heur_init.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) 2002-2024 Zuse Institute Berlin (ZIB)                      */
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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
 
/**@file   heur_init.c
 * @brief  initial primal heuristic for the vertex coloring problem
 * @author Gerald Gamrath
 *
 * This file implements a heuristic which computes a starting solution for the coloring problem. It
 * therefore computes maximal stable sets and creates one variable for each set, which is added to the
 * LP.
 *
 * The heuristic is called only one time: before solving the root node.
 *
 * It checks, whether a solution-file was read in and a starting solution already exists.  If this
 * is not the case, an initial possible coloring is computed by a greedy method.  After that, a
 * tabu-search is called, which tries to reduce the number of colors needed. The tabu-search algorithm
 * follows the description in
 *
 * "A Survey of Local Search Methods for Graph Coloring"@n
 * by P. Galinier and A. Hertz@n
 * Computers & Operations Research, 33 (2006)
 *
 * The tabu-search works as follows: given the graph and a number of colors it tries to color the
 * nodes of the graph with at most the given number of colors.  It starts with a random coloring. In
 * each iteration, it counts the number of violated edges, that is, edges for which both incident
 * nodes have the same color. It now switches one node to another color in each iteration, taking
 * the node and color, that cause the greatest reduction of the number of violated edges, or if no
 * such combination exists, the node and color that cause the smallest increase of that number.  The
 * former color of the node is forbidden for a couple of iterations in order to give the possibility
 * to leave a local minimum.
 *
 * As long as the tabu-search finds a solution with the given number of colors, this number is reduced
 * by 1 and the tabu-search is called another time. If no coloring was found after a given number
 * of iterations, the tabu-search is stopped and variables for all sets of the last feasible coloring
 * are created and added to the LP (after possible extension to maximal stable sets).
 *
 * The variables of these sets result in a feasible starting solution of the coloring problem.
 *
 * The tabu-search can be deactivated by setting the parameter <heuristics/initcol/usetabu> to
 * FALSE.  The number of iterations after which the tabu-search stops if no solution was yet found
 * can be changed by the param <heuristics/initcol/maxiter>. A great effect is also obtained by
 * changing the parameters <heuristics/initcol/tabubase> and <heuristics/initcol/tabugamma>, which
 * determine the number of iterations for which the former color of a node is forbidden; more
 * precisely, this number is <tabubase> + ncritical * <tabugamma>, where ncritical is the number
 * of nodes, which are incident to violated edges.  Finally, the level of output and the frequency of
 * status lines can be changed by <heuristics/initcol/output> and <heuristics/initcol/dispfreq>.
 */
 
/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/
 
#include <assert.h>
#include <string.h>
 
#include "heur_init.h"
#include "pricer_coloring.h"
#include "probdata_coloring.h"
#include "reader_col.h"
#include "scip/cons_setppc.h"
#include "cons_storeGraph.h"
#include "tclique/tclique.h"
 
#define HEUR_NAME             "initcol"
#define HEUR_DESC             "initial primal heuristic for coloring"
#define HEUR_DISPCHAR         't'
#define HEUR_PRIORITY         1
#define HEUR_FREQ             1
#define HEUR_FREQOFS          0
#define HEUR_MAXDEPTH         0
#define HEUR_TIMING           SCIP_HEURTIMING_BEFORENODE
#define HEUR_USESSUBSCIP      FALSE  /**< does the heuristic use a secondary SCIP instance? */
 
 
/* default values for parameters */
#define DEFAULT_USETABU    TRUE
#define DEFAULT_MAXITER    100000
#define DEFAULT_TABUBASE   50
#define DEFAULT_TABUGAMMA  0.9
#define DEFAULT_OUTPUT     1
#define DEFAULT_DISPFREQ   10000
 
 
 
/*
 * Data structures
 */
 
/** primal heuristic data */
struct SCIP_HeurData
{
   SCIP_Bool             usetabu;            /**< should the tabu search heuristic be used in order to improve the greedy-solution? */
   int                   maxiter;            /**< maximal number of iterations to be performed in each tabu-run */
   int                   tabubase;           /**< constant part of the tabu-duration */
   SCIP_Real             tabugamma;          /**< factor for the linear part of the tabu-duration */
   int                   output;             /**< verbosity level for the output of the tabu search, 0: no output, 1: normal, 2: high */
   int                   dispfreq;           /**< frequency for displaying status information, only active with output verbosity level 2 */
};
 
 
 
 
/*
 * Local methods
 */
 
 
 
/** checks whether one of the nodes has no color respectively has color -1 in the given array */
static
SCIP_Bool hasUncoloredNode(
   int                   nnodes,             /**< the graph that should be colored */
   int*                  colors              /**< array of ints representing the colors */
   )
{
   int i;
 
   assert(colors != NULL);
 
   for( i = 0; i < nnodes; i++)
   {
      /* node not yet colored */
      if(colors[i] == -1)
      {
         return TRUE;
      }
   }
   return FALSE;
}
 
 
/** computes a stable set with a greedy-method and colors its nodes */
static
SCIP_RETCODE greedyStableSet(
   SCIP*                 scip,               /**< SCIP data structure */
   TCLIQUE_GRAPH*        graph,              /**< pointer to graph data structure */
   int*                  colors,             /**< array of ints representing the different colors, -1 means uncolored */
   int                   nextcolor           /**< color in which the stable set will be colored */
   )
{
   SCIP_Bool indNode;
   int nnodes;
   int i;
   int j;
   int* degrees;
   int* sortednodes;
   int* values;
   int* stablesetnodes;
   int nstablesetnodes;
 
   assert(graph != NULL);
   assert(colors != NULL);
 
   /* get number of nodes */
   nnodes = tcliqueGetNNodes(graph);
 
   /* get the  degrees and weights for the nodes in the graph */
   degrees = tcliqueGetDegrees(graph);
   SCIP_CALL( SCIPallocBufferArray(scip, &stablesetnodes, nnodes) );
   SCIP_CALL( SCIPallocBufferArray(scip, &values, nnodes) );
   SCIP_CALL( SCIPallocBufferArray(scip, &sortednodes, nnodes) );
 
   /* set values to the nodes which are used for sorting them */
   /* value = degree of the node + number of nodes if the node is yet uncolored,
      therefore the yet colored nodes have lower values than the not yet colored nodes */
   for( i = 0; i < nnodes; i++ )
   {
      sortednodes[i] = i;
      values[i] = degrees[i] + ( colors[i] == -1 ? nnodes : 0);
   }
 
   /* sort the nodes w.r.t. the computed values */
   SCIPsortDownIntInt(values, sortednodes, nnodes);
 
   /* insert first node */
   stablesetnodes[0] = sortednodes[0];
   nstablesetnodes = 1;
   for( i = 1; i < nnodes; i++)
   {
      if( colors[sortednodes[i]] != -1 )
      {
         break;
      }
      indNode = TRUE;
      for( j = 0; j < nstablesetnodes; j++ )
      {
         if( tcliqueIsEdge(graph, sortednodes[i], stablesetnodes[j]) )
         {
            indNode = FALSE;
            break;
         }
      }
      if( indNode == TRUE )
      {
         stablesetnodes[nstablesetnodes] = sortednodes[i];
         nstablesetnodes++;
      }
 
   }
   for( i = 0; i < nstablesetnodes; i++ )
   {
      assert(colors[stablesetnodes[i]] == -1);
      colors[stablesetnodes[i]] = nextcolor;
   }
   SCIPfreeBufferArray(scip, &stablesetnodes);
   SCIPfreeBufferArray(scip, &sortednodes);
   SCIPfreeBufferArray(scip, &values);
 
   return SCIP_OKAY;
}
 
 
static
/** computes the initial coloring with a greedy method */
SCIP_RETCODE greedyInitialColoring(
   SCIP*                 scip,               /**< SCIP data structure */
   TCLIQUE_GRAPH*        graph,              /**< pointer to graph data structure */
   int*                  colors,             /**< array of ints representing the different colors */
   int*                  ncolors             /**< number of colors needed */
   )
{
   int nnodes;
   int i;
   int color;
 
   assert(scip != NULL);
   assert(graph != NULL);
   assert(colors != NULL);
 
   nnodes = COLORprobGetNNodes(scip);
   assert(nnodes > 0);
 
   for( i = 0; i < nnodes; i++ )
   {
      colors[i] = -1;
   }
 
   color = 0;
   /* create stable sets until all Nodes are covered */
   while( hasUncoloredNode(nnodes, colors) )
   {
      SCIP_CALL( greedyStableSet(scip, graph, colors, color) );
      color++;
   }
   *ncolors = color;
 
   return SCIP_OKAY;
 
}
 
 
#ifndef NDEBUG
/** computes the number of violated edges, that means the number of edges (i,j) where i and j have the same color */
static
int getNViolatedEdges(
   TCLIQUE_GRAPH*        graph,              /**< the graph */
   int*                  colors              /**< colors of the nodes */
   )
{
   int nnodes;
   int i;
   int* j;
   int cnt;
 
   assert(graph != NULL);
   assert(colors != NULL);
 
   /* get the number of nodes */
   nnodes = tcliqueGetNNodes(graph);
   cnt = 0;
 
   /* count the number of violated edges, only consider edges (i,j) with i > j since the graph is undirected bu */
   for( i = 0; i < nnodes; i++ )
   {
      for( j = tcliqueGetFirstAdjedge(graph,i);  j <= tcliqueGetLastAdjedge(graph,i) && *j < i; j++ )
      {
         if( colors[i] == colors[*j] )
            cnt++;
      }
   }
   return cnt;
}
#endif
 
 
/** runs tabu coloring heuristic, gets a graph and a number of colors
 *  and tries to color the graph with at most that many colors;
 *  starts with a random coloring and switches one node to another color in each iteration,
 *  forbidding the old color for a couple of iterations
 */
static
SCIP_RETCODE runTabuCol(
   TCLIQUE_GRAPH*        graph,              /**< the graph, that should be colored */
   int                   seed,               /**< seed for the first random coloring */
   int                   maxcolors,          /**< number of colors, which are allowed */
   int*                  colors,             /**< output: the computed coloring */
   SCIP_HEURDATA*        heurdata,           /**< data of the heuristic */
   SCIP_Bool*            success             /**< pointer to store if something went wrong */
   )
{
   int nnodes;
   int** tabu;
   int** adj;
   int obj;
   int bestobj;
   int i;
   int j;
   int node1;
   int node2;
   int color1;
   int color2;
   int* firstedge;
   int* lastedge;
   SCIP_Bool restrictive;
   int iter;
   int minnode;
   int mincolor;
   int minvalue;
   int ncritical;
   SCIP_Bool aspiration;
   int d;
   int oldcolor;
 
   assert(graph != NULL);
   assert(heurdata != NULL);
   assert(success != NULL);
 
   if( heurdata->output >= 1 )
      printf("Running tabu coloring with maxcolors = %d...\n", maxcolors);
 
   /* get size */
   nnodes = tcliqueGetNNodes(graph);
 
   srand( seed ); /*lint !e732*/
 
   /* init random coloring, optionally keeping colors from a previous coloring */
   for( i = 0; i < nnodes; i++ )
   {
      if( colors[i] < 0 || colors[i] >= maxcolors )
      {
         int rnd = rand();
         colors[i] = rnd % maxcolors;
      }
      assert( 0 <= colors[i] && colors[i] < maxcolors );
   }
 
   /* init matrices */
   SCIP_CALL( SCIPallocMemoryArray(scip, &tabu, nnodes) );   /* stores iteration at which tabu node/color pair will
                                                              * expire to be tabu
                                                              */
   SCIP_CALL( SCIPallocMemoryArray(scip, &adj, nnodes) );    /* stores number of adjacent nodes using specified color */
 
   for( i = 0; i < nnodes; i++ )
   {
      SCIP_CALL( SCIPallocMemoryArray(scip, &(tabu[i]), maxcolors) ); /*lint !e866*/
      SCIP_CALL( SCIPallocMemoryArray(scip, &(adj[i]), maxcolors) ); /*lint !e866*/
      for( j = 0; j < maxcolors; j++ )
      {
         tabu[i][j] = 0;
         adj[i][j] = 0;
      }
   }
 
   /* objective */
   obj = 0;
 
   /* init adj-matrix and objective */
   for( node1 = 0; node1 < nnodes; node1++ )
   {
      color1 = colors[node1];
      firstedge = tcliqueGetFirstAdjedge(graph, node1);
      lastedge = tcliqueGetLastAdjedge(graph, node1);
      while(  firstedge <= lastedge )
      {
         node2 = *firstedge;
         color2 = colors[node2];
         assert( 0 <= color2 && color2 < maxcolors );
         (adj[node1][color2])++;
         if( color1 == color2 )
            obj++;
         firstedge++;
      }
   }
   assert( obj % 2 == 0 );
   obj = obj / 2;
   assert( obj == getNViolatedEdges(graph, colors) );
 
   bestobj = obj;
   restrictive = FALSE;
   iter = 0;
   if( obj > 0 )
   {
      /* perform predefined number of iterations */
      for( iter = 1; iter <= heurdata->maxiter; iter++ )
      {
         /* find best 1-move among those with critical vertex */
         minnode = -1;
         mincolor = -1;
         minvalue = nnodes * nnodes;
         ncritical = 0;
         for( node1 = 0; node1 < nnodes; node1++ )
         {
            aspiration = FALSE;
            color1 = colors[node1];
            assert( 0 <= color1 && color1 < maxcolors );
 
            /* if node is critical (has incident violated edges) */
            if( adj[node1][color1] > 0 )
            {
               ncritical++;
               /* check all colors */
               for( j = 0; j < maxcolors; j++ )
               {
                  /* if color is new */
                  if( j != color1 )
                  {
                     /* change in the number of violated edges: */
                     d = adj[node1][j] - adj[node1][color1];
 
                     /* 'aspiration criterion': stop if we get feasible solution */
                     if( obj + d == 0 )
                     {
                        if( heurdata->output >= 1 )
                           printf("   Feasible solution found after %d iterations!\n\n", iter);
                        minnode = node1;
                        mincolor = j;
                        minvalue = d;
                        aspiration = TRUE;
                        break;
                     }
 
                     /* if not tabu and better value */
                     if( tabu[node1][j] < iter &&  d < minvalue )
                     {
                        minnode = node1;
                        mincolor = j;
                        minvalue = d;
                     }
                  }
               }
            }
            if( aspiration )
               break;
         }
 
         /* if no candidate could be found - tabu list is too restrictive: just skip current iteration */
         if( minnode == -1 )
         {
            restrictive = TRUE;
            continue;
         }
         assert( minnode != -1 );
         assert( mincolor >= 0 );
 
         /* perform changes */
         assert( colors[minnode] != mincolor );
         oldcolor = colors[minnode];
         colors[minnode] = mincolor;
         obj += minvalue;
         assert( obj == getNViolatedEdges(graph, colors) );
         if( obj < bestobj )
            bestobj = obj;
 
         if( heurdata->output == 2 && (iter) % (heurdata->dispfreq) == 0 )
         {
            printf("Iter: %d  obj: %d  critical: %d   node: %d  color: %d  delta: %d\n", iter, obj, ncritical, minnode,
                  mincolor, minvalue);
         }
 
         /* terminate if valid coloring has been found */
         if( obj == 0 )
            break;
 
         /* update tabu list */
         assert( tabu[minnode][oldcolor] < iter );
         tabu[minnode][oldcolor] = iter + (heurdata->tabubase) + (int) (((double) ncritical) * (heurdata->tabugamma));
 
         /* update adj matrix */
         for( firstedge = tcliqueGetFirstAdjedge(graph, minnode); firstedge <= tcliqueGetLastAdjedge(graph, minnode); firstedge++ )
         {
            (adj[*firstedge][mincolor])++;
            (adj[*firstedge][oldcolor])--;
         }
      }
   }
   if( heurdata->output == 2 )
   {
      printf("Best objective: %d\n ", bestobj);
      if( restrictive )
      {
         printf("\nTabu list is probably too restrictive.\n");
      }
      printf("\n");
   }
   if( heurdata->output >= 1 && bestobj != 0 )
   {
      printf("   No feasible solution found after %d iterations!\n\n", iter-1);
   }
 
   for( i = 0; i < nnodes; i++ )
   {
      SCIPfreeMemoryArray(scip, &(adj[i]));
      SCIPfreeMemoryArray(scip, &(tabu[i]));
   }
   SCIPfreeMemoryArray(scip, &adj);
   SCIPfreeMemoryArray(scip, &tabu);
 
   /* check whether valid coloring has been found */
   *success = (obj == 0);
 
   return SCIP_OKAY;
}
 
 
/*
 * Callback methods of primal heuristic
 */
 
/** copy method for primal heuristic plugins (called when SCIP copies plugins) */
static
SCIP_DECL_HEURCOPY(heurCopyInit)
{  /*lint --e{715}*/
   assert(scip != NULL);
   assert(heur != NULL);
   assert(strcmp(SCIPheurGetName(heur), HEUR_NAME) == 0);
 
   return SCIP_OKAY;
}
 
/** destructor of primal heuristic to free user data (called when SCIP is exiting) */
/**! [SnippetHeurFreeInit] */
static
SCIP_DECL_HEURFREE(heurFreeInit)
{
   SCIP_HEURDATA* heurdata;
 
   /* free heuristic rule data */
   heurdata = SCIPheurGetData(heur);
   SCIPfreeBlockMemory(scip, &heurdata);
   SCIPheurSetData(heur, NULL);
 
   return SCIP_OKAY;
}
/**! [SnippetHeurFreeInit] */
 
 
/** execution method of primal heuristic */
static
SCIP_DECL_HEUREXEC(heurExecInit)
{
   int i;
   int j;
   int k;
   int nnodes;
   SCIP_SOL* sol;
   SCIP_Bool stored;
   SCIP_Bool success;
   SCIP_Bool indnode;
   int* colors;
   int* bestcolors;
   int ncolors;
   int nstablesetnodes;
   int setnumber;
   SCIP_VAR* var;
   SCIP_CONS** constraints;
   TCLIQUE_GRAPH* graph;
   SCIP_HEURDATA* heurdata;
   SCIP_Bool onlybest;
   int maxvarsround;
 
   heurdata = SCIPheurGetData(heur);
   assert(heurdata != NULL);
 
   *result = SCIP_DIDNOTFIND;
   nnodes = COLORprobGetNNodes(scip);
   graph = COLORprobGetGraph(scip);
 
   /* create stable sets if no solution was read */
   if( COLORprobGetNStableSets(scip) == 0 )
   {
      /* get memory for arrays */
      SCIP_CALL( SCIPallocBufferArray(scip, &colors, nnodes) );
      SCIP_CALL( SCIPallocBufferArray(scip, &bestcolors, nnodes) );
 
      /* get the node-constraits */
      constraints = COLORprobGetConstraints(scip);
      assert(constraints != NULL);
 
      /* compute an initial coloring with a greedy method */
      SCIP_CALL( greedyInitialColoring(scip, graph, bestcolors, &ncolors) );
 
      if( heurdata->usetabu )
      {
         /* try to find better colorings with tabu search method */
         success = TRUE;
         while( success )
         {
            ncolors--;
 
            /* initialize with colors from previous iteration; the last color is randomized */
            SCIP_CALL( runTabuCol(graph, 0, ncolors, colors, heurdata, &success) );
 
            if( success )
            {
               for( i = 0; i < nnodes; i++ )
                  bestcolors[i] = colors[i];
            }
         }
      }
 
      /* create vars for the computed coloring */
      for( i = 0; i <= ncolors; i++ )
      {
         /* save nodes with color i in the array colors and the number of such nodes in nstablesetnodes */
         nstablesetnodes = 0;
         for( j = 0; j < nnodes; j++ )
         {
            if( bestcolors[j] == i )
            {
               colors[nstablesetnodes] = j;
               nstablesetnodes++;
            }
         }
 
         /* try to add more nodes to the stable set without violating the stability */
         for( j = 0; j < nnodes; j++ )
         {
            indnode = TRUE;
            for( k = 0; k < nstablesetnodes; k++ )
            {
               if( j == colors[k] || tcliqueIsEdge(graph, j, colors[k]) )
               {
                  indnode = FALSE;
                  break;
               }
            }
 
            if( indnode == TRUE )
            {
               colors[nstablesetnodes] = j;
               nstablesetnodes++;
            }
         }
 
         /* create variable for the stable set and add it to SCIP */
         SCIPsortDownInt(colors, nstablesetnodes);
         SCIP_CALL( COLORprobAddNewStableSet(scip, colors, nstablesetnodes, &setnumber) );
         assert(setnumber != -1);
 
         /* create variable for the stable set and add it to SCIP */
         SCIP_CALL( SCIPcreateVar(scip, &var, NULL, 0.0, 1.0, 1.0, SCIP_VARTYPE_BINARY,
               TRUE, TRUE, NULL, NULL, NULL, NULL, (SCIP_VARDATA*)(size_t)setnumber) ); /*lint !e571*/
 
         SCIP_CALL( COLORprobAddVarForStableSet(scip, setnumber, var) );
         SCIP_CALL( SCIPaddVar(scip, var) );
         SCIP_CALL( SCIPchgVarUbLazy(scip, var, 1.0) );
 
         for( j = 0; j < nstablesetnodes; j++ )
         {
            /* add variable to node constraints of nodes in the set */
            SCIP_CALL( SCIPaddCoefSetppc(scip, constraints[colors[j]], var) );
         }
      }
 
      SCIPfreeBufferArray(scip, &bestcolors);
      SCIPfreeBufferArray(scip, &colors);
 
   }
 
   /* create solution consisting of all yet created stable sets, i.e., all sets of the solution given by the solution
    * file or created by the greedy and tabu search */
   SCIP_CALL( SCIPcreateSol(scip, &sol, NULL) );
   assert(sol != NULL);
   for( i = 0; i < COLORprobGetNStableSets(scip); i++ )
   {
      SCIP_CALL( SCIPsetSolVal(scip, sol, COLORprobGetVarForStableSet(scip, i), 1.0) );
   }
   SCIP_CALL( SCIPtrySolFree(scip, &sol, TRUE, FALSE, FALSE, FALSE, FALSE, &stored) );
   assert(stored);
 
   /* set maximal number of variables to be priced in each round */
   SCIP_CALL( SCIPgetBoolParam(scip, "pricers/coloring/onlybest", &onlybest) );
   if( onlybest )
      maxvarsround = COLORprobGetNStableSets(scip) * COLORprobGetNNodes(scip)/50;
   else
      maxvarsround = 1;
   SCIP_CALL( SCIPsetIntParam(scip, "pricers/coloring/maxvarsround", maxvarsround) );
 
   *result = SCIP_FOUNDSOL;
 
   return SCIP_OKAY;
}/*lint !e715*/
 
/*
 * primal heuristic specific interface methods
 */
 
/** creates the init primal heuristic and includes it in SCIP */
SCIP_RETCODE SCIPincludeHeurInit(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   SCIP_HEURDATA* heurdata;
   SCIP_HEUR* heur;
 
   /* create init primal heuristic data */
   SCIP_CALL( SCIPallocBlockMemory(scip, &heurdata) );
 
   heur = NULL;
   /* include primal heuristic */
   SCIP_CALL( SCIPincludeHeurBasic(scip, &heur, HEUR_NAME, HEUR_DESC, HEUR_DISPCHAR, HEUR_PRIORITY, HEUR_FREQ, HEUR_FREQOFS,
         HEUR_MAXDEPTH, HEUR_TIMING, HEUR_USESSUBSCIP, heurExecInit, heurdata) );
   assert(heur != NULL);
 
   SCIP_CALL( SCIPsetHeurCopy(scip, heur, heurCopyInit) );
   SCIP_CALL( SCIPsetHeurFree(scip, heur, heurFreeInit) );
 
   /* add parameters */
   SCIP_CALL( SCIPaddBoolParam(scip,
         "heuristics/initcol/usetabu",
         "should the tabu search heuristic be used in order to improve the greedy-solution?",
         &heurdata->usetabu, FALSE, DEFAULT_USETABU, NULL, NULL) );
 
   SCIP_CALL( SCIPaddIntParam(scip,
         "heuristics/initcol/maxiter",
         "maximal number of iterations to be performed in each tabu-run",
         &heurdata->maxiter, TRUE, DEFAULT_MAXITER, 0, INT_MAX, NULL, NULL) );
 
   SCIP_CALL( SCIPaddIntParam(scip,
         "heuristics/initcol/tabubase",
         "constant part of the tabu-duration",
         &heurdata->tabubase, TRUE, DEFAULT_TABUBASE, 0, INT_MAX, NULL, NULL) );
 
   SCIP_CALL( SCIPaddRealParam(scip,
         "heuristics/initcol/tabugamma",
         "factor for the linear part of the tabu-duration",
         &heurdata->tabugamma, TRUE, DEFAULT_TABUGAMMA, -100.0, 100.0, NULL, NULL) );
 
   SCIP_CALL( SCIPaddIntParam(scip,
         "heuristics/initcol/output",
         "verbosity level for the output of the tabu search, 0: no output, 1: normal, 2: high",
         &heurdata->output, FALSE, DEFAULT_OUTPUT, 0, 2, NULL, NULL) );
 
   SCIP_CALL( SCIPaddIntParam(scip,
         "heuristics/initcol/dispfreq",
         "frequency for displaying status information, only active with output verbosity level 2",
         &heurdata->dispfreq, TRUE, DEFAULT_DISPFREQ, 0, INT_MAX, NULL, NULL) );
 
 
   return SCIP_OKAY;
}