cons_sos2.c

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
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/*         SCIP --- Solving Constraint Integer Programs                      */
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/*  Copyright 2002-2022 Zuse Institute Berlin                                */
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/**@file   cons_sos2.c
 * @ingroup DEFPLUGINS_CONS
 * @brief  constraint handler for SOS type 2 constraints
 * @author Marc Pfetsch
 *
 * A specially ordered set of type 2 (SOS2) is a sequence of variables such that at most two
 * variables are nonzero and if two variables are nonzero they must be adjacent in the specified
 * sequence. Note that it is in principle allowed that a variable appears twice, but it then can be
 * fixed to 0 if it is at least two apart in the sequence.
 *
 * This constraint is useful when considering a piecewise affine approximation of a univariate
 * (nonlinear) function \f$: [a,b] \rightarrow R\f$: Let \f$x_1 < \ldots < x_n\f$ be points in
 * \f$[a,b]\f$ and introduce variables \f$\lambda_1, \ldots, \lambda_n\f$. To evaluate \f$f(x')\f$
 * at some point \f$x' \in [a,b]\f$ one can use the following constraints:
 * \f[
 *     \lambda_1 + \cdots + \lambda_n = 1,\quad x' = x_1 \lambda_1 + \cdots + x_n \lambda_n.
 * \f]
 * The value of \f$f(x')\f$ can the be approximated as
 * \f[
 *     f(x_1) \lambda_1 + \cdots + f(x_n) \lambda_n.
 * \f]
 * To get a valid piecewise affine approximation, \f$\lambda_1, \ldots, \lambda_n\f$ have to obey an
 * SOS constraint of type 2.
 *
 * This implementation of this constraint handler is based on classical ideas, see e.g.@n
 *  "Special Facilities in General Mathematical Programming System for
 *  Non-Convex Problems Using Ordered Sets of Variables"@n
 *  E. Beale and J. Tomlin, Proc. 5th IFORS Conference, 447-454 (1970)
 *
 * The order of the variables is determined as follows:
 *
 * - If the constraint is created with SCIPcreateConsSOS2() and weights are given, the weights
 *   determine the order (decreasing weights). Additional variables can be added with
 *   SCIPaddVarSOS2(), which adds a variable with given weight.
 *
 * - If an empty constraint is created and then variables are added with SCIPaddVarSOS2(), weights
 *   are needed and stored.
 *
 * - All other calls ignore the weights, i.e., if a nonempty constraint is created or variables are
 *   added with SCIPappendVarSOS2().
 *
 * @todo Allow to adapt the order of the constraints, e.g. by priorities. This for instance
 *   determines the branching order.
 * @todo Separate the following cuts for each pair of variables x, y of at least distance 2 in the
 *   SOS2 constraint: \f$ \min \{l_x, l_y\} \leq x + y \leq \max \{u_x, u_y\}\f$, where \f$l_x, u_x,
 *   l_y, u_y\f$ are the lower and upper bounds of x and y, respectively.
 * @todo Possibly allow to generate local cuts via strengthened local cuts (would affect lhs/rhs of rows)
 * @todo Try to compute better estimations for the child nodes in enforceSOS2 when called for a relaxation solution;
 *   currently pseudo costs are used, which are not computed for the relaxation.
 */

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

#include "blockmemshell/memory.h"
#include "scip/cons_linear.h"
#include "scip/cons_sos2.h"
#include "scip/pub_cons.h"
#include "scip/pub_event.h"
#include "scip/pub_lp.h"
#include "scip/pub_message.h"
#include "scip/pub_misc.h"
#include "scip/pub_misc_sort.h"
#include "scip/pub_var.h"
#include "scip/scip_branch.h"
#include "scip/scip_conflict.h"
#include "scip/scip_cons.h"
#include "scip/scip_copy.h"
#include "scip/scip_cut.h"
#include "scip/scip_event.h"
#include "scip/scip_general.h"
#include "scip/scip_lp.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_numerics.h"
#include "scip/scip_prob.h"
#include "scip/scip_sol.h"
#include "scip/scip_var.h"
#include <ctype.h>
#include <stdlib.h>
#include <string.h>


/* constraint handler properties */
#define CONSHDLR_NAME          "SOS2"
#define CONSHDLR_DESC          "SOS2 constraint handler"
#define CONSHDLR_SEPAPRIORITY        10 /**< priority of the constraint handler for separation */
#define CONSHDLR_ENFOPRIORITY       100 /**< priority of the constraint handler for constraint enforcing */
#define CONSHDLR_CHECKPRIORITY      -10 /**< priority of the constraint handler for checking feasibility */
#define CONSHDLR_SEPAFREQ             0 /**< frequency for separating cuts; zero means to separate only in the root node */
#define CONSHDLR_PROPFREQ             1 /**< frequency for propagating domains; zero means only preprocessing propagation */
#define CONSHDLR_EAGERFREQ          100 /**< frequency for using all instead of only the useful constraints in separation,
                                         *   propagation and enforcement, -1 for no eager evaluations, 0 for first only */
#define CONSHDLR_MAXPREROUNDS        -1 /**< maximal number of presolving rounds the constraint handler participates in (-1: no limit) */
#define CONSHDLR_DELAYSEPA        FALSE /**< should separation method be delayed, if other separators found cuts? */
#define CONSHDLR_DELAYPROP        FALSE /**< should propagation method be delayed, if other propagators found reductions? */
#define CONSHDLR_NEEDSCONS         TRUE /**< should the constraint handler be skipped, if no constraints are available? */

#define CONSHDLR_PROP_TIMING             SCIP_PROPTIMING_BEFORELP
#define CONSHDLR_PRESOLTIMING            SCIP_PRESOLTIMING_FAST

/* event handler properties */
#define EVENTHDLR_NAME         "SOS2"
#define EVENTHDLR_DESC         "bound change event handler for SOS2 constraints"

#define EVENTHDLR_EVENT_TYPE   (SCIP_EVENTTYPE_BOUNDCHANGED | SCIP_EVENTTYPE_GBDCHANGED)


/** constraint data for SOS2 constraints */
struct SCIP_ConsData
{
   int                   nvars;              /**< number of variables in the constraint */
   int                   maxvars;            /**< maximal number of variables (= size of storage) */
   int                   nfixednonzeros;     /**< number of variables fixed to be nonzero */
   SCIP_VAR**            vars;               /**< variables in constraint */
   SCIP_ROW*             row;                /**< row corresponding to upper and lower bound inequalities, or NULL if not yet created */
   SCIP_Real*            weights;            /**< weights determining the order (ascending), or NULL if not used */
};

/** SOS2 constraint handler data */
struct SCIP_ConshdlrData
{
   SCIP_EVENTHDLR*       eventhdlr;          /**< event handler for bound change events */
};


/** fix variable in given node to 0 or add constraint if variable is multi-aggregated */
static
SCIP_RETCODE fixVariableZeroNode(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_VAR*             var,                /**< variable to be fixed to 0*/
   SCIP_NODE*            node,               /**< node */
   SCIP_Bool*            infeasible          /**< if fixing is infeasible */
   )
{
   /* if variable cannot be nonzero */
   *infeasible = FALSE;
   if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(var)) || SCIPisFeasNegative(scip, SCIPvarGetUbLocal(var)) )
   {
      *infeasible = TRUE;
      return SCIP_OKAY;
   }

   /* if variable is multi-aggregated */
   if ( SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR )
   {
      SCIP_CONS* cons;
      SCIP_Real val;

      val = 1.0;

      if ( ! SCIPisFeasZero(scip, SCIPvarGetLbLocal(var)) || ! SCIPisFeasZero(scip, SCIPvarGetUbLocal(var)) )
      {
         SCIPdebugMsg(scip, "creating constraint to force multi-aggregated variable <%s> to 0.\n", SCIPvarGetName(var));
         /* we have to insert a local constraint var = 0 */
         SCIP_CALL( SCIPcreateConsLinear(scip, &cons, "branch", 1, &var, &val, 0.0, 0.0, TRUE, TRUE, TRUE, TRUE, TRUE,
               TRUE, FALSE, FALSE, FALSE, FALSE) );
         SCIP_CALL( SCIPaddConsNode(scip, node, cons, NULL) );
         SCIP_CALL( SCIPreleaseCons(scip, &cons) );
      }
   }
   else
   {
      if ( ! SCIPisFeasZero(scip, SCIPvarGetLbLocal(var)) )
         SCIP_CALL( SCIPchgVarLbNode(scip, node, var, 0.0) );
      if ( ! SCIPisFeasZero(scip, SCIPvarGetUbLocal(var)) )
         SCIP_CALL( SCIPchgVarUbNode(scip, node, var, 0.0) );
   }

   return SCIP_OKAY;
}


/** fix variable in local node to 0, and return whether the operation was feasible
 *
 *  @note We do not add a linear constraint if the variable is multi-aggregated as in
 *  fixVariableZeroNode(), since this would be too time consuming.
 */
static
SCIP_RETCODE inferVariableZero(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_VAR*             var,                /**< variable to be fixed to 0*/
   SCIP_CONS*            cons,               /**< constraint */
   int                   inferinfo,          /**< info for reverse prop. */
   SCIP_Bool*            infeasible,         /**< if fixing is infeasible */
   SCIP_Bool*            tightened,          /**< if fixing was performed */
   SCIP_Bool*            success             /**< whether fixing was successful, i.e., variable is not multi-aggregated */
   )
{
   *infeasible = FALSE;
   *tightened = FALSE;
   *success = FALSE;

   /* if variable cannot be nonzero */
   if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(var)) || SCIPisFeasNegative(scip, SCIPvarGetUbLocal(var)) )
   {
      *infeasible = TRUE;
      return SCIP_OKAY;
   }

   /* directly fix variable if it is not multi-aggregated, do nothing otherwise */
   if ( SCIPvarGetStatus(var) != SCIP_VARSTATUS_MULTAGGR )
   {
      SCIP_Bool tighten;

      /* fix lower bound */
      SCIP_CALL( SCIPinferVarLbCons(scip, var, 0.0, cons, inferinfo, FALSE, infeasible, &tighten) );
      *tightened = *tightened || tighten;

      /* fix upper bound */
      SCIP_CALL( SCIPinferVarUbCons(scip, var, 0.0, cons, inferinfo, FALSE, infeasible, &tighten) );
      *tightened = *tightened || tighten;

      *success = TRUE;
   }

   return SCIP_OKAY;
}


/** add lock on variable */
static
SCIP_RETCODE lockVariableSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var                 /**< variable */
   )
{
   assert( scip != NULL );
   assert( cons != NULL );
   assert( var != NULL );

   /* rounding down == bad if lb < 0, rounding up == bad if ub > 0 */
   SCIP_CALL( SCIPlockVarCons(scip, var, cons, SCIPisFeasNegative(scip, SCIPvarGetLbGlobal(var)),
         SCIPisFeasPositive(scip, SCIPvarGetUbGlobal(var))) );

   return SCIP_OKAY;
}


/* remove lock on variable */
static
SCIP_RETCODE unlockVariableSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var                 /**< variable */
   )
{
   assert( scip != NULL );
   assert( cons != NULL );
   assert( var != NULL );

   /* rounding down == bad if lb < 0, rounding up == bad if ub > 0 */
   SCIP_CALL( SCIPunlockVarCons(scip, var, cons, SCIPisFeasNegative(scip, SCIPvarGetLbGlobal(var)),
         SCIPisFeasPositive(scip, SCIPvarGetUbGlobal(var))) );

   return SCIP_OKAY;
}


/** ensures that the vars and weights array can store at least num entries */
static
SCIP_RETCODE consdataEnsurevarsSizeSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   int                   num,                /**< minimum number of entries to store */
   SCIP_Bool             reserveWeights      /**< whether the weights array is handled */
   )
{
   assert( consdata != NULL );
   assert( consdata->nvars <= consdata->maxvars );

   if ( num > consdata->maxvars )
   {
      int newsize;

      newsize = SCIPcalcMemGrowSize(scip, num);
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &consdata->vars, consdata->maxvars, newsize) );
      if ( reserveWeights )
         SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &consdata->weights, consdata->maxvars, newsize) );
      consdata->maxvars = newsize;
   }
   assert( num <= consdata->maxvars );

   return SCIP_OKAY;
}


/** handle new variable */
static
SCIP_RETCODE handleNewVariableSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_VAR*             var,                /**< variable */
   SCIP_Bool             transformed         /**< whether original variable was transformed */
   )
{
   assert( scip != NULL );
   assert( cons != NULL );
   assert( consdata != NULL );
   assert( var != NULL );

   /* if we are in transformed problem, catch the variable's events */
   if ( transformed )
   {
      SCIP_CONSHDLR* conshdlr;
      SCIP_CONSHDLRDATA* conshdlrdata;

      /* get event handler */
      conshdlr = SCIPconsGetHdlr(cons);
      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert( conshdlrdata != NULL );
      assert( conshdlrdata->eventhdlr != NULL );

      /* catch bound change events of variable */
      SCIP_CALL( SCIPcatchVarEvent(scip, var, EVENTHDLR_EVENT_TYPE, conshdlrdata->eventhdlr,
            (SCIP_EVENTDATA*)cons, NULL) );

      /* if the variable if fixed to nonzero */
      assert( consdata->nfixednonzeros >= 0 );
      if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(var)) || SCIPisFeasNegative(scip, SCIPvarGetUbLocal(var)) )
         ++consdata->nfixednonzeros;
   }

   /* install the rounding locks for the new variable */
   SCIP_CALL( lockVariableSOS2(scip, cons, var) );

   /* add the new coefficient to the LP row, if necessary */
   if ( consdata->row != NULL )
   {
      /* this is currently dead code, since the constraint is not modifiable */
      SCIP_CALL( SCIPaddVarToRow(scip, consdata->row, var, 1.0) );

      /* update lhs and rhs if necessary */
      if ( SCIPisFeasGT(scip, SCIPvarGetUbLocal(var), SCIProwGetRhs(consdata->row)) )
         SCIP_CALL( SCIPchgRowRhs(scip, consdata->row, SCIPvarGetUbLocal(var) ) );
      if ( SCIPisFeasLT(scip, SCIPvarGetLbLocal(var), SCIProwGetLhs(consdata->row)) )
         SCIP_CALL( SCIPchgRowLhs(scip, consdata->row, SCIPvarGetLbLocal(var) ) );
   }

   return SCIP_OKAY;
}


/** adds a variable to an SOS2 constraint, a position given by weight - ascending order */
static
SCIP_RETCODE addVarSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var,                /**< variable to add to the constraint */
   SCIP_Real             weight              /**< weight to determine position */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Bool transformed;
   int j;
   int pos;

   assert( var != NULL );
   assert( cons != NULL );

   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );

   if ( consdata->weights == NULL && consdata->maxvars > 0 )
   {
      SCIPerrorMessage("cannot add variable to SOS2 constraint <%s> that does not contain weights.\n", SCIPconsGetName(cons));
      return SCIP_INVALIDCALL;
   }

   /* are we in the transformed problem? */
   transformed = SCIPconsIsTransformed(cons);

   /* always use transformed variables in transformed constraints */
   if ( transformed )
   {
      SCIP_CALL( SCIPgetTransformedVar(scip, var, &var) );
   }
   assert( var != NULL );
   assert( transformed == SCIPvarIsTransformed(var) );

   SCIP_CALL( consdataEnsurevarsSizeSOS2(scip, consdata, consdata->nvars + 1, TRUE) );
   assert( consdata->weights != NULL );
   assert( consdata->maxvars >= consdata->nvars+1 );

   /* find variable position */
   for (pos = 0; pos < consdata->nvars; ++pos)
   {
      if ( consdata->weights[pos] > weight )
         break;
   }
   assert( 0 <= pos && pos <= consdata->nvars );

   /* move other variables, if necessary */
   for (j = consdata->nvars; j > pos; --j)
   {
      consdata->vars[j] = consdata->vars[j-1];
      consdata->weights[j] = consdata->weights[j-1];
   }

   /* insert variable */
   consdata->vars[pos] = var;
   consdata->weights[pos] = weight;
   ++consdata->nvars;

   /* handle the new variable */
   SCIP_CALL( handleNewVariableSOS2(scip, cons, consdata, var, transformed) );

   return SCIP_OKAY;
}


/** appends a variable to an SOS2 constraint */
static
SCIP_RETCODE appendVarSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var                 /**< variable to add to the constraint */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Bool transformed;

   assert( var != NULL );
   assert( cons != NULL );

   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );
   assert( consdata->nvars >= 0 );

   /* are we in the transformed problem? */
   transformed = SCIPconsIsTransformed(cons);

   /* always use transformed variables in transformed constraints */
   if ( transformed )
   {
      SCIP_CALL( SCIPgetTransformedVar(scip, var, &var) );
   }
   assert( var != NULL );
   assert( transformed == SCIPvarIsTransformed(var) );

   if ( consdata->weights != NULL )
   {
      SCIP_CALL( consdataEnsurevarsSizeSOS2(scip, consdata, consdata->nvars + 1, TRUE) );
   }
   else
   {
      SCIP_CALL( consdataEnsurevarsSizeSOS2(scip, consdata, consdata->nvars + 1, FALSE) );
   }

   /* insert variable */
   consdata->vars[consdata->nvars] = var;
   if ( consdata->weights != NULL )
   {
      if ( consdata->nvars > 0 )
         consdata->weights[consdata->nvars] = consdata->weights[consdata->nvars-1] + 1.0;
      else
         consdata->weights[consdata->nvars] = 0.0;
   }
   ++consdata->nvars;

   /* handle the new variable */
   SCIP_CALL( handleNewVariableSOS2(scip, cons, consdata, var, transformed) );

   return SCIP_OKAY;
}


/** deletes a variable of an SOS2 constraint */
static
SCIP_RETCODE deleteVarSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_EVENTHDLR*       eventhdlr,          /**< corresponding event handler */
   int                   pos                 /**< position of variable in array */
   )
{
   int j;

   assert( 0 <= pos && pos < consdata->nvars );

   /* remove lock of variable */
   SCIP_CALL( unlockVariableSOS2(scip, cons, consdata->vars[pos]) );

   /* drop events on variable */
   SCIP_CALL( SCIPdropVarEvent(scip, consdata->vars[pos], EVENTHDLR_EVENT_TYPE, eventhdlr, (SCIP_EVENTDATA*)cons, -1) );

   /* delete variable - need to copy since order is important */
   for (j = pos; j < consdata->nvars-1; ++j)
   {
      consdata->vars[j] = consdata->vars[j+1]; /*lint !e679*/
      if ( consdata->weights != NULL )
         consdata->weights[j] = consdata->weights[j+1]; /*lint !e679*/
   }
   --consdata->nvars;

   return SCIP_OKAY;
}


/** perform one presolving round
 *
 *  We perform the following presolving steps.
 *
 *  - If the bounds of one variable force it to be nonzero, we can fix all other variables with distance at least two to
 *    zero. If two variables are certain to be nonzero, we can fix all other variables to 0 and remove the constraint.
 *  - All variables fixed to zero, that are at the beginning or end of the constraint can be removed.
 *  - We substitute appregated variables.
 *  - If a constraint has at most two variables, we delete it.
 *
 *  We currently do not handle the following:
 *
 *  - If we have at least two variables fixed to zero next to each-other, that are positioned in the inner part of this
 *    constraint, we can delete all but one of these variables.
 *  - If a variable appears twice not next to each-other, it can be fixed to 0. If one variable appears next to
 *    each-other and is already certain to be nonzero, we can fix all variables.
 *  - If a binary variable and its negation appear in the constraint, we might fix variables to zero or can forbid a zero
 *    value for them.
 *  - When, after removing all zero "border" variables, a constraint with more than two variables has at most two
 *    variables that are not fixed to 0, only one of these can take a nonzero value, because these variables need to be
 *    the "border" variables of this constraint. The same holds if we have exactly three variables in one constraint and
 *    the middle variable is certain to be not zero. In both cases we can upgrade this constraint constraint to an sos1
 *    consisting only of the "border" variables. If these "border" variables are negations of each other, we can delete
 *    this constraint.
 *  - When, after removing all variables fixed to 0, that are possible, in a constraint each even positioned variable is
 *    fixed to 0, we can upgrade this constraint to an sos1 that holds all non-fixed variables.
 *  - Extract cliques for all odd and also for all even positioned binary variables
 */
static
SCIP_RETCODE presolRoundSOS2(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler */
   SCIP_Bool*            cutoff,             /**< whether a cutoff happened */
   SCIP_Bool*            success,            /**< whether we performed a successful reduction */
   int*                  ndelconss,          /**< number of deleted constraints */
   int*                  nfixedvars,         /**< number of fixed variables */
   int*                  nremovedvars        /**< number of variables removed */
   )
{
   SCIP_VAR** vars;
   SCIP_Bool infeasible;
   SCIP_Bool fixed;
   int nfixednonzeros;
   int lastFixedNonzero;
   int lastzero;
   int localnremovedvars;
   int oldnfixedvars;
   int j;

   assert( scip != NULL );
   assert( cons != NULL );
   assert( consdata != NULL );
   assert( eventhdlr != NULL );
   assert( cutoff != NULL );
   assert( success != NULL );
   assert( ndelconss != NULL );
   assert( nfixedvars != NULL );
   assert( nremovedvars != NULL );

   *cutoff = FALSE;
   *success = FALSE;

   SCIPdebugMsg(scip, "Presolving SOS2 constraint <%s>.\n", SCIPconsGetName(cons) );

   /* if the number of variables is at most 2 */
   if( consdata->nvars <= 2 )
   {
      SCIPdebugMsg(scip, "Deleting constraint with <= 2 variables.\n");

      /* delete constraint */
      assert( ! SCIPconsIsModifiable(cons) );
      SCIP_CALL( SCIPdelCons(scip, cons) );
      ++(*ndelconss);
      *success = TRUE;

      return SCIP_OKAY;
   }

   nfixednonzeros = 0;
   lastFixedNonzero = -1;
   vars = consdata->vars;
   lastzero = consdata->nvars;
   localnremovedvars = 0;

   /* check for variables fixed to 0 and bounds that guarantee a variable to be nonzero; downward loop is important */
   for( j = consdata->nvars - 1; j >= 0; --j )
   {
      SCIP_VAR* var;
      SCIP_Real lb;
      SCIP_Real ub;
      SCIP_Real scalar;
      SCIP_Real constant;

      /* check that our vars array is still correct */
      assert(vars == consdata->vars);

      scalar = 1.0;
      constant = 0.0;

      /* check aggregation: if the constant is zero, the variable is zero iff the aggregated variable is 0 */
      var = vars[j];
      SCIP_CALL( SCIPgetProbvarSum(scip, &var, &scalar, &constant) );

      /* if constant is zero and we get a different variable, substitute variable */
      if ( SCIPisZero(scip, constant) && ! SCIPisZero(scip, scalar) && var != vars[j] )
      {
         SCIPdebugMsg(scip, "substituted variable <%s> by <%s>.\n", SCIPvarGetName(vars[j]), SCIPvarGetName(var));
         SCIP_CALL( SCIPdropVarEvent(scip, consdata->vars[j], EVENTHDLR_EVENT_TYPE, eventhdlr, (SCIP_EVENTDATA*)cons, -1) );
         SCIP_CALL( SCIPcatchVarEvent(scip, var, EVENTHDLR_EVENT_TYPE, eventhdlr, (SCIP_EVENTDATA*)cons, NULL) );

         /* change the rounding locks */
         SCIP_CALL( unlockVariableSOS2(scip, cons, consdata->vars[j]) );
         SCIP_CALL( lockVariableSOS2(scip, cons, var) );

         vars[j] = var;
      }

      /* get bounds */
      lb = SCIPvarGetLbLocal(vars[j]);
      ub = SCIPvarGetUbLocal(vars[j]);

      /* if the variable if fixed to nonzero */
      if ( SCIPisFeasPositive(scip, lb) || SCIPisFeasNegative(scip, ub) )
      {
         ++nfixednonzeros;

         /* two variables certain to be nonzero which are not next to each other, so we are infeasible */
         if( lastFixedNonzero != -1 && lastFixedNonzero != j + 1 )
         {
            SCIPdebugMsg(scip, "The problem is infeasible: two non-consecutive variables have bounds that keep them from being 0.\n");
            *cutoff = TRUE;
            return SCIP_OKAY;
         }

         /* if more than two variables are fixed to be nonzero, we are infeasible */
         if( nfixednonzeros > 2 )
         {
            SCIPdebugMsg(scip, "The problem is infeasible: more than two variables have bounds that keep them from being 0.\n");
            *cutoff = TRUE;
            return SCIP_OKAY;
         }

         if( lastFixedNonzero == -1)
            lastFixedNonzero = j;
      }

      /* if the variable is fixed to 0 we may delete it from our constraint */
      if( SCIPisFeasZero(scip, lb) && SCIPisFeasZero(scip, ub) )
      {
         /* all rear variables fixed to 0 can be deleted */
         if( j == consdata->nvars - 1 )
         {
            ++(*nremovedvars);

            SCIPdebugMsg(scip, "deleting variable <%s> fixed to 0.\n", SCIPvarGetName(vars[j]));
            SCIP_CALL( deleteVarSOS2(scip, cons, consdata, eventhdlr, j) );

            *success = TRUE;
         }
         /* remember position of last variable for which all up front and this one are fixed to 0 */
         else if( lastzero > j + 1 )
            lastzero = j;
      }
      else
         lastzero = consdata->nvars;
   }

   /* check that our vars array is still correct */
   assert(vars == consdata->vars);

   /* remove first "lastzero" many variables, that are already fixed to 0 */
   if( lastzero < consdata->nvars )
   {
      assert(lastzero >= 0);

      for( j = lastzero; j >= 0; --j )
      {
         /* the variables should all be fixed to zero */
         assert(SCIPisFeasZero(scip, SCIPvarGetLbGlobal(vars[j])) && SCIPisFeasZero(scip, SCIPvarGetUbGlobal(vars[j])));

         SCIPdebugMsg(scip, "deleting variable <%s> fixed to 0.\n", SCIPvarGetName(vars[j]));
         SCIP_CALL( deleteVarSOS2(scip, cons, consdata, eventhdlr, j) );
      }
      localnremovedvars += (lastzero + 1);
      *success = TRUE;
   }

   /* check that our variable array is still correct */
   assert(vars == consdata->vars);

   *nremovedvars += localnremovedvars;

   /* we might need to correct the position of the first variable which is certain to be not zero */
   if( lastFixedNonzero >= 0 )
   {
      lastFixedNonzero -= localnremovedvars;
      assert(0 <= lastFixedNonzero && lastFixedNonzero < consdata->nvars);
      assert(SCIPisFeasPositive(scip, SCIPvarGetLbGlobal(vars[lastFixedNonzero])) || SCIPisFeasNegative(scip, SCIPvarGetUbGlobal(vars[lastFixedNonzero])));
   }

   /* if the number of variables is at most 2 */
   if( consdata->nvars <= 2 )
   {
      SCIPdebugMsg(scip, "Deleting constraint with <= 2 variables.\n");

      /* delete constraint */
      assert( ! SCIPconsIsModifiable(cons) );
      SCIP_CALL( SCIPdelCons(scip, cons) );
      ++(*ndelconss);
      *success = TRUE;

      return SCIP_OKAY;
   }

   oldnfixedvars = *nfixedvars;

   /* if there is exactly one fixed nonzero variable */
   if ( nfixednonzeros == 1 )
   {
      assert(0 <= lastFixedNonzero && lastFixedNonzero < consdata->nvars);
      assert(SCIPisFeasPositive(scip, SCIPvarGetLbGlobal(vars[lastFixedNonzero])) ||
         SCIPisFeasNegative(scip, SCIPvarGetUbGlobal(vars[lastFixedNonzero])));

      /* fix all other variables with distance two to zero */
      for( j = 0; j < lastFixedNonzero - 1; ++j )
      {
         SCIPdebugMsg(scip, "fixing variable <%s> to 0.\n", SCIPvarGetName(vars[j]));
         SCIP_CALL( SCIPfixVar(scip, vars[j], 0.0, &infeasible, &fixed) );

         if( infeasible )
         {
            *cutoff = TRUE;
            return SCIP_OKAY;
         }

         if ( fixed )
            ++(*nfixedvars);
      }
      for( j = lastFixedNonzero + 2; j < consdata->nvars; ++j )
      {
         SCIPdebugMsg(scip, "fixing variable <%s> to 0.\n", SCIPvarGetName(vars[j]));
         SCIP_CALL( SCIPfixVar(scip, vars[j], 0.0, &infeasible, &fixed) );

         if( infeasible )
         {
            *cutoff = TRUE;
            return SCIP_OKAY;
         }

         if ( fixed )
            ++(*nfixedvars);
      }

      if( *nfixedvars > oldnfixedvars )
         *success = TRUE;
   }
   /* if there are exactly two fixed nonzero variables */
   else if ( nfixednonzeros == 2 )
   {
      assert(0 < lastFixedNonzero && lastFixedNonzero < consdata->nvars);
      assert(SCIPisFeasPositive(scip, SCIPvarGetLbGlobal(vars[lastFixedNonzero])) ||
         SCIPisFeasNegative(scip, SCIPvarGetUbGlobal(vars[lastFixedNonzero])));
      /* the previous variable need also to be nonzero, otherwise the infeasibility should have been detected earlier */
      assert(SCIPisFeasPositive(scip, SCIPvarGetLbGlobal(vars[lastFixedNonzero - 1])) ||
         SCIPisFeasNegative(scip, SCIPvarGetUbGlobal(vars[lastFixedNonzero - 1])));

      /* fix all variables before lastFixedNonzero to zero */
      for( j = 0; j < lastFixedNonzero - 1; ++j )
      {
         SCIPdebugMsg(scip, "fixing variable <%s> to 0.\n", SCIPvarGetName(vars[j]));
         SCIP_CALL( SCIPfixVar(scip, vars[j], 0.0, &infeasible, &fixed) );

         if( infeasible )
         {
            *cutoff = TRUE;
            return SCIP_OKAY;
         }
         if ( fixed )
            ++(*nfixedvars);
      }
      /* fix all variables after lastFixedNonzero + 1 to zero */
      for( j = lastFixedNonzero + 1; j < consdata->nvars; ++j )
      {
         SCIPdebugMsg(scip, "fixing variable <%s> to 0.\n", SCIPvarGetName(vars[j]));
         SCIP_CALL( SCIPfixVar(scip, vars[j], 0.0, &infeasible, &fixed) );

         if( infeasible )
         {
            *cutoff = TRUE;
            return SCIP_OKAY;
         }
         if ( fixed )
            ++(*nfixedvars);
      }

      /* delete constraint */
      assert( ! SCIPconsIsModifiable(cons) );
      SCIP_CALL( SCIPdelCons(scip, cons) );
      ++(*ndelconss);
      *success = TRUE;
   }

   return SCIP_OKAY;
}


/** propagate variables */
static
SCIP_RETCODE propSOS2(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_Bool*            cutoff,             /**< whether a cutoff happened */
   int*                  ngen                /**< pointer to incremental counter for domain changes */
   )
{
   int ngenold;

   assert( scip != NULL );
   assert( cons != NULL );
   assert( consdata != NULL );
   assert( cutoff != NULL );
   assert( ngen != NULL );

   *cutoff = FALSE;
   ngenold = *ngen;

   /* if more than two variables are fixed to be nonzero */
   if ( consdata->nfixednonzeros > 2 )
   {
      SCIPdebugMsg(scip, "the node is infeasible, more than 2 variables are fixed to be nonzero.\n");
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      *cutoff = TRUE;
      return SCIP_OKAY;
   }

   /* if exactly one variable is fixed to be nonzero */
   if ( consdata->nfixednonzeros == 1 )
   {
      SCIP_VAR** vars;
      SCIP_Bool infeasible;
      SCIP_Bool tightened;
      SCIP_Bool success;
      int firstFixedNonzero;
      int nvars;
      int j;

      firstFixedNonzero = -1;
      nvars = consdata->nvars;
      vars = consdata->vars;
      assert( vars != NULL );

      /* search nonzero variable */
      for (j = 0; j < nvars; ++j)
      {
         if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(vars[j])) || SCIPisFeasNegative(scip, SCIPvarGetUbLocal(vars[j])) )
         {
            firstFixedNonzero = j;
            break;
         }
      }
      assert( firstFixedNonzero >= 0 );

      SCIPdebugMsg(scip, "variable <%s> is nonzero, fixing variables with distance at least 2 to 0.\n", SCIPvarGetName(vars[firstFixedNonzero]));

      /* fix variables before firstFixedNonzero-1 to 0 */
      for (j = 0; j < firstFixedNonzero-1; ++j)
      {
         /* fix variable */
         SCIP_CALL( inferVariableZero(scip, vars[j], cons, firstFixedNonzero, &infeasible, &tightened, &success) );
         assert( ! infeasible );

         if ( tightened )
            ++(*ngen);
      }

      /* fix variables after firstFixedNonzero+1 to 0 */
      for (j = firstFixedNonzero+2; j < nvars; ++j)
      {
         /* fix variable */
         SCIP_CALL( inferVariableZero(scip, vars[j], cons, firstFixedNonzero, &infeasible, &tightened, &success) );

         /* no variable after firstFixedNonzero+1 should be fixed to be nonzero */
         if ( infeasible )
         {
            assert( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(vars[j])) || SCIPisFeasNegative(scip, SCIPvarGetUbLocal(vars[j])) );
            SCIPdebugMsg(scip, "the node is infeasible: variable <%s> is fixed nonzero and variable <%s> with distance at least 2 as well.\n",
               SCIPvarGetName(vars[firstFixedNonzero]), SCIPvarGetName(vars[j]));
            *cutoff = TRUE;
            return SCIP_OKAY;
         }

         if ( tightened )
            ++(*ngen);
      }
      /* cannot locally delete constraint, since position of second entry is not fixed! */
   } /*lint !e438*/
   /* if exactly two variables are fixed to be nonzero */
   else if ( consdata->nfixednonzeros == 2 )
   {
      SCIP_VAR** vars;
      SCIP_Bool infeasible;
      SCIP_Bool tightened;
      SCIP_Bool success;
      SCIP_Bool allVarFixed;
      int firstFixedNonzero;
      int nvars;
      int j;

      firstFixedNonzero = -1;
      nvars = consdata->nvars;
      vars = consdata->vars;
      assert( vars != NULL );

      /* search nonzero variable */
      for (j = 0; j < nvars; ++j)
      {
         if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(vars[j])) || SCIPisFeasNegative(scip, SCIPvarGetUbLocal(vars[j])) )
         {
            firstFixedNonzero = j;
            break;
         }
      }
      assert( 0 <= firstFixedNonzero && firstFixedNonzero < nvars-1 );

      SCIPdebugMsg(scip, "variable <%s> is fixed to be nonzero, fixing variables to 0.\n", SCIPvarGetName(vars[firstFixedNonzero]));

      /* fix variables before firstFixedNonzero to 0 */
      allVarFixed = TRUE;
      for (j = 0; j < firstFixedNonzero; ++j)
      {
         /* fix variable */
         SCIP_CALL( inferVariableZero(scip, vars[j], cons, firstFixedNonzero+1, &infeasible, &tightened, &success) );
         assert( ! infeasible );
         allVarFixed = allVarFixed && success;
         if ( tightened )
            ++(*ngen);
      }

      /* fix variables after firstFixedNonzero+1 to 0 */
      for (j = firstFixedNonzero+2; j < nvars; ++j)
      {
         /* fix variable */
         SCIP_CALL( inferVariableZero(scip, vars[j], cons, firstFixedNonzero, &infeasible, &tightened, &success) );

         /* no variable after firstFixedNonzero+1 should be fixed to be nonzero */
         if ( infeasible )
         {
            assert( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(vars[j])) || SCIPisFeasNegative(scip, SCIPvarGetUbLocal(vars[j])) );
            SCIPdebugMsg(scip, "the node is infeasible: variable <%s> is fixed nonzero and variable <%s> with distance at least 2 as well.\n",
               SCIPvarGetName(vars[firstFixedNonzero]), SCIPvarGetName(vars[j]));
            *cutoff = TRUE;
            return SCIP_OKAY;
         }
         allVarFixed = allVarFixed && success;

         if ( tightened )
            ++(*ngen);
      }

      /* delete constraint locally, since the nonzero positions are fixed */
      if ( allVarFixed )
      {
         SCIPdebugMsg(scip, "locally deleting constraint <%s>.\n", SCIPconsGetName(cons));
         assert( !SCIPconsIsModifiable(cons) );
         SCIP_CALL( SCIPdelConsLocal(scip, cons) );
      }
   }

   /* reset constraint age counter */
   if ( *ngen > ngenold )
      SCIP_CALL( SCIPresetConsAge(scip, cons) );

   return SCIP_OKAY;
}


/** enforcement method
 *
 *  We check whether the current solution is feasible, i.e., contains
 *  at most one nonzero variable. If not, we branch along the lines
 *  indicated by Beale and Tomlin:
 *
 *  We first compute \f$W = \sum_{j=1}^n |x_i|\f$ and \f$w =
 *  \sum_{j=1}^n j\, |x_i|\f$. Then we search for the index \f$k\f$ that
 *  satisfies
 *  \f[
 *        k \leq \frac{w}{W} < k+1.
 *  \f]
 *  The branches are then
 *  \f[
 *        x_1 = 0, \ldots, x_{k-1} = 0 \qquad \mbox{and}\qquad
 *        x_{k+1} = 0, \ldots, x_n = 0.
 *  \f]
 *
 *  There is one special case that we have to consider: It can happen
 *  that \f$k\f$ is one too small. Example: \f$x_1 = 1 - \epsilon, x_2
 *  = 0, x_3 = \epsilon\f$. Then \f$w = 1 - \epsilon + 3 \epsilon = 1
 *  + 2 \epsilon\f$. This yields \f$k = 1\f$ and hence the first
 *  branch does not change the solution. We therefore increase \f$k\f$
 *  by one if \f$x_k \neq 0\f$. This is valid, since we know that
 *  \f$x_{k+1} \neq 0\f$ (with respect to the original \f$k\f$); the
 *  corresponding branch will cut off the current solution, since
 *  \f$x_k \neq 0\f$.
 */
static
SCIP_RETCODE enforceSOS2(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss,              /**< indicator constraints */
   SCIP_SOL*             sol,                /**< solution to be enforced (NULL for LP solution) */
   SCIP_RESULT*          result              /**< result */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Bool infeasible;
   SCIP_NODE* node1;
   SCIP_NODE* node2;
   SCIP_CONS* branchCons = NULL;
   SCIP_VAR** vars;
   SCIP_Real nodeselest;
   SCIP_Real objest;
   int nvars;
   int maxNonzeros;
   int maxInd;
   int j;
   int c;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( result != NULL );

   maxNonzeros = 0;
   maxInd = -1;

   SCIPdebugMsg(scip, "Enforcing SOS2 constraints <%s>.\n", SCIPconshdlrGetName(conshdlr) );
   *result = SCIP_FEASIBLE;

   /* check each constraint */
   for (c = 0; c < nconss; ++c)
   {
      SCIP_CONS* cons;
      SCIP_Bool cutoff;
      SCIP_Real weight1;
      SCIP_Real weight2;
      SCIP_Real w;
      int lastNonzero;
      int ngen;
      int cnt;
      int ind;

      cons = conss[c];
      assert( cons != NULL );

      consdata = SCIPconsGetData(cons);
      assert( consdata != NULL );

      nvars = consdata->nvars;
      vars = consdata->vars;

      /* do nothing if there are not enough variables - this is usually eliminated by preprocessing */
      if ( nvars <= 2 )
         return SCIP_OKAY;

      ngen = 0;

      /* first perform propagation (it might happen that standard propagation is turned off) */
      SCIP_CALL( propSOS2(scip, cons, consdata, &cutoff, &ngen) );
      SCIPdebugMsg(scip, "propagating <%s> in enforcing (cutoff: %u, domain reductions: %d).\n", SCIPconsGetName(cons), cutoff, ngen);
      if ( cutoff )
      {
         *result = SCIP_CUTOFF;
         return SCIP_OKAY;
      }
      if ( ngen > 0 )
      {
         *result = SCIP_REDUCEDDOM;
         return SCIP_OKAY;
      }

      cnt = 0;
      weight1 = 0.0;
      weight2 = 0.0;
      lastNonzero = -1;

      /* compute weight */
      for (j = 0; j < nvars; ++j)
      {
         SCIP_Real val;

         val = REALABS(SCIPgetSolVal(scip, sol, vars[j]));
         weight1 += val * (SCIP_Real) j;
         weight2 += val;

         if ( ! SCIPisFeasZero(scip, val) )
         {
            lastNonzero = j;
            ++cnt;
         }
      }

      /* if at most one variable is nonzero, the constraint is feasible */
      if ( cnt < 2 )
         continue;

      /* if two adjacent variables are nonzero */
      assert( 0 < lastNonzero && lastNonzero < nvars );
      if ( cnt == 2 && ! SCIPisFeasZero(scip, SCIPgetSolVal(scip, sol, vars[lastNonzero-1])) )
         continue;

      assert( !SCIPisFeasZero(scip, weight2) );
      w = weight1/weight2;  /*lint !e795*/

      ind = (int) SCIPfeasFloor(scip, w);
      assert( 0 <= ind && ind < nvars-1 );

      /* correct index if necessary - see above for an explanation */
      if ( ! SCIPisFeasZero(scip, SCIPgetSolVal(scip, sol, vars[ind])) && ind < lastNonzero-1 )
         ++ind;

      /* check if the constraint has more nonzeros */
      if ( cnt > maxNonzeros )
      {
         maxNonzeros = cnt;
         branchCons = cons;
         maxInd = ind;
      }
   }

   /* if all constraints are feasible */
   if ( branchCons == NULL )
   {
      SCIPdebugMsg(scip, "All SOS2 constraints are feasible.\n");
      return SCIP_OKAY;
   }

   /* create branches */
   consdata = SCIPconsGetData(branchCons);
   assert( consdata != NULL );
   nvars = consdata->nvars;
   vars = consdata->vars;

   assert( 0 < maxInd && maxInd < nvars-1 );

   /* branch on variable ind: either all variables before ind or all variables after ind are zero */
   SCIPdebugMsg(scip, "Branching on variable <%s> in constraint <%s> (nonzeros: %d).\n", SCIPvarGetName(vars[maxInd]),
      SCIPconsGetName(branchCons), maxNonzeros);

   /* calculate node selection and objective estimate for node 1 */
   nodeselest = 0.0;
   objest = SCIPgetLocalTransEstimate(scip);
   for (j = 0; j < maxInd; ++j)
   {
      objest += SCIPcalcChildEstimateIncrease(scip, vars[j], SCIPgetSolVal(scip, sol, vars[j]), 0.0);
      nodeselest += SCIPcalcNodeselPriority(scip, vars[j], SCIP_BRANCHDIR_DOWNWARDS, 0.0);
   }
   assert( objest >= SCIPgetLocalTransEstimate(scip) );

   /* create node 1 */
   SCIP_CALL( SCIPcreateChild(scip, &node1, nodeselest, objest) );

   for (j = 0; j < maxInd; ++j)
   {
      SCIP_CALL( fixVariableZeroNode(scip, vars[j], node1, &infeasible) );
      assert( ! infeasible );
   }

   /* calculate node selection and objective estimate for node 2 */
   nodeselest = 0.0;
   objest = SCIPgetLocalTransEstimate(scip);
   for (j = maxInd+1; j < nvars; ++j)
   {
      objest += SCIPcalcChildEstimateIncrease(scip, vars[j], SCIPgetSolVal(scip, sol, vars[j]), 0.0);
      nodeselest += SCIPcalcNodeselPriority(scip, vars[j], SCIP_BRANCHDIR_DOWNWARDS, 0.0);
   }
   assert( objest >= SCIPgetLocalTransEstimate(scip) );

   /* create node 2 */
   SCIP_CALL( SCIPcreateChild(scip, &node2, nodeselest, objest) );
   for (j = maxInd+1; j < nvars; ++j)
   {
      SCIP_CALL( fixVariableZeroNode(scip, vars[j], node2, &infeasible) );
      assert( ! infeasible );
   }
   SCIP_CALL( SCIPresetConsAge(scip, branchCons) );
   *result = SCIP_BRANCHED;

   return SCIP_OKAY;
}


/** Generate basic row
 *
 *  We generate the row corresponding to the following simple valid
 *  inequalities. Let \f$U\f$ and \f$U'\f$ be the largest and second
 *  largest upper bound of variables appearing in the
 *  constraint. Similarly let \f$L\f$ and \f$L'\f$ be the smallest and
 *  second smallest lower bound. The inequalities are:
 *  \f[
 *        x_1 + \ldots + x_n \leq U + U' \qquad\mbox{and}\qquad
 *        x_1 + \ldots + x_n \geq L + L'.
 *  \f]
 *  Of course, these inequalities are only added if the upper and
 *  lower bounds are all finite and \f$L+L' < 0\f$ or \f$U+U' > 0\f$.
 */
static
SCIP_RETCODE generateRowSOS2(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_Bool             local               /**< produce local cut? */
   )
{
   char name[SCIP_MAXSTRLEN];
   SCIP_CONSDATA* consdata;
   SCIP_VAR** vars;
   SCIP_Real minLb = SCIPinfinity(scip);
   SCIP_Real minLb2 = SCIPinfinity(scip);
   SCIP_Real maxUb = -SCIPinfinity(scip);
   SCIP_Real maxUb2 = -SCIPinfinity(scip);
   SCIP_Real lhs;
   SCIP_Real rhs;
   SCIP_ROW* row;
   int nvars;
   int j;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( cons != NULL );

   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );
   assert( consdata->row == NULL );

   nvars = consdata->nvars;
   vars = consdata->vars;
   assert( vars != NULL );

   /* find minimum and maximum lower and upper bounds */
   for (j = 0; j < nvars; ++j)
   {
      SCIP_Real val;

      if ( local )
         val = SCIPvarGetLbLocal(vars[j]);
      else
         val = SCIPvarGetLbGlobal(vars[j]);

      if ( val < minLb )
      {
         minLb2 = minLb;
         minLb = val;
      }
      else
      {
         if ( val < minLb2 )
            minLb2 = val;
      }

      if ( local )
         val = SCIPvarGetUbLocal(vars[j]);
      else
         val = SCIPvarGetUbGlobal(vars[j]);

      if ( val > maxUb )
      {
         maxUb2 = maxUb;
         maxUb = val;
      }
      else
      {
         if ( val > maxUb2 )
            maxUb2 = val;
      }
   }
   lhs = minLb + minLb2;
   rhs = maxUb + maxUb2;

   /* ignore trivial inequality if left hand side would be 0 */
   if ( SCIPisFeasZero(scip, lhs) )
      lhs = -SCIPinfinity(scip);

   /* ignore trivial inequality if right hand side would be 0 */
   if ( SCIPisFeasZero(scip, rhs) )
      rhs = SCIPinfinity(scip);

   /* create upper and lower bound inequality if one of the bounds is finite */
   if ( ! SCIPisInfinity(scip, REALABS(lhs)) || ! SCIPisInfinity(scip, REALABS(rhs)) )
   {
      (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "sos2bnd#%s", SCIPconsGetName(cons));
      SCIP_CALL( SCIPcreateEmptyRowCons(scip, &row, cons, name, lhs, rhs, local, FALSE, FALSE) );
      SCIP_CALL( SCIPaddVarsToRowSameCoef(scip, row, nvars, vars, 1.0) );
      consdata->row = row;

      SCIPdebug( SCIP_CALL( SCIPprintRow(scip, row, NULL) ) );
   }

   return SCIP_OKAY;
}


/* ---------------------------- constraint handler callback methods ----------------------*/

/** copy method for constraint handler plugins (called when SCIP copies plugins) */
static
SCIP_DECL_CONSHDLRCOPY(conshdlrCopySOS2)
{  /*lint --e{715}*/
   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );

   /* call inclusion method of constraint handler */
   SCIP_CALL( SCIPincludeConshdlrSOS2(scip) );

   *valid = TRUE;

   return SCIP_OKAY;
}


/** destructor of constraint handler to free constraint handler data (called when SCIP is exiting) */
static
SCIP_DECL_CONSFREE(consFreeSOS2)
{
   SCIP_CONSHDLRDATA* conshdlrdata;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   SCIPfreeBlockMemory(scip, &conshdlrdata);

   return SCIP_OKAY;
}


/** solving process deinitialization method of constraint handler (called before branch and bound process data is freed) */
static
SCIP_DECL_CONSEXITSOL(consExitsolSOS2)
{  /*lint --e{715}*/
   int c;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );

   /* check each constraint */
   for (c = 0; c < nconss; ++c)
   {
      SCIP_CONSDATA* consdata;

      assert( conss != NULL );
      assert( conss[c] != NULL );
      consdata = SCIPconsGetData(conss[c]);
      assert( consdata != NULL );

      SCIPdebugMsg(scip, "Exiting SOS2 constraint <%s>.\n", SCIPconsGetName(conss[c]) );

      /* free row */
      if ( consdata->row != NULL )
      {
         SCIP_CALL( SCIPreleaseRow(scip, &consdata->row) );
      }
   }
   return SCIP_OKAY;
}


/** frees specific constraint data */
static
SCIP_DECL_CONSDELETE(consDeleteSOS2)
{
   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( cons != NULL );
   assert( consdata != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );

   SCIPdebugMsg(scip, "Deleting SOS2 constraint <%s>.\n", SCIPconsGetName(cons) );

   /* drop events on transformed variables */
   if ( SCIPconsIsTransformed(cons) )
   {
      SCIP_CONSHDLRDATA* conshdlrdata;
      int j;

      /* get constraint handler data */
      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert( conshdlrdata != NULL );
      assert( conshdlrdata->eventhdlr != NULL );

      for (j = 0; j < (*consdata)->nvars; ++j)
      {
         SCIP_CALL( SCIPdropVarEvent(scip, (*consdata)->vars[j], EVENTHDLR_EVENT_TYPE, conshdlrdata->eventhdlr,
               (SCIP_EVENTDATA*)cons, -1) );
      }
   }

   SCIPfreeBlockMemoryArray(scip, &(*consdata)->vars, (*consdata)->maxvars);
   if ( (*consdata)->weights != NULL )
   {
      SCIPfreeBlockMemoryArray(scip, &(*consdata)->weights, (*consdata)->maxvars);
   }

   /* free row */
   if ( (*consdata)->row != NULL )
   {
      SCIP_CALL( SCIPreleaseRow(scip, &(*consdata)->row) );
   }
   assert( (*consdata)->row == NULL );

   SCIPfreeBlockMemory(scip, consdata);

   return SCIP_OKAY;
}


/** transforms constraint data into data belonging to the transformed problem */
static
SCIP_DECL_CONSTRANS(consTransSOS2)
{
   SCIP_CONSDATA* consdata;
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* sourcedata;
   char s[SCIP_MAXSTRLEN];
   int j;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( sourcecons != NULL );
   assert( targetcons != NULL );

   /* get constraint handler data */
   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );
   assert( conshdlrdata->eventhdlr != NULL );

   SCIPdebugMsg(scip, "Transforming SOS2 constraint: <%s>.\n", SCIPconsGetName(sourcecons) );

   /* get data of original constraint */
   sourcedata = SCIPconsGetData(sourcecons);
   assert( sourcedata != NULL );
   assert( sourcedata->nvars > 0 );
   assert( sourcedata->nvars <= sourcedata->maxvars );

   /* create constraint data */
   SCIP_CALL( SCIPallocBlockMemory(scip, &consdata) );

   consdata->nvars = sourcedata->nvars;
   consdata->maxvars = sourcedata->nvars;
   consdata->row = NULL;
   consdata->nfixednonzeros = 0;
   SCIP_CALL( SCIPallocBlockMemoryArray(scip, &consdata->vars, consdata->nvars) );

   /* if weights were used */
   if ( sourcedata->weights != NULL )
   {
      SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &consdata->weights, sourcedata->weights, consdata->nvars) );
   }
   else
      consdata->weights = NULL;

   for (j = 0; j < sourcedata->nvars; ++j)
   {
      assert( sourcedata->vars[j] != 0 );
      SCIP_CALL( SCIPgetTransformedVar(scip, sourcedata->vars[j], &(consdata->vars[j])) );

      /* if variable is fixed to be nonzero */
      if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(consdata->vars[j])) || SCIPisFeasNegative(scip, SCIPvarGetUbLocal(consdata->vars[j])) )
         ++(consdata->nfixednonzeros);
   }

   /* create transformed constraint with the same flags */
   (void) SCIPsnprintf(s, SCIP_MAXSTRLEN, "t_%s", SCIPconsGetName(sourcecons));
   SCIP_CALL( SCIPcreateCons(scip, targetcons, s, conshdlr, consdata,
         SCIPconsIsInitial(sourcecons), SCIPconsIsSeparated(sourcecons),
         SCIPconsIsEnforced(sourcecons), SCIPconsIsChecked(sourcecons),
         SCIPconsIsPropagated(sourcecons), SCIPconsIsLocal(sourcecons),
         SCIPconsIsModifiable(sourcecons), SCIPconsIsDynamic(sourcecons),
         SCIPconsIsRemovable(sourcecons), SCIPconsIsStickingAtNode(sourcecons)) );

   /* catch bound change events on variable */
   for (j = 0; j < consdata->nvars; ++j)
   {
      SCIP_CALL( SCIPcatchVarEvent(scip, consdata->vars[j], EVENTHDLR_EVENT_TYPE, conshdlrdata->eventhdlr,
            (SCIP_EVENTDATA*)*targetcons, NULL) );
   }

#ifdef SCIP_DEBUG
   if ( consdata->nfixednonzeros > 0 )
   {
      SCIPdebugMsg(scip, "constraint <%s> has %d variables fixed to be nonzero.\n", SCIPconsGetName(*targetcons), consdata->nfixednonzeros );
   }
#endif

   return SCIP_OKAY;
}


/** presolving method of constraint handler */
static
SCIP_DECL_CONSPRESOL(consPresolSOS2)
{  /*lint --e{715}*/
   SCIPdebug( int oldnfixedvars = *nfixedvars; )
   SCIPdebug( int oldndelconss = *ndelconss; )
   int nremovedvars;
   SCIP_EVENTHDLR* eventhdlr;
   int c;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( result != NULL );

   *result = SCIP_DIDNOTRUN;
   nremovedvars = 0;

   /* only run if success is possible */
   if( nrounds == 0 || nnewfixedvars > 0 || nnewaggrvars > 0 || nnewchgcoefs > 0 )
   {
      /* get constraint handler data */
      assert( SCIPconshdlrGetData(conshdlr) != NULL );
      eventhdlr = SCIPconshdlrGetData(conshdlr)->eventhdlr;
      assert( eventhdlr != NULL );

      *result = SCIP_DIDNOTFIND;

      /* check each constraint */
      for (c = 0; c < nconss; ++c)
      {
         SCIP_CONSDATA* consdata;
         SCIP_CONS* cons;
         SCIP_Bool cutoff;
         SCIP_Bool success;

         assert( conss != NULL );
         assert( conss[c] != NULL );

         cons = conss[c];
         consdata = SCIPconsGetData(cons);

         assert( consdata != NULL );
         assert( consdata->nvars >= 0 );
         assert( consdata->nvars <= consdata->maxvars );
         assert( ! SCIPconsIsModifiable(cons) );

         /* perform one presolving round */
         SCIP_CALL( presolRoundSOS2(scip, cons, consdata, eventhdlr, &cutoff, &success, ndelconss, nfixedvars, &nremovedvars) );

         if ( cutoff )
         {
            *result = SCIP_CUTOFF;
            return SCIP_OKAY;
         }

         if ( success )
            *result = SCIP_SUCCESS;
      }
   }
   (*nchgcoefs) += nremovedvars;

   SCIPdebug( SCIPdebugMsg(scip, "presolving fixed %d variables, removed %d variables, and deleted %d constraints.\n",
      *nfixedvars - oldnfixedvars, nremovedvars, *ndelconss - oldndelconss); )

   return SCIP_OKAY;
}


/** LP initialization method of constraint handler (called before the initial LP relaxation at a node is solved) */
static
SCIP_DECL_CONSINITLP(consInitlpSOS2)
{
   int c;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );

   *infeasible = FALSE;

   /* check each constraint */
   for (c = 0; c < nconss && !(*infeasible); ++c)
   {
      SCIP_CONSDATA* consdata;

      assert( conss != NULL );
      assert( conss[c] != NULL );
      consdata = SCIPconsGetData(conss[c]);
      assert( consdata != NULL );

      SCIPdebugMsg(scip, "Checking for initial rows for SOS2 constraint <%s>.\n", SCIPconsGetName(conss[c]) );

      /* possibly generate row if not yet done */
      if ( consdata->row == NULL )
      {
         SCIP_CALL( generateRowSOS2(scip, conshdlr, conss[c], FALSE) );
      }

      /* put corresponding rows into LP */
      if ( consdata->row != NULL && ! SCIProwIsInLP(consdata->row) )
      {
         assert( ! SCIPisInfinity(scip, REALABS(SCIProwGetLhs(consdata->row))) || ! SCIPisInfinity(scip, REALABS(SCIProwGetRhs(consdata->row))) );

         SCIP_CALL( SCIPaddRow(scip, consdata->row, FALSE, infeasible) );
         SCIPdebug( SCIP_CALL( SCIPprintRow(scip, consdata->row, NULL) ) );
      }
   }

   return SCIP_OKAY;
}


/** separation method of constraint handler for LP solutions */
static
SCIP_DECL_CONSSEPALP(consSepalpSOS2)
{  /*lint --e{715}*/
   SCIP_Bool cutoff = FALSE;
   int c;
   int ngen = 0;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( result != NULL );

   *result = SCIP_DIDNOTRUN;

   /* check each constraint */
   for (c = 0; c < nconss && ! cutoff; ++c)
   {
      SCIP_CONSDATA* consdata;
      SCIP_ROW* row;

      *result = SCIP_DIDNOTFIND;
      assert( conss[c] != NULL );
      consdata = SCIPconsGetData(conss[c]);
      assert( consdata != NULL );
      SCIPdebugMsg(scip, "Separating inequalities for SOS2 constraint <%s>.\n", SCIPconsGetName(conss[c]) );

      /* put corresponding rows into LP if they are useful */
      row = consdata->row;

      /* possibly generate row if not yet done */
      if ( row == NULL )
      {
         SCIP_CALL( generateRowSOS2(scip, conshdlr, conss[c], FALSE) );
      }

      /* possibly add row to LP if it is useful */
      if ( row != NULL && ! SCIProwIsInLP(row) && SCIPisCutEfficacious(scip, NULL, row) )
      {
         SCIP_CALL( SCIPaddRow(scip, row, FALSE, &cutoff) );
         SCIPdebug( SCIP_CALL( SCIPprintRow(scip, row, NULL) ) );
         SCIP_CALL( SCIPresetConsAge(scip, conss[c]) );
         ++ngen;
      }
   }
   SCIPdebugMsg(scip, "Separated %d SOS2 constraints.\n", ngen);
   if ( cutoff )
      *result = SCIP_CUTOFF;
   else if ( ngen > 0 )
      *result = SCIP_SEPARATED;

   return SCIP_OKAY;
}


/** separation method of constraint handler for arbitrary primal solutions */
static
SCIP_DECL_CONSSEPASOL(consSepasolSOS2)
{  /*lint --e{715}*/
   SCIP_Bool cutoff = FALSE;
   int c;
   int ngen = 0;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( result != NULL );

   *result = SCIP_DIDNOTRUN;

   /* check each constraint */
   for (c = 0; c < nconss && ! cutoff; ++c)
   {
      SCIP_CONSDATA* consdata;
      SCIP_ROW* row;

      *result = SCIP_DIDNOTFIND;
      assert( conss[c] != NULL );
      consdata = SCIPconsGetData(conss[c]);
      assert( consdata != NULL );
      SCIPdebugMsg(scip, "Separating solution for SOS2 constraint <%s>.\n", SCIPconsGetName(conss[c]) );

      /* put corresponding row into LP if it is useful */
      row = consdata->row;

      /* possibly generate row if not yet done */
      if ( row == NULL )
      {
         SCIP_CALL( generateRowSOS2(scip, conshdlr, conss[c], FALSE) );
      }

      /* possibly add row to LP if it is useful */
      if ( row != NULL && ! SCIProwIsInLP(row) && SCIPisCutEfficacious(scip, sol, row) )
      {
         SCIP_CALL( SCIPaddRow(scip, row, FALSE, &cutoff) );
         SCIPdebug( SCIP_CALL( SCIPprintRow(scip, row, NULL) ) );
         SCIP_CALL( SCIPresetConsAge(scip, conss[c]) );
         ++ngen;
      }
   }
   SCIPdebugMsg(scip, "Separated %d SOS2 constraints.\n", ngen);
   if ( cutoff )
      *result = SCIP_CUTOFF;
   else if ( ngen > 0 )
      *result = SCIP_SEPARATED;

   return SCIP_OKAY;
}


/** constraint enforcing method of constraint handler for LP solutions */
static
SCIP_DECL_CONSENFOLP(consEnfolpSOS2)
{  /*lint --e{715}*/
   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( result != NULL );

   SCIP_CALL( enforceSOS2(scip, conshdlr, nconss, conss, NULL, result) );

   return SCIP_OKAY;
}


/** constraint enforcing method of constraint handler for relaxation solutions */
static
SCIP_DECL_CONSENFORELAX(consEnforelaxSOS2)
{  /*lint --e{715}*/
   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( result != NULL );

   SCIP_CALL( enforceSOS2(scip, conshdlr, nconss, conss, sol, result) );

   return SCIP_OKAY;
}


/** constraint enforcing method of constraint handler for pseudo solutions */
static
SCIP_DECL_CONSENFOPS(consEnfopsSOS2)
{  /*lint --e{715}*/
   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( result != NULL );

   SCIP_CALL( enforceSOS2(scip, conshdlr, nconss, conss, NULL, result) );

   return SCIP_OKAY;
}


/** feasibility check method of constraint handler for integral solutions
 *
 *  We simply check whether at most two variable are nonzero and in the
 *  case there are exactly two nonzero, then they have to be direct
 *  neighbors in the given solution.
 */
static
SCIP_DECL_CONSCHECK(consCheckSOS2)
{  /*lint --e{715}*/
   int c;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( result != NULL );

   *result = SCIP_FEASIBLE;

   /* check each constraint */
   for (c = 0; c < nconss && (*result == SCIP_FEASIBLE || completely); ++c)
   {
      SCIP_CONSDATA* consdata;
      int firstNonzero;
      int j;

      firstNonzero = -1;
      assert( conss[c] != NULL );
      consdata = SCIPconsGetData(conss[c]);
      assert( consdata != NULL );
      SCIPdebugMsg(scip, "Checking SOS2 constraint <%s>.\n", SCIPconsGetName(conss[c]));

      /* check all variables */
      for (j = 0; j < consdata->nvars; ++j)
      {
         /* if variable is nonzero */
         if ( ! SCIPisFeasZero(scip, SCIPgetSolVal(scip, sol, consdata->vars[j])) )
         {
            if ( firstNonzero < 0 )
               firstNonzero = j;
            else
            {
               /* if we are more than one position away from the firstNonzero variable */
               if ( j > firstNonzero+1 )
               {
                  SCIP_CALL( SCIPresetConsAge(scip, conss[c]) );
                  *result = SCIP_INFEASIBLE;

                  /* update constraint violation in solution */
                  if ( sol != NULL )
                     SCIPupdateSolConsViolation(scip, sol, 1.0, 1.0);

                  if ( printreason )
                  {
                     SCIP_CALL( SCIPprintCons(scip, conss[c], NULL) );

                     SCIPinfoMessage(scip, NULL, ";\nviolation: <%s> = %.15g and  <%s> = %.15g\n",
                        SCIPvarGetName(consdata->vars[firstNonzero]),
                        SCIPgetSolVal(scip, sol, consdata->vars[firstNonzero]),
                        SCIPvarGetName(consdata->vars[j]),
                        SCIPgetSolVal(scip, sol, consdata->vars[j]));
                  }

                  SCIPdebugMsg(scip, "SOS2 constraint <%s> infeasible.\n", SCIPconsGetName(conss[c]));
               }
            }
         }
      }
   }

   return SCIP_OKAY;
}


/** domain propagation method of constraint handler */
static
SCIP_DECL_CONSPROP(consPropSOS2)
{  /*lint --e{715}*/
   int c;
   int ngen = 0;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( result != NULL );
   *result = SCIP_DIDNOTRUN;

   assert( SCIPisTransformed(scip) );

   /* check each constraint */
   for (c = 0; c < nconss; ++c)
   {
      SCIP_CONS* cons;
      SCIP_CONSDATA* consdata;
      SCIP_Bool cutoff;

      assert( conss[c] != NULL );
      cons = conss[c];
      consdata = SCIPconsGetData(cons);
      assert( consdata != NULL );
      SCIPdebugMsg(scip, "Propagating SOS2 constraint <%s>.\n", SCIPconsGetName(cons) );

      *result = SCIP_DIDNOTFIND;
      SCIP_CALL( propSOS2(scip, cons, consdata, &cutoff, &ngen) );
      if ( cutoff )
      {
         *result = SCIP_CUTOFF;
         return SCIP_OKAY;
      }
   }
   SCIPdebugMsg(scip, "Propagated %d domains.\n", ngen);
   if ( ngen > 0 )
      *result = SCIP_REDUCEDDOM;

   return SCIP_OKAY;
}


/** propagation conflict resolving method of constraint handler
 *
 *  We check which bound changes were the reason for infeasibility. We
 *  use that @a inferinfo stores the index of the variable that has
 *  bounds that fix it to be nonzero (these bounds are the reason). */
static
SCIP_DECL_CONSRESPROP(consRespropSOS2)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;
   SCIP_VAR* var;

   assert( scip != NULL );
   assert( cons != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert( infervar != NULL );
   assert( bdchgidx != NULL );
   assert( result != NULL );

   *result = SCIP_DIDNOTFIND;
   SCIPdebugMsg(scip, "Propagation resolution method of SOS2 constraint <%s>.\n", SCIPconsGetName(cons));

   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );
   assert( 0 <= inferinfo && inferinfo < consdata->nvars );
   var = consdata->vars[inferinfo];
   assert( var != infervar );

   /* check if lower bound of var was the reason */
   if ( SCIPisFeasPositive(scip, SCIPgetVarLbAtIndex(scip, var, bdchgidx, FALSE)) )
   {
      SCIP_CALL( SCIPaddConflictLb(scip, var, bdchgidx) );
      *result = SCIP_SUCCESS;
   }

   /* check if upper bound of var was the reason */
   if ( SCIPisFeasNegative(scip, SCIPgetVarUbAtIndex(scip, var, bdchgidx, FALSE)) )
   {
      SCIP_CALL( SCIPaddConflictUb(scip, var, bdchgidx) );
      *result = SCIP_SUCCESS;
   }

   return SCIP_OKAY;
}


/** variable rounding lock method of constraint handler
 *
 *  Let lb and ub be the lower and upper bounds of a
 *  variable. Preprocessing usually makes sure that lb <= 0 <= ub.
 *
 *  - If lb < 0 then rounding down may violate the constraint.
 *  - If ub > 0 then rounding up may violated the constraint.
 *  - If lb > 0 or ub < 0 then the constraint is infeasible and we do
 *    not have to deal with it here.
 *  - If lb == 0 then rounding down does not violate the constraint.
 *  - If ub == 0 then rounding up does not violate the constraint.
 */
static
SCIP_DECL_CONSLOCK(consLockSOS2)
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR** vars;
   int nvars;
   int j;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( cons != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );
   assert(locktype == SCIP_LOCKTYPE_MODEL);

   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );

   SCIPdebugMsg(scip, "Locking constraint <%s>.\n", SCIPconsGetName(cons));

   vars = consdata->vars;
   nvars = consdata->nvars;
   assert( vars != NULL );

   for (j = 0; j < nvars; ++j)
   {
      SCIP_VAR* var;
      var = vars[j];

      /* if lower bound is negative, rounding down may violate constraint */
      if ( SCIPisFeasNegative(scip, SCIPvarGetLbGlobal(var)) )
         SCIP_CALL( SCIPaddVarLocksType(scip, var, locktype, nlockspos, nlocksneg) );

      /* additionally: if upper bound is positive, rounding up may violate constraint */
      if ( SCIPisFeasPositive(scip, SCIPvarGetUbGlobal(var)) )
         SCIP_CALL( SCIPaddVarLocksType(scip, var, locktype, nlocksneg, nlockspos) );
   }

   return SCIP_OKAY;
}


/** constraint display method of constraint handler */
static
SCIP_DECL_CONSPRINT(consPrintSOS2)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;
   int j;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( cons != NULL );
   assert( strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0 );

   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );

   for (j = 0; j < consdata->nvars; ++j)
   {
      if ( j > 0 )
         SCIPinfoMessage(scip, file, ", ");
      SCIP_CALL( SCIPwriteVarName(scip, file, consdata->vars[j], FALSE) );
      if ( consdata->weights == NULL )
         SCIPinfoMessage(scip, file, " (%d)", j+1);
      else
         SCIPinfoMessage(scip, file, " (%3.2f)", consdata->weights[j]);
   }

   return SCIP_OKAY;
}


/** constraint copying method of constraint handler */
static
SCIP_DECL_CONSCOPY(consCopySOS2)
{  /*lint --e{715}*/
   SCIP_CONSDATA* sourceconsdata;
   SCIP_VAR** sourcevars;
   SCIP_VAR** targetvars;
   SCIP_Real* targetweights = NULL;
   const char* consname;
   int nvars;
   int v;

   assert( scip != NULL );
   assert( sourcescip != NULL );
   assert( sourcecons != NULL );
   assert( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(sourcecons)), CONSHDLR_NAME) == 0 );
   assert( valid != NULL );

   *valid = TRUE;

   if ( name != NULL )
      consname = name;
   else
      consname = SCIPconsGetName(sourcecons);

   SCIPdebugMsg(scip, "Copying SOS2 constraint <%s> ...\n", consname);

   sourceconsdata = SCIPconsGetData(sourcecons);
   assert( sourceconsdata != NULL );

   /* get variables and weights of the source constraint */
   nvars = sourceconsdata->nvars;
   assert( nvars >= 0 );

   /* duplicate weights array */
   if ( sourceconsdata->weights != NULL )
   {
      SCIP_CALL( SCIPduplicateBufferArray(sourcescip, &targetweights, sourceconsdata->weights, nvars) );
   }

   /* get copied variables in target SCIP */
   sourcevars = sourceconsdata->vars;
   SCIP_CALL( SCIPallocBufferArray(sourcescip, &targetvars, nvars) );
   for (v = 0; v < nvars && *valid; ++v)
   {
      assert( sourcevars != NULL );
      SCIP_CALL( SCIPgetVarCopy(sourcescip, scip, sourcevars[v], &(targetvars[v]), varmap, consmap, global, valid) );
   }

   /* only create the target constraint, if all variables could be copied */
   if( *valid )
   {
      SCIP_CALL( SCIPcreateConsSOS2(scip, cons, consname, nvars, targetvars, targetweights,
            initial, separate, enforce, check, propagate, local, dynamic, removable, stickingatnode) );
   }

   /* free buffer array */
   SCIPfreeBufferArray(sourcescip, &targetvars);
   SCIPfreeBufferArrayNull(sourcescip, &targetweights);

   return SCIP_OKAY;
}


/** constraint parsing method of constraint handler */
static
SCIP_DECL_CONSPARSE(consParseSOS2)
{  /*lint --e{715}*/
   SCIP_VAR* var;
   SCIP_Real weight;
   const char* s;
   char* t;

   *success = TRUE;
   s = str;

   /* create empty SOS2 constraint */
   SCIP_CALL( SCIPcreateConsSOS2(scip, cons, name, 0, NULL, NULL, initial, separate, enforce, check, propagate, local, dynamic, removable, stickingatnode) );

   /* loop through string */
   do
   {
      /* parse variable name */
      SCIP_CALL( SCIPparseVarName(scip, s, &var, &t) );
      s = t;

      /* skip until beginning of weight */
      while ( *s != '\0' && *s != '(' )
         ++s;

      if ( *s == '\0' )
      {
         SCIPverbMessage(scip, SCIP_VERBLEVEL_MINIMAL, NULL, "Syntax error: expected weight at input: %s\n", s);
         *success = FALSE;
         return SCIP_OKAY;
      }
      /* skip '(' */
      ++s;

      /* find weight */
      weight = strtod(s, &t);
      if ( t == NULL )
      {
         SCIPverbMessage(scip, SCIP_VERBLEVEL_MINIMAL, NULL, "Syntax error during parsing of the weight: %s\n", s);
         *success = FALSE;
         return SCIP_OKAY;
      }
      s = t;

      /* skip white space, ',', and ')' */
      while ( *s != '\0' && ( isspace((unsigned char)*s) ||  *s == ',' || *s == ')' ) )
         ++s;

      /* add variable */
      SCIP_CALL( SCIPaddVarSOS2(scip, *cons, var, weight) );
   }
   while ( *s != '\0' );

   return SCIP_OKAY;
}


/** constraint method of constraint handler which returns the variables (if possible) */
static
SCIP_DECL_CONSGETVARS(consGetVarsSOS2)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( varssize < consdata->nvars )
      (*success) = FALSE;
   else
   {
      assert(vars != NULL);

      BMScopyMemoryArray(vars, consdata->vars, consdata->nvars);
      (*success) = TRUE;
   }

   return SCIP_OKAY;
}


/** constraint method of constraint handler which returns the number of variables (if possible) */
static
SCIP_DECL_CONSGETNVARS(consGetNVarsSOS2)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   (*nvars) = consdata->nvars;
   (*success) = TRUE;

   return SCIP_OKAY;
}


/* ---------------- Callback methods of event handler ---------------- */

/* exec the event handler
 *
 * We update the number of variables fixed to be nonzero
 */
static
SCIP_DECL_EVENTEXEC(eventExecSOS2)
{
   SCIP_EVENTTYPE eventtype;
   SCIP_CONS* cons;
   SCIP_CONSDATA* consdata;
   SCIP_VAR* var;
   SCIP_Real oldbound, newbound;

   assert( eventhdlr != NULL );
   assert( eventdata != NULL );
   assert( strcmp(SCIPeventhdlrGetName(eventhdlr), EVENTHDLR_NAME) == 0 );
   assert( event != NULL );

   cons = (SCIP_CONS*)eventdata;
   assert( cons != NULL );
   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );
   assert( 0 <= consdata->nfixednonzeros && consdata->nfixednonzeros <= consdata->nvars );

   oldbound = SCIPeventGetOldbound(event);
   newbound = SCIPeventGetNewbound(event);

   eventtype = SCIPeventGetType(event);
   switch ( eventtype )
   {
   case SCIP_EVENTTYPE_LBTIGHTENED:
      /* if variable is now fixed to be nonzero */
      if ( ! SCIPisFeasPositive(scip, oldbound) && SCIPisFeasPositive(scip, newbound) )
         ++(consdata->nfixednonzeros);
      break;
   case SCIP_EVENTTYPE_UBTIGHTENED:
      /* if variable is now fixed to be nonzero */
      if ( ! SCIPisFeasNegative(scip, oldbound) && SCIPisFeasNegative(scip, newbound) )
         ++(consdata->nfixednonzeros);
      break;
   case SCIP_EVENTTYPE_LBRELAXED:
      /* if variable is not fixed to be nonzero anymore */
      if ( SCIPisFeasPositive(scip, oldbound) && ! SCIPisFeasPositive(scip, newbound) )
         --(consdata->nfixednonzeros);
      break;
   case SCIP_EVENTTYPE_UBRELAXED:
      /* if variable is not fixed to be nonzero anymore */
      if ( SCIPisFeasNegative(scip, oldbound) && ! SCIPisFeasNegative(scip, newbound) )
         --(consdata->nfixednonzeros);
      break;
   case SCIP_EVENTTYPE_GLBCHANGED:
      var = SCIPeventGetVar(event);
      assert(var != NULL);

      /* global lower bound is not negative anymore -> remove down lock */
      if ( SCIPisFeasNegative(scip, oldbound) && ! SCIPisFeasNegative(scip, newbound) )
         SCIP_CALL( SCIPunlockVarCons(scip, var, cons, TRUE, FALSE) );
      /* global lower bound turned negative -> add down lock */
      else if ( ! SCIPisFeasNegative(scip, oldbound) && SCIPisFeasNegative(scip, newbound) )
         SCIP_CALL( SCIPlockVarCons(scip, var, cons, TRUE, FALSE) );
      break;
   case SCIP_EVENTTYPE_GUBCHANGED:
      var = SCIPeventGetVar(event);
      assert(var != NULL);

      /* global upper bound is not positive anymore -> remove up lock */
      if ( SCIPisFeasPositive(scip, oldbound) && ! SCIPisFeasPositive(scip, newbound) )
         SCIP_CALL( SCIPunlockVarCons(scip, var, cons, FALSE, TRUE) );
      /* global upper bound turned positive -> add up lock */
      else if ( ! SCIPisFeasPositive(scip, oldbound) && SCIPisFeasPositive(scip, newbound) )
         SCIP_CALL( SCIPlockVarCons(scip, var, cons, FALSE, TRUE) );
      break;
   default:
      SCIPerrorMessage("invalid event type.\n");
      return SCIP_INVALIDDATA;
   }
   assert( 0 <= consdata->nfixednonzeros && consdata->nfixednonzeros <= consdata->nvars );

   SCIPdebugMsg(scip, "changed bound of variable <%s> from %f to %f (nfixednonzeros: %d).\n", SCIPvarGetName(SCIPeventGetVar(event)),
      oldbound, newbound, consdata->nfixednonzeros);

   return SCIP_OKAY;
}


/* ---------------- Constraint specific interface methods ---------------- */

/** creates the handler for SOS2 constraints and includes it in SCIP */
SCIP_RETCODE SCIPincludeConshdlrSOS2(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSHDLR* conshdlr;

   /* create constraint handler data */
   SCIP_CALL( SCIPallocBlockMemory(scip, &conshdlrdata) );

   conshdlrdata->eventhdlr = NULL;
   /* create event handler for bound change events */
   SCIP_CALL( SCIPincludeEventhdlrBasic(scip, &(conshdlrdata->eventhdlr), EVENTHDLR_NAME, EVENTHDLR_DESC,
         eventExecSOS2, NULL) );
   if ( conshdlrdata->eventhdlr == NULL )
   {
      SCIPerrorMessage("event handler for SOS2 constraints not found.\n");
      return SCIP_PLUGINNOTFOUND;
   }

   /* include constraint handler */
   SCIP_CALL( SCIPincludeConshdlrBasic(scip, &conshdlr, CONSHDLR_NAME, CONSHDLR_DESC,
         CONSHDLR_ENFOPRIORITY, CONSHDLR_CHECKPRIORITY, CONSHDLR_EAGERFREQ, CONSHDLR_NEEDSCONS,
         consEnfolpSOS2, consEnfopsSOS2, consCheckSOS2, consLockSOS2, conshdlrdata) );
   assert(conshdlr != NULL);

   /* set non-fundamental callbacks via specific setter functions */
   SCIP_CALL( SCIPsetConshdlrCopy(scip, conshdlr, conshdlrCopySOS2, consCopySOS2) );
   SCIP_CALL( SCIPsetConshdlrDelete(scip, conshdlr, consDeleteSOS2) );
   SCIP_CALL( SCIPsetConshdlrExitsol(scip, conshdlr, consExitsolSOS2) );
   SCIP_CALL( SCIPsetConshdlrFree(scip, conshdlr, consFreeSOS2) );
   SCIP_CALL( SCIPsetConshdlrGetVars(scip, conshdlr, consGetVarsSOS2) );
   SCIP_CALL( SCIPsetConshdlrGetNVars(scip, conshdlr, consGetNVarsSOS2) );
   SCIP_CALL( SCIPsetConshdlrInitlp(scip, conshdlr, consInitlpSOS2) );
   SCIP_CALL( SCIPsetConshdlrParse(scip, conshdlr, consParseSOS2) );
   SCIP_CALL( SCIPsetConshdlrPresol(scip, conshdlr, consPresolSOS2, CONSHDLR_MAXPREROUNDS, CONSHDLR_PRESOLTIMING) );
   SCIP_CALL( SCIPsetConshdlrPrint(scip, conshdlr, consPrintSOS2) );
   SCIP_CALL( SCIPsetConshdlrProp(scip, conshdlr, consPropSOS2, CONSHDLR_PROPFREQ, CONSHDLR_DELAYPROP, CONSHDLR_PROP_TIMING) );
   SCIP_CALL( SCIPsetConshdlrResprop(scip, conshdlr, consRespropSOS2) );
   SCIP_CALL( SCIPsetConshdlrSepa(scip, conshdlr, consSepalpSOS2, consSepasolSOS2, CONSHDLR_SEPAFREQ, CONSHDLR_SEPAPRIORITY, CONSHDLR_DELAYSEPA) );
   SCIP_CALL( SCIPsetConshdlrTrans(scip, conshdlr, consTransSOS2) );
   SCIP_CALL( SCIPsetConshdlrEnforelax(scip, conshdlr, consEnforelaxSOS2) );

   return SCIP_OKAY;
}


/** creates and captures a SOS2 constraint
 *
 *  We set the constraint to not be modifable. If the weights are non
 *  NULL, the variables are ordered according to these weights (in
 *  ascending order).
 *
 *  @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 */
SCIP_RETCODE SCIPcreateConsSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           cons,               /**< pointer to hold the created constraint */
   const char*           name,               /**< name of constraint */
   int                   nvars,              /**< number of variables in the constraint */
   SCIP_VAR**            vars,               /**< array with variables of constraint entries */
   SCIP_Real*            weights,            /**< weights determining the variable order, or NULL if natural order should be used */
   SCIP_Bool             initial,            /**< should the LP relaxation of constraint be in the initial LP?
                                              *   Usually set to TRUE. Set to FALSE for 'lazy constraints'. */
   SCIP_Bool             separate,           /**< should the constraint be separated during LP processing?
                                              *   Usually set to TRUE. */
   SCIP_Bool             enforce,            /**< should the constraint be enforced during node processing?
                                              *   TRUE for model constraints, FALSE for additional, redundant constraints. */
   SCIP_Bool             check,              /**< should the constraint be checked for feasibility?
                                              *   TRUE for model constraints, FALSE for additional, redundant constraints. */
   SCIP_Bool             propagate,          /**< should the constraint be propagated during node processing?
                                              *   Usually set to TRUE. */
   SCIP_Bool             local,              /**< is constraint only valid locally?
                                              *   Usually set to FALSE. Has to be set to TRUE, e.g., for branching constraints. */
   SCIP_Bool             dynamic,            /**< is constraint subject to aging?
                                              *   Usually set to FALSE. Set to TRUE for own cuts which
                                              *   are separated as constraints. */
   SCIP_Bool             removable,          /**< should the relaxation be removed from the LP due to aging or cleanup?
                                              *   Usually set to FALSE. Set to TRUE for 'lazy constraints' and 'user cuts'. */
   SCIP_Bool             stickingatnode      /**< should the constraint always be kept at the node where it was added, even
                                              *   if it may be moved to a more global node?
                                              *   Usually set to FALSE. Set to TRUE to for constraints that represent node data. */
   )
{
   SCIP_CONSHDLR* conshdlr;
   SCIP_CONSDATA* consdata;
   SCIP_Bool modifiable;

   modifiable = FALSE;

   /* find the SOS2 constraint handler */
   conshdlr = SCIPfindConshdlr(scip, CONSHDLR_NAME);
   if ( conshdlr == NULL )
   {
      SCIPerrorMessage("<%s> constraint handler not found\n", CONSHDLR_NAME);
      return SCIP_PLUGINNOTFOUND;
   }

   /* create constraint data */
   SCIP_CALL( SCIPallocBlockMemory(scip, &consdata) );
   consdata->vars = NULL;
   consdata->nvars = nvars;
   consdata->maxvars = nvars;
   consdata->row = NULL;
   consdata->nfixednonzeros = -1;
   consdata->weights = NULL;
   if ( nvars > 0 )
   {
      SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &consdata->vars, vars, nvars) );

      /* check weights */
      if ( weights != NULL )
      {
         /* store weights */
         SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &consdata->weights, weights, nvars) );

         /* sort variables - ascending order */
         SCIPsortRealPtr(consdata->weights, (void**)consdata->vars, nvars);
      }
   }
   else
      assert( weights == NULL );

   /* create constraint */
   SCIP_CALL( SCIPcreateCons(scip, cons, name, conshdlr, consdata, initial, separate, enforce, check, propagate,
         local, modifiable, dynamic, removable, stickingatnode) );

   return SCIP_OKAY;
}


/** creates and captures a SOS2 constraint with all constraint flags set to their default values.
 *
 *  @warning Do NOT set the constraint to be modifiable manually, because this might lead
 *  to wrong results as the variable array will not be resorted
 *
 *  @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 */
SCIP_RETCODE SCIPcreateConsBasicSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           cons,               /**< pointer to hold the created constraint */
   const char*           name,               /**< name of constraint */
   int                   nvars,              /**< number of variables in the constraint */
   SCIP_VAR**            vars,               /**< array with variables of constraint entries */
   SCIP_Real*            weights             /**< weights determining the variable order, or NULL if natural order should be used */
   )
{
   SCIP_CALL( SCIPcreateConsSOS2( scip, cons, name, nvars, vars, weights, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE) );

   return SCIP_OKAY;
}


/** adds variable to SOS2 constraint, the position is determined by the given weight */
SCIP_RETCODE SCIPaddVarSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var,                /**< variable to add to the constraint */
   SCIP_Real             weight              /**< weight determining position of variable */
   )
{
   assert( scip != NULL );
   assert( var != NULL );
   assert( cons != NULL );

   SCIPdebugMsg(scip, "adding variable <%s> to constraint <%s> with weight %g\n", SCIPvarGetName(var), SCIPconsGetName(cons), weight);

   if ( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not an SOS2 constraint.\n");
      return SCIP_INVALIDDATA;
   }

   SCIP_CALL( addVarSOS2(scip, cons, var, weight) );

   return SCIP_OKAY;
}


/** appends variable to SOS2 constraint */
SCIP_RETCODE SCIPappendVarSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_VAR*             var                 /**< variable to add to the constraint */
   )
{
   assert( scip != NULL );
   assert( var != NULL );
   assert( cons != NULL );

   SCIPdebugMsg(scip, "appending variable <%s> to constraint <%s>\n", SCIPvarGetName(var), SCIPconsGetName(cons));

   if ( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not an SOS2 constraint.\n");
      return SCIP_INVALIDDATA;
   }

   SCIP_CALL( appendVarSOS2(scip, cons, var) );

   return SCIP_OKAY;
}


/** gets number of variables in SOS2 constraint */
int SCIPgetNVarsSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint */
   )
{
   SCIP_CONSDATA* consdata;

   assert( scip != NULL );
   assert( cons != NULL );

   if ( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not an SOS2 constraint.\n");
      SCIPABORT();
      return -1;  /*lint !e527*/
   }

   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );

   return consdata->nvars;
}


/** gets array of variables in SOS2 constraint */
SCIP_VAR** SCIPgetVarsSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint data */
   )
{
   SCIP_CONSDATA* consdata;

   assert( scip != NULL );
   assert( cons != NULL );

   if ( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not an SOS2 constraint.\n");
      SCIPABORT();
      return NULL;  /*lint !e527*/
   }

   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );

   return consdata->vars;
}


/** gets array of weights in SOS2 constraint (or NULL if not existent) */
SCIP_Real* SCIPgetWeightsSOS2(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint data */
   )
{
   SCIP_CONSDATA* consdata;

   assert( scip != NULL );
   assert( cons != NULL );

   if ( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not an SOS2 constraint.\n");
      SCIPABORT();
      return NULL;  /*lint !e527*/
   }

   consdata = SCIPconsGetData(cons);
   assert( consdata != NULL );

   return consdata->weights;
}