdigraphGetNNodes(adjacencygraph);
 
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &insubtour, nstates) );
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &subtours, nstates) );
 
   for( k = 0; k < nstates; ++k )
   {
      SCIP_CALL( SCIPallocClearBlockMemoryArray(scip, &subtours[k], cyclelength + 1) ); /*lint !e866, !e776*/
      insubtour[k] = -1;
   }
 
   /* for each state, check if a subtour inequality is violated */
   for( anchor = 0; anchor < nstates; ++anchor )
   {
      /* while reconstructing the subtour, count the number of contractions */
      ncontractions = 0;
 
      /* a cycle inequality is violated if the following is true */
      if( SCIPisGT(scip, getDist(adjacencymatrix, cyclelength - 1, anchor, anchor), cyclelength - 1.0) )
      {
         subtours[anchor][0] = anchor;
         if( insubtour[anchor] == -1 )
            insubtour[anchor] = anchor;
 
         /* traverse the cycle */
         for( k = 0; k < cyclelength -1; ++k )
         {
            currentnode = subtours[anchor][k];
 
            assert(0 <= currentnode && currentnode < nstates);
 
            successors = SCIPdigraphGetSuccessors(adjacencygraph, currentnode);
            nsuccessors = SCIPdigraphGetNSuccessors(adjacencygraph, currentnode);
 
            /* find the next state along the subtour */
            for( l = 0; l < nsuccessors; l++ )
            {
               successor = successors[l];
 
               assert(0 <= successor && successor < nstates);
 
               /* check if this successor of the current node is the one in the cycle. If so add it. */
               if( SCIPisEQ(scip, getDist(adjacencymatrix, 0, currentnode, successor)
                  + getDist(adjacencymatrix, cyclelength - (k + 2), successor, anchor),
                  getDist(adjacencymatrix, cyclelength - (k + 1), currentnode, anchor)) )
               {
                  subtours[anchor][k + 1] = successor;
                  insubtour[successor] = anchor;
 
                  if( iscontracted[currentnode][successor] != -1 )
                     ncontractions++;
 
                  break;
               }
            }
         }
 
         /* start and endnode are always the same in a cycle */
         subtours[anchor][cyclelength] = anchor;
 
         /* check last arc for a contraction */
         if( iscontracted[subtours[anchor][cyclelength - 1]][anchor] != -1 )
            ncontractions++;
 
         isduplicate = FALSE;
 
         /* if this anchor is already in another subtour, we check if the subtour is the same, since we don't want to
          * add duplicates
          */
         if( insubtour[anchor] != anchor )
         {
            c = 0;
            isduplicate = TRUE;
 
            while( subtours[insubtour[anchor]][c] != anchor )
               c++;
 
            for( k = 0; k < cyclelength && isduplicate; ++k )
            {
               if( subtours[insubtour[anchor]][(k + c) % cyclelength] != subtours[anchor][k] )
                  isduplicate = FALSE;
            }
         }
 
         if( isduplicate )
            continue;
 
         /* set the amount of y and z variables that we can still lift into the inequality */
         liftabley = cyclelength - 1;
         liftablez = SCIPcycGetNCluster(scip) - cyclelength - 1;
 
         /* Now build the cut and add the subtour inequality */
         (void)SCIPsnprintf(cutname, SCIP_MAXSTRLEN, "subtour_%d_length_%d_contracted_%d", anchor,
            cyclelength, ncontractions );
         SCIP_CALL( SCIPcreateEmptyRowSepa(scip, &cut,sepa, cutname, -SCIPinfinity(scip),
            cyclelength + ncontractions - 1.0, FALSE, FALSE, TRUE) );
 
         SCIP_CALL( SCIPcacheRowExtensions(scip, cut) );
 
         for( k = 0; k < cyclelength; ++k )
         {
            currentnode = subtours[anchor][k];
            successor = subtours[anchor][k+1];
            intermediate = iscontracted[currentnode][successor];
 
            if( intermediate != -1 )
            {
               SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, currentnode, intermediate, CONSECUTIVE_CLUSTER), 1.0) );
               SCIP_CALL( SCIPaddVarToRow(scip, cut,
                  getEdgevar(edgevars, MAX(intermediate, successor), MIN(intermediate, successor), INCLUSTER), 1.0) );
 
               greater = intermediate > currentnode ? intermediate : currentnode;
               smaller = intermediate < currentnode ? intermediate : currentnode;
 
               if( liftabley > 0 && SCIPvarGetLPSol(getEdgevar(edgevars, greater, smaller, INCLUSTER)) > 0 )
               {
                  SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, greater, smaller, INCLUSTER), 1.0) );
                  liftabley--;
               }
               if( liftablez > 0 && SCIPvarGetLPSol(getEdgevar(edgevars, intermediate, successor, CONSECUTIVE_CLUSTER)) > 0 )
               {
                  SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, intermediate, successor, CONSECUTIVE_CLUSTER), 1.0) );
                  liftablez--;
               }
            }
            else
            {
               SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, currentnode, successor, CONSECUTIVE_CLUSTER), 1.0) );
               if( SCIPvarGetLPSol(getEdgevar(edgevars, MAX(currentnode, successor), MIN(currentnode, successor), INCLUSTER))
                  > 0 && liftabley > 0  )
               {
                  SCIP_CALL( SCIPaddVarToRow(scip, cut,
                     getEdgevar(edgevars, MAX(currentnode, successor), MIN(currentnode, successor), INCLUSTER), 1.0) );
                  liftabley--;
               }
            }
         }
 
         SCIP_CALL( SCIPflushRowExtensions(scip, cut) );
         SCIP_CALL( SCIPaddPoolCut(scip, cut) );
 
         /* print for debugging purposes */
         SCIPdebug( SCIP_CALL( SCIPprintRow(scip, cut, NULL) ) );
 
         /* release data and increment cut counter */
         SCIP_CALL( SCIPreleaseRow(scip, &cut) );
 
         *result = SCIP_SEPARATED;
         (*ncuts)++;
      }
   }
 
   for( k = 0; k < nstates; ++k )
   {
      SCIPfreeBlockMemoryArray(scip, &(subtours[k]), cyclelength + 1);
   }
   SCIPfreeBlockMemoryArray(scip, &subtours, nstates);
   SCIPfreeBlockMemoryArray(scip, &insubtour, nstates);
 
   return SCIP_OKAY;
}
 
/** Detect if path inequalities are violated and if so, add them to scip */
static
SCIP_RETCODE addPathCuts(
   SCIP*                 scip,               /**< SCIP data structure. */
   SCIP_SEPA*            sepa,               /**< the subtour separator */
   SCIP_Real***          adjacencymatrix,    /**< the adjacency-matrix of all paths with 1,...,|Clutster| arcs */
   SCIP_DIGRAPH*         adjacencygraph,     /**< the directed edge-graph */
   int**                 iscontracted,       /**< information of intermediate contraction-nodes for contracted arcs */
   int                   pathlength,         /**< the length of the subtours to add */
   SCIP_RESULT*          result,             /**< pointer to store the result of separation */
   int*                  ncuts               /**< pointer to store number of cuts */
   )
{
   SCIP_VAR**** edgevars;
   char cutname[SCIP_MAXSTRLEN];
   SCIP_ROW* cut;
   int* path;
   int nstates;
   int currentnode;
   int successor;
   int* successors;
   int nsuccessors;
   int intermediate;
   int start;
   int end;
   int ncontractions;
   int k;
   int i;
   int j;
   int nz;
   int ny;
 
   edgevars = SCIPcycGetEdgevars(scip);
   nstates = SCIPdigraphGetNNodes(adjacencygraph);
 
   SCIP_CALL( SCIPallocMemoryArray(scip, &path, pathlength + 1) );
 
   for( start = 0; start < nstates; ++start )
   {
      path[0] =  start;
 
      for( j = 0; j < SCIPdigraphGetNSuccessors(adjacencygraph, start); ++j )
      {
         ncontractions = 0;
 
         end = SCIPdigraphGetSuccessors(adjacencygraph, start)[j];
         path[pathlength] = end;
 
         /* check if path-inequality is violated */
         if( SCIPisGT(scip, getDist(adjacencymatrix, pathlength - 1, start, end)
            + getDist(adjacencymatrix, 0, start, end), (SCIP_Real) pathlength) )
         {
            /*reconstruct the path */
            for( k = 0; k < pathlength - 1; ++k )
            {
               currentnode = path[k];
 
               assert(0 <= currentnode && currentnode < nstates);
 
               successors = SCIPdigraphGetSuccessors(adjacencygraph, currentnode);
               nsuccessors = SCIPdigraphGetNSuccessors(adjacencygraph, currentnode);
 
               for( i = 0; i < nsuccessors; ++i )
               {
                  successor = successors[i];
 
                  assert(0 <= successor && successor < nstates);
 
                  if( SCIPisEQ(scip, getDist(adjacencymatrix, 0, currentnode, successor)
                     + getDist(adjacencymatrix, pathlength - (k + 2), successor, end),
                     getDist(adjacencymatrix, pathlength - (k + 1), currentnode, end)) )
                  {
                     path[k + 1] = successor;
 
                     if( iscontracted[currentnode][successor] != -1 )
                        ncontractions++;
 
                     break;
                  }
               }
            }
 
            /* check the last arc along the path and the direct arc from start to end for contractions */
            if( iscontracted[path[pathlength - 1]][end] != -1 )
               ncontractions++;
 
            if( iscontracted[start][end] != -1 )
               ncontractions++;
 
            nz = pathlength;
            ny = 0;
 
            /* construct the corresponding inequality and add it to scip */
            (void)SCIPsnprintf(cutname, SCIP_MAXSTRLEN, "path_%d_%d_length_%d_contracted_%d",
               start, end, pathlength, ncontractions );
            SCIP_CALL( SCIPcreateEmptyRowSepa(scip, &cut,sepa, cutname, -SCIPinfinity(scip),
               (SCIP_Real) pathlength + ncontractions, FALSE, FALSE, TRUE) );
 
            SCIP_CALL( SCIPcacheRowExtensions(scip, cut) );
 
            for( k = 0; k < pathlength; ++k )
            {
               currentnode = path[k];
               successor = path[k+1];
               intermediate = iscontracted[currentnode][successor];
 
               if( intermediate != -1 )
               {
                  SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, currentnode, intermediate, CONSECUTIVE_CLUSTER), 1.0) );
                  SCIP_CALL( SCIPaddVarToRow(scip, cut,
                     getEdgevar(edgevars, MAX(intermediate, successor), MIN(intermediate, successor), INCLUSTER), 1.0) );
 
                  if( nz < SCIPcycGetNCluster(scip)
                     && SCIPisPositive(scip, SCIPvarGetLPSol(getEdgevar(edgevars, intermediate, successor, CONSECUTIVE_CLUSTER))) )
                  {
                     SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, intermediate, successor, CONSECUTIVE_CLUSTER), 1.0) );
                     nz++;
                  }
 
                  if( ny < pathlength - 2 && SCIPisPositive(scip, SCIPvarGetLPSol(
                     getEdgevar(edgevars, MAX(currentnode, intermediate), MIN(currentnode, intermediate), INCLUSTER))) )
                  {
                     SCIP_CALL( SCIPaddVarToRow(scip, cut,
                        getEdgevar(edgevars, MAX(currentnode, intermediate), MIN(currentnode, intermediate), INCLUSTER), 1.0) );
                     ny++;
                  }
               }
               else
               {
                  SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, currentnode, successor, CONSECUTIVE_CLUSTER), 1.0) );
 
                  if( ny < pathlength - 2 && SCIPisPositive(scip, SCIPvarGetLPSol(
                     getEdgevar(edgevars, MAX(currentnode, successor), MIN(currentnode, successor), INCLUSTER))) )
                  {
                     SCIP_CALL( SCIPaddVarToRow(scip, cut,
                        getEdgevar(edgevars, MAX(currentnode, successor), MIN(currentnode, successor), INCLUSTER), 1.0) );
                     ny++;
                  }
               }
            }
 
            /* add the direct arc from start to end */
            intermediate = iscontracted[start][end];
 
            if( iscontracted[start][end] != -1 )
            {
               SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, start, intermediate, CONSECUTIVE_CLUSTER), 1.0) );
               SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars,
                  MAX(intermediate, end), MIN(intermediate, end), INCLUSTER), 1.0) );
            }
            else
            {
               assert( NULL != getEdgevar(edgevars, start, end, CONSECUTIVE_CLUSTER));
 
               SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, start, end, CONSECUTIVE_CLUSTER), 1.0) );
            }
 
            SCIP_CALL( SCIPflushRowExtensions(scip, cut) );
 
            /* print row if in debug mode */
            SCIPdebug( SCIPprintRow(scip, cut, NULL) );
 
            /* if an arc appears twice then the path inequality should not be used */
            if( SCIPisEQ(scip, SCIPgetRowMaxCoef(scip, cut), 1.0) )
            {
               SCIP_CALL( SCIPaddPoolCut(scip, cut) );
               *result = SCIP_SEPARATED;
               (*ncuts)++;
            }
 
            SCIP_CALL( SCIPreleaseRow(scip, &cut) );
         }
      }
   }
 
   SCIPfreeMemoryArray(scip, &path);
 
   return SCIP_OKAY;
}
 
/** detect if path inequalities are violated and if so, add them to scip */
static
SCIP_RETCODE addTourCuts(
   SCIP*                 scip,               /**< SCIP data structure. */
   SCIP_SEPA*            sepa,               /**< the subtour separator */
   SCIP_Real***          adjacencymatrix,    /**< the adjacency-matrix of all paths with 1,...,|Clutster| arcs */
   SCIP_DIGRAPH*         adjacencygraph,     /**< the directed edge-graph */
   int**                 iscontracted,       /**< information of intermediate contraction-nodes for contracted arcs */
   int                   tourlength,         /**< the length of the subtours to add */
   SCIP_RESULT*          result,             /**< pointer to store the result of separation */
   int*                  ncuts               /**< pointer to store number of cuts */
   )
{
   SCIP_VAR**** edgevars;
   char cutname[SCIP_MAXSTRLEN];
   SCIP_ROW* cut;
   int* tour;
   int* successors;
   int* succerssorsstart;
   int nsuccessorsstart;
   int nsuccessors;
   int nstates;
   int currentnode;
   int successor;
   int intermediate;
   int start;
   int end;
   int ncontractions;
   int k;
   int i;
   int j;
 
   edgevars = SCIPcycGetEdgevars(scip);
   nstates = SCIPdigraphGetNNodes(adjacencygraph);
 
   SCIP_CALL( SCIPallocMemoryArray(scip, &tour, tourlength + 1) );
 
   for( start = 0; start < nstates; ++start )
   {
      tour[0] =  start;
      succerssorsstart = SCIPdigraphGetSuccessors(adjacencygraph, start);
      nsuccessorsstart = SCIPdigraphGetNSuccessors(adjacencygraph, start);
 
      for( j = 0; j < nsuccessorsstart; ++j )
      {
         ncontractions = 0;
 
         end = succerssorsstart[j];
         tour[tourlength] = end;
 
         /* check if tour-inequality is violated */
         if( SCIPisGT(scip, getDist(adjacencymatrix, tourlength - 1, start, end)
            - getDist(adjacencymatrix, 0, end, start), (SCIP_Real) tourlength - 1) )
         {
            /*reconstruct the tour */
            for( k = 0; k < tourlength - 1; ++k )
            {
               currentnode = tour[k];
               successors = SCIPdigraphGetSuccessors(adjacencygraph, currentnode);
               nsuccessors = SCIPdigraphGetNSuccessors(adjacencygraph, currentnode);
 
               for( i = 0; i < nsuccessors; ++i )
               {
                  successor = successors[i];
 
                  if( SCIPisEQ(scip, getDist(adjacencymatrix, 0, currentnode, successor)
                     + getDist(adjacencymatrix, tourlength - (k + 2), successor, end)
                     , getDist(adjacencymatrix, tourlength - (k + 1), currentnode, end)) )
                  {
                     tour[k + 1] = successor;
 
                     if( iscontracted[currentnode][successor] != -1 )
                        ncontractions++;
                     break;
                  }
               }
            }
 
            /* check the last arc along the tour and the direct arc from start to end for contractions */
            if( iscontracted[tour[tourlength - 1]][end] != -1 )
               ncontractions++;
            if( iscontracted[end][start] != -1 )
               ncontractions++;
 
            /* construct the corresponding inequality and add it to scip */
            (void)SCIPsnprintf(cutname, SCIP_MAXSTRLEN, "tour_%d_%d_length_%d_contracted_%d",
               start, end, tourlength, ncontractions );
            SCIP_CALL( SCIPcreateEmptyRowSepa(scip, &cut,sepa, cutname, -SCIPinfinity(scip),
               (SCIP_Real) tourlength + ncontractions - 1, FALSE, FALSE, TRUE) );
 
            SCIP_CALL( SCIPcacheRowExtensions(scip, cut) );
 
            for( k = 0; k < tourlength; ++k )
            {
               currentnode = tour[k];
               successor = tour[k+1];
               intermediate = iscontracted[currentnode][successor];
 
               if( intermediate != -1 )
               {
                  SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, currentnode, intermediate, CONSECUTIVE_CLUSTER), 1.0) );
                  SCIP_CALL( SCIPaddVarToRow(scip, cut,
                     getEdgevar(edgevars, MAX(intermediate, successor), MIN(intermediate, successor), INCLUSTER), 1.0) );
               }
               else
               {
                  SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, currentnode, successor, CONSECUTIVE_CLUSTER), 1.0) );
               }
            }
 
            /* add the direct arc from start to end */
            intermediate = iscontracted[end][start];
            if( iscontracted[end][start] != -1 )
            {
               SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, end, intermediate, CONSECUTIVE_CLUSTER), -1.0) );
               SCIP_CALL( SCIPaddVarToRow(scip, cut,
                  getEdgevar(edgevars, MAX(intermediate, start), MIN(intermediate, start), INCLUSTER), 1.0) );
            }
            else
            {
               SCIP_CALL( SCIPaddVarToRow(scip, cut, getEdgevar(edgevars, end, start, CONSECUTIVE_CLUSTER), -1.0) );
            }
 
            SCIP_CALL( SCIPflushRowExtensions(scip, cut) );
 
            /* print row if in debug mode */
            SCIPdebug( SCIPprintRow(scip, cut, NULL) );
 
            /* if an arc appears twice then the tour inequality should not be used */
            if( SCIPisEQ(scip, SCIPgetRowMaxCoef(scip, cut), 1.0) )
            {
               SCIP_CALL( SCIPaddPoolCut(scip, cut) );
               *result = SCIP_SEPARATED;
               (*ncuts)++;
            }
 
            SCIP_CALL( SCIPreleaseRow(scip, &cut) );
         }
      }
   }
 
   SCIPfreeMemoryArray(scip, &tour);
 
   return SCIP_OKAY;
}
 
/** compute the next matrix with the weight off all the longest paths with exactly narcs and store it in
 *  adjacencymatrix[narcs - 1]. For this, simply compute
 * \f{align*}{ d^{k}(currentnode,successor) = max_{l=1,\ldots,n} \{d^{k-1}(currentnode,l) + d^1(l,successor) \} \f}.
 */
static
SCIP_Bool computeNextAdjacency
(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_Real***          adjacencymatrix,    /**< the max-distance matrices for all number of arcs less than narcs. */
   SCIP_DIGRAPH*         adjacencygraph,     /**< the directed edge-graph */
   int                   narcs               /**< the current number of arcs in the paths */
)
{
   int* intermediates;
   int nintermediates;
   int currentnode;
   int intermediate;
   int successor;
   int l;
   int nnodes;
   SCIP_Bool foundviolation;
 
   foundviolation = FALSE;
   nnodes = SCIPdigraphGetNNodes(adjacencygraph);
 
   for( currentnode = 0; currentnode < nnodes; ++currentnode )
   {
      intermediates = SCIPdigraphGetSuccessors(adjacencygraph, currentnode);
      nintermediates = SCIPdigraphGetNSuccessors(adjacencygraph, currentnode);
 
      for( l = 0; l < nintermediates; ++l )
      {
         intermediate = intermediates[l];
 
         assert(0 <= intermediate && intermediate < nnodes);
 
         for( successor = 0; successor < nnodes; ++successor )
         {
            if( SCIPisPositive(scip, getDist(adjacencymatrix, 0, currentnode, intermediate))
               && SCIPisPositive(scip, getDist(adjacencymatrix, narcs - 2, intermediate, successor)) )
            {
               if( SCIPisGT(scip, getDist(adjacencymatrix, 0, currentnode, intermediate)
                  + getDist(adjacencymatrix, narcs - 2, intermediate, successor),
                  getDist(adjacencymatrix, narcs - 1, currentnode, successor)) )
               {
                  adjacencymatrix[narcs - 1][currentnode][successor] = getDist(adjacencymatrix, 0, currentnode, intermediate)
                     + getDist(adjacencymatrix, narcs - 2, intermediate, successor);
               }
            }
         }
      }
   }
 
   /* check if we have found a violated subtour constraint */
   for( currentnode = 0; currentnode < nnodes; ++currentnode )
   {
      if( SCIPisGT(scip, getDist(adjacencymatrix, narcs - 1, currentnode, currentnode), narcs - 1.0) )
         foundviolation = TRUE;
   }
   return foundviolation;
}
 
/** copy method for separator plugins (called when SCIP copies plugins) */
static
SCIP_DECL_SEPACOPY(sepaCopySubtour)
{  /*lint --e{715}*/
   assert(scip != NULL);
   assert(sepa != NULL);
   assert(strcmp(SCIPsepaGetName(sepa), SEPA_NAME) == 0);
 
   /* call inclusion method of constraint handler */
   SCIP_CALL( SCIPincludeSepaSubtour(scip) );
 
   return SCIP_OKAY;
}
 
/** LP solution separation method of separator */
static
SCIP_DECL_SEPAEXECLP(sepaExeclpSubtour)
{  /*lint --e{715}*/
   SCIP_VAR**** edgevars;
   SCIP_Real*** adjacencymatrix;
   SCIP_DIGRAPH* adjacencygraph;
   SCIP_DIGRAPH* edgegraph;
   int** iscontracted;
   SCIP_Bool violation;
   int* successors1;
   int* successors2;
   int nsuccessors1;
   int nsuccessors2;
   int ncuts;
   int nstates;
   int ncluster;
   int cyclelength;
   int rounds;
   int i;
   int j;
   int k;
   int state1;
   int state2;
   int state3;
 
   /* get problem information */
   rounds = SCIPsepaGetNCallsAtNode(sepa);
   ncluster = SCIPcycGetNCluster(scip);
   edgevars = SCIPcycGetEdgevars(scip);
   nstates = SCIPcycGetNBins(scip);
   edgegraph = SCIPcycGetEdgeGraph(scip);
   ncuts = 0;
 
   if( rounds >= MAXROUNDS )
   {
      *result =  SCIP_DIDNOTRUN;
      return SCIP_OKAY;
   }
 
   assert(nstates > 0);
   assert(ncluster > 0 && ncluster < nstates);
   assert(NULL != edgevars);
   assert(NULL != edgegraph);
 
   /* allocate memory */
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &adjacencymatrix, ncluster) );
 
   for( k = 0; k < ncluster; ++k )
   {
      SCIP_CALL( SCIPallocBlockMemoryArray(scip, &adjacencymatrix[k], nstates) ); /*lint !e866*/
 
      for( j = 0; j < nstates; ++j )
      {
         SCIP_CALL( SCIPallocClearBlockMemoryArray(scip, &adjacencymatrix[k][j], nstates) ); /*lint !e866*/
      }
   }
 
   /* create Digraph from the current LP-Solution */
   SCIP_CALL( SCIPcreateDigraph(scip, &adjacencygraph, nstates) );
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &iscontracted, nstates) );
 
 
   /* get the values of the lp-solution */
   for( i = 0; i < nstates; ++i )
   {
      SCIP_CALL( SCIPallocBlockMemoryArray(scip, &iscontracted[i], nstates) );
 
      for( j = 0; j < nstates; ++j )
      {
         iscontracted[i][j] = -1;
 
         if( edgevars[i] != NULL && edgevars[i][j] != NULL && getEdgevar(edgevars, i, j, CONSECUTIVE_CLUSTER) != NULL )
            adjacencymatrix[0][i][j] = SCIPvarGetLPSol(getEdgevar(edgevars, i, j, CONSECUTIVE_CLUSTER));
      }
   }
 
   /* contract the adjacency matrix if it is better to take z_{ij} + y_{jk} rather than z_{ik} directly,
    * this stores j at position (i,k)
    */
   for( i = 0; i < nstates; ++i )
   {
      state1 = i;
 
      assert( edgevars[state1] != NULL);
 
      successors1 = SCIPdigraphGetSuccessors(edgegraph, state1);
      nsuccessors1 = SCIPdigraphGetNSuccessors(edgegraph, state1);
 
      for( j = 0; j < nsuccessors1; ++j )
      {
         state2 = successors1[j];
 
         assert( edgevars[state2] != NULL);
 
         successors2 = SCIPdigraphGetSuccessors(edgegraph, state2);
         nsuccessors2 = SCIPdigraphGetNSuccessors(edgegraph, state2);
 
         for( k = 0 ; k < nsuccessors2; ++k )
         {
            state3 = successors2[k];
 
            if( edgevars[state1][state2] == NULL || edgevars[state2][state3] == NULL || edgevars[state1][state3] == NULL )
               continue;
 
            if( SCIPisLT( scip, getDist(adjacencymatrix, 0, state1, state3),
               SCIPvarGetLPSol(getEdgevar(edgevars, state1, state2, CONSECUTIVE_CLUSTER))
               + SCIPvarGetLPSol(getEdgevar(edgevars, MAX(state2, state3), MIN(state2, state3), INCLUSTER)) - 1) )
            {
               adjacencymatrix[0][state1][state3] = SCIPvarGetLPSol(getEdgevar(edgevars, state1, state2, CONSECUTIVE_CLUSTER))
                  + SCIPvarGetLPSol(getEdgevar(edgevars, MAX(state2, state3), MIN(state2, state3), INCLUSTER)) - 1;
 
               iscontracted[state1][state3] = state2;
            }
         }
      }
   }
 
   /* save the contracted matrix as a digraph to be able to reuse it quicker */
   for( i = 0; i < nstates; ++i )
   {
      for( j = 0; j < nstates; ++j )
      {
         if( !SCIPisZero(scip, getDist(adjacencymatrix, 0, i, j)) )
         {
            SCIP_CALL( SCIPdigraphAddArc(adjacencygraph, i , j, NULL) );
         }
      }
   }
 
   /* a cyclelength of one does not make sense as there are no loops */
   cyclelength = 2;
   *result = SCIP_DIDNOTFIND;
 
   /* Iterate until we have found a sufficient number of cuts or until we have checked all possible violations */
   while( cyclelength < ncluster )
   {
      /* Compute the next adjacency matrix */
      violation = computeNextAdjacency(scip, adjacencymatrix, adjacencygraph, cyclelength);
 
      /* if we found a violation separate it */
      if( violation )
      {
         SCIP_CALL( addSubtourCuts(scip, sepa, adjacencymatrix, adjacencygraph, iscontracted, cyclelength,
            result, &ncuts) );
      }
 
      /* check if any path-inequalities are violated and sepatare them */
      SCIP_CALL( addPathCuts(scip, sepa, adjacencymatrix, adjacencygraph, iscontracted, cyclelength, result, &ncuts) );
 
      if( cyclelength == ncluster - 1 )
      {
         SCIP_CALL( addTourCuts(scip, sepa, adjacencymatrix, adjacencygraph, iscontracted, cyclelength,
            result, &ncuts) );
      }
 
      /* stop if we added maximal number of cuts */
      if( ncuts >= MAXCUTS )
         break;
 
      cyclelength++;
   }
 
   SCIPdigraphFreeComponents(adjacencygraph);
   SCIPdigraphFree(&adjacencygraph);
 
   /* free allocated memory */
   for( i = 0; i < nstates; ++i )
   {
      SCIPfreeBlockMemoryArray(scip, &iscontracted[i], nstates);
   }
   SCIPfreeBlockMemoryArray(scip, &iscontracted, nstates);
 
   for( i = 0; i < ncluster; ++i )
   {
      for( j = 0; j < nstates; ++j )
      {
         SCIPfreeBlockMemoryArray(scip, &adjacencymatrix[i][j], nstates);
      }
      SCIPfreeBlockMemoryArray(scip, &adjacencymatrix[i], nstates);
   }
   SCIPfreeBlockMemoryArray(scip, &adjacencymatrix, ncluster);
 
   return SCIP_OKAY;
}
 
 
/** creates the Subtour separator and includes it in SCIP */
SCIP_RETCODE SCIPincludeSepaSubtour(
   SCIP*                 scip                /**< SCIP data structure */
)
{
   SCIP_SEPA* sepa;
 
   /* include separator */
 
   SCIP_CALL( SCIPincludeSepaBasic(scip, &sepa, SEPA_NAME, SEPA_DESC, SEPA_PRIORITY, SEPA_FREQ, SEPA_MAXBOUNDDIST,
      SEPA_USESSUBSCIP, SEPA_DELAY,
      sepaExeclpSubtour, NULL,
      NULL) );
 
   assert(sepa != NULL);
 
   /* set non fundamental callbacks via setter functions */
   SCIP_CALL( SCIPsetSepaCopy(scip, sepa, sepaCopySubtour) );
 
 
   return SCIP_OKAY;
}