Scippy

    SCIP

    Solving Constraint Integer Programs

    Detailed Description

    constraint handler for SOS type 2 constraints

    Author
    Marc Pfetsch

    A specially ordered set of type 2 (SOS2) is a sequence of variables such that at most two variables are nonzero and if two variables are nonzero they must be adjacent in the specified sequence. Note that it is in principle allowed that a variable appears twice, but it then can be fixed to 0 if it is at least two apart in the sequence.

    This constraint is useful when considering a piecewise affine approximation of a univariate (nonlinear) function \(: [a,b] \rightarrow R\): Let \(x_1 < \ldots < x_n\) be points in \([a,b]\) and introduce variables \(\lambda_1, \ldots, \lambda_n\). To evaluate \(f(x')\) at some point \(x' \in [a,b]\) one can use the following constraints:

    \[ \lambda_1 + \cdots + \lambda_n = 1,\quad x' = x_1 \lambda_1 + \cdots + x_n \lambda_n. \]

    The value of \(f(x')\) can the be approximated as

    \[ f(x_1) \lambda_1 + \cdots + f(x_n) \lambda_n. \]

    To get a valid piecewise affine approximation, \(\lambda_1, \ldots, \lambda_n\) have to obey an SOS constraint of type 2.

    This implementation of this constraint handler is based on classical ideas, see e.g.
    "Special Facilities in General Mathematical Programming System for Non-Convex Problems Using Ordered Sets of Variables"
    E. Beale and J. Tomlin, Proc. 5th IFORS Conference, 447-454 (1970)

    The order of the variables is determined as follows:

    • If the constraint is created with SCIPcreateConsSOS2() and weights are given, the weights determine the order (decreasing weights). Additional variables can be added with SCIPaddVarSOS2(), which adds a variable with given weight.
    • If an empty constraint is created and then variables are added with SCIPaddVarSOS2(), weights are needed and stored.
    • All other calls ignore the weights, i.e., if a nonempty constraint is created or variables are added with SCIPappendVarSOS2().

    Definition in file cons_sos2.c.

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

    Go to the source code of this file.

    Macros

    #define CONSHDLR_NAME   "SOS2"
     
    #define CONSHDLR_DESC   "SOS2 constraint handler"
     
    #define CONSHDLR_SEPAPRIORITY   10
     
    #define CONSHDLR_ENFOPRIORITY   100
     
    #define CONSHDLR_CHECKPRIORITY   -10
     
    #define CONSHDLR_SEPAFREQ   0
     
    #define CONSHDLR_PROPFREQ   1
     
    #define CONSHDLR_EAGERFREQ   100
     
    #define CONSHDLR_MAXPREROUNDS   -1
     
    #define CONSHDLR_DELAYSEPA   FALSE
     
    #define CONSHDLR_DELAYPROP   FALSE
     
    #define CONSHDLR_NEEDSCONS   TRUE
     
    #define CONSHDLR_PROP_TIMING   SCIP_PROPTIMING_BEFORELP
     
    #define CONSHDLR_PRESOLTIMING   SCIP_PRESOLTIMING_FAST
     
    #define EVENTHDLR_NAME   "SOS2"
     
    #define EVENTHDLR_DESC   "bound change event handler for SOS2 constraints"
     
    #define EVENTHDLR_EVENT_TYPE   (SCIP_EVENTTYPE_BOUNDCHANGED | SCIP_EVENTTYPE_GBDCHANGED)
     

    Functions

    static SCIP_RETCODE fixVariableZeroNode (SCIP *scip, SCIP_VAR *var, SCIP_NODE *node, SCIP_Bool *infeasible)
     
    static SCIP_RETCODE inferVariableZero (SCIP *scip, SCIP_VAR *var, SCIP_CONS *cons, int inferinfo, SCIP_Bool *infeasible, SCIP_Bool *tightened, SCIP_Bool *success)
     
    static SCIP_RETCODE lockVariableSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var)
     
    static SCIP_RETCODE unlockVariableSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var)
     
    static SCIP_RETCODE consdataEnsurevarsSizeSOS2 (SCIP *scip, SCIP_CONSDATA *consdata, int num, SCIP_Bool reserveWeights)
     
    static SCIP_RETCODE handleNewVariableSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_CONSDATA *consdata, SCIP_VAR *var, SCIP_Bool transformed)
     
    static SCIP_RETCODE addVarSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var, SCIP_Real weight)
     
    static SCIP_RETCODE appendVarSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var)
     
    static SCIP_RETCODE deleteVarSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_CONSDATA *consdata, SCIP_EVENTHDLR *eventhdlr, int pos)
     
    static SCIP_RETCODE presolRoundSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_CONSDATA *consdata, SCIP_EVENTHDLR *eventhdlr, SCIP_Bool *cutoff, SCIP_Bool *success, int *ndelconss, int *nfixedvars, int *nremovedvars)
     
    static SCIP_RETCODE propSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_CONSDATA *consdata, SCIP_Bool *cutoff, int *ngen)
     
    static SCIP_RETCODE enforceSOS2 (SCIP *scip, SCIP_CONSHDLR *conshdlr, int nconss, SCIP_CONS **conss, SCIP_SOL *sol, SCIP_RESULT *result)
     
    static SCIP_RETCODE generateRowSOS2 (SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_CONS *cons, SCIP_Bool local)
     
    static SCIP_DECL_CONSHDLRCOPY (conshdlrCopySOS2)
     
    static SCIP_DECL_CONSFREE (consFreeSOS2)
     
    static SCIP_DECL_CONSEXITSOL (consExitsolSOS2)
     
    static SCIP_DECL_CONSDELETE (consDeleteSOS2)
     
    static SCIP_DECL_CONSTRANS (consTransSOS2)
     
    static SCIP_DECL_CONSPRESOL (consPresolSOS2)
     
    static SCIP_DECL_CONSINITLP (consInitlpSOS2)
     
    static SCIP_DECL_CONSSEPALP (consSepalpSOS2)
     
    static SCIP_DECL_CONSSEPASOL (consSepasolSOS2)
     
    static SCIP_DECL_CONSENFOLP (consEnfolpSOS2)
     
    static SCIP_DECL_CONSENFORELAX (consEnforelaxSOS2)
     
    static SCIP_DECL_CONSENFOPS (consEnfopsSOS2)
     
    static SCIP_DECL_CONSCHECK (consCheckSOS2)
     
    static SCIP_DECL_CONSPROP (consPropSOS2)
     
    static SCIP_DECL_CONSRESPROP (consRespropSOS2)
     
    static SCIP_DECL_CONSLOCK (consLockSOS2)
     
    static SCIP_DECL_CONSPRINT (consPrintSOS2)
     
    static SCIP_DECL_CONSCOPY (consCopySOS2)
     
    static SCIP_DECL_CONSPARSE (consParseSOS2)
     
    static SCIP_DECL_CONSGETVARS (consGetVarsSOS2)
     
    static SCIP_DECL_CONSGETNVARS (consGetNVarsSOS2)
     
    static SCIP_DECL_CONSGETPERMSYMGRAPH (consGetPermsymGraphSOS2)
     
    static SCIP_DECL_CONSGETSIGNEDPERMSYMGRAPH (consGetSignedPermsymGraphSOS2)
     
    static SCIP_DECL_EVENTEXEC (eventExecSOS2)
     
    SCIP_RETCODE SCIPincludeConshdlrSOS2 (SCIP *scip)
     
    SCIP_RETCODE SCIPcreateConsSOS2 (SCIP *scip, SCIP_CONS **cons, const char *name, int nvars, SCIP_VAR **vars, SCIP_Real *weights, SCIP_Bool initial, SCIP_Bool separate, SCIP_Bool enforce, SCIP_Bool check, SCIP_Bool propagate, SCIP_Bool local, SCIP_Bool dynamic, SCIP_Bool removable, SCIP_Bool stickingatnode)
     
    SCIP_RETCODE SCIPcreateConsBasicSOS2 (SCIP *scip, SCIP_CONS **cons, const char *name, int nvars, SCIP_VAR **vars, SCIP_Real *weights)
     
    SCIP_RETCODE SCIPaddVarSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var, SCIP_Real weight)
     
    SCIP_RETCODE SCIPappendVarSOS2 (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var)
     
    int SCIPgetNVarsSOS2 (SCIP *scip, SCIP_CONS *cons)
     
    SCIP_VAR ** SCIPgetVarsSOS2 (SCIP *scip, SCIP_CONS *cons)
     
    SCIP_RealSCIPgetWeightsSOS2 (SCIP *scip, SCIP_CONS *cons)
     

    Macro Definition Documentation

    ◆ CONSHDLR_NAME

    #define CONSHDLR_NAME   "SOS2"

    Definition at line 110 of file cons_sos2.c.

    ◆ CONSHDLR_DESC

    #define CONSHDLR_DESC   "SOS2 constraint handler"

    Definition at line 111 of file cons_sos2.c.

    ◆ CONSHDLR_SEPAPRIORITY

    #define CONSHDLR_SEPAPRIORITY   10

    priority of the constraint handler for separation

    Definition at line 112 of file cons_sos2.c.

    ◆ CONSHDLR_ENFOPRIORITY

    #define CONSHDLR_ENFOPRIORITY   100

    priority of the constraint handler for constraint enforcing

    Definition at line 113 of file cons_sos2.c.

    ◆ CONSHDLR_CHECKPRIORITY

    #define CONSHDLR_CHECKPRIORITY   -10

    priority of the constraint handler for checking feasibility

    Definition at line 114 of file cons_sos2.c.

    ◆ CONSHDLR_SEPAFREQ

    #define CONSHDLR_SEPAFREQ   0

    frequency for separating cuts; zero means to separate only in the root node

    Definition at line 115 of file cons_sos2.c.

    ◆ CONSHDLR_PROPFREQ

    #define CONSHDLR_PROPFREQ   1

    frequency for propagating domains; zero means only preprocessing propagation

    Definition at line 116 of file cons_sos2.c.

    ◆ CONSHDLR_EAGERFREQ

    #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

    Definition at line 118 of file cons_sos2.c.

    ◆ CONSHDLR_MAXPREROUNDS

    #define CONSHDLR_MAXPREROUNDS   -1

    maximal number of presolving rounds the constraint handler participates in (-1: no limit)

    Definition at line 119 of file cons_sos2.c.

    ◆ CONSHDLR_DELAYSEPA

    #define CONSHDLR_DELAYSEPA   FALSE

    should separation method be delayed, if other separators found cuts?

    Definition at line 120 of file cons_sos2.c.

    ◆ CONSHDLR_DELAYPROP

    #define CONSHDLR_DELAYPROP   FALSE

    should propagation method be delayed, if other propagators found reductions?

    Definition at line 121 of file cons_sos2.c.

    ◆ CONSHDLR_NEEDSCONS

    #define CONSHDLR_NEEDSCONS   TRUE

    should the constraint handler be skipped, if no constraints are available?

    Definition at line 122 of file cons_sos2.c.

    ◆ CONSHDLR_PROP_TIMING

    #define CONSHDLR_PROP_TIMING   SCIP_PROPTIMING_BEFORELP

    Definition at line 124 of file cons_sos2.c.

    ◆ CONSHDLR_PRESOLTIMING

    #define CONSHDLR_PRESOLTIMING   SCIP_PRESOLTIMING_FAST

    Definition at line 125 of file cons_sos2.c.

    ◆ EVENTHDLR_NAME

    #define EVENTHDLR_NAME   "SOS2"

    Definition at line 128 of file cons_sos2.c.

    ◆ EVENTHDLR_DESC

    #define EVENTHDLR_DESC   "bound change event handler for SOS2 constraints"

    Definition at line 129 of file cons_sos2.c.

    ◆ EVENTHDLR_EVENT_TYPE

    #define EVENTHDLR_EVENT_TYPE   (SCIP_EVENTTYPE_BOUNDCHANGED | SCIP_EVENTTYPE_GBDCHANGED)

    Definition at line 131 of file cons_sos2.c.

    Function Documentation

    ◆ fixVariableZeroNode()

    static SCIP_RETCODE fixVariableZeroNode ( SCIP scip,
    SCIP_VAR var,
    SCIP_NODE node,
    SCIP_Bool infeasible 
    )
    static

    fix variable in given node to 0 or add constraint if variable is multi-aggregated

    Parameters
    scipSCIP pointer
    varvariable to be fixed to 0
    nodenode
    infeasibleif fixing is infeasible

    Definition at line 154 of file cons_sos2.c.

    References FALSE, NULL, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIP_VARSTATUS_MULTAGGR, SCIPaddConsNode(), SCIPchgVarLbNode(), SCIPchgVarUbNode(), SCIPcreateConsLinear(), SCIPdebugMsg, SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPisFeasZero(), SCIPreleaseCons(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetStatus(), SCIPvarGetUbLocal(), and TRUE.

    Referenced by enforceSOS2().

    ◆ inferVariableZero()

    static SCIP_RETCODE inferVariableZero ( SCIP scip,
    SCIP_VAR var,
    SCIP_CONS cons,
    int  inferinfo,
    SCIP_Bool infeasible,
    SCIP_Bool tightened,
    SCIP_Bool success 
    )
    static

    fix variable in local node to 0, and return whether the operation was feasible

    Note
    We do not add a linear constraint if the variable is multi-aggregated as in fixVariableZeroNode(), since this would be too time consuming.
    Parameters
    scipSCIP pointer
    varvariable to be fixed to 0
    consconstraint
    inferinfoinfo for reverse prop.
    infeasibleif fixing is infeasible
    tightenedif fixing was performed
    successwhether fixing was successful, i.e., variable is not multi-aggregated

    Definition at line 205 of file cons_sos2.c.

    References FALSE, SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIP_VARSTATUS_MULTAGGR, SCIPinferVarLbCons(), SCIPinferVarUbCons(), SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPvarGetLbLocal(), SCIPvarGetStatus(), SCIPvarGetUbLocal(), and TRUE.

    Referenced by propSOS2().

    ◆ lockVariableSOS2()

    static SCIP_RETCODE lockVariableSOS2 ( SCIP scip,
    SCIP_CONS cons,
    SCIP_VAR var 
    )
    static

    add lock on variable

    Parameters
    scipSCIP data structure
    consconstraint
    varvariable

    Definition at line 248 of file cons_sos2.c.

    References NULL, SCIP_CALL, SCIP_OKAY, SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPlockVarCons(), SCIPvarGetLbGlobal(), and SCIPvarGetUbGlobal().

    Referenced by handleNewVariableSOS2(), and presolRoundSOS2().

    ◆ unlockVariableSOS2()

    static SCIP_RETCODE unlockVariableSOS2 ( SCIP scip,
    SCIP_CONS cons,
    SCIP_VAR var 
    )
    static

    remove lock on variable

    Parameters
    scipSCIP data structure
    consconstraint
    varvariable

    Definition at line 268 of file cons_sos2.c.

    References NULL, SCIP_CALL, SCIP_OKAY, SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPunlockVarCons(), SCIPvarGetLbGlobal(), and SCIPvarGetUbGlobal().

    Referenced by deleteVarSOS2(), and presolRoundSOS2().

    ◆ consdataEnsurevarsSizeSOS2()

    static SCIP_RETCODE consdataEnsurevarsSizeSOS2 ( SCIP scip,
    SCIP_CONSDATA consdata,
    int  num,
    SCIP_Bool  reserveWeights 
    )
    static

    ensures that the vars and weights array can store at least num entries

    Parameters
    scipSCIP data structure
    consdataconstraint data
    numminimum number of entries to store
    reserveWeightswhether the weights array is handled

    Definition at line 288 of file cons_sos2.c.

    References NULL, SCIP_CALL, SCIP_OKAY, SCIPcalcMemGrowSize(), and SCIPreallocBlockMemoryArray.

    Referenced by addVarSOS2(), and appendVarSOS2().

    ◆ handleNewVariableSOS2()

    static SCIP_RETCODE handleNewVariableSOS2 ( SCIP scip,
    SCIP_CONS cons,
    SCIP_CONSDATA consdata,
    SCIP_VAR var,
    SCIP_Bool  transformed 
    )
    static

    handle new variable

    Parameters
    scipSCIP data structure
    consconstraint
    consdataconstraint data
    varvariable
    transformedwhether original variable was transformed

    Definition at line 316 of file cons_sos2.c.

    References EVENTHDLR_EVENT_TYPE, lockVariableSOS2(), NULL, SCIP_CALL, SCIP_OKAY, SCIPaddVarToRow(), SCIPcatchVarEvent(), SCIPchgRowLhs(), SCIPchgRowRhs(), SCIPconsGetHdlr(), SCIPconshdlrGetData(), SCIPisFeasGT(), SCIPisFeasLT(), SCIPisFeasNegative(), SCIPisFeasPositive(), SCIProwGetLhs(), SCIProwGetRhs(), SCIPvarGetLbLocal(), and SCIPvarGetUbLocal().

    Referenced by addVarSOS2(), and appendVarSOS2().

    ◆ addVarSOS2()

    static SCIP_RETCODE addVarSOS2 ( SCIP scip,
    SCIP_CONS cons,
    SCIP_VAR var,
    SCIP_Real  weight 
    )
    static

    adds a variable to an SOS2 constraint, a position given by weight - ascending order

    Parameters
    scipSCIP data structure
    consconstraint
    varvariable to add to the constraint
    weightweight to determine position

    Definition at line 373 of file cons_sos2.c.

    References consdataEnsurevarsSizeSOS2(), handleNewVariableSOS2(), NULL, SCIP_Bool, SCIP_CALL, SCIP_INVALIDCALL, SCIP_OKAY, SCIPconsGetData(), SCIPconsGetName(), SCIPconsIsTransformed(), SCIPerrorMessage, SCIPgetTransformedVar(), SCIPvarIsTransformed(), and TRUE.

    Referenced by SCIPaddVarSOS2().

    ◆ appendVarSOS2()

    static SCIP_RETCODE appendVarSOS2 ( SCIP scip,
    SCIP_CONS cons,
    SCIP_VAR var 
    )
    static

    appends a variable to an SOS2 constraint

    Parameters
    scipSCIP data structure
    consconstraint
    varvariable to add to the constraint

    Definition at line 441 of file cons_sos2.c.

    References consdataEnsurevarsSizeSOS2(), FALSE, handleNewVariableSOS2(), NULL, SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIPconsGetData(), SCIPconsIsTransformed(), SCIPgetTransformedVar(), SCIPvarIsTransformed(), and TRUE.

    Referenced by SCIPappendVarSOS2().

    ◆ deleteVarSOS2()

    static SCIP_RETCODE deleteVarSOS2 ( SCIP scip,
    SCIP_CONS cons,
    SCIP_CONSDATA consdata,
    SCIP_EVENTHDLR eventhdlr,
    int  pos 
    )
    static

    deletes a variable of an SOS2 constraint

    Parameters
    scipSCIP data structure
    consconstraint
    consdataconstraint data
    eventhdlrcorresponding event handler
    posposition of variable in array

    Definition at line 497 of file cons_sos2.c.

    References EVENTHDLR_EVENT_TYPE, NULL, SCIP_CALL, SCIP_OKAY, SCIPdropVarEvent(), and unlockVariableSOS2().

    Referenced by presolRoundSOS2().

    ◆ presolRoundSOS2()

    static SCIP_RETCODE presolRoundSOS2 ( SCIP scip,
    SCIP_CONS cons,
    SCIP_CONSDATA consdata,
    SCIP_EVENTHDLR eventhdlr,
    SCIP_Bool cutoff,
    SCIP_Bool success,
    int *  ndelconss,
    int *  nfixedvars,
    int *  nremovedvars 
    )
    static

    perform one presolving round

    We perform the following presolving steps.

    • If the bounds of one variable force it to be nonzero, we can fix all other variables with distance at least two to zero. If two variables are certain to be nonzero, we can fix all other variables to 0 and remove the constraint.
    • All variables fixed to zero, that are at the beginning or end of the constraint can be removed.
    • We substitute appregated variables.
    • If a constraint has at most two variables, we delete it.

    We currently do not handle the following:

    • If we have at least two variables fixed to zero next to each-other, that are positioned in the inner part of this constraint, we can delete all but one of these variables.
    • If a variable appears twice not next to each-other, it can be fixed to 0. If one variable appears next to each-other and is already certain to be nonzero, we can fix all variables.
    • If a binary variable and its negation appear in the constraint, we might fix variables to zero or can forbid a zero value for them.
    • When, after removing all zero "border" variables, a constraint with more than two variables has at most two variables that are not fixed to 0, only one of these can take a nonzero value, because these variables need to be the "border" variables of this constraint. The same holds if we have exactly three variables in one constraint and the middle variable is certain to be not zero. In both cases we can upgrade this constraint constraint to an sos1 consisting only of the "border" variables. If these "border" variables are negations of each other, we can delete this constraint.
    • When, after removing all variables fixed to 0, that are possible, in a constraint each even positioned variable is fixed to 0, we can upgrade this constraint to an sos1 that holds all non-fixed variables.
    • Extract cliques for all odd and also for all even positioned binary variables
    Parameters
    scipSCIP pointer
    consconstraint
    consdataconstraint data
    eventhdlrevent handler
    cutoffwhether a cutoff happened
    successwhether we performed a successful reduction
    ndelconssnumber of deleted constraints
    nfixedvarsnumber of fixed variables
    nremovedvarsnumber of variables removed

    Definition at line 557 of file cons_sos2.c.

    References deleteVarSOS2(), EVENTHDLR_EVENT_TYPE, FALSE, lockVariableSOS2(), NULL, SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIPcatchVarEvent(), SCIPconsGetName(), SCIPconsIsModifiable(), SCIPdebugMsg, SCIPdelCons(), SCIPdropVarEvent(), SCIPfixVar(), SCIPgetProbvarSum(), SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPisFeasZero(), SCIPisZero(), SCIPvarGetLbGlobal(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetUbGlobal(), SCIPvarGetUbLocal(), TRUE, and unlockVariableSOS2().

    Referenced by SCIP_DECL_CONSPRESOL().

    ◆ propSOS2()

    static SCIP_RETCODE propSOS2 ( SCIP scip,
    SCIP_CONS cons,
    SCIP_CONSDATA consdata,
    SCIP_Bool cutoff,
    int *  ngen 
    )
    static

    propagate variables

    Parameters
    scipSCIP pointer
    consconstraint
    consdataconstraint data
    cutoffwhether a cutoff happened
    ngenpointer to incremental counter for domain changes

    Definition at line 838 of file cons_sos2.c.

    References FALSE, inferVariableZero(), NULL, SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIPconsGetName(), SCIPconsIsModifiable(), SCIPdebugMsg, SCIPdelConsLocal(), SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPresetConsAge(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetUbLocal(), and TRUE.

    Referenced by enforceSOS2(), and SCIP_DECL_CONSPROP().

    ◆ enforceSOS2()

    static SCIP_RETCODE enforceSOS2 ( SCIP scip,
    SCIP_CONSHDLR conshdlr,
    int  nconss,
    SCIP_CONS **  conss,
    SCIP_SOL sol,
    SCIP_RESULT result 
    )
    static

    enforcement method

    We check whether the current solution is feasible, i.e., contains at most one nonzero variable. If not, we branch along the lines indicated by Beale and Tomlin:

    We first compute \(W = \sum_{j=1}^n |x_i|\) and \(w = \sum_{j=1}^n j\, |x_i|\). Then we search for the index \(k\) that satisfies

    \[ k \leq \frac{w}{W} < k+1. \]

    The branches are then

    \[ x_1 = 0, \ldots, x_{k-1} = 0 \qquad \mbox{and}\qquad x_{k+1} = 0, \ldots, x_n = 0. \]

    There is one special case that we have to consider: It can happen that \(k\) is one too small. Example: \(x_1 = 1 - \epsilon, x_2 = 0, x_3 = \epsilon\). Then \(w = 1 - \epsilon + 3 \epsilon = 1 + 2 \epsilon\). This yields \(k = 1\) and hence the first branch does not change the solution. We therefore increase \(k\) by one if \(x_k \neq 0\). This is valid, since we know that \(x_{k+1} \neq 0\) (with respect to the original \(k\)); the corresponding branch will cut off the current solution, since \(x_k \neq 0\).

    Parameters
    scipSCIP pointer
    conshdlrconstraint handler
    nconssnumber of constraints
    conssindicator constraints
    solsolution to be enforced (NULL for LP solution)
    resultresult

    Definition at line 1036 of file cons_sos2.c.

    References branchCons(), fixVariableZeroNode(), NULL, propSOS2(), REALABS, SCIP_Bool, SCIP_BRANCHDIR_DOWNWARDS, SCIP_BRANCHED, SCIP_CALL, SCIP_CUTOFF, SCIP_FEASIBLE, SCIP_OKAY, SCIP_Real, SCIP_REDUCEDDOM, SCIPcalcChildEstimateIncrease(), SCIPcalcNodeselPriority(), SCIPconsGetData(), SCIPconsGetName(), SCIPconshdlrGetName(), SCIPcreateChild(), SCIPdebugMsg, SCIPfeasFloor(), SCIPgetLocalTransEstimate(), SCIPgetSolVal(), SCIPisFeasZero(), SCIPresetConsAge(), SCIPvarGetName(), and w.

    Referenced by SCIP_DECL_CONSENFOLP(), SCIP_DECL_CONSENFOPS(), and SCIP_DECL_CONSENFORELAX().

    ◆ generateRowSOS2()

    static SCIP_RETCODE generateRowSOS2 ( SCIP scip,
    SCIP_CONSHDLR conshdlr,
    SCIP_CONS cons,
    SCIP_Bool  local 
    )
    static

    Generate basic row

    We generate the row corresponding to the following simple valid inequalities. Let \(U\) and \(U'\) be the largest and second largest upper bound of variables appearing in the constraint. Similarly let \(L\) and \(L'\) be the smallest and second smallest lower bound. The inequalities are:

    \[ x_1 + \ldots + x_n \leq U + U' \qquad\mbox{and}\qquad x_1 + \ldots + x_n \geq L + L'. \]

    Of course, these inequalities are only added if the upper and lower bounds are all finite and \(L+L' < 0\) or \(U+U' > 0\).

    Parameters
    scipSCIP pointer
    conshdlrconstraint handler
    consconstraint
    localproduce local cut?

    Definition at line 1238 of file cons_sos2.c.

    References FALSE, NULL, REALABS, SCIP_CALL, SCIP_MAXSTRLEN, SCIP_OKAY, SCIP_Real, SCIPaddVarsToRowSameCoef(), SCIPconsGetData(), SCIPconsGetName(), SCIPcreateEmptyRowCons(), SCIPdebug, SCIPinfinity(), SCIPisFeasZero(), SCIPisInfinity(), SCIPprintRow(), SCIPsnprintf(), SCIPvarGetLbGlobal(), SCIPvarGetLbLocal(), SCIPvarGetUbGlobal(), and SCIPvarGetUbLocal().

    Referenced by SCIP_DECL_CONSINITLP(), SCIP_DECL_CONSSEPALP(), and SCIP_DECL_CONSSEPASOL().

    ◆ SCIP_DECL_CONSHDLRCOPY()

    static SCIP_DECL_CONSHDLRCOPY ( conshdlrCopySOS2  )
    static

    copy method for constraint handler plugins (called when SCIP copies plugins)

    Definition at line 1337 of file cons_sos2.c.

    References CONSHDLR_NAME, NULL, SCIP_CALL, SCIP_OKAY, SCIPconshdlrGetName(), SCIPincludeConshdlrSOS2(), and TRUE.

    ◆ SCIP_DECL_CONSFREE()

    static SCIP_DECL_CONSFREE ( consFreeSOS2  )
    static

    destructor of constraint handler to free constraint handler data (called when SCIP is exiting)

    Definition at line 1354 of file cons_sos2.c.

    References CONSHDLR_NAME, NULL, SCIP_OKAY, SCIPconshdlrGetData(), SCIPconshdlrGetName(), and SCIPfreeBlockMemory.

    ◆ SCIP_DECL_CONSEXITSOL()

    static SCIP_DECL_CONSEXITSOL ( consExitsolSOS2  )
    static

    solving process deinitialization method of constraint handler (called before branch and bound process data is freed)

    Definition at line 1373 of file cons_sos2.c.

    References CONSHDLR_NAME, NULL, SCIP_CALL, SCIP_OKAY, SCIPconsGetData(), SCIPconsGetName(), SCIPconshdlrGetName(), SCIPdebugMsg, and SCIPreleaseRow().

    ◆ SCIP_DECL_CONSDELETE()

    static SCIP_DECL_CONSDELETE ( consDeleteSOS2  )
    static

    ◆ SCIP_DECL_CONSTRANS()

    ◆ SCIP_DECL_CONSPRESOL()

    static SCIP_DECL_CONSPRESOL ( consPresolSOS2  )
    static

    ◆ SCIP_DECL_CONSINITLP()

    static SCIP_DECL_CONSINITLP ( consInitlpSOS2  )
    static

    LP initialization method of constraint handler (called before the initial LP relaxation at a node is solved)

    Definition at line 1606 of file cons_sos2.c.

    References CONSHDLR_NAME, FALSE, generateRowSOS2(), NULL, REALABS, SCIP_CALL, SCIP_OKAY, SCIPaddRow(), SCIPconsGetData(), SCIPconsGetName(), SCIPconshdlrGetName(), SCIPdebug, SCIPdebugMsg, SCIPisInfinity(), SCIPprintRow(), SCIProwGetLhs(), SCIProwGetRhs(), and SCIProwIsInLP().

    ◆ SCIP_DECL_CONSSEPALP()

    static SCIP_DECL_CONSSEPALP ( consSepalpSOS2  )
    static

    ◆ SCIP_DECL_CONSSEPASOL()

    static SCIP_DECL_CONSSEPASOL ( consSepasolSOS2  )
    static

    ◆ SCIP_DECL_CONSENFOLP()

    static SCIP_DECL_CONSENFOLP ( consEnfolpSOS2  )
    static

    constraint enforcing method of constraint handler for LP solutions

    Definition at line 1762 of file cons_sos2.c.

    References CONSHDLR_NAME, enforceSOS2(), NULL, SCIP_CALL, SCIP_OKAY, and SCIPconshdlrGetName().

    ◆ SCIP_DECL_CONSENFORELAX()

    static SCIP_DECL_CONSENFORELAX ( consEnforelaxSOS2  )
    static

    constraint enforcing method of constraint handler for relaxation solutions

    Definition at line 1778 of file cons_sos2.c.

    References CONSHDLR_NAME, enforceSOS2(), NULL, SCIP_CALL, SCIP_OKAY, and SCIPconshdlrGetName().

    ◆ SCIP_DECL_CONSENFOPS()

    static SCIP_DECL_CONSENFOPS ( consEnfopsSOS2  )
    static

    constraint enforcing method of constraint handler for pseudo solutions

    Definition at line 1794 of file cons_sos2.c.

    References CONSHDLR_NAME, enforceSOS2(), NULL, SCIP_CALL, SCIP_OKAY, and SCIPconshdlrGetName().

    ◆ SCIP_DECL_CONSCHECK()

    static SCIP_DECL_CONSCHECK ( consCheckSOS2  )
    static

    feasibility check method of constraint handler for integral solutions

    We simply check whether at most two variable are nonzero and in the case there are exactly two nonzero, then they have to be direct neighbors in the given solution.

    Definition at line 1815 of file cons_sos2.c.

    References CONSHDLR_NAME, NULL, SCIP_CALL, SCIP_FEASIBLE, SCIP_INFEASIBLE, SCIP_OKAY, SCIPconsGetData(), SCIPconsGetName(), SCIPconshdlrGetName(), SCIPdebugMsg, SCIPgetSolVal(), SCIPinfoMessage(), SCIPisFeasZero(), SCIPprintCons(), SCIPresetConsAge(), SCIPupdateSolConsViolation(), and SCIPvarGetName().

    ◆ SCIP_DECL_CONSPROP()

    static SCIP_DECL_CONSPROP ( consPropSOS2  )
    static

    ◆ SCIP_DECL_CONSRESPROP()

    static SCIP_DECL_CONSRESPROP ( consRespropSOS2  )
    static

    propagation conflict resolving method of constraint handler

    We check which bound changes were the reason for infeasibility. We use that inferinfo stores the index of the variable that has bounds that fix it to be nonzero (these bounds are the reason).

    Definition at line 1933 of file cons_sos2.c.

    References CONSHDLR_NAME, FALSE, NULL, SCIP_CALL, SCIP_DIDNOTFIND, SCIP_OKAY, SCIP_SUCCESS, SCIPaddConflictLb(), SCIPaddConflictUb(), SCIPconsGetData(), SCIPconsGetName(), SCIPconshdlrGetName(), SCIPdebugMsg, SCIPgetVarLbAtIndex(), SCIPgetVarUbAtIndex(), SCIPisFeasNegative(), and SCIPisFeasPositive().

    ◆ SCIP_DECL_CONSLOCK()

    static SCIP_DECL_CONSLOCK ( consLockSOS2  )
    static

    variable rounding lock method of constraint handler

    Let lb and ub be the lower and upper bounds of a variable. Preprocessing usually makes sure that lb <= 0 <= ub.

    • If lb < 0 then rounding down may violate the constraint.
    • If ub > 0 then rounding up may violated the constraint.
    • If lb > 0 or ub < 0 then the constraint is infeasible and we do not have to deal with it here.
    • If lb == 0 then rounding down does not violate the constraint.
    • If ub == 0 then rounding up does not violate the constraint.

    Definition at line 1985 of file cons_sos2.c.

    References CONSHDLR_NAME, NULL, SCIP_CALL, SCIP_LOCKTYPE_MODEL, SCIP_OKAY, SCIPaddVarLocksType(), SCIPconsGetData(), SCIPconsGetName(), SCIPconshdlrGetName(), SCIPdebugMsg, SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPvarGetLbGlobal(), and SCIPvarGetUbGlobal().

    ◆ SCIP_DECL_CONSPRINT()

    static SCIP_DECL_CONSPRINT ( consPrintSOS2  )
    static

    constraint display method of constraint handler

    Definition at line 2027 of file cons_sos2.c.

    References CONSHDLR_NAME, FALSE, NULL, SCIP_CALL, SCIP_OKAY, SCIPconsGetData(), SCIPconshdlrGetName(), SCIPinfoMessage(), and SCIPwriteVarName().

    ◆ SCIP_DECL_CONSCOPY()

    ◆ SCIP_DECL_CONSPARSE()

    static SCIP_DECL_CONSPARSE ( consParseSOS2  )
    static

    constraint parsing method of constraint handler

    Definition at line 2121 of file cons_sos2.c.

    References FALSE, NULL, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIPaddVarSOS2(), SCIPcreateConsSOS2(), SCIPerrorMessage, SCIPparseVarName(), SCIPreleaseCons(), SCIPskipSpace(), separate(), and TRUE.

    ◆ SCIP_DECL_CONSGETVARS()

    static SCIP_DECL_CONSGETVARS ( consGetVarsSOS2  )
    static

    constraint method of constraint handler which returns the variables (if possible)

    Definition at line 2205 of file cons_sos2.c.

    References BMScopyMemoryArray, FALSE, NULL, SCIP_OKAY, SCIPconsGetData(), and TRUE.

    ◆ SCIP_DECL_CONSGETNVARS()

    static SCIP_DECL_CONSGETNVARS ( consGetNVarsSOS2  )
    static

    constraint method of constraint handler which returns the number of variables (if possible)

    Definition at line 2228 of file cons_sos2.c.

    References NULL, SCIP_OKAY, SCIPconsGetData(), and TRUE.

    ◆ SCIP_DECL_CONSGETPERMSYMGRAPH()

    ◆ SCIP_DECL_CONSGETSIGNEDPERMSYMGRAPH()

    ◆ SCIP_DECL_EVENTEXEC()