cons_indicator.c

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the program and library             */
/*         SCIP --- Solving Constraint Integer Programs                      */
/*                                                                           */
/*    Copyright (C) 2002-2019 Konrad-Zuse-Zentrum                            */
/*                            fuer Informationstechnik Berlin                */
/*                                                                           */
/*  SCIP is distributed under the terms of the ZIB Academic License.         */
/*                                                                           */
/*  You should have received a copy of the ZIB Academic License              */
/*  along with SCIP; see the file COPYING. If not visit scip.zib.de.         */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/**@file   cons_indicator.c
 * @brief  constraint handler for indicator constraints
 * @author Marc Pfetsch
 *
 * An indicator constraint is given by a binary variable \f$y\f$ and an inequality \f$ax \leq
 * b\f$. It states that if \f$y = 1\f$ then \f$ax \leq b\f$ holds.
 *
 * This constraint is handled by adding a slack variable \f$s:\; ax - s \leq b\f$ with \f$s \geq
 * 0\f$. The constraint is enforced by fixing \f$s\f$ to 0 if \f$y = 1\f$.
 *
 * @note The constraint only implements an implication not an equivalence, i.e., it does not ensure
 * that \f$y = 1\f$ if \f$ax \leq b\f$ or equivalently if \f$s = 0\f$ holds.
 *
 * This constraint is equivalent to a linear constraint \f$ax - s \leq b\f$ and an SOS1 constraint on
 * \f$y\f$ and \f$s\f$ (at most one should be nonzero). In the indicator context we can, however,
 * separate more inequalities.
 *
 * The name indicator apparently comes from CPLEX.
 *
 *
 * @section SEPARATION Separation Methods
 *
 * We now explain the handling of indicator constraints in more detail.  The indicator constraint
 * handler adds an inequality for each indicator constraint. We assume that this system (with added
 * slack variables) is \f$ Ax - s \leq b \f$, where \f$ x \f$ are the original variables and \f$ s
 * \f$ are the slack variables added by the indicator constraint. Variables \f$ y \f$ are the binary
 * variables corresponding to the indicator constraints.
 *
 * @note In the implementation, we assume that bounds on the original variables \f$x\f$ cannot be
 * influenced by the indicator constraint. If it should be possible to relax these constraints as
 * well, then these constraints have to be added as indicator constraints.
 *
 * We separate inequalities by using the so-called alternative polyhedron.
 *
 *
 * @section ALTERNATIVEPOLYHEDRON Separation via the Alternative Polyhedron
 *
 * We now describe the separation method of the first method in more detail.
 *
 * Consider the LP-relaxation of the current subproblem:
 * \f[
 * \begin{array}{ll}
 *  min & c^T x + d^T z\\
 *      & A x - s \leq b, \\
 *      & D x + C z \leq f, \\
 *      & l \leq x \leq u, \\
 *      & u \leq z \leq v, \\
 *      & 0 \leq s.
 * \end{array}
 * \f]
 * As above \f$Ax - s \leq b\f$ contains all inequalities corresponding to indicator constraints,
 * while the system \f$Dx + Cy \leq f\f$ contains all other inequalities (which are ignored in the
 * following). Similarly, variables \f$z\f$ not appearing in indicator constraints are
 * ignored. Bounds for the variables \f$x_j\f$ can be given, in particular, variables can be
 * fixed. Note that \f$s \leq 0\f$ renders the system infeasible.
 *
 * To generate cuts, we construct the so-called @a alternative @a polyhedron:
 * \f[
 * \begin{array}{ll}
 *      P = \{ (w,r,t) : & A^T w - r + t = 0,\\
 *                       & b^T w - l^T r + u^T t = -1,\\
 *                       & w, r, t \geq 0 \}.
 * \end{array}
 * \f]
 * Here, \f$r\f$ and \f$t\f$ correspond to the lower and upper bounds on \f$x\f$, respectively.
 *
 * It turns out that the vertices of \f$P\f$ correspond to minimal infeasible subsystems of \f$A x
 * \leq b\f$, \f$l \leq x \leq u\f$. If \f$I\f$ is the index set of such a system, it follows that not all \f$s_i\f$ for
 * \f$i \in I\f$ can be 0, i.e., \f$y_i\f$ can be 1. In other words, the following cut is valid:
 * \f[
 *      \sum_{i \in I} y_i \leq |I| - 1.
 * \f]
 *
 *
 * @subsection DETAIL Separation heuristic
 *
 * We separate the above inequalities by a heuristic described in
 *
 *   Branch-And-Cut for the Maximum Feasible Subsystem Problem,@n
 *   Marc Pfetsch, SIAM Journal on Optimization 19, No.1, 21-38 (2008)
 *
 * The first step in the separation heuristic is to apply the transformation \f$\bar{y} = 1 - y\f$, which
 * transforms the above inequality into the constraint
 * \f[
 *      \sum_{i \in I} \bar{y}_i \geq 1,
 * \f]
 * that is, it is a set covering constraint on the negated variables.
 *
 * The basic idea is to use the current solution to the LP relaxation and use it as the objective,
 * when optimizing of the alternative polyhedron. Since any vertex corresponds to such an
 * inequality, we can check whether it is violated. To enlarge the chance that we find a @em
 * violated inequality, we perform a fixing procedure, in which the variable corresponding to an
 * arbitrary element of the last IIS \f$I\f$ is fixed to zero, i.e., cannot be used in the next
 * IISs. This is repeated until the corresponding alternative polyhedron is infeasible, i.e., we
 * have obtained an IIS-cover. For more details see the paper above.
 *
 *
 * @subsection PREPROC Preprocessing
 *
 * Since each indicator constraint adds a linear constraint to the formulation, preprocessing of the
 * linear constraints change the above approach as follows.
 *
 * The system as present in the formulation is the following (ignoring variables that are not
 * contained in indicator constraints and the objective function):
 * \f[
 *    \begin{array}{ll}
 *      & A x - s \leq b, \\
 *      & l \leq x \leq u, \\
 *      & s \leq 0.
 *    \end{array}
 * \f]
 * Note again that the requirement \f$s \leq 0\f$ leads to an infeasible system. Consider now the
 * preprocessing of the linear constraint (aggregation, bound strengthening, etc.) and assume that
 * this changes the above system to the following:
 * \f[
 *    \begin{array}{ll}
 *      & \tilde{A} x - \tilde{B} s \leq \tilde{b}, \\
 *      & \tilde{l} \leq x \leq \tilde{u}, \\
 *      & s \leq 0. \\
 *    \end{array}
 * \f]
 * Note that we forbid multi-aggregation of the \f$s\f$ variables in order to be able to change their
 * bounds in propagation/branching. The corresponding alternative system is the following:
 * \f[
 *    \begin{array}{ll}
 *      & \tilde{A}^T w - r + t = 0,\\
 *      & - \tilde{B}^T w + v = 0,\\
 *      & b^T w - l^T r + u^T t = -1,\\
 *      & w, v, r, t \geq 0
 *    \end{array}
 *    \qquad \Leftrightarrow \qquad
 *    \begin{array}{ll}
 *      & \tilde{A}^T w - r + t = 0,\\
 *      & \tilde{B}^T w \geq 0,\\
 *      & b^T w - l^T r + u^T t = -1,\\
 *      & w, r, t \geq 0,
 *    \end{array}
 * \f]
 * where the second form arises by substituting \f$v \geq 0\f$. A closer look at this system reveals
 * that it is not larger than the original one:
 *
 * - (Multi-)Aggregation of variables \f$x\f$ will remove these variables from the formulation, such that
 *   the corresponding column of \f$\tilde{A}\f$ (row of \f$\tilde{A}^T\f$) will be zero.
 *
 * - The rows of \f$\tilde{B}^T\f$ are not unit vectors, i.e., do not correspond to redundant
 *   nonnegativity constraints, only if the corresponding slack variables appear in an aggregation.
 *
 * Taken together, these two observations yield the conclusion that the new system is roughly as
 * large as the original one.
 *
 * @note Because of possible (multi-)aggregation it might happen that the linear constraint
 * corresponding to an indicator constraint becomes redundant and is deleted. From this we cannot
 * conclude that the indicator constraint is redundant as well (i.e. always fulfilled), because the
 * corresponding slack variable is still present and its setting to 0 might influence other
 * (linear) constraints. Thus, we have to rely on the dual presolving of the linear constraints to
 * detect this case: If the linear constraint is really redundant, i.e., is always fulfilled, it is
 * deleted and the slack variable can be fixed to 0. In this case, the indicator constraint can be
 * deleted as well.
 *
 * @todo Accept arbitrary ranged linear constraints as input (in particular: equations). Internally
 * create two indicator constraints or correct alternative polyhedron accordingly (need to split the
 * variables there, but not in original problem).
 *
 * @todo Treat variable upper bounds in a special way: Do not create the artificial slack variable,
 * but directly enforce the propagations etc.
 *
 * @todo Turn off separation if the alternative polyhedron is infeasible and updateBounds is false.
 *
 * @todo Improve parsing of indicator constraint in CIP-format. Currently, we have to rely on a particular name, i.e.,
 * the slack variable has to start with "indslack" and end with the name of the corresponding linear constraint.
 *
 * @todo Check whether one can further use the fact that the slack variable is aggregated.
 */

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

#include "blockmemshell/memory.h"
#include "lpi/lpi.h"
#include "lpi/type_lpi.h"
#include "nlpi/type_expr.h"
#include "scip/cons_indicator.h"
#include "scip/cons_linear.h"
#include "scip/cons_logicor.h"
#include "scip/cons_quadratic.h"
#include "scip/cons_varbound.h"
#include "scip/heur_indicator.h"
#include "scip/heur_trysol.h"
#include "scip/pub_conflict.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_paramset.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_heur.h"
#include "scip/scip_lp.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_nlp.h"
#include "scip/scip_numerics.h"
#include "scip/scip_param.h"
#include "scip/scip_prob.h"
#include "scip/scip_probing.h"
#include "scip/scip_sol.h"
#include "scip/scip_solve.h"
#include "scip/scip_solvingstats.h"
#include "scip/scip_tree.h"
#include "scip/scip_var.h"
#include <string.h>

/* #define SCIP_OUTPUT */
/* #define SCIP_ENABLE_IISCHECK */

/* constraint handler properties */
#define CONSHDLR_NAME          "indicator"
#define CONSHDLR_DESC          "indicator 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 -6000000 /**< priority of the constraint handler for checking feasibility */
#define CONSHDLR_SEPAFREQ            10 /**< 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_PRESOLTIMING      SCIP_PRESOLTIMING_FAST
#define CONSHDLR_PROP_TIMING       SCIP_PROPTIMING_BEFORELP


/* event handler properties */
#define EVENTHDLR_BOUND_NAME       "indicatorbound"
#define EVENTHDLR_BOUND_DESC       "bound change event handler for indicator constraints"

#define EVENTHDLR_RESTART_NAME     "indicatorrestart"
#define EVENTHDLR_RESTART_DESC     "force restart if absolute gap is 1 or enough binary variables have been fixed"


/* conflict handler properties */
#define CONFLICTHDLR_NAME          "indicatorconflict"
#define CONFLICTHDLR_DESC          "replace slack variables and generate logicor constraints"
#define CONFLICTHDLR_PRIORITY      200000

/* upgrade properties */
#define LINCONSUPGD_PRIORITY      +100000    /**< priority of the constraint handler for upgrading of linear constraints */

/* default values for parameters */
#define DEFAULT_BRANCHINDICATORS    FALSE    /**< Branch on indicator constraints in enforcing? */
#define DEFAULT_GENLOGICOR          FALSE    /**< Generate logicor constraints instead of cuts? */
#define DEFAULT_ADDCOUPLING          TRUE    /**< Add coupling constraints or rows if big-M is small enough? */
#define DEFAULT_MAXCOUPLINGVALUE      1e4    /**< maximum coefficient for binary variable in coupling constraint */
#define DEFAULT_ADDCOUPLINGCONS     FALSE    /**< Add initial variable upper bound constraints, if 'addcoupling' is true? */
#define DEFAULT_SEPACOUPLINGCUTS     TRUE    /**< Should the coupling inequalities be separated dynamically? */
#define DEFAULT_SEPACOUPLINGLOCAL   FALSE    /**< Allow to use local bounds in order to separate coupling inequalities? */
#define DEFAULT_SEPACOUPLINGVALUE     1e4    /**< maximum coefficient for binary variable in separated coupling constraint */
#define DEFAULT_SEPAALTERNATIVELP   FALSE    /**< Separate using the alternative LP? */
#define DEFAULT_SEPAPERSPECTIVE     FALSE    /**< Separate cuts based on perspective formulation? */
#define DEFAULT_SEPAPERSPLOCAL       TRUE    /**< Allow to use local bounds in order to separate perspectice cuts? */
#define DEFAULT_MAXSEPANONVIOLATED      3    /**< maximal number of separated non violated IISs, before separation is stopped */
#define DEFAULT_TRYSOLFROMCOVER     FALSE    /**< Try to construct a feasible solution from a cover? */
#define DEFAULT_UPGRADELINEAR       FALSE    /**< Try to upgrade linear constraints to indicator constraints? */
#define DEFAULT_USEOTHERCONSS       FALSE    /**< Collect other constraints to alternative LP? */
#define DEFAULT_USEOBJECTIVECUT     FALSE    /**< Use objective cut with current best solution to alternative LP? */
#define DEFAULT_UPDATEBOUNDS        FALSE    /**< Update bounds of original variables for separation? */
#define DEFAULT_MAXCONDITIONALTLP     0.0    /**< max. estimated condition of the solution basis matrix of the alt. LP to be trustworthy (0.0 to disable check) */
#define DEFAULT_MAXSEPACUTS           100    /**< maximal number of cuts separated per separation round */
#define DEFAULT_MAXSEPACUTSROOT      2000    /**< maximal number of cuts separated per separation round in the root node */
#define DEFAULT_REMOVEINDICATORS    FALSE    /**< Remove indicator constraint if corresponding variable bound constraint has been added? */
#define DEFAULT_GENERATEBILINEAR    FALSE    /**< Do not generate indicator constraint, but a bilinear constraint instead? */
#define DEFAULT_SCALESLACKVAR       FALSE    /**< Scale slack variable coefficient at construction time? */
#define DEFAULT_NOLINCONSCONT       FALSE    /**< Decompose problem (do not generate linear constraint if all variables are continuous)? */
#define DEFAULT_TRYSOLUTIONS         TRUE    /**< Try to make solutions feasible by setting indicator variables? */
#define DEFAULT_ENFORCECUTS         FALSE    /**< In enforcing try to generate cuts (only if sepaalternativelp is true)? */
#define DEFAULT_DUALREDUCTIONS       TRUE    /**< Should dual reduction steps be performed? */
#define DEFAULT_ADDOPPOSITE         FALSE    /**< Add opposite inequality in nodes in which the binary variable has been fixed to 0? */
#define DEFAULT_CONFLICTSUPGRADE    FALSE    /**< Try to upgrade bounddisjunction conflicts by replacing slack variables? */
#define DEFAULT_FORCERESTART        FALSE    /**< Force restart if absolute gap is 1 or enough binary variables have been fixed? */
#define DEFAULT_RESTARTFRAC           0.9    /**< fraction of binary variables that need to be fixed before restart occurs (in forcerestart) */


/* other values */
#define OBJEPSILON                  0.001    /**< value to add to objective in alt. LP if the binary variable is 1 to get small IISs */
#define SEPAALTTHRESHOLD               10    /**< only separate IIS cuts if the number of separated coupling cuts is less than this value */
#define MAXROUNDINGROUNDS               1    /**< maximal number of rounds that produced cuts in separation */


/** constraint data for indicator constraints */
struct SCIP_ConsData
{
   SCIP_VAR*             binvar;             /**< binary variable for indicator constraint */
   SCIP_VAR*             slackvar;           /**< slack variable of inequality of indicator constraint */
   SCIP_CONS*            lincons;            /**< linear constraint corresponding to indicator constraint */
   int                   nfixednonzero;      /**< number of variables among binvar and slackvar fixed to be nonzero */
   int                   colindex;           /**< column index in alternative LP */
   unsigned int          linconsactive:1;    /**< whether linear constraint and slack variable are active */
   unsigned int          implicationadded:1; /**< whether corresponding implication has been added */
   unsigned int          slacktypechecked:1; /**< whether it has been checked to convert the slack variable to be implicit integer */
};


/** indicator constraint handler data */
struct SCIP_ConshdlrData
{
   SCIP_EVENTHDLR*       eventhdlrbound;     /**< event handler for bound change events */
   SCIP_EVENTHDLR*       eventhdlrrestart;   /**< event handler for performing restarts */
   SCIP_Bool             removable;          /**< whether the separated cuts should be removable */
   SCIP_Bool             scaled;             /**< if first row of alt. LP has been scaled */
   SCIP_Bool             objindicatoronly;   /**< whether the objective is nonzero only for indicator variables */
   SCIP_Bool             objothervarsonly;   /**< whether the objective is nonzero only for non-indicator variables */
   SCIP_Real             minabsobj;          /**< minimum absolute nonzero objective of indicator variables */
   SCIP_LPI*             altlp;              /**< alternative LP for cut separation */
   int                   nrows;              /**< # rows in the alt. LP corr. to original variables in linear constraints and slacks */
   int                   nlbbounds;          /**< # lower bounds of original variables */
   int                   nubbounds;          /**< # upper bounds of original variables */
   SCIP_HASHMAP*         varhash;            /**< hash map from variable to row index in alternative LP */
   SCIP_HASHMAP*         lbhash;             /**< hash map from variable to index of lower bound column in alternative LP */
   SCIP_HASHMAP*         ubhash;             /**< hash map from variable to index of upper bound column in alternative LP */
   SCIP_HASHMAP*         slackhash;          /**< hash map from slack variable to row index in alternative LP */
   SCIP_HASHMAP*         binvarhash;         /**< hash map from binary indicator variable to indicator constraint */
   int                   nslackvars;         /**< # slack variables */
   int                   niiscutsgen;        /**< number of IIS-cuts generated */
   int                   nperspcutsgen;      /**< number of cuts based on perspective formulation generated */
   int                   objcutindex;        /**< index of objective cut in alternative LP (-1 if not added) */
   SCIP_Real             objupperbound;      /**< best upper bound on objective known */
   SCIP_Real             objaltlpbound;      /**< upper objective bound stored in alternative LP (infinity if not added) */
   int                   maxroundingrounds;  /**< maximal number of rounds that produced cuts in separation */
   SCIP_Real             roundingminthres;   /**< minimal value for rounding in separation */
   SCIP_Real             roundingmaxthres;   /**< maximal value for rounding in separation */
   SCIP_Real             roundingoffset;     /**< offset for rounding in separation */
   SCIP_Bool             branchindicators;   /**< Branch on indicator constraints in enforcing? */
   SCIP_Bool             genlogicor;         /**< Generate logicor constraints instead of cuts? */
   SCIP_Bool             addcoupling;        /**< whether the coupling inequalities should be added at the beginning */
   SCIP_Bool             addcouplingcons;    /**< Add initial variable upper bound constraints, if 'addcoupling' is true? */
   SCIP_Bool             sepacouplingcuts;   /**< Should the coupling inequalities be separated dynamically? */
   SCIP_Bool             sepacouplinglocal;  /**< Allow to use local bounds in order to separate coupling inequalities? */
   SCIP_Bool             sepaperspective;    /**< Separate cuts based on perspective formulation? */
   SCIP_Bool             sepapersplocal;     /**< Allow to use local bounds in order to separate perspectice cuts? */
   SCIP_Bool             removeindicators;   /**< Remove indicator constraint if corresponding variable bound constraint has been added? */
   SCIP_Bool             updatebounds;       /**< whether the bounds of the original variables should be changed for separation */
   SCIP_Bool             trysolutions;       /**< Try to make solutions feasible by setting indicator variables? */
   SCIP_Bool             enforcecuts;        /**< in enforcing try to generate cuts (only if sepaalternativelp is true) */
   SCIP_Bool             dualreductions;     /**< Should dual reduction steps be performed? */
   SCIP_Bool             addopposite;        /**< Add opposite inequality in nodes in which the binary variable has been fixed to 0? */
   SCIP_Bool             generatebilinear;   /**< Do not generate indicator constraint, but a bilinear constraint instead? */
   SCIP_Bool             scaleslackvar;      /**< Scale slack variable coefficient at construction time? */
   SCIP_Bool             conflictsupgrade;   /**< Try to upgrade bounddisjunction conflicts by replacing slack variables? */
   SCIP_Bool             performedrestart;   /**< whether a restart has been performed already */
   int                   maxsepacuts;        /**< maximal number of cuts separated per separation round */
   int                   maxsepacutsroot;    /**< maximal number of cuts separated per separation round in root node */
   int                   maxsepanonviolated; /**< maximal number of separated non violated IISs, before separation is stopped */
   int                   nbinvarszero;       /**< binary variables globally fixed to zero */
   int                   ninitconss;         /**< initial number of indicator constraints (needed in event handlers) */
   SCIP_Real             maxcouplingvalue;   /**< maximum coefficient for binary variable in initial coupling constraint */
   SCIP_Real             sepacouplingvalue;  /**< maximum coefficient for binary variable in separated coupling constraint */
   SCIP_Real             maxconditionaltlp;  /**< maximum estimated condition number of the alternative LP to trust its solution */
   SCIP_Real             restartfrac;        /**< fraction of binary variables that need to be fixed before restart occurs (in forcerestart) */
   SCIP_HEUR*            heurtrysol;         /**< trysol heuristic */
   SCIP_Bool             addedcouplingcons;  /**< whether the coupling constraints have been added already */
   SCIP_CONS**           addlincons;         /**< additional linear constraints that should be added to the alternative LP */
   int                   naddlincons;        /**< number of additional constraints */
   int                   maxaddlincons;      /**< maximal number of additional constraints */
   SCIP_Bool             useotherconss;      /**< Collect other constraints to alternative LP? */
   SCIP_Bool             useobjectivecut;    /**< Use objective cut with current best solution to alternative LP? */
   SCIP_Bool             trysolfromcover;    /**< Try to construct a feasible solution from a cover? */
   SCIP_Bool             upgradelinear;      /**< Try to upgrade linear constraints to indicator constraints? */
   char                  normtype;           /**< norm type for cut computation */
   /* parameters that should not be changed after problem stage: */
   SCIP_Bool             sepaalternativelp;  /**< Separate using the alternative LP? */
   SCIP_Bool             sepaalternativelp_; /**< used to store the sepaalternativelp parameter */
   SCIP_Bool             nolinconscont;      /**< decompose problem - do not generate linear constraint if all variables are continuous */
   SCIP_Bool             nolinconscont_;     /**< used to store the nolinconscont parameter */
   SCIP_Bool             forcerestart;       /**< Force restart if absolute gap is 1 or enough binary variables have been fixed? */
   SCIP_Bool             forcerestart_;      /**< used to store the forcerestart parameter */
};


/** indicator conflict handler data */
struct SCIP_ConflicthdlrData
{
   SCIP_CONSHDLR*        conshdlr;           /**< indicator constraint handler */
   SCIP_CONSHDLRDATA*    conshdlrdata;       /**< indicator constraint handler data */
};


/* macro for parameters */
#define SCIP_CALL_PARAM(x) /*lint -e527 */ do                                                   \
{                                                                                               \
   SCIP_RETCODE _restat_;                                                                       \
   if ( (_restat_ = (x)) != SCIP_OKAY && (_restat_ != SCIP_PARAMETERUNKNOWN) )                  \
   {                                                                                            \
      SCIPerrorMessage("[%s:%d] Error <%d> in function call\n", __FILE__, __LINE__, _restat_);  \
      SCIPABORT();                                                                              \
      return _restat_;                                                                          \
   }                                                                                            \
}                                                                                               \
while ( FALSE )


/* ---------------- Callback methods of event handlers ---------------- */

/** exec the event handler for getting variable bound changes
 *
 *  We update the number of variables fixed to be nonzero.
 */
static
SCIP_DECL_EVENTEXEC(eventExecIndicatorBound)
{
   SCIP_EVENTTYPE eventtype;
   SCIP_CONSDATA* consdata;
   SCIP_Real oldbound;
   SCIP_Real newbound;

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

   consdata = (SCIP_CONSDATA*)eventdata;
   assert( consdata != NULL );
   assert( 0 <= consdata->nfixednonzero && consdata->nfixednonzero <= 2 );
   assert( consdata->linconsactive );

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

   eventtype = SCIPeventGetType(event);
   switch ( eventtype )
   {
   case SCIP_EVENTTYPE_LBTIGHTENED:
      /* if variable is now fixed to be positive */
      if ( ! SCIPisFeasPositive(scip, oldbound) && SCIPisFeasPositive(scip, newbound) )
         ++(consdata->nfixednonzero);
#ifdef SCIP_MORE_DEBUG
      SCIPdebugMsg(scip, "Changed lower bound of variable <%s> from %g to %g (nfixednonzero: %d).\n",
         SCIPvarGetName(SCIPeventGetVar(event)), oldbound, newbound, consdata->nfixednonzero);
#endif
      break;

   case SCIP_EVENTTYPE_UBTIGHTENED:
      /* if variable is now fixed to be negative */
      if ( ! SCIPisFeasNegative(scip, oldbound) && SCIPisFeasNegative(scip, newbound) )
         ++(consdata->nfixednonzero);
#ifdef SCIP_MORE_DEBUG
      SCIPdebugMsg(scip, "Changed upper bound of variable <%s> from %g to %g (nfixednonzero: %d).\n",
         SCIPvarGetName(SCIPeventGetVar(event)), oldbound, newbound, consdata->nfixednonzero);
#endif
      break;

   case SCIP_EVENTTYPE_LBRELAXED:
      /* if variable is not fixed to be positive anymore */
      if ( SCIPisFeasPositive(scip, oldbound) && ! SCIPisFeasPositive(scip, newbound) )
         --(consdata->nfixednonzero);
#ifdef SCIP_MORE_DEBUG
      SCIPdebugMsg(scip, "Changed lower bound of variable <%s> from %g to %g (nfixednonzero: %d).\n",
         SCIPvarGetName(SCIPeventGetVar(event)), oldbound, newbound, consdata->nfixednonzero);
#endif
      break;

   case SCIP_EVENTTYPE_UBRELAXED:
      /* if variable is not fixed to be negative anymore */
      if ( SCIPisFeasNegative(scip, oldbound) && ! SCIPisFeasNegative(scip, newbound) )
         --(consdata->nfixednonzero);
#ifdef SCIP_MORE_DEBUG
      SCIPdebugMsg(scip, "Changed upper bound of variable <%s> from %g to %g (nfixednonzero: %d).\n",
         SCIPvarGetName(SCIPeventGetVar(event)), oldbound, newbound, consdata->nfixednonzero);
#endif
      break;

   default:
      SCIPerrorMessage("Invalid event type.\n");
      SCIPABORT();
      return SCIP_INVALIDDATA; /*lint !e527*/
   }
   assert( 0 <= consdata->nfixednonzero && consdata->nfixednonzero <= 2 );

   return SCIP_OKAY;
}


/** exec the event handler for forcing a restart
 *
 *  There are two cases in which we perform a (user) restart:
 *  - If we have a max FS instance, i.e., the objective is 1 for indicator variables and 0 otherwise,
 *    we can force a restart if the gap is 1. In this case, the remaining work consists of proving
 *    infeasibility of the non-fixed indicators.
 *  - If a large fraction of the binary indicator variables have been globally fixed, it makes sense
 *    to force a restart.
 */
static
SCIP_DECL_EVENTEXEC(eventExecIndicatorRestart)
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_EVENTTYPE eventtype;

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

   conshdlrdata = (SCIP_CONSHDLRDATA*)eventdata;
   assert( conshdlrdata != NULL );
   assert( conshdlrdata->forcerestart );

   eventtype = SCIPeventGetType(event);
   switch ( eventtype )
   {
   case SCIP_EVENTTYPE_GUBCHANGED:
   case SCIP_EVENTTYPE_GLBCHANGED:
   {
#ifndef NDEBUG
      SCIP_Real oldbound;
      SCIP_Real newbound;

      assert( SCIPvarGetType(SCIPeventGetVar(event)) == SCIP_VARTYPE_BINARY );
      oldbound = SCIPeventGetOldbound(event);
      newbound = SCIPeventGetNewbound(event);
      assert( SCIPisIntegral(scip, oldbound) );
      assert( SCIPisIntegral(scip, newbound) );
      assert( ! SCIPisEQ(scip, oldbound, newbound) );
      assert( SCIPisZero(scip, oldbound) || SCIPisEQ(scip, oldbound, 1.0) );
      assert( SCIPisZero(scip, newbound) || SCIPisEQ(scip, newbound, 1.0) );
#endif

      /* do not treat this case if we have performed a restart already */
      if ( conshdlrdata->performedrestart )
         return SCIP_OKAY;

      /* variable is now fixed */
      ++(conshdlrdata->nbinvarszero);
      SCIPdebugMsg(scip, "Fixed variable <%s> (nbinvarszero: %d, total: %d).\n",
         SCIPvarGetName(SCIPeventGetVar(event)), conshdlrdata->nbinvarszero, conshdlrdata->ninitconss);

      if ( SCIPgetStage(scip) != SCIP_STAGE_SOLVING )
         break;

      /* if enough variables have been fixed */
      if ( conshdlrdata->nbinvarszero > (int) ((SCIP_Real) conshdlrdata->ninitconss * conshdlrdata->restartfrac) )
      {
         SCIPverbMessage(scip, SCIP_VERBLEVEL_NORMAL, NULL,
            "Forcing restart, since %d binary variables among %d have been fixed.\n", conshdlrdata->nbinvarszero, conshdlrdata->ninitconss);
         SCIP_CALL( SCIPrestartSolve(scip) );

         /* drop event */
         if ( conshdlrdata->objindicatoronly )
         {
            SCIP_CALL( SCIPdropEvent(scip, SCIP_EVENTTYPE_BESTSOLFOUND, eventhdlr, (SCIP_EVENTDATA*) conshdlrdata, -1) );
         }
         conshdlrdata->performedrestart = TRUE;
      }
      break;
   }

   case SCIP_EVENTTYPE_BESTSOLFOUND:
      assert( SCIPisIntegral(scip, conshdlrdata->minabsobj) );
      assert( SCIPisGE(scip, conshdlrdata->minabsobj, 1.0 ) );

      if ( SCIPgetStage(scip) != SCIP_STAGE_SOLVING )
         break;

      if ( ! conshdlrdata->objindicatoronly )
         break;

      /* if the absolute gap is equal to minabsobj */
      if ( SCIPisEQ(scip, REALABS(SCIPgetPrimalbound(scip) - SCIPgetDualbound(scip)), conshdlrdata->minabsobj) )
      {
         SCIPverbMessage(scip, SCIP_VERBLEVEL_NORMAL, NULL, "Forcing restart, since the absolute gap is %f.\n", conshdlrdata->minabsobj);
         SCIP_CALL( SCIPrestartSolve(scip) );

         /* use inference branching, since the objective is not meaningful */
         if ( SCIPfindBranchrule(scip, "inference") != NULL && !SCIPisParamFixed(scip, "branching/inference/priority") )
         {
            SCIP_CALL( SCIPsetIntParam(scip, "branching/inference/priority", INT_MAX/4) );
         }

         /* drop event */
         SCIP_CALL( SCIPdropEvent(scip, SCIP_EVENTTYPE_BESTSOLFOUND, eventhdlr, (SCIP_EVENTDATA*) conshdlrdata, -1) );
         conshdlrdata->performedrestart = TRUE;
      }
      break;

   default:
      SCIPerrorMessage("invalid event type.\n");
      SCIPABORT();
      return SCIP_INVALIDDATA; /*lint !e527*/
   }

   return SCIP_OKAY;
}


/* ------------------------ conflict handler ---------------------------------*/

/** destructor of conflict handler to free conflict handler data (called when SCIP is exiting) */
static
SCIP_DECL_CONFLICTFREE(conflictFreeIndicator)
{
   SCIP_CONFLICTHDLRDATA* conflicthdlrdata;

   assert( scip != NULL );
   assert( conflicthdlr != NULL );
   assert( strcmp(SCIPconflicthdlrGetName(conflicthdlr), CONFLICTHDLR_NAME) == 0 );

   conflicthdlrdata = SCIPconflicthdlrGetData(conflicthdlr);
   SCIPfreeBlockMemory(scip, &conflicthdlrdata);

   return SCIP_OKAY;
}


/** conflict processing method of conflict handler (called when conflict was found)
 *
 *  In this conflict handler we try to replace slack variables by binary indicator variables and
 *  generate a logicor constraint if possible.
 *
 *  @todo Extend to integral case.
 */
static
SCIP_DECL_CONFLICTEXEC(conflictExecIndicator)
{  /*lint --e{715}*/
   SCIP_CONFLICTHDLRDATA* conflicthdlrdata;
   SCIP_Bool haveslack;
   SCIP_VAR* var;
   int i;

   assert( conflicthdlr != NULL );
   assert( strcmp(SCIPconflicthdlrGetName(conflicthdlr), CONFLICTHDLR_NAME) == 0 );
   assert( bdchginfos != NULL || nbdchginfos == 0 );
   assert( result != NULL );

   /* don't process already resolved conflicts */
   if ( resolved )
   {
      *result = SCIP_DIDNOTRUN;
      return SCIP_OKAY;
   }

   SCIPdebugMsg(scip, "Indicator conflict handler.\n");

   conflicthdlrdata = SCIPconflicthdlrGetData(conflicthdlr);
   assert( conflicthdlrdata != NULL );

   /* possibly skip conflict handler */
   if ( ! ((SCIP_CONFLICTHDLRDATA*) conflicthdlrdata)->conshdlrdata->conflictsupgrade )
      return SCIP_OKAY;

   *result = SCIP_DIDNOTFIND;

   /* check whether there seems to be one slack variable and all other variables are binary */
   haveslack = FALSE;
   for (i = 0; i < nbdchginfos; ++i)
   {
      assert( bdchginfos != NULL ); /* for flexelint */
      assert( bdchginfos[i] != NULL );

      var = SCIPbdchginfoGetVar(bdchginfos[i]);

      /* quick check for slack variable that is implicitly integral or continuous */
      if ( SCIPvarGetType(var) == SCIP_VARTYPE_IMPLINT || SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS )
      {
         /* check string */
         if ( strstr(SCIPvarGetName(var), "indslack") != NULL )
         {
            /* make sure that the slack variable occurs with its lower bound */
            if ( SCIPboundtypeOpposite(SCIPbdchginfoGetBoundtype(bdchginfos[i])) != SCIP_BOUNDTYPE_LOWER )
               break;

            /* make sure that the lower bound is 0 */
            if ( ! SCIPisFeasZero(scip, SCIPbdchginfoGetNewbound(bdchginfos[i])) )
               break;

            haveslack = TRUE;
            continue;
         }
      }

      /* we only treat binary variables (other than slack variables) */
      if ( ! SCIPvarIsBinary(var) )
         break;
   }

   /* if we have found at least one slack variable and all other variables are binary */
   if ( haveslack && i == nbdchginfos )
   {
      SCIP_CONS** conss;
      SCIP_VAR** vars;
      int nconss;
      int j;

      SCIPdebugMsg(scip, "Found conflict involving slack variables that can be remodelled.\n");

      assert( conflicthdlrdata->conshdlr != NULL );
      assert( strcmp(SCIPconshdlrGetName(conflicthdlrdata->conshdlr), CONSHDLR_NAME) == 0 );

      nconss = SCIPconshdlrGetNConss(conflicthdlrdata->conshdlr);
      conss = SCIPconshdlrGetConss(conflicthdlrdata->conshdlr);

      /* create array of variables in conflict constraint */
      SCIP_CALL( SCIPallocBufferArray(scip, &vars, nbdchginfos) );
      for (i = 0; i < nbdchginfos; ++i)
      {
         assert( bdchginfos != NULL ); /* for flexelint */
         assert( bdchginfos[i] != NULL );

         var = SCIPbdchginfoGetVar(bdchginfos[i]);

         SCIPdebugMsg(scip, " <%s> %s %g\n", SCIPvarGetName(var), SCIPbdchginfoGetBoundtype(bdchginfos[i]) == SCIP_BOUNDTYPE_LOWER ? ">=" : "<=",
            SCIPbdchginfoGetNewbound(bdchginfos[i]));

         /* quick check for slack variable that is implicitly integral or continuous */
         if ( (SCIPvarGetType(var) == SCIP_VARTYPE_IMPLINT || SCIPvarGetType(var) == SCIP_VARTYPE_CONTINUOUS) && strstr(SCIPvarGetName(var), "indslack") != NULL )
         {
            SCIP_VAR* slackvar;

            /* search for slack variable */
            for (j = 0; j < nconss; ++j)
            {
               assert( conss[j] != NULL );
               slackvar = SCIPgetSlackVarIndicator(conss[j]);
               assert( slackvar != NULL );

               /* check whether we found the variable */
               if ( slackvar == var )
               {
                  /* replace slack variable by binary variable */
                  var = SCIPgetBinaryVarIndicator(conss[j]);
                  break;
               }
            }

            /* check whether we found the slack variable */
            if ( j >= nconss )
            {
               SCIPdebugMsg(scip, "Could not find slack variable <%s>.\n", SCIPvarGetName(var));
               break;
            }
         }
         else
         {
            /* if the variable is fixed to one in the conflict set, we have to use its negation */
            if ( SCIPbdchginfoGetNewbound(bdchginfos[i]) > 0.5 )
            {
               SCIP_CALL( SCIPgetNegatedVar(scip, var, &var) );
            }
         }

         vars[i] = var;
      }

      /* whether all slack variables have been found */
      if ( i == nbdchginfos )
      {
         SCIP_CONS* cons;
         char consname[SCIP_MAXSTRLEN];

         SCIPdebugMsg(scip, "Generated logicor conflict constraint.\n");

         /* create a logicor constraint out of the conflict set */
         (void) SCIPsnprintf(consname, SCIP_MAXSTRLEN, "cf%d_%" SCIP_LONGINT_FORMAT, SCIPgetNRuns(scip), SCIPgetNConflictConssApplied(scip));
         SCIP_CALL( SCIPcreateConsLogicor(scip, &cons, consname, nbdchginfos, vars, 
               FALSE, separate, FALSE, FALSE, TRUE, local, FALSE, dynamic, removable, FALSE) );

#ifdef SCIP_OUTPUT
         SCIP_CALL( SCIPprintCons(scip, cons, NULL) );
         SCIPinfoMessage(scip, NULL, ";\n");
#endif

         /* add constraint to SCIP */
         SCIP_CALL( SCIPaddConflict(scip, node, cons, validnode, conftype, cutoffinvolved) );

         *result = SCIP_CONSADDED;
      }

      /* free temporary memory */
      SCIPfreeBufferArray(scip, &vars);
   }

   return SCIP_OKAY;
}


/* ------------------------ parameter handling ---------------------------------*/

/** check whether we transfer a changed parameter to the given value
 *
 *  @see paramChangedIndicator()
 */
static
SCIP_RETCODE checkTransferBoolParam(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_PARAM*           param,              /**< parameter */
   const char*           name,               /**< parameter name to check */
   SCIP_Bool             newvalue,           /**< new value */
   SCIP_Bool*            value               /**< old and possibly changed value of parameter */
   )
{
   const char* paramname;

   assert( scip != NULL );
   assert( param != NULL );
   assert( name != NULL );
   assert( value != NULL );

   if ( SCIPparamGetType(param) != SCIP_PARAMTYPE_BOOL )
      return SCIP_OKAY;

   if ( *value == newvalue )
      return SCIP_OKAY;

   paramname = SCIPparamGetName(param);
   assert( paramname != NULL );

   /* check whether the change parameter corresponds to our name to check */
   if ( strcmp(paramname, name) == 0 )
   {
      /* check stage and possibly ignore parameter change */
      if ( SCIPgetStage(scip) > SCIP_STAGE_PROBLEM )
      {
         SCIPwarningMessage(scip, "Cannot change parameter <%s> stage %d - reset to old value %s.\n", name, SCIPgetStage(scip), *value ? "true" : "false");
         /* Note that the following command will create a recursive call, but then *value == newvalue above. */
         SCIP_CALL( SCIPchgBoolParam(scip, param, *value) );
      }
      else
      {
         /* otherwise copy value */
         *value = newvalue;
      }
   }

   return SCIP_OKAY;
}


/** called after a parameter has been changed */
static
SCIP_DECL_PARAMCHGD(paramChangedIndicator)
{
   SCIP_CONSHDLR* conshdlr;
   SCIP_CONSHDLRDATA* conshdlrdata;

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

   /* get indicator constraint handler */
   conshdlr = SCIPfindConshdlr(scip, "indicator");
   assert( conshdlr != NULL );

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

   SCIP_CALL( checkTransferBoolParam(scip, param, "constraints/indicator/sepaalternativelp", conshdlrdata->sepaalternativelp_, &conshdlrdata->sepaalternativelp) );
   SCIP_CALL( checkTransferBoolParam(scip, param, "constraints/indicator/forcerestart", conshdlrdata->forcerestart_, &conshdlrdata->forcerestart) );
   SCIP_CALL( checkTransferBoolParam(scip, param, "constraints/indicator/nolinconscont", conshdlrdata->nolinconscont_, &conshdlrdata->nolinconscont) );

   return SCIP_OKAY;
}


/* ------------------------ debugging routines ---------------------------------*/

#ifdef SCIP_ENABLE_IISCHECK
/** Check that indicator constraints corresponding to nonnegative entries in @a vector are infeasible in original problem
 *
 *  @note This function will probably fail if the has been presolved by the cons_linear presolver. To make it complete
 *  we would have to substitute active variables.
 */
static
SCIP_RETCODE checkIIS(
   SCIP*                 scip,               /**< SCIP pointer */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss,              /**< indicator constraints */
   SCIP_Real*            vector              /**< vector */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSHDLR* conshdlr;
   SCIP_HASHMAP* varhash;   /* hash map from variable to column index in auxiliary LP */
   SCIP_LPI* lp;
   int nvars = 0;
   int c;

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

   SCIPdebugMsg(scip, "Checking IIS ...\n");

   /* now check indicator constraints */
   conshdlr = SCIPfindConshdlr(scip, "indicator");
   assert( conshdlr != NULL );

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

   conss = SCIPconshdlrGetConss(conshdlr);
   nconss = SCIPconshdlrGetNConss(conshdlr);

   /* create LP */
   SCIP_CALL( SCIPlpiCreate(&lp, SCIPgetMessagehdlr(scip), "checkLP", SCIP_OBJSEN_MINIMIZE) );

   /* set up hash map */
   SCIP_CALL( SCIPhashmapCreate(&varhash, SCIPblkmem(scip), SCIPgetNVars(scip)) );

   /* loop through indicator constraints */
   for (c = 0; c < nconss; ++c)
   {
      SCIP_CONSDATA* consdata;
      consdata = SCIPconsGetData(conss[c]);
      assert( consdata != NULL );

      /* check whether constraint should be included */
      if ( consdata->colindex >= 0 && (! SCIPisFeasZero(scip, vector[consdata->colindex]) || ! SCIPconsIsEnabled(conss[c])) )
      {
         SCIP_CONS* lincons;
         SCIP_VAR** linvars;
         SCIP_Real* linvals;
         SCIP_Real linrhs;
         SCIP_Real linlhs;
         SCIP_VAR* slackvar;
         int nlinvars;
         SCIP_Real sign = 1.0;
         int matbeg;
         int* matind;
         SCIP_Real* matval;
         SCIP_VAR** newvars;
         int nnewvars;
         SCIP_Real lhs;
         SCIP_Real rhs;
         int cnt;
         int v;

         lincons = consdata->lincons;
         assert( lincons != NULL );
         assert( ! SCIPconsIsEnabled(conss[c]) || SCIPconsIsActive(lincons) );
         assert( ! SCIPconsIsEnabled(conss[c]) || SCIPconsIsEnabled(lincons) );

         slackvar = consdata->slackvar;
         assert( slackvar != NULL );

         /* if the slack variable is aggregated (multi-aggregation should not happen) */
         assert( SCIPvarGetStatus(slackvar) != SCIP_VARSTATUS_MULTAGGR );
         if ( SCIPvarGetStatus(slackvar) == SCIP_VARSTATUS_AGGREGATED )
         {
            SCIP_VAR* var;
            SCIP_Real scalar = 1.0;
            SCIP_Real constant = 0.0;

            var = slackvar;

            SCIP_CALL( SCIPgetProbvarSum(scip, &var, &scalar, &constant) );
            assert( ! SCIPisZero(scip, scalar) );

            /*  SCIPdebugMsg(scip, "slack variable aggregated (scalar: %f, constant: %f)\n", scalar, constant); */

            /* otherwise construct a linear constraint */
            SCIP_CALL( SCIPallocBufferArray(scip, &linvars, 1) );
            SCIP_CALL( SCIPallocBufferArray(scip, &linvals, 1) );
            linvars[0] = var;
            linvals[0] = scalar;
            nlinvars = 1;
            linlhs = -SCIPinfinity(scip);
            linrhs = constant;
         }
         else
         {
            /* in this case, the linear constraint is directly usable */
            linvars = SCIPgetVarsLinear(scip, lincons);
            linvals = SCIPgetValsLinear(scip, lincons);
            nlinvars = SCIPgetNVarsLinear(scip, lincons);
            linlhs = SCIPgetLhsLinear(scip, lincons);
            linrhs = SCIPgetRhsLinear(scip, lincons);
         }

         /* adapt rhs of linear constraint */
         assert( SCIPisInfinity(scip, -linlhs) || SCIPisInfinity(scip, linrhs) );
         if ( SCIPisInfinity(scip, linrhs) )
         {
            linrhs = -linlhs;
            assert( linrhs > -SCIPinfinity(scip) );
            sign = -1.0;
         }

         SCIP_CALL( SCIPallocBufferArray(scip, &matind, 4*nlinvars) );
         SCIP_CALL( SCIPallocBufferArray(scip, &matval, 4*nlinvars) );
         SCIP_CALL( SCIPallocBufferArray(scip, &newvars, nlinvars) );

         /* set up row */
         nnewvars = 0;
         for (v = 0; v < nlinvars; ++v)
         {
            SCIP_VAR* var;
            var = linvars[v];
            assert( var != NULL );

            /* skip slack variable */
            if ( var == slackvar )
               continue;

            /* if variable is new */
            if ( ! SCIPhashmapExists(varhash, var) )
            {
               /* add variable in map */
               SCIP_CALL( SCIPhashmapInsertInt(varhash, var, nvars) );
               assert( nvars == SCIPhashmapGetImageInt(varhash, var) );
               /* SCIPdebugMsg(scip, "Inserted variable <%s> into hashmap (%d).\n", SCIPvarGetName(var), nvars); */
               nvars++;

               /* store new variables */
               newvars[nnewvars++] = var;
            }
            assert( SCIPhashmapExists(varhash, var) );
         }

         /* add new columns */
         if ( nnewvars > 0 )
         {
            SCIP_Real* lb;
            SCIP_Real* ub;
            SCIP_Real* obj;
            char** colnames;

            SCIP_CALL( SCIPallocBufferArray(scip, &lb, nnewvars) );
            SCIP_CALL( SCIPallocBufferArray(scip, &ub, nnewvars) );
            SCIP_CALL( SCIPallocBufferArray(scip, &obj, nnewvars) );
            SCIP_CALL( SCIPallocBufferArray(scip, &colnames, nnewvars) );

            for (v = 0; v < nnewvars; ++v)
            {
               SCIP_VAR* var;
               var = newvars[v];
               obj[v] = 0.0;
               lb[v] = SCIPvarGetLbLocal(var);
               ub[v] = SCIPvarGetUbLocal(var);
               SCIP_CALL( SCIPallocBufferArray(scip, &(colnames[v]), SCIP_MAXSTRLEN) ); /*lint !e866*/
               (void) SCIPsnprintf(colnames[v], SCIP_MAXSTRLEN, "%s", SCIPvarGetName(var));
            }

            /* now add columns */
            SCIP_CALL( SCIPlpiAddCols(lp, nnewvars, obj, lb, ub, colnames, 0, NULL, NULL, NULL) );

            for (v = nnewvars - 1; v >= 0; --v)
            {
               SCIPfreeBufferArray(scip, &(colnames[v]));
            }
            SCIPfreeBufferArray(scip, &colnames);
            SCIPfreeBufferArray(scip, &obj);
            SCIPfreeBufferArray(scip, &ub);
            SCIPfreeBufferArray(scip, &lb);
         }

         /* set up row */
         cnt = 0;
         for (v = 0; v < nlinvars; ++v)
         {
            SCIP_VAR* var;
            var = linvars[v];
            assert( var != NULL );

            /* skip slack variable */
            if ( var == slackvar )
               continue;

            assert( SCIPhashmapExists(varhash, var) );
            matind[cnt] = SCIPhashmapGetImageInt(varhash, var);
            matval[cnt] = sign * linvals[v];
            ++cnt;
         }

         lhs = -SCIPlpiInfinity(lp);
         rhs = linrhs;

         /* add new row */
         matbeg = 0;
         SCIP_CALL( SCIPlpiAddRows(lp, 1, &lhs, &rhs, NULL, cnt, &matbeg, matind, matval) );

         SCIPfreeBufferArray(scip, &matind);
         SCIPfreeBufferArray(scip, &matval);
         SCIPfreeBufferArray(scip, &newvars);

         assert( slackvar != NULL );
         if ( SCIPvarGetStatus(slackvar) == SCIP_VARSTATUS_AGGREGATED )
         {
            SCIPfreeBufferArray(scip, &linvals);
            SCIPfreeBufferArray(scip, &linvars);
         }
      }
   }

   /* possibly handle additional linear constraints */
   if ( conshdlrdata->useotherconss )
   {
      /* get all linear constraints */
      conss = SCIPgetConss(scip);
      nconss = SCIPgetNConss(scip);

      /* loop through constraints */
      for (c = 0; c < nconss; ++c)
      {
         SCIP_CONS* cons;
         SCIP_VAR** linvars;
         SCIP_Real* linvals;
         SCIP_Real linrhs;
         SCIP_Real linlhs;
         SCIP_Real* matval;
         SCIP_VAR** newvars;
         int nnewvars = 0;
         int* matind;
         int nlinvars;
         int matbeg = 0;
         int cnt = 0;
         int v;

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

         /* avoid non-active, local constraints */
         if ( ! SCIPconsIsEnabled(cons) || ! SCIPconsIsActive(cons) || SCIPconsIsLocal(cons) )
            continue;

         /* check type of constraint (only take linear constraints) */
         if ( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), "linear") != 0 )
            continue;

         /* avoid adding linear constraints that correspond to indicator constraints */
         if ( strncmp(SCIPconsGetName(cons), "indlin", 6) == 0 )
            continue;

         /* get data of linear constraint */
         linvars = SCIPgetVarsLinear(scip, cons);
         linvals = SCIPgetValsLinear(scip, cons);
         nlinvars = SCIPgetNVarsLinear(scip, cons);
         linlhs = SCIPgetLhsLinear(scip, cons);
         linrhs = SCIPgetRhsLinear(scip, cons);

         /* reserve space */
         SCIP_CALL( SCIPallocBufferArray(scip, &matind, 4*nlinvars) );
         SCIP_CALL( SCIPallocBufferArray(scip, &matval, 4*nlinvars) );
         SCIP_CALL( SCIPallocBufferArray(scip, &newvars, nlinvars) );

         /* collect possibly new variables */
         for (v = 0; v < nlinvars; ++v)
         {
            SCIP_VAR* var;
            var = linvars[v];
            assert( var != NULL );

            /* if variable is new */
            if ( ! SCIPhashmapExists(varhash, var) )
            {
               /* add variable in map */
               SCIP_CALL( SCIPhashmapInsertInt(varhash, var, nvars) );
               assert( nvars == SCIPhashmapGetImageInt(varhash, var) );
               /* SCIPdebugMsg(scip, "Inserted variable <%s> into hashmap (%d).\n", SCIPvarGetName(var), nvars); */
               nvars++;

               /* store new variables */
               newvars[nnewvars++] = var;
            }
            assert( SCIPhashmapExists(varhash, var) );
         }

         /* add new columns */
         if ( nnewvars > 0 )
         {
            SCIP_Real* lb;
            SCIP_Real* ub;
            SCIP_Real* obj;
            char** colnames;

            SCIP_CALL( SCIPallocBufferArray(scip, &lb, nnewvars) );
            SCIP_CALL( SCIPallocBufferArray(scip, &ub, nnewvars) );
            SCIP_CALL( SCIPallocBufferArray(scip, &obj, nnewvars) );
            SCIP_CALL( SCIPallocBufferArray(scip, &colnames, nnewvars) );

            for (v = 0; v < nnewvars; ++v)
            {
               SCIP_VAR* var;
               var = newvars[v];
               obj[v] = 0.0;
               lb[v] = SCIPvarGetLbLocal(var);
               ub[v] = SCIPvarGetUbLocal(var);
               SCIP_CALL( SCIPallocBufferArray(scip, &(colnames[v]), SCIP_MAXSTRLEN) ); /*lint !e866*/
               (void) SCIPsnprintf(colnames[v], SCIP_MAXSTRLEN, "%s", SCIPvarGetName(var));
            }

            /* now add columns */
            SCIP_CALL( SCIPlpiAddCols(lp, nnewvars, obj, lb, ub, colnames, 0, NULL, NULL, NULL) );

            for (v = nnewvars - 1; v >= 0; --v)
            {
               SCIPfreeBufferArray(scip, &(colnames[v]));
            }
            SCIPfreeBufferArray(scip, &colnames);
            SCIPfreeBufferArray(scip, &obj);
            SCIPfreeBufferArray(scip, &ub);
            SCIPfreeBufferArray(scip, &lb);
         }

         /* set up row */
         for (v = 0; v < nlinvars; ++v)
         {
            SCIP_VAR* var;
            var = linvars[v];
            assert( var != NULL );

            assert( SCIPhashmapExists(varhash, var) );
            matind[cnt] = SCIPhashmapGetImageInt(varhash, var);
            matval[cnt] = linvals[v];
            ++cnt;
         }

         /* add new row */
         SCIP_CALL( SCIPlpiAddRows(lp, 1, &linlhs, &linrhs, NULL, cnt, &matbeg, matind, matval) );

         SCIPfreeBufferArray(scip, &matind);
         SCIPfreeBufferArray(scip, &matval);
         SCIPfreeBufferArray(scip, &newvars);
      }
   }

   /* solve LP and check status */
   SCIP_CALL( SCIPlpiSolvePrimal(lp) );

   if ( ! SCIPlpiIsPrimalInfeasible(lp) )
   {
      SCIPerrorMessage("Detected IIS is not infeasible in original problem!\n");

      SCIP_CALL( SCIPlpiWriteLP(lp, "check.lp") );
      SCIP_CALL( SCIPlpiWriteLP(conshdlrdata->altlp, "altdebug.lp") );
      SCIPABORT();
      return SCIP_ERROR; /*lint !e527*/
   }
   SCIPdebugMsg(scip, "Check successful!\n");

   SCIPhashmapFree(&varhash);
   SCIP_CALL( SCIPlpiFree(&lp) );

   return SCIP_OKAY;
}
#endif


/* ------------------------ auxiliary operations -------------------------------*/

/** return objective contribution of variable
 *
 *  Special treatment of negated variables: return negative of objective of original
 *  variable. SCIPvarGetObj() would return 0 in these cases.
 */
static
SCIP_Real varGetObjDelta(
   SCIP_VAR*             var                 /**< variable */
   )
{
   if ( SCIPvarIsBinary(var) && SCIPvarIsNegated(var) )
   {
      assert( SCIPvarGetNegatedVar(var) != NULL );
      return -SCIPvarGetObj(SCIPvarGetNegatedVar(var));
   }
   else if ( SCIPvarGetStatus(var) == SCIP_VARSTATUS_AGGREGATED )
   {
      assert( SCIPvarGetAggrVar(var) != NULL );
      return SCIPvarGetAggrScalar(var) * SCIPvarGetObj(SCIPvarGetAggrVar(var));
   }

   return SCIPvarGetObj(var);
}


/** ensures that the addlincons array can store at least num entries */
static
SCIP_RETCODE consdataEnsureAddLinConsSize(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   int                   num                 /**< minimum number of entries to store */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;

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

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );
   assert( conshdlrdata->naddlincons <= conshdlrdata->maxaddlincons );

   if ( num > conshdlrdata->maxaddlincons )
   {
      int newsize;

      newsize = SCIPcalcMemGrowSize(scip, num);
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &conshdlrdata->addlincons, conshdlrdata->maxaddlincons, newsize) );
      conshdlrdata->maxaddlincons = newsize;
   }
   assert( num <= conshdlrdata->maxaddlincons );

   return SCIP_OKAY;
}


/* ------------------------ operations on the alternative LP -------------------*/

/** initialize alternative LP
 *
 *  The alternative system is organized as follows:
 *  - The first row corresponds to the right hand side of the original system.
 *  - The next nconss constraints correspond to the slack variables.
 *  - The rows after that correspond to the original variables.
 */
static
SCIP_RETCODE initAlternativeLP(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr            /**< constraint handler */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_Real lhs = -1.0;
   SCIP_Real rhs = -1.0;

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

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );
   assert( conshdlrdata->altlp == NULL );
   assert( conshdlrdata->varhash == NULL );
   assert( conshdlrdata->lbhash == NULL );
   assert( conshdlrdata->ubhash == NULL );
   assert( conshdlrdata->slackhash != NULL );

   /* create hash map of variables */
   SCIP_CALL( SCIPhashmapCreate(&conshdlrdata->varhash, SCIPblkmem(scip), SCIPgetNVars(scip)) );
   SCIP_CALL( SCIPhashmapCreate(&conshdlrdata->lbhash, SCIPblkmem(scip), SCIPgetNVars(scip)) );
   SCIP_CALL( SCIPhashmapCreate(&conshdlrdata->ubhash, SCIPblkmem(scip), SCIPgetNVars(scip)) );

   /* create alternative LP */
   SCIP_CALL( SCIPlpiCreate(&conshdlrdata->altlp, SCIPgetMessagehdlr(scip), "altlp", SCIP_OBJSEN_MINIMIZE) );

   /* add first row */
   SCIP_CALL( SCIPlpiAddRows(conshdlrdata->altlp, 1, &lhs, &rhs, NULL, 0, NULL, NULL, NULL) );
   conshdlrdata->nrows = 1;

   /* set parameters */
   SCIP_CALL_PARAM( SCIPlpiSetIntpar(conshdlrdata->altlp, SCIP_LPPAR_FROMSCRATCH, FALSE) );
   SCIP_CALL_PARAM( SCIPlpiSetIntpar(conshdlrdata->altlp, SCIP_LPPAR_PRESOLVING, TRUE) );
   SCIP_CALL_PARAM( SCIPlpiSetIntpar(conshdlrdata->altlp, SCIP_LPPAR_SCALING, 1) );
   SCIP_CALL_PARAM( SCIPlpiSetIntpar(conshdlrdata->altlp, SCIP_LPPAR_FASTMIP, FALSE) );

   SCIPdebugMsg(scip, "Initialized alternative LP.\n");

   /* uncomment the following for debugging */
   /* SCIP_CALL_PARAM( SCIPlpiSetIntpar(conshdlrdata->altlp, SCIP_LPPAR_LPINFO, TRUE) ); */

   return SCIP_OKAY;
}


/** check whether the bounds in given (alternative) LP are set correctly (for debugging) */
#ifndef NDEBUG
static
SCIP_RETCODE checkLPBoundsClean(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_LPI*             lp,                 /**< LP for which bounds should be checked */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss               /**< constraints */
   )
{
   SCIP_Real* lb;
   SCIP_Real* ub;
   SCIP_Bool* covered;
   int nCols;
   int j;

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

   SCIP_CALL( SCIPlpiGetNCols(lp, &nCols) );

   SCIP_CALL( SCIPallocBufferArray(scip, &lb, nCols) );
   SCIP_CALL( SCIPallocBufferArray(scip, &ub, nCols) );
   SCIP_CALL( SCIPallocBufferArray(scip, &covered, nCols) );

   for (j = 0; j < nCols; ++j)
      covered[j] = FALSE;

   /* check columns used by constraints */
   SCIP_CALL( SCIPlpiGetBounds(lp, 0, nCols-1, lb, ub) );
   for (j = 0; j < nconss; ++j)
   {
      SCIP_CONSDATA* consdata;
      int ind;

      assert( conss[j] != NULL );
      consdata = SCIPconsGetData(conss[j]);
      assert( consdata != NULL );
      ind = consdata->colindex;

      if ( ind >= 0 )
      {
         assert( ind < nCols );
         covered[ind] = TRUE;
         if ( ! SCIPisFeasZero(scip, lb[ind]) || ! SCIPlpiIsInfinity(lp, ub[ind]) )
         {
            SCIPABORT();
         }
      }
   }

   /* check other columns */
   for (j = 0; j < nCols; ++j)
   {
      if (! covered[j] )
      {
         /* some columns can be fixed to 0, since they correspond to disabled constraints */
         if ( ( ! SCIPlpiIsInfinity(lp, -lb[j]) && ! SCIPisFeasZero(scip, lb[j])) || (! SCIPlpiIsInfinity(lp, ub[j]) && ! SCIPisFeasZero(scip, ub[j])) )
         {
            SCIPABORT();
         }
      }
   }

   SCIPfreeBufferArray(scip, &covered);
   SCIPfreeBufferArray(scip, &lb);
   SCIPfreeBufferArray(scip, &ub);

   return SCIP_OKAY;
}
#endif


/** set the alternative system objective function
 *
 *  We assume that the objective function coefficients of the variables other than the binary
 *  indicators are always 0 and hence do not have to be changed.
 *
 *  We already use the tranformation \f$y' = 1 - y\f$.
 */
static
SCIP_RETCODE setAltLPObj(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_LPI*             lp,                 /**< alternative LP */
   SCIP_SOL*             sol,                /**< solution to be dealt with */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss               /**< indicator constraints */
   )
{
   int j;
   SCIP_Real* obj = NULL;
   int* indices = NULL;
   int cnt = 0;

   assert( scip != NULL );
   assert( lp != NULL );
   assert( conss != NULL );

   SCIP_CALL( SCIPallocBufferArray(scip, &obj, nconss) );
   SCIP_CALL( SCIPallocBufferArray(scip, &indices, nconss) );

   for (j = 0; j < nconss; ++j)
   {
      SCIP_CONSDATA* consdata;

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

      if ( consdata->colindex >= 0 )
      {
         SCIP_Real val = SCIPgetSolVal(scip, sol, consdata->binvar);
         if ( SCIPisFeasEQ(scip, val, 1.0) )
            obj[cnt] = OBJEPSILON;      /* set objective to some small number to get small IISs */
         else
            obj[cnt] = 1.0 - val;
         indices[cnt++] = consdata->colindex;
      }
   }

   if ( cnt > 0 )
   {
      SCIP_CALL( SCIPlpiChgObj(lp, cnt, indices, obj) );
   }

   SCIPfreeBufferArray(scip, &indices);
   SCIPfreeBufferArray(scip, &obj);

   return SCIP_OKAY;
}


/** set the alternative system objective function to some small value */
static
SCIP_RETCODE setAltLPObjZero(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_LPI*             lp,                 /**< alternative LP */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss               /**< indicator constraints */
   )
{
   int j;
   SCIP_Real* obj = NULL;
   int* indices = NULL;
   int cnt = 0;

   assert( scip != NULL );
   assert( lp != NULL );
   assert( conss != NULL );

   SCIP_CALL( SCIPallocBufferArray(scip, &obj, nconss) );
   SCIP_CALL( SCIPallocBufferArray(scip, &indices, nconss) );

   for (j = 0; j < nconss; ++j)
   {
      SCIP_CONSDATA* consdata;

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

      if ( consdata->colindex >= 0 )
      {
         obj[cnt] = OBJEPSILON;
         indices[cnt++] = consdata->colindex;
      }
   }

   if ( cnt > 0 )
   {
      SCIP_CALL( SCIPlpiChgObj(lp, cnt, indices, obj) );
   }

   SCIPfreeBufferArray(scip, &indices);
   SCIPfreeBufferArray(scip, &obj);

   return SCIP_OKAY;
}


/** fix variable given by @a S to 0 */
static
SCIP_RETCODE fixAltLPVariables(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_LPI*             lp,                 /**< alternative LP */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss,              /**< indicator constraints */
   SCIP_Bool*            S                   /**< bitset of variables */
   )
{
   SCIP_Real* lb = NULL;
   SCIP_Real* ub = NULL;
   int* indices = NULL;
   int cnt = 0;
   int j;

   assert( scip != NULL );
   assert( lp != NULL );
   assert( conss != NULL );

   SCIP_CALL( SCIPallocBufferArray(scip, &lb, nconss) );
   SCIP_CALL( SCIPallocBufferArray(scip, &ub, nconss) );
   SCIP_CALL( SCIPallocBufferArray(scip, &indices, nconss) );

   /* collect bounds to be changed */
   for (j = 0; j < nconss; ++j)
   {
      SCIP_CONSDATA* consdata;

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

      if ( consdata->colindex >= 0 )
      {
         if ( S[j] )
         {
            indices[cnt] = consdata->colindex;
            lb[cnt] = 0.0;
            ub[cnt] = 0.0;
            ++cnt;
         }
      }
   }

   /* change bounds */
   if ( cnt > 0 )
   {
      SCIP_CALL( SCIPlpiChgBounds(lp, cnt, indices, lb, ub) );
   }

   SCIPfreeBufferArray(scip, &indices);
   SCIPfreeBufferArray(scip, &ub);
   SCIPfreeBufferArray(scip, &lb);

   return SCIP_OKAY;
}


/** fix variable @a ind to 0 */
static
SCIP_RETCODE fixAltLPVariable(
   SCIP_LPI*             lp,                 /**< alternative LP */
   int                   ind                 /**< variable that should be fixed to 0 */
   )
{
   SCIP_Real lb = 0.0;
   SCIP_Real ub = 0.0;

   /* change bounds */
   SCIP_CALL( SCIPlpiChgBounds(lp, 1, &ind, &lb, &ub) );

   return SCIP_OKAY;
}


/** unfix variable @a ind to 0 */
static
SCIP_RETCODE unfixAltLPVariable(
   SCIP_LPI*             lp,                 /**< alternative LP */
   int                   ind                 /**< variable that should be fixed to 0 */
   )
{
   SCIP_Real lb = 0.0;
   SCIP_Real ub = SCIPlpiInfinity(lp);

   /* change bounds */
   SCIP_CALL( SCIPlpiChgBounds(lp, 1, &ind, &lb, &ub) );

   return SCIP_OKAY;
}

/** unfix variable given by @a S to 0 */
static
SCIP_RETCODE unfixAltLPVariables(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_LPI*             lp,                 /**< alternative LP */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss,              /**< indicator constraints */
   SCIP_Bool*            S                   /**< bitset of variables */
   )
{
   SCIP_Real* lb = NULL;
   SCIP_Real* ub = NULL;
   int* indices = NULL;
   int cnt = 0;
   int j;

   assert( scip != NULL );
   assert( lp != NULL );
   assert( conss != NULL );

   SCIP_CALL( SCIPallocBufferArray(scip, &lb, nconss) );
   SCIP_CALL( SCIPallocBufferArray(scip, &ub, nconss) );
   SCIP_CALL( SCIPallocBufferArray(scip, &indices, nconss) );

   /* collect bounds to be changed */
   for (j = 0; j < nconss; ++j)
   {
      if ( S[j] )
      {
         SCIP_CONSDATA* consdata;

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

         if ( consdata->colindex >= 0 )
         {
            indices[cnt] = consdata->colindex;
            lb[cnt] = 0.0;
            ub[cnt] = SCIPlpiInfinity(lp);
            ++cnt;
         }
      }
   }

   /* change bounds */
   if ( cnt > 0 )
   {
      SCIP_CALL( SCIPlpiChgBounds(lp, cnt, indices, lb, ub) );
   }

   SCIPfreeBufferArray(scip, &indices);
   SCIPfreeBufferArray(scip, &ub);
   SCIPfreeBufferArray(scip, &lb);

   return SCIP_OKAY;
}


/** update bounds in first row to the current ones */
static
SCIP_RETCODE updateFirstRow(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLRDATA*    conshdlrdata        /**< constraint handler */
   )
{
   SCIP_HASHMAP* lbhash;
   SCIP_HASHMAP* ubhash;
   SCIP_VAR** vars;
   SCIP_LPI* altlp;
   int nvars;
   int cnt;
   int v;

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

   altlp = conshdlrdata->altlp;
   lbhash = conshdlrdata->lbhash;
   ubhash = conshdlrdata->ubhash;
   assert( lbhash != NULL && ubhash != NULL );

   /* check all variables */
   vars = SCIPgetVars(scip);
   nvars = SCIPgetNVars(scip);
   cnt = 0;

   for (v = 0; v < nvars; ++v)
   {
      SCIP_VAR* var;
      var = vars[v];
      if ( SCIPhashmapExists(lbhash, var) )
      {
         int col;

         col = SCIPhashmapGetImageInt(lbhash, var);
         SCIP_CALL( SCIPlpiChgCoef(altlp, 0, col, -SCIPvarGetLbLocal(var)) );
         if ( ! SCIPisEQ(scip, SCIPvarGetLbLocal(var), SCIPvarGetLbGlobal(var)) )
            ++cnt;
      }
      if ( SCIPhashmapExists(ubhash, var) )
      {
         int col;

         col = SCIPhashmapGetImageInt(ubhash, var);
         SCIP_CALL( SCIPlpiChgCoef(altlp, 0, col, SCIPvarGetUbLocal(var)) );
         if ( ! SCIPisEQ(scip, SCIPvarGetUbLocal(var), SCIPvarGetUbGlobal(var)) )
            ++cnt;
      }
   }
   if ( cnt > 10 )
   {
      /* possible force a rescaling: */
      conshdlrdata->scaled = FALSE;

      /* SCIP_CALL( SCIPlpiWriteLP(altlp, "altChg.lp") ); */
      SCIPdebugMsg(scip, "Updated bounds of original variables: %d.\n", cnt);
   }

   return SCIP_OKAY;
}


/** update bounds in first row to the global bounds */
static
SCIP_RETCODE updateFirstRowGlobal(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLRDATA*    conshdlrdata        /**< constraint handler */
   )
{
   SCIP_HASHMAP* lbhash;
   SCIP_HASHMAP* ubhash;
   SCIP_VAR** vars;
   SCIP_LPI* altlp;
   int nvars;
   int cnt;
   int v;

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

   altlp = conshdlrdata->altlp;
   lbhash = conshdlrdata->lbhash;
   ubhash = conshdlrdata->ubhash;
   assert( lbhash != NULL && ubhash != NULL );

   /* check all variables */
   vars = SCIPgetVars(scip);
   nvars = SCIPgetNVars(scip);
   cnt = 0;

   for (v = 0; v < nvars; ++v)
   {
      SCIP_VAR* var;
      int col;

      var = vars[v];
      if ( SCIPhashmapExists(lbhash, var) )
      {
         col = SCIPhashmapGetImageInt(lbhash, var);
         SCIP_CALL( SCIPlpiChgCoef(altlp, 0, col, -SCIPvarGetLbGlobal(var)) );
         ++cnt;
      }
      if ( SCIPhashmapExists(ubhash, var) )
      {
         col = SCIPhashmapGetImageInt(ubhash, var);
         SCIP_CALL( SCIPlpiChgCoef(altlp, 0, col, SCIPvarGetUbGlobal(var)) );
         ++cnt;
      }
   }

   if ( cnt > 0 )
   {
      /* SCIP_CALL( SCIPlpiWriteLP(altlp, "altChg.lp") ); */
      SCIPdebugMsg(scip, "Updated bounds of original variables: %d.\n", cnt);
   }

   /* possible force a rescaling: */
   /* conshdlrdata->scaled = FALSE; */

   return SCIP_OKAY;
}


/** check whether IIS defined by @a vector corresponds to a local cut */
static
SCIP_RETCODE checkIISlocal(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLRDATA*    conshdlrdata,       /**< constraint handler */
   SCIP_Real*            vector,             /**< solution to alternative LP defining IIS */
   SCIP_Bool*            isLocal             /**< whether the IIS uses local bounds different from the global ones */
   )
{
   SCIP_HASHMAP* lbhash;
   SCIP_HASHMAP* ubhash;
   SCIP_VAR** vars;
#ifndef NDEBUG
   int nCols;
#endif
   int nvars;
   int v;

   assert( scip != NULL );
   assert( conshdlrdata != NULL );
   assert( vector != NULL );
   assert( isLocal != NULL );

   *isLocal = FALSE;

#ifndef NDEBUG
   SCIP_CALL( SCIPlpiGetNCols(conshdlrdata->altlp, &nCols) );
#endif

   lbhash = conshdlrdata->lbhash;
   ubhash = conshdlrdata->ubhash;
   assert( lbhash != NULL && ubhash != NULL );

   /* get all variables */
   vars = SCIPgetVars(scip);
   nvars = SCIPgetNVars(scip);

   /* check all variables */
   for (v = 0; v < nvars; ++v)
   {
      SCIP_VAR* var;
      var = vars[v];

      /* if local bound is different from global bound */
      if ( ! SCIPisEQ(scip, SCIPvarGetLbLocal(var), SCIPvarGetLbGlobal(var)) )
      {
         /* check whether the variable corresponding to the lower bounds has been used */
         if ( SCIPhashmapExists(lbhash, var) )
         {
            int col;

            col = SCIPhashmapGetImageInt(lbhash, var);
            assert( 0 <= col && col < nCols );
            if ( ! SCIPisFeasZero(scip, vector[col]) )
            {
               *isLocal = TRUE;
               return SCIP_OKAY;
            }
         }
      }

      /* if local bound is different from global bound */
      if ( ! SCIPisEQ(scip, SCIPvarGetUbLocal(var), SCIPvarGetUbGlobal(var)) )
      {
         /* check whether the variable corresponding to the upper bounds has been used */
         if ( SCIPhashmapExists(ubhash, var) )
         {
            int col;

            col = SCIPhashmapGetImageInt(ubhash, var);
            assert( 0 <= col && col < nCols );
            if ( ! SCIPisFeasZero(scip, vector[col]) )
            {
               *isLocal = TRUE;
               return SCIP_OKAY;
            }
         }
      }
   }

   return SCIP_OKAY;
}


/** compute scaling for first row
 *
 *  If the coefficients in the first row are large, a right hand side of -1 might not be
 *  adequate. Here, we replace the right hand side by the sum of the coefficients divided by the
 *  number of nonzeros.
 */
static
SCIP_RETCODE scaleFirstRow(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLRDATA*    conshdlrdata        /**< constraint handler */
   )
{
   assert( scip != NULL );
   assert( conshdlrdata != NULL );

   if ( ! conshdlrdata->scaled )
   {
      SCIP_Real* val;
      SCIP_LPI* altlp;
      int* ind;
      SCIP_Real sum = 0.0;
      int beg[1];
      int nCols;
      int cnt;
      int j;

      altlp = conshdlrdata->altlp;
      SCIP_CALL( SCIPlpiGetNCols(altlp, &nCols) );
      SCIP_CALL( SCIPallocBufferArray(scip, &ind, nCols) );
      SCIP_CALL( SCIPallocBufferArray(scip, &val, nCols) );

      SCIP_CALL( SCIPlpiGetRows(altlp, 0, 0, NULL, NULL, &cnt, beg, ind, val) );

      if ( cnt > 0 )
      {
         /* compute sum */
         for (j = 0; j < cnt; ++j)
            sum += REALABS(val[j]);

         /* set rhs */
         sum = - REALABS(sum) / ((double) cnt);
         j = 0;
         SCIP_CALL( SCIPlpiChgSides(altlp, 1, &j, &sum, &sum) );
      }

      SCIPfreeBufferArray(scip, &val);
      SCIPfreeBufferArray(scip, &ind);

      conshdlrdata->scaled = TRUE;
   }

   return SCIP_OKAY;
}


/** add column to alternative LP
 *
 *  See the description at the top of the file for more information.
 */
static
SCIP_RETCODE addAltLPColumn(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONSHDLRDATA*    conshdlrdata,       /**< data of constraint handler */
   SCIP_VAR*             slackvar,           /**< slack variable or NULL */
   int                   nvars,              /**< number of variables in column */
   SCIP_VAR**            vars,               /**< variables for column */
   SCIP_Real*            vals,               /**< values for column */
   SCIP_Real             rhscoef,            /**< coefficient for first row */
   SCIP_Real             objcoef,            /**< objective in alternative LP */
   SCIP_Real             sign,               /**< sign (+1,-1) for column */
   SCIP_Bool             colfree,            /**< whether column should be free, e.g., for equations */
   int*                  colindex            /**< index of new column (return value) */
   )
{
   SCIP_VAR** newvars;
   SCIP_Real val;
   SCIP_Real* matval;
   SCIP_Bool* newrowsslack;
   SCIP_Real* obj;
   SCIP_Real* lb;
   SCIP_Real* ub;
   int* matbeg;
   int* matind;
   int nnewvars = 0;
   int nnewcols = 0;
   int nnewrows = 0;
   int ncols = 0;
   int cnt = 0;
   int v;

   assert( scip != NULL );
   assert( conshdlrdata != NULL );
   assert( vars != NULL );
   assert( vals != NULL );
   assert( ! SCIPisInfinity(scip, rhscoef) && ! SCIPisInfinity(scip, -rhscoef) );
   assert( SCIPisEQ(scip, sign, 1.0) || SCIPisEQ(scip, sign, -1.0) );
   assert( colindex != NULL );

   *colindex = -1;

   if ( conshdlrdata->altlp == NULL )
   {
      SCIP_CALL( initAlternativeLP(scip, conshdlr) );
   }
   assert( conshdlrdata->altlp != NULL );
   assert( conshdlrdata->varhash != NULL );
   assert( conshdlrdata->lbhash != NULL );
   assert( conshdlrdata->ubhash != NULL );
   assert( conshdlrdata->slackhash != NULL );

#ifndef NDEBUG
   {
      int nrows;
      SCIP_CALL( SCIPlpiGetNRows(conshdlrdata->altlp, &nrows) );
      assert( nrows == conshdlrdata->nrows );
   }
#endif

   /* set up data for construction */
   SCIP_CALL( SCIPallocBufferArray(scip, &matbeg, nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &matind, 4 * nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &matval, 4 * nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &obj, 2 * nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &lb, 2 * nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &ub, 2 * nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &newvars, nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &newrowsslack, 2 * nvars) );

   /* store index of column in constraint */
   /* coverity[var_deref_model] */
   SCIP_CALL( SCIPlpiGetNCols(conshdlrdata->altlp, &ncols) );
   *colindex = ncols;

   /* handle first row */
   if ( ! SCIPisFeasZero(scip, rhscoef) )
   {
      matind[cnt] = 0;
      matval[cnt++] = sign * rhscoef;
   }

   /* set up column (recognize new original variables) */
   for (v = 0; v < nvars; ++v)
   {
      SCIP_VAR* var;

      var = vars[v];
      assert( var != NULL );

      /* if variable is a slack variable */
      if ( SCIPhashmapExists(conshdlrdata->slackhash, var) )
      {
         /* to avoid trivial rows: only add row corresponding to slack variable if it appears outside its own constraint */
         if ( var != slackvar )
         {
            int ind;

            ind = SCIPhashmapGetImageInt(conshdlrdata->slackhash, var);

            if ( ind < INT_MAX )
               matind[cnt] = ind;
            else
            {
               /* correct number of variable already in map/array and remember to add a new row */
               SCIP_CALL( SCIPhashmapSetImageInt(conshdlrdata->slackhash, var, conshdlrdata->nrows) );
               assert( conshdlrdata->nrows == SCIPhashmapGetImageInt(conshdlrdata->slackhash, var) );
               SCIPdebugMsg(scip, "Inserted slack variable <%s> into hashmap (row: %d).\n", SCIPvarGetName(var), conshdlrdata->nrows);
               matind[cnt] = (conshdlrdata->nrows)++;

               /* store new variables */
               newrowsslack[nnewrows++] = TRUE;
            }
            assert( conshdlrdata->nrows >= SCIPhashmapGetImageInt(conshdlrdata->slackhash, var) );
            matval[cnt++] = sign * vals[v];
         }
      }
      else
      {
         /* if variable exists */
         if ( SCIPhashmapExists(conshdlrdata->varhash, var) )
            matind[cnt] = SCIPhashmapGetImageInt(conshdlrdata->varhash, var);
         else
         {
            /* add variable in map and array and remember to add a new row */
            SCIP_CALL( SCIPhashmapInsertInt(conshdlrdata->varhash, var, conshdlrdata->nrows) );
            assert( conshdlrdata->nrows == SCIPhashmapGetImageInt(conshdlrdata->varhash, var) );
            SCIPdebugMsg(scip, "Inserted variable <%s> into hashmap (row: %d).\n", SCIPvarGetName(var), conshdlrdata->nrows);
            matind[cnt] = (conshdlrdata->nrows)++;

            /* store new variables */
            newrowsslack[nnewrows++] = FALSE;
            newvars[nnewvars++] = var;
         }
         assert( SCIPhashmapExists(conshdlrdata->varhash, var) );
         matval[cnt++] = sign * vals[v];
      }
   }

   /* add new rows */
   if ( nnewrows > 0 )
   {
      SCIP_Real* lhs;
      SCIP_Real* rhs;
      int i;

      SCIP_CALL( SCIPallocBufferArray(scip, &lhs, nnewrows) );
      SCIP_CALL( SCIPallocBufferArray(scip, &rhs, nnewrows) );
      for (i = 0; i < nnewrows; ++i)
      {
         if ( newrowsslack[i] )
            lhs[i] = -SCIPlpiInfinity(conshdlrdata->altlp);
         else
            lhs[i] = 0.0;
         rhs[i] = 0.0;
      }
      /* add new rows */
      SCIP_CALL( SCIPlpiAddRows(conshdlrdata->altlp, nnewrows, lhs, rhs, NULL, 0, NULL, NULL, NULL) );

      SCIPfreeBufferArray(scip, &lhs);
      SCIPfreeBufferArray(scip, &rhs);
   }

   /* now add column */
   obj[0] = objcoef;
   if ( colfree )
   {
      /* create a free variable -> should only happen for additional linear constraints */
      assert( slackvar == NULL );
      lb[0] = -SCIPlpiInfinity(conshdlrdata->altlp);
   }
   else
      lb[0] = 0.0;
   ub[0] = SCIPlpiInfinity(conshdlrdata->altlp);
   matbeg[0] = 0;

   SCIP_CALL( SCIPlpiAddCols(conshdlrdata->altlp, 1, obj, lb, ub, NULL, cnt, matbeg, matind, matval) );

   /* add columns corresponding to bounds of original variables - no bounds needed for slack vars */
   cnt = 0;
   for (v = 0; v < nnewvars; ++v)
   {
      SCIP_VAR* var = newvars[v];
      assert( var != NULL );

      /* if the lower bound is finite */
      val  = SCIPvarGetLbGlobal(var);
      if ( ! SCIPisInfinity(scip, -val) )
      {
         matbeg[nnewcols] = cnt;
         if ( ! SCIPisZero(scip, val) )
         {
            matind[cnt] = 0;
            matval[cnt++] = -val;
         }
         assert( SCIPhashmapExists(conshdlrdata->varhash, var) );

         matind[cnt] = SCIPhashmapGetImageInt(conshdlrdata->varhash, var);
         matval[cnt++] = -1.0;
         obj[nnewcols] = 0.0;
         lb[nnewcols] = 0.0;
         ub[nnewcols] = SCIPlpiInfinity(conshdlrdata->altlp);
         ++conshdlrdata->nlbbounds;

         SCIP_CALL( SCIPhashmapInsertInt(conshdlrdata->lbhash, var, ncols + 1 + nnewcols) );
         assert( SCIPhashmapExists(conshdlrdata->lbhash, var) );
         SCIPdebugMsg(scip, "Added column for lower bound (%f) of variable <%s> to alternative polyhedron (col: %d).\n",
            val, SCIPvarGetName(var), ncols + 1 + nnewcols);
         ++nnewcols;
      }

      /* if the upper bound is finite */
      val = SCIPvarGetUbGlobal(var);
      if ( ! SCIPisInfinity(scip, val) )
      {
         matbeg[nnewcols] = cnt;
         if ( ! SCIPisZero(scip, val) )
         {
            matind[cnt] = 0;
            matval[cnt++] = val;
         }
         assert( SCIPhashmapExists(conshdlrdata->varhash, var) );

         matind[cnt] = SCIPhashmapGetImageInt(conshdlrdata->varhash, var);
         matval[cnt++] = 1.0;
         obj[nnewcols] = 0.0;
         lb[nnewcols] = 0.0;
         ub[nnewcols] = SCIPlpiInfinity(conshdlrdata->altlp);
         ++conshdlrdata->nubbounds;

         SCIP_CALL( SCIPhashmapInsertInt(conshdlrdata->ubhash, var, ncols + 1 + nnewcols) );
         assert( SCIPhashmapExists(conshdlrdata->ubhash, var) );
         SCIPdebugMsg(scip, "Added column for upper bound (%f) of variable <%s> to alternative polyhedron (col: %d).\n",
            val, SCIPvarGetName(var), ncols + 1 + nnewcols);
         ++nnewcols;
      }
   }

   /* add columns if necessary */
   if ( nnewcols > 0 )
   {
      SCIP_CALL( SCIPlpiAddCols(conshdlrdata->altlp, nnewcols, obj, lb, ub, NULL, cnt, matbeg, matind, matval) );
   }

#ifndef NDEBUG
   SCIP_CALL( SCIPlpiGetNCols(conshdlrdata->altlp, &cnt) );
   assert( cnt == ncols + nnewcols + 1 );
#endif

   SCIPfreeBufferArray(scip, &ub);
   SCIPfreeBufferArray(scip, &lb);
   SCIPfreeBufferArray(scip, &obj);
   SCIPfreeBufferArray(scip, &matind);
   SCIPfreeBufferArray(scip, &matval);
   SCIPfreeBufferArray(scip, &matbeg);
   SCIPfreeBufferArray(scip, &newvars);
   SCIPfreeBufferArray(scip, &newrowsslack);

   conshdlrdata->scaled = FALSE;

#ifdef SCIP_OUTPUT
   SCIP_CALL( SCIPlpiWriteLP(conshdlrdata->altlp, "alt.lp") );
#endif

   return SCIP_OKAY;
}


/** add column corresponding to constraint to alternative LP
 *
 *  See the description at the top of the file for more information.
 */
static
SCIP_RETCODE addAltLPConstraint(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            lincons,            /**< linear constraint */
   SCIP_VAR*             slackvar,           /**< slack variable or NULL */
   SCIP_Real             objcoef,            /**< objective coefficient */
   int*                  colindex            /**< index of new column */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_VAR** linvars;
   SCIP_Real* linvals;
   SCIP_Real linrhs;
   SCIP_Real linlhs;
   int nlinvars;

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

   *colindex = -1;

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

   /* if the slack variable is aggregated (multi-aggregation should not happen) */
   assert( slackvar == NULL || SCIPvarGetStatus(slackvar) != SCIP_VARSTATUS_MULTAGGR );
   if ( slackvar != NULL && SCIPvarGetStatus(slackvar) == SCIP_VARSTATUS_AGGREGATED )
   {
      SCIP_VAR* var;
      SCIP_Real scalar = 1.0;
      SCIP_Real constant = 0.0;

      var = slackvar;

      SCIP_CALL( SCIPgetProbvarSum(scip, &var, &scalar, &constant) );

      SCIPdebugMsg(scip, "Slack variable is aggregated (scalar: %f, constant: %f).\n", scalar, constant);

      /* if the slack variable is fixed */
      if ( SCIPisZero(scip, scalar) && ! SCIPconsIsActive(lincons) )
         return SCIP_OKAY;

      /* otherwise construct a linear constraint */
      SCIP_CALL( SCIPallocBufferArray(scip, &linvars, 1) );
      SCIP_CALL( SCIPallocBufferArray(scip, &linvals, 1) );
      linvars[0] = var;
      linvals[0] = scalar;
      nlinvars = 1;
      linlhs = -SCIPinfinity(scip);
      linrhs = constant;
   }
   else
   {
      /* exit if linear constraint is not active */
      if ( ! SCIPconsIsActive(lincons) && slackvar != NULL )
         return SCIP_OKAY;

      /* in this case, the linear constraint is directly usable */
      linvars = SCIPgetVarsLinear(scip, lincons);
      linvals = SCIPgetValsLinear(scip, lincons);
      nlinvars = SCIPgetNVarsLinear(scip, lincons);
      linlhs = SCIPgetLhsLinear(scip, lincons);
      linrhs = SCIPgetRhsLinear(scip, lincons);
   }

   /* create column */
   if ( SCIPisEQ(scip, linlhs, linrhs) )
   {
      /* create free variable for equations (should only happen for additional linear constraints) */
      SCIP_CALL( addAltLPColumn(scip, conshdlr, conshdlrdata, slackvar, nlinvars, linvars, linvals, linrhs, objcoef, 1.0, TRUE, colindex) );
   }
   else if ( ! SCIPisInfinity(scip, linrhs) )
   {
      /* create column for rhs */
      SCIP_CALL( addAltLPColumn(scip, conshdlr, conshdlrdata, slackvar, nlinvars, linvars, linvals, linrhs, objcoef, 1.0, FALSE, colindex) );
   }
   else
   {
      /* create column for lhs */
      assert( ! SCIPisInfinity(scip, -linlhs) );
      SCIP_CALL( addAltLPColumn(scip, conshdlr, conshdlrdata, slackvar, nlinvars, linvars, linvals, linlhs, objcoef, -1.0, FALSE, colindex) );
   }

   if ( slackvar != NULL && SCIPvarGetStatus(slackvar) == SCIP_VARSTATUS_AGGREGATED )
   {
      SCIPfreeBufferArray(scip, &linvals);
      SCIPfreeBufferArray(scip, &linvars);
   }

   return SCIP_OKAY;
}


/** add column corresponding to row to alternative LP
 *
 *  See the description at the top of the file for more information.
 */
static
SCIP_RETCODE addAltLPRow(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_ROW*             row,                /**< row to add */
   SCIP_Real             objcoef,            /**< objective coefficient */
   int*                  colindex            /**< index of new column */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_COL** rowcols;
   SCIP_Real* rowvals;
   SCIP_VAR** rowvars;
   SCIP_Real rowrhs;
   SCIP_Real rowlhs;
   int nrowcols;
   int j;

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

   /* initialize data */
   *colindex = -1;

   /* exit if row is not global */
   if ( SCIProwIsLocal(row) )
      return SCIP_OKAY;

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

   /* get row data */
   rowcols = SCIProwGetCols(row);
   rowvals = SCIProwGetVals(row);
   nrowcols = SCIProwGetNNonz(row);
   rowlhs = SCIProwGetLhs(row) - SCIProwGetConstant(row);
   rowrhs = SCIProwGetRhs(row) - SCIProwGetConstant(row);

   SCIP_CALL( SCIPallocBufferArray(scip, &rowvars, nrowcols) );
   for (j = 0; j < nrowcols; ++j)
   {
      rowvars[j] = SCIPcolGetVar(rowcols[j]);
      assert( rowvars[j] != NULL );
   }

   /* create column */
   if ( SCIPisEQ(scip, rowlhs, rowrhs) )
   {
      /* create free variable for equations (should only happen for additional linear constraints) */
      SCIP_CALL( addAltLPColumn(scip, conshdlr, conshdlrdata, NULL, nrowcols, rowvars, rowvals, rowrhs, objcoef, 1.0, TRUE, colindex) );
   }
   else if ( ! SCIPisInfinity(scip, rowrhs) )
   {
      /* create column for rhs */
      SCIP_CALL( addAltLPColumn(scip, conshdlr, conshdlrdata, NULL, nrowcols, rowvars, rowvals, rowrhs, objcoef, 1.0, FALSE, colindex) );
   }
   else
   {
      /* create column for lhs */
      assert( ! SCIPisInfinity(scip, -rowlhs) );
      SCIP_CALL( addAltLPColumn(scip, conshdlr, conshdlrdata, NULL, nrowcols, rowvars, rowvals, rowlhs, objcoef, -1.0, FALSE, colindex) );
   }

   SCIPfreeBufferArray(scip, &rowvars);

   return SCIP_OKAY;
}


/** try to add objective cut as column to alternative LP */
static
SCIP_RETCODE addObjcut(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr            /**< constraint handler */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_VAR** objvars;
   SCIP_Real* objvals;
   SCIP_VAR** vars;
   int nobjvars = 0;
   int nvars;
   int v;

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

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

   /* skip procedure if already added */
   if ( conshdlrdata->objcutindex >= 0 )
      return SCIP_OKAY;

   /* check whether we can add objective cut: all indicator variables have zero objective */
   if ( ! conshdlrdata->objothervarsonly )
      return SCIP_OKAY;

   assert( ! SCIPisInfinity(scip, conshdlrdata->objupperbound) );
   SCIPdebugMsg(scip, "Add objective cut to alternative LP (obj. bound: %g).\n", conshdlrdata->objupperbound);

   SCIP_CALL( SCIPgetVarsData(scip, &vars, &nvars, NULL, NULL, NULL, NULL) );
   SCIP_CALL( SCIPallocBufferArray(scip, &objvars, nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &objvals, nvars) );

   /* collect nonzeros */
   for (v = 0; v < nvars; ++v)
   {
      SCIP_VAR* var;
      SCIP_Real objval;

      var = vars[v];
      assert( var != NULL );
      objval = SCIPvarGetObj(var);

      /* skip variables with zero objective - this includes slack and indicator variables */
      if ( ! SCIPisZero(scip, objval) )
      {
         objvars[nobjvars] = var;
         objvals[nobjvars++] = objval;
      }
   }

   /* create column (with rhs = upperbound, objective 0, and scaling factor 1.0) */
   SCIP_CALL( addAltLPColumn(scip, conshdlr, conshdlrdata, NULL, nobjvars, objvars, objvals, conshdlrdata->objupperbound, 0.0, 1.0, FALSE, &conshdlrdata->objcutindex) );
   assert( conshdlrdata->objcutindex >= 0 );
   conshdlrdata->objaltlpbound = conshdlrdata->objupperbound;

   SCIPfreeBufferArray(scip, &objvals);
   SCIPfreeBufferArray(scip, &objvars);

   return SCIP_OKAY;
}


/** delete column corresponding to constraint in alternative LP
 *
 *  We currently just fix the corresponding variable to 0.
 */
static
SCIP_RETCODE deleteAltLPConstraint(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONS*            cons                /**< indicator constraint */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;

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

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

   if ( conshdlrdata->altlp != NULL )
   {
      SCIP_CONSDATA* consdata;

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

      if ( consdata->colindex >= 0 )
      {
         SCIP_CALL( fixAltLPVariable(conshdlrdata->altlp, consdata->colindex) );
      }
      consdata->colindex = -1;

      SCIPdebugMsg(scip, "Fixed variable for column %d (constraint: <%s>) from alternative LP to 0.\n", consdata->colindex, SCIPconsGetName(cons));
   }
   conshdlrdata->scaled = FALSE;

   return SCIP_OKAY;
}


/** update upper bound in alternative LP */
static
SCIP_RETCODE updateObjUpperbound(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONSHDLRDATA*    conshdlrdata        /**< constraint handler data */
   )
{
   SCIP_Real objbnd;

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

   if ( ! conshdlrdata->useobjectivecut )
      return SCIP_OKAY;

   if ( conshdlrdata->altlp == NULL )
      return SCIP_OKAY;

   /* first check whether we can improve the upper bound */
   objbnd = SCIPgetUpperbound(scip);
   if ( ! SCIPisInfinity(scip, objbnd) )
   {
      if ( SCIPisObjIntegral(scip) )
         objbnd = SCIPfeasCeil(scip, objbnd) - (1.0 - SCIPcutoffbounddelta(scip));
      else
         objbnd -= SCIPcutoffbounddelta(scip);

      if ( SCIPisLT(scip, objbnd, conshdlrdata->objupperbound) )
         conshdlrdata->objupperbound = objbnd;
   }

   if ( SCIPisInfinity(scip, conshdlrdata->objupperbound) )
      return SCIP_OKAY;

   /* if we can improve on the bound stored in the alternative LP */
   if ( SCIPisLT(scip, conshdlrdata->objupperbound, conshdlrdata->objaltlpbound) )
   {
      SCIPdebugMsg(scip, "Update objective bound to %g.\n", conshdlrdata->objupperbound);

      /* possibly add column for objective cut */
      if ( conshdlrdata->objcutindex < 0 )
      {
         SCIP_CALL( addObjcut(scip, conshdlr) );
      }
      else
      {
#ifndef NDEBUG
         SCIP_Real oldbnd;
         SCIP_CALL( SCIPlpiGetCoef(conshdlrdata->altlp, 0, conshdlrdata->objcutindex, &oldbnd) );
         assert( SCIPisEQ(scip, oldbnd, conshdlrdata->objaltlpbound) );
#endif

         /* update bound */
         SCIP_CALL( SCIPlpiChgCoef(conshdlrdata->altlp, 0, conshdlrdata->objcutindex, conshdlrdata->objupperbound) );
         conshdlrdata->objaltlpbound = conshdlrdata->objupperbound;

#ifdef SCIP_OUTPUT
         SCIP_CALL( SCIPlpiWriteLP(conshdlrdata->altlp, "alt.lp") );
#endif
      }
   }

   return SCIP_OKAY;
}


/** check whether the given LP is infeasible
 *
 *  If @a primal is false we assume that the problem is <em>dual feasible</em>, e.g., the problem
 *  was only changed by fixing bounds!
 *
 *  This is the workhorse for all methods that have to solve the alternative LP. We try in several
 *  ways to recover from possible stability problems.
 *
 *  @pre It is assumed that all parameters for the alternative LP are set.
 */
static
SCIP_RETCODE checkAltLPInfeasible(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_LPI*             lp,                 /**< LP */
   SCIP_Real             maxcondition,       /**< maximal allowed condition of LP solution basis matrix */
   SCIP_Bool             primal,             /**< whether we are using the primal or dual simplex */
   SCIP_Bool*            infeasible,         /**< output: whether the LP is infeasible */
   SCIP_Bool*            error               /**< output: whether an error occurred */
   )
{
   SCIP_RETCODE retcode;
   SCIP_Real condition;

   assert( scip != NULL );
   assert( lp != NULL );
   assert( infeasible != NULL );
   assert( error != NULL );

   *error = FALSE;

   /* solve LP */
   if ( primal )
      retcode = SCIPlpiSolvePrimal(lp);  /* use primal simplex */
   else
      retcode = SCIPlpiSolveDual(lp);    /* use dual simplex */
   if ( retcode == SCIP_LPERROR )
   {
      *error = TRUE;
      return SCIP_OKAY;
   }
   SCIP_CALL( retcode );

   /* resolve if LP is not stable */
   if ( ! SCIPlpiIsStable(lp) )
   {
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_FROMSCRATCH, TRUE) );
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_PRESOLVING, FALSE) );
      SCIPwarningMessage(scip, "Numerical problems, retrying ...\n");

      /* re-solve LP */
      if ( primal )
         retcode = SCIPlpiSolvePrimal(lp);  /* use primal simplex */
      else
         retcode = SCIPlpiSolveDual(lp);    /* use dual simplex */

      /* reset parameters */
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_FROMSCRATCH, FALSE) );
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_PRESOLVING, TRUE) );

      if ( retcode == SCIP_LPERROR )
      {
         *error = TRUE;
         return SCIP_OKAY;
      }
      SCIP_CALL( retcode );
   }

   /* check whether we want to ignore the result, because the condition number is too large */
   if ( maxcondition > 0.0 )
   {
      /* check estimated condition number of basis matrix */
      SCIP_CALL( SCIPlpiGetRealSolQuality(lp, SCIP_LPSOLQUALITY_ESTIMCONDITION, &condition) );
      if ( condition != SCIP_INVALID && condition > maxcondition )  /*lint !e777*/
      {
         SCIPdebugMsg(scip, "Estimated condition number of basis matrix (%e) exceeds maximal allowance (%e).\n", condition, maxcondition);

         *error = TRUE;

         return SCIP_OKAY;
      }
      else if ( condition != SCIP_INVALID )  /*lint !e777*/
      {
         SCIPdebugMsg(scip, "Estimated condition number of basis matrix (%e) is below maximal allowance (%e).\n", condition, maxcondition);
      }
      else
      {
         SCIPdebugMsg(scip, "Estimated condition number of basis matrix not available.\n");
      }
   }

   /* check whether we are in the paradoxical situation that
    * - the primal is not infeasible
    * - the primal is not unbounded
    * - the LP is not optimal
    * - we have a primal ray
    *
    * If we ran the dual simplex algorithm, then we run again with the primal simplex
    */
   if ( ! SCIPlpiIsPrimalInfeasible(lp) && ! SCIPlpiIsPrimalUnbounded(lp) &&
        ! SCIPlpiIsOptimal(lp) && SCIPlpiExistsPrimalRay(lp) && ! primal )
   {
      SCIPwarningMessage(scip, "The dual simplex produced a primal ray. Retrying with primal ...\n");

      /* the following settings might be changed: */
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_FROMSCRATCH, TRUE) );
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_PRESOLVING, TRUE) );
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_SCALING, 1) );

      SCIP_CALL( SCIPlpiSolvePrimal(lp) );   /* use primal simplex */

      /* reset parameters */
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_FROMSCRATCH, FALSE) );
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_PRESOLVING, TRUE) );
      SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_SCALING, 1) );
   }

   /* examine LP solution status */
   if ( SCIPlpiIsPrimalInfeasible(lp) )     /* the LP is provably infeasible */
   {
      assert( ! SCIPlpiIsPrimalUnbounded(lp) );   /* can't be unbounded or optimal */
      assert( ! SCIPlpiIsOptimal(lp) );           /* if it is infeasible! */

      *infeasible = TRUE;                         /* LP is infeasible */
      return SCIP_OKAY;
   }
   else
   {
      /* By assumption the dual is feasible if the dual simplex is run, therefore
       * the status has to be primal unbounded or optimal. */
      if ( ! SCIPlpiIsPrimalUnbounded(lp) && ! SCIPlpiIsOptimal(lp) )
      {
         /* We have a status different from unbounded or optimal. This should not be the case ... */
         if (primal)
            SCIPwarningMessage(scip, "Primal simplex returned with unknown status: %d\n", SCIPlpiGetInternalStatus(lp));
         else
            SCIPwarningMessage(scip, "Dual simplex returned with unknown status: %d\n", SCIPlpiGetInternalStatus(lp));

         /* SCIP_CALL( SCIPlpiWriteLP(lp, "debug.lp") ); */
         *error = TRUE;
         return SCIP_OKAY;
      }
   }

   /* at this point we have a feasible solution */
   *infeasible = FALSE;
   return SCIP_OKAY;
}


/** tries to extend a given set of variables to a cover
 *
 *  At each step we include a variable which covers a new IIS. The corresponding IIS inequalities are added to the LP,
 *  if this not already happened.
 *
 *  @pre It is assumed that all parameters for the alternative LP are set and that the variables
 *  corresponding to @a S are fixed. Furthermore @c xVal_ should contain the current LP solution.
 */
static
SCIP_RETCODE extendToCover(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONSHDLRDATA*    conshdlrdata,       /**< constraint handler data */
   SCIP_LPI*             lp,                 /**< LP */
   SCIP_SOL*             sol,                /**< solution to be separated */
   SCIP_Bool             removable,          /**< whether cuts should be removable */
   SCIP_Bool             genlogicor,         /**< should logicor constraints be generated? */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss,              /**< indicator constraints */
   SCIP_Bool*            S,                  /**< bitset of variables */
   int*                  size,               /**< size of S */
   SCIP_Real*            value,              /**< objective value of S */
   SCIP_Bool*            error,              /**< output: whether an error occurred */
   SCIP_Bool*            cutoff,             /**< whether we detected a cutoff by an infeasible inequality */
   int*                  nGen                /**< number of generated cuts */
   )
{
#ifdef SCIP_DEBUG
   char name[SCIP_MAXSTRLEN];
#endif
   SCIP_Real* primsol;
   int nnonviolated = 0;
   int step = 0;
   int nCols;

   assert( scip != NULL );
   assert( lp != NULL );
   assert( conss != NULL );
   assert( S != NULL );
   assert( size != NULL );
   assert( value != NULL );
   assert( error != NULL );
   assert( cutoff != NULL );
   assert( nGen != NULL );

   *error = FALSE;
   *cutoff = FALSE;
   *nGen = 0;

   SCIP_CALL( SCIPlpiGetNCols(lp, &nCols) );
   SCIP_CALL( SCIPallocBufferArray(scip, &primsol, nCols) );
   assert( nconss <= nCols );

   do
   {
      SCIP_Bool infeasible;
      SCIP_Real sum = 0.0;
      SCIP_Real candobj = -1.0;
      SCIP_Real candval = 2.0;
      SCIP_Real norm = 1.0;
      int sizeIIS = 0;
      int candidate = -1;
      int candindex = -1;
      int j;

      if ( step == 0 )
      {
         /* the first LP is solved without warm start, after that we use a warmstart. */
         SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_FROMSCRATCH, TRUE) );
         SCIP_CALL( checkAltLPInfeasible(scip, lp, conshdlrdata->maxconditionaltlp, TRUE, &infeasible, error) );
         SCIP_CALL_PARAM( SCIPlpiSetIntpar(lp, SCIP_LPPAR_FROMSCRATCH, FALSE) );
      }
      else
         SCIP_CALL( checkAltLPInfeasible(scip, lp, conshdlrdata->maxconditionaltlp, FALSE, &infeasible, error) );

      if ( *error )
         break;

      /* if the alternative polyhedron is infeasible, we found a cover */
      if ( infeasible )
      {
         /* Note: checking for a primal solution is done in extendToCover(). */
         SCIPdebugMsg(scip, "   size: %4d  produced possible cover with indicator variable objective value %f.\n", *size, *value);

         /* we currently cannot call probing if there are cuts in the sepastore; @todo fix this */
         if ( conshdlrdata->trysolfromcover )
         {
            /* Check whether we want to try to construct a feasible solution: there should be no integer/binary variables
             * except the indicator variables. Thus, there should be no integral variables and the number of indicator
             * variables should be at least (actually equal to) the number of binary variables. */
            if ( SCIPgetNIntVars(scip) == 0 && nconss >= SCIPgetNBinVars(scip) )
            {
               SCIP_HEUR* heurindicator;

               heurindicator = SCIPfindHeur(scip, "indicator");
               if ( heurindicator == NULL )
               {
                  SCIPerrorMessage("Could not find heuristic \"indicator\".\n");
                  return SCIP_PLUGINNOTFOUND;
               }

               SCIP_CALL( SCIPheurPassIndicator(scip, heurindicator, nconss, conss, S, -*value) );
               SCIPdebugMsg(scip, "Passed feasible solution to indicator heuristic.\n");
            }
         }
         break;
      }

      /* get solution of alternative LP */
      SCIP_CALL( SCIPlpiGetSol(lp, NULL, primsol, NULL, NULL, NULL) );

      /* get value of cut and find candidate for variable to add */
      for (j = 0; j < nconss; ++j)
      {
         SCIP_CONSDATA* consdata;
         int ind;

         consdata = SCIPconsGetData(conss[j]);
         assert( consdata != NULL );
         ind = consdata->colindex;

         if ( ind >= 0 )
         {
            assert( ind < nCols );

            /* check support of the solution, i.e., the corresponding IIS */
            if ( ! SCIPisFeasZero(scip, primsol[ind]) )
            {
               SCIP_Real val;

               assert( ! S[j] );
               ++sizeIIS;
               val = SCIPgetSolVal(scip, sol, consdata->binvar);
               sum += val;

               /* take element with smallest relaxation value */
               if ( val < candval )
               {
                  candidate = j;
                  candindex = ind;
                  candval = val;
                  candobj = varGetObjDelta(consdata->binvar);
               }
            }
         }
      }

      /* check for error */
      if ( candidate < 0 )
      {
         /* Because of numerical problems it might happen that the solution primsol above is zero
          * within the tolerances. In this case we quit. */
         break;
      }
      assert( candidate >= 0 );
      assert( ! S[candidate] );
      assert( sizeIIS > 0 );

      /* get the type of norm to use for efficacy calculations */
      switch ( conshdlrdata->normtype )
      {
      case 'e':
         norm = sqrt((SCIP_Real) sizeIIS);
         break;
      case 'm':
         norm = 1.0;
         break;
      case 's':
         norm = (SCIP_Real) sizeIIS;
         break;
      case 'd':
         norm = 1.0;
         break;
      default:
         SCIPerrorMessage("Invalid efficacy norm parameter '%c'.\n", conshdlrdata->normtype);
         SCIPABORT();
         norm = 1.0; /*lint !e527*/
      }

      SCIPdebugMsg(scip, "   size: %4d, add var. %4d (obj: %-6g, alt-LP sol: %-8.4f); IIS size: %4d, eff.: %g.\n",
         *size, candidate, candobj, primsol[SCIPconsGetData(conss[candidate])->colindex], sizeIIS, (sum - (SCIP_Real) (sizeIIS - 1))/norm);

      /* update new set S */
      S[candidate] = TRUE;
      ++(*size);
      *value += candobj;

      /* fix chosen variable to 0 */
      SCIP_CALL( fixAltLPVariable(lp, candindex) );

      /* if cut is violated, i.e., sum - sizeIIS + 1 > 0 */
      if ( SCIPisEfficacious(scip, (sum - (SCIP_Real) (sizeIIS - 1))/norm) )
      {
         SCIP_Bool isLocal = FALSE;

#ifdef SCIP_ENABLE_IISCHECK
         /* check whether we really have an infeasible subsystem */
         SCIP_CALL( checkIIS(scip, nconss, conss, primsol) );
#endif

         /* check whether IIS corresponds to a local cut */
         if (  conshdlrdata->updatebounds )
         {
            SCIP_CALL( checkIISlocal(scip, conshdlrdata, primsol, &isLocal) );
         }

         if ( genlogicor )
         {
            SCIP_CONS* cons;
            SCIP_VAR** vars;
            int cnt = 0;

            SCIP_CALL( SCIPallocBufferArray(scip, &vars, nconss) );

            /* collect variables corresponding to support to cut */
            for (j = 0; j < nconss; ++j)
            {
               SCIP_CONSDATA* consdata;
               int ind;

               consdata = SCIPconsGetData(conss[j]);
               ind = consdata->colindex;

               if ( ind >= 0 )
               {
                  assert( ind < nCols );
                  assert( consdata->binvar != NULL );

                  /* check support of the solution, i.e., the corresponding IIS */
                  if ( ! SCIPisFeasZero(scip, primsol[ind]) )
                  {
                     SCIP_VAR* var;
                     SCIP_CALL( SCIPgetNegatedVar(scip, consdata->binvar, &var) );
                     vars[cnt++] = var;
                  }
               }
            }
            assert( cnt == sizeIIS );

#ifdef SCIP_DEBUG
            (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "iis%d", conshdlrdata->niiscutsgen + *nGen);
            SCIP_CALL( SCIPcreateConsLogicor(scip, &cons, name, cnt, vars, FALSE, TRUE, TRUE, TRUE, TRUE, isLocal, FALSE, TRUE, removable, FALSE) );
#else
            SCIP_CALL( SCIPcreateConsLogicor(scip, &cons, "", cnt, vars, FALSE, TRUE, TRUE, TRUE, TRUE, isLocal, FALSE, TRUE, removable, FALSE) );
#endif

#ifdef SCIP_OUTPUT
            SCIP_CALL( SCIPprintCons(scip, cons, NULL) );
            SCIPinfoMessage(scip, NULL, ";\n");
#endif

            SCIP_CALL( SCIPaddCons(scip, cons) );
            SCIP_CALL( SCIPreleaseCons(scip, &cons) );

            SCIPfreeBufferArray(scip, &vars);
            ++(*nGen);
         }
         else
         {
            SCIP_ROW* row;

            /* create row */
#ifdef SCIP_DEBUG
            (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "iis%d", conshdlrdata->niiscutsgen + *nGen);
            SCIP_CALL( SCIPcreateEmptyRowCons(scip, &row, conshdlr, name, -SCIPinfinity(scip), (SCIP_Real) (sizeIIS - 1), isLocal, FALSE, removable) );
#else
            SCIP_CALL( SCIPcreateEmptyRowCons(scip, &row, conshdlr, "", -SCIPinfinity(scip), (SCIP_Real) (sizeIIS - 1), isLocal, FALSE, removable) );
#endif
            SCIP_CALL( SCIPcacheRowExtensions(scip, row) );

            /* add variables corresponding to support to cut */
            for (j = 0; j < nconss; ++j)
            {
               int ind;
               SCIP_CONSDATA* consdata;

               consdata = SCIPconsGetData(conss[j]);
               ind = consdata->colindex;

               if ( ind >= 0 )
               {
                  assert( ind < nCols );
                  assert( consdata->binvar != NULL );

                  /* check support of the solution, i.e., the corresponding IIS */
                  if ( ! SCIPisFeasZero(scip, primsol[ind]) )
                  {
                     SCIP_VAR* var = consdata->binvar;
                     SCIP_CALL( SCIPaddVarToRow(scip, row, var, 1.0) );
                  }
               }
            }
            SCIP_CALL( SCIPflushRowExtensions(scip, row) );
#ifdef SCIP_OUTPUT
            SCIP_CALL( SCIPprintRow(scip, row, NULL) );
#endif
            SCIP_CALL( SCIPaddRow(scip, row, FALSE, cutoff) );
            if ( *cutoff )
            {
               SCIPfreeBufferArray(scip, &primsol);
               return SCIP_OKAY;
            }

            /* cut should be violated: */
            assert( SCIPisFeasNegative(scip, SCIPgetRowSolFeasibility(scip, row, sol)) );

            /* add cuts to pool if they are globally valid */
            if ( ! isLocal )
               SCIP_CALL( SCIPaddPoolCut(scip, row) );
            SCIP_CALL( SCIPreleaseRow(scip, &row));
            ++(*nGen);
         }
         nnonviolated = 0;
      }
      else
         ++nnonviolated;
      ++step;

      if ( nnonviolated > conshdlrdata->maxsepanonviolated )
      {
         SCIPdebugMsg(scip, "Stop separation after %d non violated IISs.\n", nnonviolated);
         break;
      }
   }
   while (step < nconss);

   SCIPfreeBufferArray(scip, &primsol);

   return SCIP_OKAY;
}


/* ---------------------------- constraint handler local methods ----------------------*/

/** creates and initializes consdata */
static
SCIP_RETCODE consdataCreate(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_CONSHDLRDATA*    conshdlrdata,       /**< constraint handler data */
   const char*           consname,           /**< name of constraint (or NULL) */
   SCIP_CONSDATA**       consdata,           /**< pointer to linear constraint data */
   SCIP_EVENTHDLR*       eventhdlrbound,     /**< event handler for bound change events */
   SCIP_EVENTHDLR*       eventhdlrrestart,   /**< event handler for handling restarts */
   SCIP_VAR*             binvar,             /**< binary variable (or NULL) */
   SCIP_VAR*             slackvar,           /**< slack variable */
   SCIP_CONS*            lincons,            /**< linear constraint (or NULL) */
   SCIP_Bool             linconsactive       /**< whether the linear constraint is active */
   )
{
   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conshdlrdata != NULL );
   assert( consdata != NULL );
   assert( slackvar != NULL );
   assert( eventhdlrbound != NULL );
   assert( eventhdlrrestart != NULL );

   /* create constraint data */
   SCIP_CALL( SCIPallocBlockMemory(scip, consdata) );
   (*consdata)->nfixednonzero = 0;
   (*consdata)->colindex = -1;
   (*consdata)->linconsactive = linconsactive;
   (*consdata)->binvar = binvar;
   (*consdata)->slackvar = slackvar;
   (*consdata)->lincons = lincons;
   (*consdata)->implicationadded = FALSE;
   (*consdata)->slacktypechecked = FALSE;

   /* if we are transformed, obtain transformed variables and catch events */
   if ( SCIPisTransformed(scip) )
   {
      SCIP_VAR* var;

      /* handle binary variable */
      if ( binvar != NULL )
      {
         SCIP_CALL( SCIPgetTransformedVar(scip, binvar, &var) );
         assert( var != NULL );
         (*consdata)->binvar = var;

         /* check type */
         if ( SCIPvarGetType(var) != SCIP_VARTYPE_BINARY )
         {
            SCIPerrorMessage("Indicator variable <%s> is not binary %d.\n", SCIPvarGetName(var), SCIPvarGetType(var));
            return SCIP_ERROR;
         }

         /* catch local bound change events on binary variable */
         if ( linconsactive )
         {
            SCIP_CALL( SCIPcatchVarEvent(scip, var, SCIP_EVENTTYPE_BOUNDCHANGED, eventhdlrbound, (SCIP_EVENTDATA*)*consdata, NULL) );
         }

         /* catch global bound change events on binary variable */
         if ( conshdlrdata->forcerestart )
         {
            SCIPdebugMsg(scip, "Catching GBDCHANGED event for <%s>.\n", SCIPvarGetName(var));
            SCIP_CALL( SCIPcatchVarEvent(scip, var, SCIP_EVENTTYPE_GBDCHANGED, eventhdlrrestart, (SCIP_EVENTDATA*) conshdlrdata, NULL) );
         }

         /* if binary variable is fixed to be nonzero */
         if ( SCIPvarGetLbLocal(var) > 0.5 )
            ++((*consdata)->nfixednonzero);
      }

      /* handle slack variable */
      SCIP_CALL( SCIPgetTransformedVar(scip, slackvar, &var) );
      assert( var != NULL );
      (*consdata)->slackvar = var;

      /* catch bound change events on slack variable and adjust nfixednonzero */
      if ( linconsactive )
      {
         SCIP_CALL( SCIPcatchVarEvent(scip, var, SCIP_EVENTTYPE_BOUNDCHANGED, eventhdlrbound, (SCIP_EVENTDATA*)*consdata, NULL) );

         /* if slack variable is fixed to be nonzero */
         if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(var)) )
            ++((*consdata)->nfixednonzero);
      }

      /* add corresponding column to alternative LP if the constraint is new */
      if ( conshdlrdata->sepaalternativelp && SCIPgetStage(scip) >= SCIP_STAGE_INITSOLVE && lincons != NULL )
      {
         assert( lincons != NULL );
         assert( consname != NULL );

         SCIP_CALL( addAltLPConstraint(scip, conshdlr, lincons, var, 1.0, &(*consdata)->colindex) );

         SCIPdebugMsg(scip, "Added column for <%s> to alternative LP with column index %d.\n", consname, (*consdata)->colindex);
#ifdef SCIP_OUTPUT
         SCIP_CALL( SCIPprintCons(scip, lincons, NULL) );
         SCIPinfoMessage(scip, NULL, ";\n");
#endif
      }

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

   return SCIP_OKAY;
}


/** create variable upper bounds for constraints */
static
SCIP_RETCODE createVarUbs(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLRDATA*    conshdlrdata,       /**< constraint handler data */
   SCIP_CONS**           conss,              /**< constraints */
   int                   nconss,             /**< number of constraints */
   int*                  ngen                /**< number of successful operations */
   )
{
   char name[50];
   int c;

   assert( scip != NULL );
   assert( conshdlrdata != NULL );
   assert( ngen != NULL );

   *ngen = 0;

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

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

      ub = SCIPvarGetUbGlobal(consdata->slackvar);
      assert( ! SCIPisNegative(scip, ub) );

      /* insert corresponding row if helpful and coefficient is not too large */
      if ( ub <= conshdlrdata->maxcouplingvalue )
      {
         SCIP_CONS* cons;

#ifndef NDEBUG
         (void) SCIPsnprintf(name, 50, "couple%d", c);
#else
         name[0] = '\0';
#endif

         SCIPdebugMsg(scip, "Insert coupling varbound constraint for indicator constraint <%s> (coeff: %f).\n", SCIPconsGetName(conss[c]), ub);

         /* add variable upper bound:
          * - check constraint if we remove the indicator constraint afterwards
          * - constraint is dynamic if we do not remove indicator constraints
          * - constraint is removable if we do not remove indicator constraints
          */
         SCIP_CALL( SCIPcreateConsVarbound(scip, &cons, name, consdata->slackvar, consdata->binvar, ub, -SCIPinfinity(scip), ub,
               TRUE, TRUE, TRUE, conshdlrdata->removeindicators, TRUE, FALSE, FALSE,
               !conshdlrdata->removeindicators, !conshdlrdata->removeindicators, FALSE) );

         SCIP_CALL( SCIPaddCons(scip, cons) );
         SCIP_CALL( SCIPreleaseCons(scip, &cons) );

         /* remove indicator constraint if required */
         if ( conshdlrdata->removeindicators )
         {
            SCIPdebugMsg(scip, "Removing indicator constraint <%s>.\n", SCIPconsGetName(conss[c]));
            assert( ! SCIPconsIsModifiable(conss[c]) );

            /* mark linear constraint to be upgrade-able */
            if ( SCIPconsIsActive(consdata->lincons) )
            {
               SCIPconsAddUpgradeLocks(consdata->lincons, -1);
               assert( SCIPconsGetNUpgradeLocks(consdata->lincons) == 0 );
            }

            SCIP_CALL( SCIPdelCons(scip, conss[c]) );
         }

         ++(*ngen);
      }
   }

   return SCIP_OKAY;
}


/** perform one presolving round */
static
SCIP_RETCODE presolRoundIndicator(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLRDATA*    conshdlrdata,       /**< constraint handler data */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_Bool             dualreductions,     /**< should dual reductions be performed? */
   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 */
   )
{
   SCIP_Bool infeasible;
   SCIP_Bool fixed;

   assert( scip != NULL );
   assert( cons != NULL );
   assert( consdata != NULL );
   assert( cutoff != NULL );
   assert( success != NULL );
   assert( ndelconss != NULL );
   assert( nfixedvars != NULL );
   assert( consdata->binvar != NULL );
   assert( consdata->slackvar != NULL );

   *cutoff = FALSE;
   *success = FALSE;

   /* if the binary variable is fixed to nonzero */
   if ( SCIPvarGetLbLocal(consdata->binvar) > 0.5 )
   {
      SCIPdebugMsg(scip, "Presolving <%s>: Binary variable fixed to 1.\n", SCIPconsGetName(cons));

      /* if slack variable is fixed to nonzero, we are infeasible */
      if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(consdata->slackvar)) )
      {
         SCIPdebugMsg(scip, "The problem is infeasible: binary and slack variable are fixed to be nonzero.\n");
         *cutoff = TRUE;
         return SCIP_OKAY;
      }

      /* otherwise fix slack variable to 0 */
      SCIPdebugMsg(scip, "Fix slack variable to 0 and delete constraint.\n");
      SCIP_CALL( SCIPfixVar(scip, consdata->slackvar, 0.0, &infeasible, &fixed) );
      assert( ! infeasible );
      if ( fixed )
         ++(*nfixedvars);

      /* mark linear constraint to be update-able */
      if ( SCIPconsIsActive(consdata->lincons) )
      {
         SCIPconsAddUpgradeLocks(consdata->lincons, -1);
         assert( SCIPconsGetNUpgradeLocks(consdata->lincons) == 0 );
      }

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

   /* if the binary variable is fixed to zero */
   if ( SCIPvarGetUbLocal(consdata->binvar) < 0.5 )
   {
      SCIPdebugMsg(scip, "Presolving <%s>: Binary variable fixed to 0, deleting indicator constraint.\n", SCIPconsGetName(cons));

      /* mark linear constraint to be update-able */
      if ( SCIPconsIsActive(consdata->lincons) )
      {
         SCIPconsAddUpgradeLocks(consdata->lincons, -1);
         assert( SCIPconsGetNUpgradeLocks(consdata->lincons) == 0 );
      }

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

   /* if the slack variable is fixed to nonzero */
   if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(consdata->slackvar)) )
   {
      SCIPdebugMsg(scip, "Presolving <%s>: Slack variable fixed to nonzero.\n", SCIPconsGetName(cons));

      /* if binary variable is fixed to nonzero, we are infeasible */
      if ( SCIPvarGetLbLocal(consdata->binvar) > 0.5 )
      {
         SCIPdebugMsg(scip, "The problem is infeasible: binary and slack variable are fixed to be nonzero.\n");
         *cutoff = TRUE;
         return SCIP_OKAY;
      }

      /* otherwise fix binary variable to 0 */
      SCIPdebugMsg(scip, "Fix binary variable to 0 and delete indicator constraint.\n");
      SCIP_CALL( SCIPfixVar(scip, consdata->binvar, 0.0, &infeasible, &fixed) );
      assert( ! infeasible );
      if ( fixed )
         ++(*nfixedvars);

      /* mark linear constraint to be update-able */
      if ( SCIPconsIsActive(consdata->lincons) )
      {
         SCIPconsAddUpgradeLocks(consdata->lincons, -1);
         assert( SCIPconsGetNUpgradeLocks(consdata->lincons) == 0 );
      }

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

   /* if the slack variable is fixed to zero */
   if ( SCIPisFeasZero(scip, SCIPvarGetUbLocal(consdata->slackvar)) )
   {
      /* perform dual reductions - if required */
      if ( dualreductions )
      {
         SCIP_VAR* binvar;
         SCIP_Real obj;

         /* check objective of binary variable */
         binvar = consdata->binvar;
         obj = varGetObjDelta(binvar);

         /* if obj = 0, we prefer fixing the binary variable to 1 (if possible) */
         if ( obj <= 0.0 )
         {
            /* In this case we would like to fix the binary variable to 1, if it is not locked up
               except by this indicator constraint. If more than one indicator constraint is
               effected, we have to hope that they are all fulfilled - in this case the last
               constraint will fix the binary variable to 1. */
            if ( SCIPvarGetNLocksUpType(binvar, SCIP_LOCKTYPE_MODEL) <= 1 )
            {
               if ( SCIPvarGetUbGlobal(binvar) > 0.5 )
               {
                  SCIPdebugMsg(scip, "Presolving <%s> - dual reduction: Slack variable fixed to 0, fix binary variable to 1.\n", SCIPconsGetName(cons));
                  SCIP_CALL( SCIPfixVar(scip, binvar, 1.0, &infeasible, &fixed) );
                  assert( ! infeasible );
                  if ( fixed )
                     ++(*nfixedvars);
                  /* make sure that the other case does not occur */
                  obj = -1.0;
               }
            }
         }
         if ( obj >= 0.0 )
         {
            /* In this case we would like to fix the binary variable to 0, if it is not locked down
               (should also have been performed by other dual reductions). */
            if ( SCIPvarGetNLocksDownType(binvar, SCIP_LOCKTYPE_MODEL) == 0 )
            {
               if ( SCIPvarGetLbGlobal(binvar) < 0.5 )
               {
                  SCIPdebugMsg(scip, "Presolving <%s> - dual reduction: Slack variable fixed to 0, fix binary variable to 0.\n", SCIPconsGetName(cons));
                  SCIP_CALL( SCIPfixVar(scip, binvar, 0.0, &infeasible, &fixed) );
                  assert( ! infeasible );
                  if ( fixed )
                     ++(*nfixedvars);
               }
            }
         }
      }

      SCIPdebugMsg(scip, "Presolving <%s>: Slack variable fixed to zero, delete redundant indicator constraint.\n", SCIPconsGetName(cons));

      /* mark linear constraint to be upgrade-able */
      if ( SCIPconsIsActive(consdata->lincons) )
      {
         SCIPconsAddUpgradeLocks(consdata->lincons, -1);
         assert( SCIPconsGetNUpgradeLocks(consdata->lincons) == 0 );
      }

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

   /* check whether indicator variable is aggregated  */
   if ( SCIPvarGetStatus(consdata->binvar) == SCIP_VARSTATUS_AGGREGATED )
   {
      SCIP_Bool negated = FALSE;
      SCIP_VAR* var;

      /* possibly get representation of indicator variable by active variable */
      var = consdata->binvar;
      SCIP_CALL( SCIPvarGetProbvarBinary(&var, &negated) );
      assert( var == consdata->binvar || SCIPvarIsActive(var) || SCIPvarIsNegated(var) );

      /* we can replace the binary variable by the active variable if it is not negated */
      if ( var != consdata->binvar && ! negated )
      {
         SCIPdebugMsg(scip, "Indicator variable <%s> is aggregated and replaced by active/negated variable <%s>.\n", SCIPvarGetName(consdata->binvar), SCIPvarGetName(var) );

         /* we need to update the events and locks */
         assert( conshdlrdata->eventhdlrbound != NULL );
         SCIP_CALL( SCIPdropVarEvent(scip, consdata->binvar, SCIP_EVENTTYPE_BOUNDCHANGED, conshdlrdata->eventhdlrbound, (SCIP_EVENTDATA*) consdata, -1) );
         SCIP_CALL( SCIPcatchVarEvent(scip, var, SCIP_EVENTTYPE_BOUNDCHANGED, conshdlrdata->eventhdlrbound, (SCIP_EVENTDATA*) consdata, NULL) );

         SCIP_CALL( SCIPaddVarLocksType(scip, consdata->binvar, SCIP_LOCKTYPE_MODEL, 0, -1) );
         SCIP_CALL( SCIPaddVarLocksType(scip, var, SCIP_LOCKTYPE_MODEL, 0, 1) );

         /* change binvary variable */
         consdata->binvar = var;
      }
   }
   else if ( SCIPvarGetStatus(consdata->binvar) == SCIP_VARSTATUS_NEGATED )
   {
      SCIP_VAR* var;

      var = SCIPvarGetNegatedVar(consdata->binvar);
      assert( var != NULL );

      /* if the binary variable is the negated slack variable, we have 1 - s = 1 -> s = 0, i.e., the constraint is redundant */
      if ( var == consdata->slackvar )
      {
         /* delete constraint */
         assert( ! SCIPconsIsModifiable(cons) );
         SCIP_CALL( SCIPdelCons(scip, cons) );
         ++(*ndelconss);
         *success = TRUE;
         return SCIP_OKAY;
      }
   }

   /* check whether slack variable is aggregated  */
   if ( SCIPvarGetStatus(consdata->slackvar) == SCIP_VARSTATUS_AGGREGATED || SCIPvarGetStatus(consdata->slackvar) == SCIP_VARSTATUS_NEGATED )
   {
      SCIP_BOUNDTYPE boundtype = SCIP_BOUNDTYPE_LOWER;
      SCIP_Real bound;
      SCIP_VAR* var;

      /* possibly get representation of slack variable by active variable */
      var = consdata->slackvar;
      bound = SCIPvarGetLbGlobal(var);

      SCIP_CALL( SCIPvarGetProbvarBound(&var, &bound, &boundtype) );
      assert( var != consdata->slackvar );

      /* we can replace the slack variable by the active variable if it is also a >= variable */
      if ( var != consdata->binvar && boundtype == SCIP_BOUNDTYPE_LOWER && SCIPisGE(scip, bound, 0.0) )
      {
         assert( SCIPvarIsActive(var) );
         SCIPdebugMsg(scip, "Slack variable <%s> is aggregated or negated and replaced by active variable <%s>.\n", SCIPvarGetName(consdata->slackvar), SCIPvarGetName(var) );

         /* we need to update the events, locks, and captures */
         assert( conshdlrdata->eventhdlrbound != NULL );
         SCIP_CALL( SCIPdropVarEvent(scip, consdata->slackvar, SCIP_EVENTTYPE_BOUNDCHANGED, conshdlrdata->eventhdlrbound, (SCIP_EVENTDATA*) consdata, -1) );
         SCIP_CALL( SCIPcatchVarEvent(scip, var, SCIP_EVENTTYPE_BOUNDCHANGED, conshdlrdata->eventhdlrbound, (SCIP_EVENTDATA*) consdata, NULL) );

         SCIP_CALL( SCIPaddVarLocksType(scip, consdata->slackvar, SCIP_LOCKTYPE_MODEL, 0, -1) );
         SCIP_CALL( SCIPaddVarLocksType(scip, var, SCIP_LOCKTYPE_MODEL, 0, 1) );

         SCIP_CALL( SCIPreleaseVar(scip, &consdata->slackvar) );
         SCIP_CALL( SCIPcaptureVar(scip, var) );

         /* change slack variable */
         consdata->slackvar = var;
      }
      else if ( var == consdata->binvar )
      {
         /* check special case that aggregating variable is equal to the indicator variable */
         assert( SCIPisEQ(scip, bound, 0.0) || SCIPisEQ(scip, bound, 1.0) );

         /* if the lower bound is transformed to an upper bound, we have "y = 1 -> 1 - y = 0", i.e., the constraint is redundant */
         if ( boundtype == SCIP_BOUNDTYPE_UPPER )
         {
            SCIPdebugMsg(scip, "Slack variable <%s> is aggregated to negated indicator variable <%s> -> constraint redundant.\n",
               SCIPvarGetName(consdata->slackvar), SCIPvarGetName(consdata->binvar));
            assert( SCIPisEQ(scip, bound, 1.0) );

            /* delete constraint */
            assert( ! SCIPconsIsModifiable(cons) );
            SCIP_CALL( SCIPdelCons(scip, cons) );
            ++(*ndelconss);
            *success = TRUE;
            return SCIP_OKAY;
         }
         else
         {
            /* if the lower bound is transformed to a lower bound, we have "y = 1 -> y = 0", i.e., we can fix the binary variable to 0 */
            SCIPdebugMsg(scip, "Slack variable <%s> is aggregated to the indicator variable <%s> -> fix indicator variable to 0.\n",
               SCIPvarGetName(consdata->slackvar), SCIPvarGetName(consdata->binvar));
            assert( boundtype == SCIP_BOUNDTYPE_LOWER );
            assert( SCIPisEQ(scip, bound, 0.0) );

            SCIP_CALL( SCIPfixVar(scip, consdata->binvar, 0.0, &infeasible, &fixed) );
            assert( ! infeasible );

            if ( fixed )
               ++(*nfixedvars);

            SCIP_CALL( SCIPdelCons(scip, cons) );

            ++(*ndelconss);
            *success = TRUE;

            return SCIP_OKAY;
         }
      }
   }

   /* Note that because of possible multi-aggregation we cannot simply remove the indicator
    * constraint if the linear constraint is not active or disabled - see the note in @ref
    * PREPROC. */

   return SCIP_OKAY;
}


/** propagate indicator constraint */
static
SCIP_RETCODE propIndicator(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONS*            cons,               /**< constraint */
   SCIP_CONSDATA*        consdata,           /**< constraint data */
   SCIP_Bool             dualreductions,     /**< should dual reductions be performed? */
   SCIP_Bool             addopposite,        /**< add opposite inequalities if binary var = 0? */
   SCIP_Bool*            cutoff,             /**< whether a cutoff happened */
   int*                  nGen                /**< number of domain changes */
   )
{
   SCIP_Bool infeasible;
   SCIP_Bool tightened;

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

   *cutoff = FALSE;
   *nGen = 0;

   /* if the linear constraint has not been generated, we do nothing */
   if ( ! consdata->linconsactive )
      return SCIP_OKAY;

   assert( consdata->slackvar != NULL );
   assert( consdata->binvar != NULL );
   assert( SCIPisFeasGE(scip, SCIPvarGetLbLocal(consdata->slackvar), 0.0) );

   /* if both slackvar and binvar are fixed to be nonzero */
   if ( consdata->nfixednonzero > 1 )
   {
      SCIPdebugMsg(scip, "The node is infeasible, both the slack variable and the binary variable are fixed to be nonzero.\n");
      *cutoff = TRUE;

      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      assert( SCIPvarGetLbLocal(consdata->binvar) > 0.5 );
      assert( SCIPisPositive(scip, SCIPvarGetLbLocal(consdata->slackvar)) );

      /* check if conflict analysis is turned on */
      if ( ! SCIPisConflictAnalysisApplicable(scip) )
         return SCIP_OKAY;

      /* conflict analysis can only be applied in solving stage */
      assert( SCIPgetStage(scip) == SCIP_STAGE_SOLVING || SCIPinProbing(scip) );

      /* perform conflict analysis */
      SCIP_CALL( SCIPinitConflictAnalysis(scip, SCIP_CONFTYPE_PROPAGATION, FALSE) );

      SCIP_CALL( SCIPaddConflictBinvar(scip, consdata->binvar) );
      SCIP_CALL( SCIPaddConflictLb(scip, consdata->slackvar, NULL) );
      SCIP_CALL( SCIPanalyzeConflictCons(scip, cons, NULL) );

      return SCIP_OKAY;
   }

   /* if exactly one of the variables is fixed to be nonzero */
   if ( consdata->nfixednonzero == 1 )
   {
      /* increase age of constraint; age is reset to zero, if a conflict or a propagation was found */
      if ( ! SCIPinRepropagation(scip) )
         SCIP_CALL( SCIPincConsAge(scip, cons) );

      /* if binvar is fixed to be nonzero */
      if ( SCIPvarGetLbLocal(consdata->binvar) > 0.5 )
      {
         assert( SCIPvarGetStatus(consdata->slackvar) != SCIP_VARSTATUS_MULTAGGR );

         /* if slack variable is not already fixed to 0 */
         if ( ! SCIPisZero(scip, SCIPvarGetUbLocal(consdata->slackvar)) )
         {
            SCIPdebugMsg(scip, "Binary variable <%s> is fixed to be nonzero, fixing slack variable <%s> to 0.\n",
               SCIPvarGetName(consdata->binvar), SCIPvarGetName(consdata->slackvar));

            /* fix slack variable to 0 */
            SCIP_CALL( SCIPinferVarUbCons(scip, consdata->slackvar, 0.0, cons, 0, FALSE, &infeasible, &tightened) );
            assert( ! infeasible );
            if ( tightened )
               ++(*nGen);
         }
      }

      /* if slackvar is fixed to be nonzero */
      if ( SCIPisFeasPositive(scip, SCIPvarGetLbLocal(consdata->slackvar)) )
      {
         /* if binary variable is not yet fixed to 0 */
         if ( SCIPvarGetUbLocal(consdata->binvar) > 0.5 )
         {
            SCIPdebugMsg(scip, "Slack variable <%s> is fixed to be nonzero, fixing binary variable <%s> to 0.\n",
               SCIPvarGetName(consdata->slackvar), SCIPvarGetName(consdata->binvar));

            /* fix binary variable to 0 */
            SCIP_CALL( SCIPinferVarUbCons(scip, consdata->binvar, 0.0, cons, 1, FALSE, &infeasible, &tightened) );
            assert( ! infeasible );
            if ( tightened )
               ++(*nGen);
         }
      }

      /* reset constraint age counter */
      if ( *nGen > 0 )
         SCIP_CALL( SCIPresetConsAge(scip, cons) );

      /* mark linear constraint to be update-able */
      if ( SCIPgetDepth(scip) == 0 && SCIPconsIsActive(consdata->lincons) )
      {
         SCIPconsAddUpgradeLocks(consdata->lincons, -1);
         assert( SCIPconsGetNUpgradeLocks(consdata->lincons) == 0 );
      }

      /* delete constraint locally */
      assert( ! SCIPconsIsModifiable(cons) );
      SCIP_CALL( SCIPdelConsLocal(scip, cons) );
   }
   else
   {
      /* if the binary variable is fixed to zero */
      if ( SCIPvarGetUbLocal(consdata->binvar) < 0.5 )
      {
         if ( addopposite && consdata->linconsactive )
         {
            char name[SCIP_MAXSTRLEN];
            SCIP_CONS* reversecons;
            SCIP_VAR** linvars;
            SCIP_Real* linvals;
            SCIP_Bool allintegral = TRUE;
            SCIP_VAR* slackvar;
            SCIP_VAR** vars;
            SCIP_Real* vals;
            SCIP_Real lhs;
            SCIP_Real rhs;
            int nlinvars;
            int nvars = 0;
            int j;

            /* determine lhs/rhs (first exchange lhs/rhs) */
            lhs = SCIPgetRhsLinear(scip, consdata->lincons);
            if ( SCIPisInfinity(scip, lhs) )
               lhs = -SCIPinfinity(scip);
            rhs = SCIPgetRhsLinear(scip, consdata->lincons);
            if ( SCIPisInfinity(scip, -rhs) )
               rhs = SCIPinfinity(scip);

            assert( ! SCIPisInfinity(scip, lhs) );
            assert( ! SCIPisInfinity(scip, -rhs) );

            /* consider only finite lhs/rhs */
            if ( ! SCIPisInfinity(scip, -lhs) || ! SCIPisInfinity(scip, rhs) )
            {
               /* ignore equations (cannot add opposite constraint) */
               if ( ! SCIPisEQ(scip, lhs, rhs) )
               {
                  assert( consdata->lincons != NULL );
                  nlinvars = SCIPgetNVarsLinear(scip, consdata->lincons);
                  linvars = SCIPgetVarsLinear(scip, consdata->lincons);
                  linvals = SCIPgetValsLinear(scip, consdata->lincons);
                  slackvar = consdata->slackvar;
                  assert( slackvar != NULL );

                  SCIP_CALL( SCIPallocBufferArray(scip, &vars, nlinvars) );
                  SCIP_CALL( SCIPallocBufferArray(scip, &vals, nlinvars) );

                  /* copy data and check whether the linear constraint is integral */
                  for (j = 0; j < nlinvars; ++j)
                  {
                     if ( linvars[j] != slackvar )
                     {
                        if (! SCIPvarIsIntegral(linvars[j]) || ! SCIPisIntegral(scip, linvals[j]) )
                           allintegral = FALSE;

                        vars[nvars] = linvars[j];
                        vals[nvars++] = linvals[j];
                     }
                  }
                  assert( nlinvars == nvars + 1 );

                  /* possibly adjust lhs/rhs */
                  if ( allintegral && ! SCIPisInfinity(scip, REALABS(lhs)) )
                     lhs += 1.0;

                  if ( allintegral && ! SCIPisInfinity(scip, REALABS(rhs)) )
                     rhs -= 1.0;

                  /* create reverse constraint */
                  (void) SCIPsnprintf(name, SCIP_MAXSTRLEN, "reverse_%s", SCIPconsGetName(consdata->lincons));

                  /* constraint is initial, separated, not enforced, not checked, propagated, local, not modifiable, dynamic, removable */
                  SCIP_CALL( SCIPcreateConsLinear(scip, &reversecons, name, nvars, vars, vals, lhs, rhs,
                        TRUE, TRUE, FALSE, FALSE, TRUE, TRUE, FALSE, TRUE, TRUE, FALSE) );

                  SCIPdebugMsg(scip, "Binary variable <%s> fixed to 0. Adding opposite linear inequality.\n", SCIPvarGetName(consdata->binvar));
                  SCIPdebugPrintCons(scip, reversecons, NULL);

                  /* add constraint */
                  SCIP_CALL( SCIPaddCons(scip, reversecons) );
                  SCIP_CALL( SCIPreleaseCons(scip, &reversecons) );

                  SCIPfreeBufferArray(scip, &vals);
                  SCIPfreeBufferArray(scip, &vars);
               }
            }
         }

         SCIP_CALL( SCIPdelConsLocal(scip, cons) );
      }

      /* if the slack variable is fixed to zero */
      if ( SCIPisFeasZero(scip, SCIPvarGetUbLocal(consdata->slackvar)) )
      {
         /* perform dual reduction - if required */
         if ( dualreductions )
         {
            SCIP_VAR* binvar;
            SCIP_Real obj;

            /* check objective of binary variable */
            binvar = consdata->binvar;
            obj = varGetObjDelta(binvar);

            /* if obj = 0, we prefer setting the binary variable to 1 (if possible) */
            if ( obj <= 0.0 )
            {
               /* In this case we would like to fix the binary variable to 1, if it is not locked up
                  except by this indicator constraint. If more than one indicator constraint is
                  affected, we have to hope that they are all fulfilled - in this case the last
                  constraint will fix the binary variable to 1. */
               if ( SCIPvarGetNLocksUpType(binvar, SCIP_LOCKTYPE_MODEL) <= 1 )
               {
                  if ( SCIPvarGetUbLocal(binvar) > 0.5 )
                  {
                     SCIPdebugMsg(scip, "Propagating <%s> - dual reduction: Slack variable fixed to 0, fix binary variable to 1.\n", SCIPconsGetName(cons));
                     SCIP_CALL( SCIPinferVarLbCons(scip, binvar, 1.0, cons, 2, FALSE, &infeasible, &tightened) );
                     assert( ! infeasible );
                     if ( tightened )
                        ++(*nGen);
                     /* Make sure that the other case does not occur, since we are not sure whether SCIPinferVarLbCons() directly changes the bounds. */
                     obj = -1.0;
                  }
               }
            }
            if ( obj >= 0.0 )
            {
               /* In this case we would like to fix the binary variable to 0, if it is not locked down
                  (should also have been performed by other dual reductions). */
               if ( SCIPvarGetNLocksDownType(binvar, SCIP_LOCKTYPE_MODEL) == 0 )
               {
                  if ( SCIPvarGetLbLocal(binvar) < 0.5 )
                  {
                     SCIPdebugMsg(scip, "Propagating <%s> - dual reduction: Slack variable fixed to 0, fix binary variable to 0.\n", SCIPconsGetName(cons));
                     SCIP_CALL( SCIPinferVarUbCons(scip, binvar, 0.0, cons, 2, FALSE, &infeasible, &tightened) );
                     assert( ! infeasible );
                     if ( tightened )
                        ++(*nGen);
                  }
               }
            }
         }

         SCIPdebugMsg(scip, "Slack variable fixed to zero, delete redundant indicator constraint <%s>.\n", SCIPconsGetName(cons));

         /* delete constraint */
         assert( ! SCIPconsIsModifiable(cons) );

         /* mark linear constraint to be update-able */
         if ( SCIPgetDepth(scip) == 0 && SCIPconsIsActive(consdata->lincons) )
         {
            SCIPconsAddUpgradeLocks(consdata->lincons, -1);
            assert( SCIPconsGetNUpgradeLocks(consdata->lincons) == 0 );
         }

         SCIP_CALL( SCIPdelConsLocal(scip, cons) );
         SCIP_CALL( SCIPresetConsAge(scip, cons) );
         ++(*nGen);
      }

      /* Note that because of possible multi-aggregation we cannot simply remove the indicator
       * constraint if the linear constraint is not active or disabled - see the note in @ref
       * PREPROC and consPresolIndicator(). Moreover, it would drastically increase memory
       * consumption, because the linear constraints have to be stored in each node. */
   }

   return SCIP_OKAY;
}


/** enforcement method that produces cuts if possible
 *
 *  This is a variant of the enforcement method that generates cuts/constraints via the alternative
 *  LP, if possible.
 */
static
SCIP_RETCODE enforceCuts(
   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 */
   SCIP_Bool             genlogicor,         /**< whether logicor constraint should be generated */
   SCIP_Bool*            cutoff,             /**< whether we detected a cutoff by an infeasible inequality */
   int*                  nGen                /**< number of cuts generated */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_LPI* lp;
   SCIP_Bool* S;
   SCIP_Real value = 0.0;
   SCIP_Bool error;
   int size = 0;
   int nCuts;
   int j;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( cutoff != NULL );
   assert( nGen != NULL );

   SCIPdebugMsg(scip, "Enforcing via cuts ...\n");
   *cutoff = FALSE;
   *nGen = 0;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );
   lp = conshdlrdata->altlp;
   assert( lp != NULL );

#ifndef NDEBUG
   SCIP_CALL( checkLPBoundsClean(scip, lp, nconss, conss) );
#endif

   /* change coefficients of bounds in alternative LP */
   if ( conshdlrdata->updatebounds )
      SCIP_CALL( updateFirstRowGlobal(scip, conshdlrdata) );

   /* possibly update upper bound */
   SCIP_CALL( updateObjUpperbound(scip, conshdlr, conshdlrdata) );

   /* scale first row if necessary */
   SCIP_CALL( scaleFirstRow(scip, conshdlrdata) );

   /* set objective function to current solution */
   SCIP_CALL( setAltLPObjZero(scip, lp, nconss, conss) );

   SCIP_CALL( SCIPallocBufferArray(scip, &S, nconss) );

   /* set up variables fixed to 1 */
   for (j = 0; j < nconss; ++j)
   {
      SCIP_CONSDATA* consdata;

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

      assert( SCIPisFeasIntegral(scip, SCIPgetSolVal(scip, sol, consdata->binvar)) );
      if ( SCIPisFeasZero(scip, SCIPgetSolVal(scip, sol, consdata->binvar)) )
      {
         ++size;
         value += varGetObjDelta(consdata->binvar);
         S[j] = TRUE;
      }
      else
         S[j] = FALSE;
   }

   /* fix the variables in S */
   SCIP_CALL( fixAltLPVariables(scip, lp, nconss, conss, S) );

   /* extend set S to a cover and generate cuts */
   error = FALSE;
   SCIP_CALL( extendToCover(scip, conshdlr, conshdlrdata, lp, sol, conshdlrdata->removable, genlogicor, nconss, conss, S, &size, &value, &error, cutoff, &nCuts) );
   *nGen = nCuts;

   /* return with an error if no cuts have been produced and and error occurred in extendToCover() */
   if ( nCuts == 0 && error )
      return SCIP_LPERROR;

   SCIPdebugMsg(scip, "Generated %d IIS-cuts.\n", nCuts);

   /* reset bounds */
   SCIP_CALL( unfixAltLPVariables(scip, lp, nconss, conss, S) );

#ifndef NDEBUG
   SCIP_CALL( checkLPBoundsClean(scip, lp, nconss, conss) );
#endif

   SCIPfreeBufferArray(scip, &S);

   return SCIP_OKAY;
}


/** enforcement method
 *
 *  We check whether the current solution is feasible, i.e., if binvar = 1
 *  implies that slackvar = 0. If not, we branch as follows:
 *
 *  In one branch we fix binvar = 1 and slackvar = 0. In the other branch
 *  we fix binvar = 0 and leave slackvar unchanged.
 */
static
SCIP_RETCODE enforceIndicators(
   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_Bool             genlogicor,         /**< whether logicor constraint should be generated */
   SCIP_RESULT*          result              /**< result */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_NODE* node1;
   SCIP_NODE* node2;
   SCIP_VAR* slackvar;
   SCIP_VAR* binvar;
   SCIP_CONS* branchCons = NULL;
   SCIP_Real maxSlack = -1.0;
   SCIP_Bool someLinconsNotActive = FALSE;
   int c;

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

   *result = SCIP_FEASIBLE;

   SCIPdebugMsg(scip, "Enforcing indicator constraints for <%s> ...\n", SCIPconshdlrGetName(conshdlr) );

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

#ifdef SCIP_OUTPUT
   SCIP_CALL( SCIPwriteTransProblem(scip, "ind.cip", "cip", FALSE) );
#endif

   /* check each constraint */
   for (c = 0; c < nconss; ++c)
   {
      SCIP_Bool cutoff;
      SCIP_Real valSlack;
      int cnt;

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

      /* if the linear constraint has not been generated, we do nothing */
      if ( ! consdata->linconsactive )
      {
         someLinconsNotActive = TRUE;
         continue;
      }

      /* first perform propagation (it might happen that standard propagation is turned off) */
      SCIP_CALL( propIndicator(scip, conss[c], consdata,
            conshdlrdata->dualreductions && SCIPallowDualReds(scip), conshdlrdata->addopposite,
            &cutoff, &cnt) );
      if ( cutoff )
      {
         SCIPdebugMsg(scip, "Propagation in enforcing <%s> detected cutoff.\n", SCIPconsGetName(conss[c]));
         *result = SCIP_CUTOFF;
         return SCIP_OKAY;
      }
      if ( cnt > 0 )
      {
         SCIPdebugMsg(scip, "Propagation in enforcing <%s> reduced domains: %d.\n", SCIPconsGetName(conss[c]), cnt);
         *result = SCIP_REDUCEDDOM;
         return SCIP_OKAY;
      }

      /* check whether constraint is infeasible */
      binvar = consdata->binvar;
      valSlack = SCIPgetSolVal(scip, sol, consdata->slackvar);
      assert( ! SCIPisFeasNegative(scip, valSlack) );
      if ( ! SCIPisFeasZero(scip, SCIPgetSolVal(scip, sol, binvar)) && ! SCIPisFeasZero(scip, valSlack) )
      {
         /* binary variable is not fixed - otherwise we would not be infeasible */
         assert( SCIPvarGetLbLocal(binvar) < 0.5 && SCIPvarGetUbLocal(binvar) > 0.5 );

         if ( valSlack > maxSlack )
         {
            maxSlack = valSlack;
            branchCons = conss[c];
#ifdef SCIP_OUTPUT
            SCIPinfoMessage(scip, NULL, "Violated indicator constraint:\n");
            SCIP_CALL( SCIPprintCons(scip, conss[c], NULL) );
            SCIPinfoMessage(scip, NULL, ";\n");
            SCIPinfoMessage(scip, NULL, "Corresponding linear constraint:\n");
            SCIP_CALL( SCIPprintCons(scip, consdata->lincons, NULL) );
            SCIPinfoMessage(scip, NULL, ";\n");
#endif
         }
      }
   }

   /* if some constraint has a linear constraint that is not active, we need to check feasibility via the alternative polyhedron */
   if ( (someLinconsNotActive || conshdlrdata->enforcecuts) && conshdlrdata->sepaalternativelp )
   {
      SCIP_Bool cutoff;
      int ngen;

      SCIP_CALL( enforceCuts(scip, conshdlr, nconss, conss, sol, genlogicor, &cutoff, &ngen) );
      if ( cutoff )
      {
         conshdlrdata->niiscutsgen += ngen;
         *result = SCIP_CUTOFF;
         return SCIP_OKAY;
      }

      if ( ngen > 0 )
      {
         conshdlrdata->niiscutsgen += ngen;
         if ( genlogicor )
         {
            SCIPdebugMsg(scip, "Generated %d constraints.\n", ngen);
            *result = SCIP_CONSADDED;
         }
         else
         {
            SCIPdebugMsg(scip, "Generated %d cuts.\n", ngen);
            *result = SCIP_SEPARATED;
         }
         return SCIP_OKAY;
      }
      SCIPdebugMsg(scip, "Enforcing produced no cuts.\n");

      assert( ! someLinconsNotActive || branchCons == NULL );
   }

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

   /* skip branching if required */
   if ( ! conshdlrdata->branchindicators )
   {
      *result = SCIP_INFEASIBLE;
      return SCIP_OKAY;
   }

   /* otherwise create branches */
   SCIPdebugMsg(scip, "Branching on constraint <%s> (slack value: %f).\n", SCIPconsGetName(branchCons), maxSlack);
   consdata = SCIPconsGetData(branchCons);
   assert( consdata != NULL );
   binvar = consdata->binvar;
   slackvar = consdata->slackvar;

   /* node1: binvar = 1, slackvar = 0 */
   SCIP_CALL( SCIPcreateChild(scip, &node1, 0.0, SCIPcalcChildEstimate(scip, binvar, 1.0) ) );

   if ( SCIPvarGetLbLocal(binvar) < 0.5 )
   {
      SCIP_CALL( SCIPchgVarLbNode(scip, node1, binvar, 1.0) );
   }

   /* if slack-variable is multi-aggregated */
   assert( SCIPvarGetStatus(slackvar) != SCIP_VARSTATUS_MULTAGGR );
   if ( ! SCIPisFeasZero(scip, SCIPvarGetUbLocal(slackvar)) )
   {
      SCIP_CALL( SCIPchgVarUbNode(scip, node1, slackvar, 0.0) );
   }

   /* node2: binvar = 0, no restriction on slackvar */
   SCIP_CALL( SCIPcreateChild(scip, &node2, 0.0, SCIPcalcChildEstimate(scip, binvar, 0.0) ) );

   if ( SCIPvarGetUbLocal(binvar) > 0.5 )
   {
      SCIP_CALL( SCIPchgVarUbNode(scip, node2, binvar, 0.0) );
   }

   SCIP_CALL( SCIPresetConsAge(scip, branchCons) );
   *result = SCIP_BRANCHED;

   return SCIP_OKAY;
}


/** separate IIS-cuts via rounding
 *
 *  @todo Check whether the cover produced at the end is a feasible solution.
 */
static
SCIP_RETCODE separateIISRounding(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_SOL*             sol,                /**< solution to be separated */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss,              /**< indicator constraints */
   int                   maxsepacuts,        /**< maximal number of cuts to be generated */
   SCIP_Bool*            cutoff,             /**< whether we detected a cutoff by an infeasible inequality */
   int*                  nGen                /**< number of domain changes */
   )
{ /*lint --e{850}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_LPI* lp;
   int rounds;
   SCIP_Real threshold;
   SCIP_Bool* S;
   SCIP_Bool error;
   int oldsize = -1;
   /* cppcheck-suppress unassignedVariable */
   int nGenOld;

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( conss != NULL );
   assert( cutoff != NULL );
   assert( nGen != NULL );

   if ( *nGen >= maxsepacuts )
      return SCIP_OKAY;

   *cutoff = FALSE;
   rounds = 0;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );
   lp = conshdlrdata->altlp;
   assert( lp != NULL );

   SCIPdebug( nGenOld = *nGen; )
   SCIPdebugMsg(scip, "Separating IIS-cuts by rounding ...\n");

#ifndef NDEBUG
   SCIP_CALL( checkLPBoundsClean(scip, lp, nconss, conss) );
#endif

   /* change coefficients of bounds in alternative LP */
   if ( conshdlrdata->updatebounds )
   {
      /* update to local bounds */
      SCIP_CALL( updateFirstRow(scip, conshdlrdata) );
   }

   /* possibly update upper bound */
   SCIP_CALL( updateObjUpperbound(scip, conshdlr, conshdlrdata) );

   /* scale first row if necessary */
   SCIP_CALL( scaleFirstRow(scip, conshdlrdata) );

   /* set objective function to current solution */
   SCIP_CALL( setAltLPObj(scip, lp, sol, nconss, conss) );

   SCIP_CALL( SCIPallocBufferArray(scip, &S, nconss) );

   /* loop through the possible thresholds */
   for (threshold = conshdlrdata->roundingmaxthres;
        rounds < conshdlrdata->maxroundingrounds && threshold >= conshdlrdata->roundingminthres && *nGen < maxsepacuts && ! (*cutoff);
        threshold -= conshdlrdata->roundingoffset )
   {
      SCIP_Real value = 0.0;
      int size = 0;
      int nCuts = 0;
      int j;
#ifdef SCIP_DEBUG
      int nvarsone = 0;
      int nvarszero = 0;
      int nvarsfrac = 0;
#endif

      SCIPdebugMsg(scip, "Threshold: %g.\n", threshold);

      /* choose variables that have a value < current threshold value */
      for (j = 0; j < nconss; ++j)
      {
         SCIP_CONSDATA* consdata;
         SCIP_Real binvarval;
         SCIP_VAR* binvarneg;

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

         binvarval = SCIPgetVarSol(scip, consdata->binvar);

#ifdef SCIP_DEBUG
         if ( SCIPisFeasEQ(scip, binvarval, 1.0) )
            ++nvarsone;
         else if ( SCIPisFeasZero(scip, binvarval) )
            ++nvarszero;
         else
            ++nvarsfrac;
#endif

         /* check whether complementary (negated) variable is present as well */
         binvarneg = SCIPvarGetNegatedVar(consdata->binvar);
         assert( binvarneg != NULL );

         /* negated variable is present as well */
         assert( conshdlrdata->binvarhash != NULL );
         if ( SCIPhashmapExists(conshdlrdata->binvarhash, (void*) binvarneg) )
         {
            SCIP_Real binvarnegval = SCIPgetVarSol(scip, binvarneg);

            /* take larger one */
            if ( binvarval > binvarnegval )
               S[j] = TRUE;
            else
               S[j] = FALSE;
            continue;
         }

         /* check for threshold */
         if ( SCIPisFeasLT(scip, SCIPgetVarSol(scip, consdata->binvar), threshold) )
         {
            S[j] = TRUE;
            value += varGetObjDelta(consdata->binvar);
            ++size;
         }
         else
            S[j] = FALSE;
      }

      if ( size == nconss )
      {
         SCIPdebugMsg(scip, "All variables in the set. Continue ...\n");
         continue;
      }

      /* skip computation if size has not changed (computation is likely the same) */
      if ( size == oldsize )
      {
         SCIPdebugMsg(scip, "Skipping computation: size support has not changed.\n");
         continue;
      }
      oldsize = size;

#ifdef SCIP_DEBUG
      SCIPdebugMsg(scip, "   Vars with value 1: %d  0: %d  and fractional: %d.\n", nvarsone, nvarszero, nvarsfrac);
#endif

      /* fix the variables in S */
      SCIP_CALL( fixAltLPVariables(scip, lp, nconss, conss, S) );

      /* extend set S to a cover and generate cuts */
      SCIP_CALL( extendToCover(scip, conshdlr, conshdlrdata, lp, sol, conshdlrdata->removable, conshdlrdata->genlogicor, nconss, conss, S, &size, &value, &error, cutoff, &nCuts) );

      /* we ignore errors in extendToCover */
      if ( nCuts > 0 )
      {
         *nGen += nCuts;
         ++rounds;
      }
      else
      {
         /* possibly update upper bound */
         SCIP_CALL( updateObjUpperbound(scip, conshdlr, conshdlrdata) );
      }

      /* reset bounds */
      SCIP_CALL( unfixAltLPVariables(scip, lp, nconss, conss, S) );
   }
   SCIPdebugMsg(scip, "Generated %d IISs.\n", *nGen - nGenOld);

#ifndef NDEBUG
   SCIP_CALL( checkLPBoundsClean(scip, lp, nconss, conss) );
#endif

   SCIPfreeBufferArray(scip, &S);

   return SCIP_OKAY;
}



/** separate cuts based on perspective formulation
 *
 *  Hijazi, Bonami, and Ouorou (2014) introduced the following cuts: We consider an indicator constraint
 *  \f[
 *  y = 1 \rightarrow \alpha^T x \leq \beta
 *  \f]
 *  and assume finite bounds \f$\ell \leq x \leq u\f$. Then for \f$I \subseteq \{1, \dots, n\}\f$ define
 *  \f[
 *    \Sigma(I,x,y) = \sum_{i \notin I} \alpha_i x_i +
 *    y \Big(\sum_{i \in I, \alpha_i < 0} \alpha_i u_i + \sum_{i \in I, \alpha_i > 0} \alpha_i \ell_i +
 *    \sum_{i \notin I, \alpha_i < 0} \alpha_i \ell_i + \sum_{i \notin I, \alpha_i > 0} \alpha_i u_i - \beta\Big).
 *  \f]
 *  Then the cuts
 *  \f[
 *  \Sigma(I,x,y) \leq \sum_{i \notin I, \alpha_i < 0} \alpha_i \ell_i + \sum_{i \notin I, \alpha_i > 0} \alpha_i u_i
 *  \f]
 *  are valid for the disjunction
 *  \f[
 *  \{y = 0,\; \ell \leq x \leq u\} \cup \{y = 1,\; \ell \leq x \leq u,\; \alpha^T x \leq \beta\}.
 *  \f]
 *  These cuts can easily be separated for a given point \f$(x^*, y^*)\f$ by checking for each \f$i \in \{1, \dots, n\}\f$ whether
 *  \f[
 *  y^*(\alpha_i\, u_i\, [\alpha_i < 0] + \alpha_i\, \ell_i\, [\alpha_i > 0]) >
 *  \alpha_i x_i^* + y^* )\alpha_i \ell_i [\alpha_i < 0] + \alpha_i u_i [\alpha_i > 0]),
 *  \f]
 *  where \f$[C] = 1\f$ if condition \f$C\f$ is satisfied, otherwise it is 0.
 *  If the above inequality holds, \f$i\f$ is included in \f$I\f$, otherwise not.
 */
static
SCIP_RETCODE separatePerspective(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   SCIP_SOL*             sol,                /**< solution to be separated */
   int                   nconss,             /**< number of constraints */
   SCIP_CONS**           conss,              /**< indicator constraints */
   int                   maxsepacuts,        /**< maximal number of cuts to be generated */
   int*                  nGen                /**< number of generated cuts */
   )
{  /*lint --e{850}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_VAR** cutvars;
   SCIP_Real* cutvals;
   int nvars;
   int c;

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

   if ( *nGen >= maxsepacuts )
      return SCIP_OKAY;

   nvars = SCIPgetNVars(scip);
   SCIP_CALL( SCIPallocBufferArray(scip, &cutvars, nvars+1) );
   SCIP_CALL( SCIPallocBufferArray(scip, &cutvals, nvars+1) );

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

   /* loop through constraints */
   for (c = 0; c < nconss; ++c)
   {
      SCIP_CONSDATA* consdata;
      SCIP_CONS* lincons;
      SCIP_VAR* slackvar;
      SCIP_VAR* binvar;
      SCIP_Real binval;

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

      lincons = consdata->lincons;
      assert( lincons != NULL );

      binvar = consdata->binvar;
      assert( binvar != NULL );
      binval = SCIPgetSolVal(scip, sol, binvar);

      if ( SCIPconsIsActive(lincons) )
      {
         SCIP_VAR** linvars;
         SCIP_Real* linvals;
         SCIP_Real linrhs;
         SCIP_Bool finitebound = TRUE;
         SCIP_Real cutrhs = 0.0;
         SCIP_Real cutval;
         SCIP_Real signfactor = 1.0;
         SCIP_Real ypart;
         SCIP_Bool islocal = FALSE;
         int nlinvars;
         int cnt = 0;
         int j;

         linvars = SCIPgetVarsLinear(scip, lincons);
         linvals = SCIPgetValsLinear(scip, lincons);
         nlinvars = SCIPgetNVarsLinear(scip, lincons);

         linrhs = SCIPgetRhsLinear(scip, lincons);
         if ( SCIPisInfinity(scip, linrhs) )
         {
            if ( ! SCIPisInfinity(scip, SCIPgetLhsLinear(scip, lincons)) )
            {
               linrhs = -SCIPgetLhsLinear(scip, lincons);
               signfactor = -1.0;
            }
            else
               continue;
         }
         ypart = -linrhs;
         cutval = binval * ypart;

         for (j = 0; j < nlinvars; ++j)
         {
            SCIP_Real linval;
            SCIP_Real lb;
            SCIP_Real ub;
            SCIP_Real din = 0.0;
            SCIP_Real dout = 0.0;
            SCIP_Real xpart;
            SCIP_Real xval;

            if ( linvars[j] == slackvar )
               continue;

            if ( conshdlrdata->sepapersplocal )
            {
               lb = SCIPvarGetLbLocal(linvars[j]);
               ub = SCIPvarGetUbLocal(linvars[j]);

               if ( lb > SCIPvarGetLbGlobal(linvars[j]) )
                  islocal = TRUE;
               if ( ub < SCIPvarGetUbGlobal(linvars[j]) )
                  islocal = TRUE;
            }
            else
            {
               lb = SCIPvarGetLbGlobal(linvars[j]);
               ub = SCIPvarGetUbGlobal(linvars[j]);
            }

            /* skip cases with unbounded variables */
            if ( SCIPisInfinity(scip, -lb) || SCIPisInfinity(scip, ub) )
            {
               finitebound = FALSE;
               break;
            }

            /* compute rest parts for i in the set (din) or not in the set (dout) */
            linval = signfactor * linvals[j];
            if ( SCIPisNegative(scip, linval) )
            {
               din += linval * ub;
               dout += linval * lb;
            }
            else if ( SCIPisPositive(scip, linval) )
            {
               din += linval * lb;
               dout += linval * ub;
            }

            xval = SCIPgetSolVal(scip, sol, linvars[j]);
            xpart = linval * xval;

            /* if din > dout, we want to include i in the set */
            if ( SCIPisGT(scip, binval * din, binval * dout + xpart) )
            {
               ypart += din;
               cutval += binval * din;
            }
            else
            {
               /* otherwise i is not in the set */
               ypart += dout;

               cutrhs += dout;
               cutval += binval * dout + xpart;

               cutvars[cnt] = linvars[j];
               cutvals[cnt++] = linval;
            }
         }

         if ( ! finitebound )
            continue;

         if ( SCIPisEfficacious(scip, cutval - cutrhs) )
         {
            SCIP_ROW* row;
            SCIP_Bool infeasible;
            char name[50];

            /* add y-variable */
            cutvars[cnt] = binvar;
            cutvals[cnt] = ypart;
            ++cnt;

            SCIPdebugMsg(scip, "Found cut of lhs value %f > %f.\n", cutval, cutrhs);
            (void) SCIPsnprintf(name, 50, "persp%d", conshdlrdata->nperspcutsgen + *nGen);
            SCIP_CALL( SCIPcreateEmptyRowCons(scip, &row, SCIPconsGetHdlr(conss[c]), name, -SCIPinfinity(scip), cutrhs, islocal, FALSE, conshdlrdata->removable) );
            SCIP_CALL( SCIPaddVarsToRow(scip, row, cnt, cutvars, cutvals) );
#ifdef SCIP_OUTPUT
            SCIP_CALL( SCIPprintRow(scip, row, NULL) );
#endif
            SCIP_CALL( SCIPaddRow(scip, row, FALSE, &infeasible) );
            assert( ! infeasible );
            SCIP_CALL( SCIPreleaseRow(scip, &row));
            SCIP_CALL( SCIPresetConsAge(scip, conss[c]) );
            ++(*nGen);
         }
      }
      if ( *nGen >= maxsepacuts )
         break;
   }

   SCIPfreeBufferArray(scip, &cutvals);
   SCIPfreeBufferArray(scip, &cutvars);

   return SCIP_OKAY;
}


/** separation method
 *
 *  We first check whether coupling inequalities can be separated (if required). If not enough of
 *  these could be generated, we check whether IIS inequalities can be separated.
 */
static
SCIP_RETCODE separateIndicators(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLR*        conshdlr,           /**< constraint handler */
   int                   nconss,             /**< number of constraints */
   int                   nusefulconss,       /**< number of useful constraints */
   SCIP_CONS**           conss,              /**< indicator constraints */
   SCIP_SOL*             sol,                /**< solution to be separated */
   SCIP_RESULT*          result              /**< result */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   int maxsepacuts;
   int ncuts;

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

   *result = SCIP_DIDNOTRUN;

   if ( nconss == 0 )
      return SCIP_OKAY;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );
   ncuts = 0;

   /* get the maximal number of cuts allowed in a separation round */
   if ( SCIPgetDepth(scip) == 0 )
      maxsepacuts = conshdlrdata->maxsepacutsroot;
   else
      maxsepacuts = conshdlrdata->maxsepacuts;

   /* first separate coupling inequalities (if required) */
   if ( conshdlrdata->sepacouplingcuts )
   {
      int c;

      *result = SCIP_DIDNOTFIND;

      /* check each constraint */
      for (c = 0; c < nusefulconss && ncuts < maxsepacuts; ++c)
      {
         SCIP_CONSDATA* consdata;
         SCIP_Bool islocal;
         SCIP_Real ub;

         assert( conss != NULL );
         assert( conss[c] != NULL );
         consdata = SCIPconsGetData(conss[c]);
         assert( consdata != NULL );
         assert( consdata->slackvar != NULL );
         assert( consdata->binvar != NULL );

         /* get upper bound for slack variable in linear constraint */
         islocal = FALSE;
         if ( conshdlrdata->sepacouplinglocal )
         {
            ub = SCIPvarGetUbLocal(consdata->slackvar);
            if ( ub < SCIPvarGetUbGlobal(consdata->slackvar) )
               islocal = TRUE;
         }
         else
            ub = SCIPvarGetUbGlobal(consdata->slackvar);
         assert( ! SCIPisFeasNegative(scip, ub) );

         /* only use coefficients that are not too large */
         if ( ub <= conshdlrdata->sepacouplingvalue )
         {
            SCIP_Real activity;

            activity = SCIPgetSolVal(scip, sol, consdata->slackvar) + ub * SCIPgetSolVal(scip, sol, consdata->binvar) - ub;
            if ( SCIPisEfficacious(scip, activity) )
            {
               SCIP_ROW* row;
               SCIP_Bool infeasible;
#ifndef NDEBUG
               char name[50];

               (void) SCIPsnprintf(name, 50, "couple%d", c);
               SCIP_CALL( SCIPcreateEmptyRowCons(scip, &row, SCIPconsGetHdlr(conss[c]), name, -SCIPinfinity(scip), ub, islocal, FALSE, conshdlrdata->removable) );
#else
               SCIP_CALL( SCIPcreateEmptyRowCons(scip, &row, SCIPconsGetHdlr(conss[c]), "", -SCIPinfinity(scip), ub, islocal, FALSE, conshdlrdata->removable) );
#endif
               SCIP_CALL( SCIPcacheRowExtensions(scip, row) );

               SCIP_CALL( SCIPaddVarToRow(scip, row, consdata->slackvar, 1.0) );
               SCIP_CALL( SCIPaddVarToRow(scip, row, consdata->binvar, ub) );
               SCIP_CALL( SCIPflushRowExtensions(scip, row) );

               SCIPdebugMsg(scip, "Separated coupling inequality for indicator constraint <%s> (coeff: %f).\n", SCIPconsGetName(conss[c]), ub);
#ifdef SCIP_OUTPUT
               SCIP_CALL( SCIPprintRow(scip, row, NULL) );
#endif
               SCIP_CALL( SCIPaddRow(scip, row, FALSE, &infeasible) );
               assert( ! infeasible );
               SCIP_CALL( SCIPreleaseRow(scip, &row));

               SCIP_CALL( SCIPresetConsAge(scip, conss[c]) );
               *result = SCIP_SEPARATED;

               ++ncuts;
            }
         }
      }
      SCIPdebugMsg(scip, "Number of separated coupling inequalities: %d.\n", ncuts);
   }

   /* separate cuts from the alternative lp (if required) */
   if ( conshdlrdata->sepaalternativelp && ncuts < SEPAALTTHRESHOLD )
   {
      SCIP_Bool cutoff;
      int noldcuts;

      SCIPdebugMsg(scip, "Separating inequalities for indicator constraints.\n");

      noldcuts = ncuts;
      if ( *result == SCIP_DIDNOTRUN )
         *result = SCIP_DIDNOTFIND;

      /* start separation */
      SCIP_CALL( separateIISRounding(scip, conshdlr, sol, nconss, conss, maxsepacuts, &cutoff, &ncuts) );
      SCIPdebugMsg(scip, "Separated %d cuts from indicator constraints.\n", ncuts - noldcuts);

      if ( cutoff )
         *result = SCIP_CUTOFF;
      else if ( ncuts > noldcuts )
      {
         conshdlrdata->niiscutsgen += ncuts;

         /* possibly overwrite result from separation above */
         if ( conshdlrdata->genlogicor )
            *result = SCIP_CONSADDED;
         else
            *result = SCIP_SEPARATED;
      }
   }

   /* separate cuts based on perspective formulation */
   if ( conshdlrdata->sepaperspective && ncuts < SEPAALTTHRESHOLD )
   {
      int noldcuts;

      SCIPdebugMsg(scip, "Separating inequalities based on perspective formulation.\n");

      noldcuts = ncuts;
      if ( *result == SCIP_DIDNOTRUN )
         *result = SCIP_DIDNOTFIND;

      /* start separation */
      SCIP_CALL( separatePerspective(scip, conshdlr, sol, nconss, conss, maxsepacuts, &ncuts) );
      SCIPdebugMsg(scip, "Separated %d cuts from perspective formulation.\n", ncuts - noldcuts);

      if ( ncuts > noldcuts )
      {
         conshdlrdata->nperspcutsgen += ncuts;

         /* possibly overwrite result from separation above */
         *result = SCIP_SEPARATED;
      }
   }

   return SCIP_OKAY;
}


/** initializes the constraint handler data */
static
void initConshdlrData(
   SCIP*                 scip,               /**< SCIP pointer */
   SCIP_CONSHDLRDATA*    conshdlrdata        /**< constraint handler data */
   )
{
   assert( conshdlrdata != NULL );

   conshdlrdata->removable = TRUE;
   conshdlrdata->scaled = FALSE;
   conshdlrdata->altlp = NULL;
   conshdlrdata->nrows = 0;
   conshdlrdata->varhash = NULL;
   conshdlrdata->slackhash = NULL;
   conshdlrdata->lbhash = NULL;
   conshdlrdata->ubhash = NULL;
   conshdlrdata->nlbbounds = 0;
   conshdlrdata->nubbounds = 0;
   conshdlrdata->nslackvars = 0;
   conshdlrdata->objcutindex = -1;
   conshdlrdata->objupperbound = SCIPinfinity(scip);
   conshdlrdata->objaltlpbound = SCIPinfinity(scip);
   conshdlrdata->roundingminthres = 0.1;
   conshdlrdata->roundingmaxthres = 0.6;
   conshdlrdata->maxroundingrounds = MAXROUNDINGROUNDS;
   conshdlrdata->roundingoffset = 0.1;
   conshdlrdata->addedcouplingcons = FALSE;
   conshdlrdata->ninitconss = 0;
   conshdlrdata->nbinvarszero = 0;
   conshdlrdata->performedrestart = FALSE;
   conshdlrdata->objindicatoronly = FALSE;
   conshdlrdata->objothervarsonly = FALSE;
   conshdlrdata->minabsobj = 0.0;
   conshdlrdata->normtype = 'e';
   conshdlrdata->niiscutsgen = 0;
   conshdlrdata->nperspcutsgen = 0;
}


/* ---------------------------- upgrading methods -----------------------------------*/

/** tries to upgrade a linear constraint into an indicator constraint
 *
 *  For some linear constraint of the form \f$a^T x + \alpha\, y \geq \beta\f$ with \f$y \in \{0,1\}\f$, we can upgrade
 *  it to an indicator constraint if for the residual value \f$a^T x \geq \gamma\f$, we have \f$\alpha + \gamma \geq
 *  \beta\f$: in this case, the constraint is always satisfied if \f$y = 1\f$.
 *
 *  Similarly, for a linear constraint in the form \f$a^T x + \alpha\, y \leq \beta\f$ with \f$y \in \{0,1\}\f$, we can
 *  upgrade it to an indicator constraint if for the residual value \f$a^T x \leq \gamma\f$, we have \f$\alpha + \gamma
 *  \leq \beta\f$.
 */
static
SCIP_DECL_LINCONSUPGD(linconsUpgdIndicator)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSHDLR* conshdlr;
   SCIP_Real minactivity = 0.0;
   SCIP_Real maxactivity = 0.0;
   SCIP_Real maxabsval = -1.0;
   SCIP_Real secabsval = -1.0;
   int maxabsvalidx = -1;
   int j;

   assert( scip != NULL );
   assert( upgdcons != NULL );
   assert( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), "linear") == 0 );
   assert( ! SCIPconsIsModifiable(cons) );

   /* do not upgrade if there are at most 2 variables (2 variables should be upgraded to a varbound constraint) */
   if ( nvars <= 2 )
      return SCIP_OKAY;

   /* cannot currently ranged constraints, since we can only return one constraint (and we would need one for each side each) */
   if ( ! SCIPisInfinity(scip, -lhs) && ! SCIPisInfinity(scip, rhs) )
      return SCIP_OKAY;

   /* check whether upgrading is turned on */
   conshdlr = SCIPfindConshdlr(scip, "indicator");
   assert( conshdlr != NULL );
   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );

   if ( ! conshdlrdata->upgradelinear )
      return SCIP_OKAY;

   /* calculate activities */
   for (j = 0; j < nvars; ++j)
   {
      SCIP_VAR* var;
      SCIP_Real val;
      SCIP_Real lb;
      SCIP_Real ub;

      val = vals[j];
      assert( ! SCIPisZero(scip, val) );

      var = vars[j];
      assert( var != NULL );

      /* store maximal (and second to largest) value of coefficients */
      if ( SCIPisGE(scip, REALABS(val), maxabsval) )
      {
         secabsval = maxabsval;
         maxabsval = REALABS(val);
         maxabsvalidx = j;
      }

      if ( val > 0 )
      {
         lb = SCIPvarGetLbGlobal(var);
         ub = SCIPvarGetUbGlobal(var);
      }
      else
      {
         ub = SCIPvarGetLbGlobal(var);
         lb = SCIPvarGetUbGlobal(var);
      }

      /* compute minimal activity */
      if ( SCIPisInfinity(scip, -lb) )
         minactivity = -SCIPinfinity(scip);
      else
      {
         if ( ! SCIPisInfinity(scip, -minactivity) )
            minactivity += val * lb;
      }

      /* compute maximal activity */
      if ( SCIPisInfinity(scip, ub) )
         maxactivity = SCIPinfinity(scip);
      else
      {
         if ( ! SCIPisInfinity(scip, maxactivity) )
            maxactivity += val * ub;
      }
   }
   assert( maxabsval >= 0.0 );
   assert( 0 <= maxabsvalidx && maxabsvalidx < nvars );

   /* exit if largest coefficient does not belong to binary variable */
   if ( ! SCIPvarIsBinary(vars[maxabsvalidx]) )
      return SCIP_OKAY;

   /* exit if the second largest coefficient is as large as largest */
   if ( SCIPisEQ(scip, secabsval, maxabsval) )
      return SCIP_OKAY;

   /* cannot upgrade if all activities are infinity */
   if ( SCIPisInfinity(scip, -minactivity) && SCIPisInfinity(scip, maxactivity) )
      return SCIP_OKAY;

   /* check each variable as indicator variable */
   for (j = 0; j < nvars; ++j)
   {
      SCIP_VAR** indconsvars;
      SCIP_Real* indconsvals;
      SCIP_Bool upgdlhs = FALSE;
      SCIP_Bool upgdrhs = FALSE;
      SCIP_Bool indneglhs = FALSE;
      SCIP_Bool indnegrhs = FALSE;
      SCIP_VAR* indvar;
      SCIP_Real indval;
      int l;

      indvar = vars[j];
      indval = vals[j];
      assert( ! SCIPisZero(scip, indval) );

      if ( ! SCIPvarIsBinary(indvar) )
         continue;

      /* check for upgrading of lhs */
      if ( ! SCIPisInfinity(scip, -minactivity) && ! SCIPisInfinity(scip, -lhs) )
      {
         /* upgrading is possible with binary variable */
         if ( SCIPisGE(scip, minactivity, lhs) )
            upgdlhs = TRUE;

         /* upgrading is possible with negated binary variable */
         if ( SCIPisGE(scip, minactivity + indval, lhs) )
         {
            upgdlhs = TRUE;
            indneglhs = TRUE;
         }
      }

      /* check for upgrading of rhs */
      if ( ! SCIPisInfinity(scip, maxactivity) && ! SCIPisInfinity(scip, rhs) )
      {
         /* upgrading is possible with binary variable */
         if ( SCIPisLE(scip, maxactivity, rhs) )
         {
            upgdrhs = TRUE;
            indnegrhs = TRUE;
         }

         /* upgrading is possible with negated binary variable */
         if ( SCIPisLE(scip, maxactivity - indval, rhs) )
            upgdrhs = TRUE;
      }

      /* upgrade constraint */
      if ( upgdlhs || upgdrhs )
      {
         SCIP_VAR* indvar2;
         SCIP_Real bnd;
         int cnt = 0;

         assert( ! upgdlhs || ! upgdrhs ); /* cannot treat ranged rows */
         SCIPdebugMsg(scip, "upgrading constraint <%s> to an indicator constraint.\n", SCIPconsGetName(cons));

         SCIP_CALL( SCIPallocBufferArray(scip, &indconsvars, nvars - 1) );
         SCIP_CALL( SCIPallocBufferArray(scip, &indconsvals, nvars - 1) );

         /* create constraint */
         for (l = 0; l < nvars; ++l)
         {
            if ( vars[l] == indvar )
               continue;
            indconsvars[cnt] = vars[l];
            if ( upgdlhs )
               indconsvals[cnt] = -vals[l];
            else
               indconsvals[cnt] = vals[l];
            ++cnt;
         }

         if ( indneglhs || indnegrhs )
         {
            SCIP_CALL( SCIPgetNegatedVar(scip, indvar, &indvar2) );
         }
         else
            indvar2 = indvar;

         if ( upgdlhs )
         {
            bnd = -lhs;
            if ( ! indneglhs )
               bnd -= indval;
            SCIP_CALL( SCIPcreateConsIndicator(scip, upgdcons, SCIPconsGetName(cons), indvar2, nvars-1, indconsvars, indconsvals, bnd,
                  SCIPconsIsInitial(cons), SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), SCIPconsIsChecked(cons), SCIPconsIsPropagated(cons),
                  SCIPconsIsLocal(cons), SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
         }
         else
         {
            bnd = rhs;
            if ( ! indnegrhs )
               bnd -= indval;
            SCIP_CALL( SCIPcreateConsIndicator(scip, upgdcons, SCIPconsGetName(cons), indvar2, nvars-1, indconsvars, indconsvals, bnd,
                  SCIPconsIsInitial(cons), SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), SCIPconsIsChecked(cons), SCIPconsIsPropagated(cons),
                  SCIPconsIsLocal(cons), SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
         }

#ifdef SCIP_DEBUG
         SCIPinfoMessage(scip, NULL, "upgrade: \n");
         SCIP_CALL( SCIPprintCons(scip, cons, NULL) );
         SCIPinfoMessage(scip, NULL, "\n");
         SCIP_CALL( SCIPprintCons(scip, *upgdcons, NULL) );
         SCIPinfoMessage(scip, NULL, "\n");
         SCIP_CALL( SCIPprintCons(scip, SCIPgetLinearConsIndicator(*upgdcons), NULL) );
         SCIPinfoMessage(scip, NULL, "  (minact: %f, maxact: %f)\n", minactivity, maxactivity);
#endif

         SCIPfreeBufferArray(scip, &indconsvars);
         SCIPfreeBufferArray(scip, &indconsvals);

         return SCIP_OKAY;
      }
   }

   return SCIP_OKAY;
}


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

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

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

   *valid = TRUE;

   return SCIP_OKAY;
}


/** initialization method of constraint handler (called after problem was transformed) */
static
SCIP_DECL_CONSINIT(consInitIndicator)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;

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

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

   initConshdlrData(scip, conshdlrdata);

   /* find trysol heuristic */
   if ( conshdlrdata->trysolutions && conshdlrdata->heurtrysol == NULL )
   {
      conshdlrdata->heurtrysol = SCIPfindHeur(scip, "trysol");
   }

   return SCIP_OKAY;
}


/** deinitialization method of constraint handler (called before transformed problem is freed) */
static
SCIP_DECL_CONSEXIT(consExitIndicator)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;

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

   conshdlrdata = SCIPconshdlrGetData(conshdlr);

   if ( conshdlrdata->binvarhash != NULL )
      SCIPhashmapFree(&conshdlrdata->binvarhash);

   SCIPfreeBlockMemoryArrayNull(scip, &conshdlrdata->addlincons, conshdlrdata->maxaddlincons);
   conshdlrdata->maxaddlincons = 0;
   conshdlrdata->naddlincons = 0;
   conshdlrdata->nrows = 0;

   return SCIP_OKAY;
}


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

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

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );
   assert( conshdlrdata->altlp == NULL );
   assert( conshdlrdata->varhash == NULL );
   assert( conshdlrdata->lbhash == NULL );
   assert( conshdlrdata->ubhash == NULL );
   assert( conshdlrdata->slackhash == NULL );

   if ( conshdlrdata->maxaddlincons > 0 )
   {
      /* if problem was not yet transformed the array may need to be freed, because we did not call the EXIT callback */
      SCIPfreeBlockMemoryArrayNull(scip, &conshdlrdata->addlincons, conshdlrdata->maxaddlincons);
   }
   assert( conshdlrdata->addlincons == NULL );
   conshdlrdata->naddlincons = 0;
   conshdlrdata->maxaddlincons = 0;

   SCIPfreeBlockMemory(scip, &conshdlrdata);

   return SCIP_OKAY;
}


/** solving process initialization method of constraint handler (called when branch and bound process is about to begin) */
static
SCIP_DECL_CONSINITSOL(consInitsolIndicator)
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   int c;

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

   if ( SCIPgetStatus(scip) == SCIP_STATUS_OPTIMAL || SCIPgetStatus(scip) == SCIP_STATUS_INFEASIBLE ||
        SCIPgetStatus(scip) == SCIP_STATUS_UNBOUNDED || SCIPgetStatus(scip) == SCIP_STATUS_INFORUNBD )
      return SCIP_OKAY;

   SCIPdebugMsg(scip, "Initsol for indicator constraints.\n");

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );
   assert( conshdlrdata->slackhash == NULL );

   SCIP_CALL( SCIPgetCharParam(scip, "separating/efficacynorm", &conshdlrdata->normtype) );

   if ( conshdlrdata->sepaalternativelp )
   {
      /* generate hash for storing all slack variables (size is just a guess) */
      SCIP_CALL( SCIPhashmapCreate(&conshdlrdata->slackhash, SCIPblkmem(scip), SCIPgetNVars(scip)) );
      assert( conshdlrdata->slackhash != NULL );

      /* first initialize slack hash */
      for (c = 0; c < nconss; ++c)
      {
         SCIP_CONSDATA* consdata;

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

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

         assert( consdata->slackvar != NULL );

         /* insert slack variable into hash */
         SCIP_CALL( SCIPhashmapInsertInt(conshdlrdata->slackhash, consdata->slackvar, INT_MAX) );
         assert( SCIPhashmapExists(conshdlrdata->slackhash, consdata->slackvar) );
         ++conshdlrdata->nslackvars;
      }

      if ( conshdlrdata->genlogicor )
      {
         SCIP_CONSHDLR* logicorconshdlr;
         int logicorsepafreq;
         int sepafreq;

         /* If we generate logicor constraints, make sure that we separate them with the same frequency */
         logicorconshdlr = SCIPfindConshdlr(scip, "logicor");
         if ( logicorconshdlr == NULL )
         {
            SCIPerrorMessage("Logicor constraint handler not included, cannot generate constraints.\n");
            return SCIP_ERROR;
         }
         logicorsepafreq = SCIPconshdlrGetSepaFreq(logicorconshdlr);
         sepafreq = SCIPconshdlrGetSepaFreq(conshdlr);
         if ( sepafreq != -1 && ((logicorsepafreq == 0 && sepafreq > 0) || sepafreq < logicorsepafreq) )
         {
            SCIPverbMessage(scip, SCIP_VERBLEVEL_MINIMAL, NULL, "Set sepafreq of logicor constraint handler to %d.\n", sepafreq);
            SCIP_CALL( SCIPsetIntParam(scip, "constraints/logicor/sepafreq", sepafreq) );
         }
      }
   }

   /* check each constraint */
   conshdlrdata->objothervarsonly = TRUE;
   for (c = 0; c < nconss; ++c)
   {
      SCIP_CONSDATA* consdata;

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

      consdata = SCIPconsGetData(conss[c]);
      assert( consdata != NULL );
      assert( consdata->binvar != NULL );
      assert( consdata->slackvar != NULL );

      /* Presolving might replace a slack variable by an active variable. Thus, the objective of a slack variables might
       * be nonzero. However, we do not need to check slack variables here. */
      if ( ! SCIPisZero(scip, varGetObjDelta(consdata->binvar)) )
         conshdlrdata->objothervarsonly = FALSE;

      /* deactivate */
      if ( ! consdata->linconsactive )
      {
         SCIP_CALL( SCIPdisableCons(scip, consdata->lincons) );
      }
      else
      {
         /* add constraint to alternative LP if not already done */
         if ( conshdlrdata->sepaalternativelp && consdata->colindex < 0 )
         {
            SCIP_CALL( addAltLPConstraint(scip, conshdlr, consdata->lincons, consdata->slackvar, 1.0, &consdata->colindex) );
            SCIPdebugMsg(scip, "Added column for <%s> to alternative LP with column index %d.\n", SCIPconsGetName(conss[c]),consdata->colindex);
#ifdef SCIP_OUTPUT
            SCIP_CALL( SCIPprintCons(scip, consdata->lincons, NULL) );
            SCIPinfoMessage(scip, NULL, ";\n");
#endif
         }
      }

      /* add nlrow representation to NLP, if NLP had been constructed
       *
       * Note, that we did not tell SCIP in exitpre that we have something to add to the NLP, thus
       * indicators are only available in the NLP for MINLPs, but not for MIPs with indicators.
       */
      if ( SCIPisNLPConstructed(scip) && SCIPconsIsChecked(conss[c]) )
      {
         SCIP_NLROW* nlrow;
         SCIP_VAR* quadvars[2];
         SCIP_QUADELEM quadelem;

         /* create nonlinear row binary variable * slack variable = 0 */
         quadvars[0] = consdata->binvar;
         quadvars[1] = consdata->slackvar;
         quadelem.idx1 = 0;
         quadelem.idx2 = 1;
         quadelem.coef = 1.0;

         SCIP_CALL( SCIPcreateNlRow(scip, &nlrow, SCIPconsGetName(conss[c]), 0.0, 0, NULL, NULL, 2, quadvars, 1,
               &quadelem, NULL, 0.0, 0.0, SCIP_EXPRCURV_UNKNOWN) );

         /* add row to NLP and forget about it */
         SCIP_CALL( SCIPaddNlRow(scip, nlrow) );
         SCIP_CALL( SCIPreleaseNlRow(scip, &nlrow) );
      }
   }

   SCIPdebugMsg(scip, "Initialized %d indicator constraints.\n", nconss);

   /* check additional constraints */
   if ( conshdlrdata->sepaalternativelp )
   {
      SCIP_CONS* cons;
      int colindex;
      int cnt = 0;

      /* add stored linear constraints if they exist */
      if ( conshdlrdata->naddlincons > 0 )
      {
         for (c = 0; c < conshdlrdata->naddlincons; ++c)
         {
            cons = conshdlrdata->addlincons[c];

            /* get transformed constraint - since it is needed only here, we do not store the information */
            if ( ! SCIPconsIsTransformed(cons) )
            {
               SCIP_CALL( SCIPgetTransformedCons(scip, conshdlrdata->addlincons[c], &cons) );

               /* @todo check when exactly the transformed constraint does not exist - SCIPisActive() does not suffice */
               if ( cons == NULL )
                  continue;
            }
            SCIP_CALL( addAltLPConstraint(scip, conshdlr, cons, NULL, 0.0, &colindex) );
            ++cnt;

#ifdef SCIP_OUTPUT
            SCIP_CALL( SCIPprintCons(scip, cons, NULL) );
            SCIPinfoMessage(scip, NULL, ";\n");
#endif
         }
         SCIPdebugMsg(scip, "Added %d additional columns to alternative LP.\n", cnt);
      }
      else
      {
         /* if no stored linear constraints are available, possibly collect other linear constraints; we only use linear
          * constraints, since most other constraints involve integral variables, and in this context we will likely
          * benefit much more from continuous variables. */
         if ( conshdlrdata->useotherconss )
         {
            const char* conshdlrname;
            SCIP_CONS** allconss;
            int nallconss;

            nallconss = SCIPgetNConss(scip);
            allconss = SCIPgetConss(scip);

            /* loop through all constraints */
            for (c = 0; c < nallconss; ++c)
            {
               /* get constraint */
               cons = allconss[c];
               assert( cons != NULL );
               assert( SCIPconsIsTransformed(cons) );

               /* get constraint handler name */
               conshdlrname = SCIPconshdlrGetName(SCIPconsGetHdlr(cons));

               /* check type of constraint (only take linear constraints) */
               if ( strcmp(conshdlrname, "linear") == 0 )
               {
                  /* avoid adding linear constraints that correspond to indicator constraints */
                  if ( strncmp(SCIPconsGetName(cons), "indlin", 6) != 0 )
                  {
                     SCIP_CALL( addAltLPConstraint(scip, conshdlr, cons, NULL, 0.0, &colindex) );
                     SCIPdebugMsg(scip, "Added column for linear constraint <%s> to alternative LP with column index %d.\n", SCIPconsGetName(cons), colindex);
                     ++cnt;
                  }
               }
            }
            SCIPdebugMsg(scip, "Added %d additional columns from linear constraints to alternative LP.\n", cnt);
         }
      }
   }

   /* initialize event handler if restart should be forced */
   if ( conshdlrdata->forcerestart )
   {
      SCIP_Bool* covered;
      SCIP_VAR** vars;
      int nvars;
      int j;

      assert( conshdlrdata->eventhdlrrestart != NULL );

      /* store number of initial constraints */
      conshdlrdata->ninitconss = SCIPconshdlrGetNActiveConss(conshdlr);

      /* reset number of fixed binary variables */
      conshdlrdata->nbinvarszero = 0;

      /* loop through variables */
      nvars = SCIPgetNVars(scip);
      vars = SCIPgetVars(scip);

      conshdlrdata->objindicatoronly = FALSE;
      conshdlrdata->minabsobj = SCIP_REAL_MAX;

      /* unmark all variables */
      SCIP_CALL( SCIPallocBufferArray(scip, &covered, nvars) );
      for (j = 0; j < nvars; ++j)
         covered[j] = FALSE;

      /* mark indicator variables */
      for (c = 0; c < nconss; ++c)
      {
         SCIP_CONSDATA* consdata;
         int probindex;

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

         /* avoid non-active indicator constraints */
         if ( ! SCIPconsIsActive(conss[c]) )
            continue;

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

         if ( SCIPvarIsNegated(consdata->binvar) )
         {
            assert( SCIPvarGetNegatedVar(consdata->binvar) != NULL );
            probindex = SCIPvarGetProbindex(SCIPvarGetNegatedVar(consdata->binvar));
         }
         else
            probindex = SCIPvarGetProbindex(consdata->binvar);

         /* if presolving detected infeasibility it might be that the binary variables are not active */
         if ( probindex < 0 )
            continue;

         assert( 0 <= probindex && probindex < nvars );
         covered[probindex] = TRUE;
      }

      /* check all variables */
      for (j = 0; j < nvars; ++j)
      {
         SCIP_Real obj;

         obj = SCIPvarGetObj(vars[j]);
         if ( ! SCIPisZero(scip, obj) )
         {
            if ( ! covered[j] )
               break;
            if ( ! SCIPisIntegral(scip, obj) )
               break;
            if ( REALABS(obj) < conshdlrdata->minabsobj )
               conshdlrdata->minabsobj = REALABS(obj);
         }
      }

      /* if all variables have integral objective and only indicator variables have nonzero objective */
      if ( j >= nvars )
      {
         /* if there are variables with nonzero objective */
         if ( conshdlrdata->minabsobj < SCIP_REAL_MAX )
         {
            assert( SCIPisIntegral(scip, conshdlrdata->minabsobj) );
            assert( SCIPisGE(scip, conshdlrdata->minabsobj, 1.0) );

            conshdlrdata->objindicatoronly = TRUE;

            assert( conshdlrdata->eventhdlrrestart != NULL );
            SCIP_CALL( SCIPcatchEvent(scip, SCIP_EVENTTYPE_BESTSOLFOUND, conshdlrdata->eventhdlrrestart, (SCIP_EVENTDATA*) conshdlrdata, NULL) );
         }
      }

      SCIPfreeBufferArray(scip, &covered);
   }

   return SCIP_OKAY;
}


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

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

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

   if ( conshdlrdata->sepaalternativelp )
   {
      if ( conshdlrdata->slackhash != NULL )
      {
#ifdef SCIP_DEBUG
         SCIPinfoMessage(scip, NULL, "\nStatistics for cons_indicator slack hash:\n");
         SCIPhashmapPrintStatistics(conshdlrdata->slackhash, SCIPgetMessagehdlr(scip));
#endif
         SCIPhashmapFree(&conshdlrdata->slackhash);
      }

      if ( conshdlrdata->altlp != NULL )
      {
         assert( conshdlrdata->varhash != NULL );
         assert( conshdlrdata->lbhash != NULL );
         assert( conshdlrdata->ubhash != NULL );

#ifdef SCIP_DEBUG
         SCIPinfoMessage(scip, NULL, "\nStatistics for cons_indicator var hash:\n");
         SCIPhashmapPrintStatistics(conshdlrdata->varhash, SCIPgetMessagehdlr(scip));
         SCIPinfoMessage(scip, NULL, "\nStatistics for cons_indicator lower bound hash:\n");
         SCIPhashmapPrintStatistics(conshdlrdata->lbhash, SCIPgetMessagehdlr(scip));
         SCIPinfoMessage(scip, NULL, "\nStatistics for cons_indicator upper bound hash:\n");
         SCIPhashmapPrintStatistics(conshdlrdata->ubhash, SCIPgetMessagehdlr(scip));
#endif

         SCIPhashmapFree(&conshdlrdata->varhash);
         SCIPhashmapFree(&conshdlrdata->lbhash);
         SCIPhashmapFree(&conshdlrdata->ubhash);

         SCIP_CALL( SCIPlpiFree(&conshdlrdata->altlp) );

         /* save the information that the columns have been deleted */
         for (c = 0; c < nconss; ++c)
         {
            SCIP_CONSDATA* consdata;

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

            consdata = SCIPconsGetData(conss[c]);
            assert( consdata != NULL );
            consdata->colindex = -1;
         }
      }
   }
   else
   {
      assert( conshdlrdata->slackhash == NULL );
      assert( conshdlrdata->varhash == NULL );
      assert( conshdlrdata->lbhash == NULL );
      assert( conshdlrdata->ubhash == NULL );
   }

   return SCIP_OKAY;
}


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

#ifdef SCIP_MORE_DEBUG
   SCIPdebugMsg(scip, "Deleting indicator constraint <%s>.\n", SCIPconsGetName(cons) );
#endif

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

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

      if ( conshdlrdata->sepaalternativelp )
      {
         SCIP_CALL( deleteAltLPConstraint(scip, conshdlr, cons) );
      }

      assert( (*consdata)->slackvar != NULL );
      assert( (*consdata)->binvar != NULL );

      /* free events only in correct stages */
      if ( SCIPgetStage(scip) >= SCIP_STAGE_TRANSFORMING && SCIPgetStage(scip) <= SCIP_STAGE_SOLVED )
      {
         if ( (*consdata)->linconsactive )
         {
            assert( conshdlrdata->eventhdlrbound != NULL );
            SCIP_CALL( SCIPdropVarEvent(scip, (*consdata)->binvar, SCIP_EVENTTYPE_BOUNDCHANGED, conshdlrdata->eventhdlrbound,
                  (SCIP_EVENTDATA*)*consdata, -1) );
            SCIP_CALL( SCIPdropVarEvent(scip, (*consdata)->slackvar, SCIP_EVENTTYPE_BOUNDCHANGED, conshdlrdata->eventhdlrbound,
                  (SCIP_EVENTDATA*)*consdata, -1) );
         }
         if ( conshdlrdata->forcerestart )
         {
            assert( conshdlrdata->eventhdlrrestart != NULL );
            SCIP_CALL( SCIPdropVarEvent(scip, (*consdata)->binvar, SCIP_EVENTTYPE_GBDCHANGED, conshdlrdata->eventhdlrrestart,
                  (SCIP_EVENTDATA*) conshdlrdata, -1) );
         }
      }
   }

   /* Can there be cases where lincons is NULL, e.g., if presolve found the problem infeasible? */
   assert( (*consdata)->lincons != NULL );

   /* release linear constraint and slack variable */
   SCIP_CALL( SCIPreleaseVar(scip, &(*consdata)->slackvar) );
   SCIP_CALL( SCIPreleaseCons(scip, &(*consdata)->lincons) );

   SCIPfreeBlockMemory(scip, consdata);

   return SCIP_OKAY;
}


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

   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->eventhdlrbound != NULL );

#ifdef SCIP_MORE_DEBUG
   SCIPdebugMsg(scip, "Transforming indicator constraint: <%s>.\n", SCIPconsGetName(sourcecons) );
#endif

   /* get data of original constraint */
   sourcedata = SCIPconsGetData(sourcecons);
   assert( sourcedata != NULL );
   assert( sourcedata->binvar != NULL );

   /* check for slackvar */
   if ( sourcedata->slackvar == NULL )
   {
      SCIPerrorMessage("The indicator constraint <%s> needs a slack variable.\n", SCIPconsGetName(sourcecons));
      return SCIP_INVALIDDATA;
   }

   /* check for linear constraint */
   if ( sourcedata->lincons == NULL )
   {
      SCIPerrorMessage("The indicator constraint <%s> needs a linear constraint variable.\n", SCIPconsGetName(sourcecons));
      return SCIP_INVALIDDATA;
   }
   assert( sourcedata->lincons != NULL );
   assert( sourcedata->slackvar != NULL );

   /* create constraint data */
   consdata = NULL;
   SCIP_CALL( consdataCreate(scip, conshdlr, conshdlrdata, SCIPconsGetName(sourcecons), &consdata, conshdlrdata->eventhdlrbound,
         conshdlrdata->eventhdlrrestart, sourcedata->binvar, sourcedata->slackvar, sourcedata->lincons, sourcedata->linconsactive) );
   assert( consdata != NULL );

   /* capture slack variable and linear constraint */
   SCIP_CALL( SCIPcaptureVar(scip, consdata->slackvar) );
   SCIP_CALL( SCIPcaptureCons(scip, consdata->lincons) );

   /* 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)) );

   /* make sure that binary variable hash exists */
   if ( conshdlrdata->sepaalternativelp )
   {
      if ( conshdlrdata->binvarhash == NULL )
      {
         SCIP_CALL( SCIPhashmapCreate(&conshdlrdata->binvarhash, SCIPblkmem(scip), SCIPgetNOrigVars(scip)) );
      }

      /* check whether binary variable is present: note that a binary variable might appear several times, but this seldomly happens. */
      assert( conshdlrdata->binvarhash != NULL );
      if ( ! SCIPhashmapExists(conshdlrdata->binvarhash, (void*) consdata->binvar) )
      {
         SCIP_CALL( SCIPhashmapInsert(conshdlrdata->binvarhash, (void*) consdata->binvar, (void*) (*targetcons)) );
      }
   }

   return SCIP_OKAY;
}


/** presolving initialization method of constraint handler (called when presolving is about to begin) */
static
SCIP_DECL_CONSINITPRE(consInitpreIndicator)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   int c;

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

   if ( SCIPgetStatus(scip) != SCIP_STATUS_UNKNOWN )
      return SCIP_OKAY;

   SCIPdebugMsg(scip, "Initpre method for indicator constraints.\n");

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

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

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

      /* if not happened already, get transformed linear constraint */
      assert( consdata->lincons != NULL );
      assert( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(consdata->lincons)), "linear") == 0 );

      /* in a restart the linear constraint might already be transformed */
      if ( ! SCIPconsIsTransformed(consdata->lincons) )
      {
         SCIP_CONS* translincons;

         SCIP_CALL( SCIPgetTransformedCons(scip, consdata->lincons, &translincons) );
         assert( translincons != NULL );

         SCIP_CALL( SCIPreleaseCons(scip, &consdata->lincons) );
         SCIP_CALL( SCIPcaptureCons(scip, translincons) );
         consdata->lincons = translincons;
      }
   }

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

   /* reset flag, in case presolve was called for some problem before */
   conshdlrdata->addedcouplingcons = FALSE;

   return SCIP_OKAY;
}


/** presolving method of constraint handler
 *
 *  For an indicator constraint with binary variable \f$y\f$ and slack variable \f$s\f$ the coupling
 *  inequality \f$s \le M (1-y)\f$ (equivalently: \f$s + M y \le M\f$) is inserted, where \f$M\f$ is
 *  an upper bound on the value of \f$s\f$. If \f$M\f$ is too large the inequality is not
 *  inserted. Depending on the parameter @a addcouplingcons we add a variable upper bound or a row
 *  (in consInitlpIndicator()).
 *
 *  @warning We can never delete linear constraints, because we need them to get the right values
 *  for the slack variables!
 */
static
SCIP_DECL_CONSPRESOL(consPresolIndicator)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_Bool noReductions;
   int oldnfixedvars;
   int oldndelconss;
   int removedvars = 0;
   int c;

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

   *result = SCIP_DIDNOTRUN;
   SCIPdebug( oldnfixedvars = *nfixedvars; )
   SCIPdebug( oldndelconss = *ndelconss; )
   /* get constraint handler data */
   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert( conshdlrdata != NULL );

   SCIPdebugMsg(scip, "Presolving indicator constraints.\n");

   /* only run if success is possible */
   if ( nrounds == 0 || nnewfixedvars > 0 || nnewchgbds > 0 || nnewaggrvars > 0 )
   {
      *result = SCIP_DIDNOTFIND;

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

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