cons_cardinality.c File Reference

Detailed Description

constraint handler for cardinality constraints

Author

Tobias Fischer

This constraint handler handles cardinality constraints of the form

\[ |\mbox{supp}(x)| \leq b \]

with integer right-hand side \(b\). Here, \(|\mbox{supp}(x)|\) denotes the number of nonzero entries of the vector \(x\).

Note that cardinality constraints generalize special ordered set of type one (SOS1) constraints in which \(b = 1\).

The implementation of this constraint handler is based on
"On the Structure of Linear Programs with Overlapping Cardinality Constraints"
T. Fischer and M. E. Pfetsch, Tech. rep., 2016

Definition in file cons_cardinality.c.

#include <assert.h>
#include "scip/cons_cardinality.h"
#include "scip/cons_linear.h"
#include "scip/cons_knapsack.h"
#include <string.h>
#include <ctype.h>

Go to the source code of this file.

Macros
#define	CONSHDLR_NAME   "cardinality"
#define	CONSHDLR_DESC   "cardinality constraint handler"
#define	CONSHDLR_SEPAPRIORITY   10
#define	CONSHDLR_ENFOPRIORITY   100
#define	CONSHDLR_CHECKPRIORITY   -10
#define	CONSHDLR_SEPAFREQ   10
#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	DEFAULT_BRANCHBALANCED   FALSE
#define	DEFAULT_BALANCEDDEPTH   20
#define	DEFAULT_BALANCEDCUTOFF   2.0
#define	EVENTHDLR_NAME   "cardinality"
#define	EVENTHDLR_DESC   "bound change event handler for cardinality constraints"

Functions
static SCIP_RETCODE	catchVarEventCardinality (SCIP *scip, SCIP_EVENTHDLR *eventhdlr, SCIP_CONSDATA *consdata, SCIP_VAR *var, SCIP_VAR *indvar, int pos, SCIP_EVENTDATA **eventdata)
static SCIP_RETCODE	dropVarEventCardinality (SCIP *scip, SCIP_EVENTHDLR *eventhdlr, SCIP_CONSDATA *consdata, SCIP_VAR *var, SCIP_VAR *indvar, SCIP_EVENTDATA **eventdata)
static SCIP_RETCODE	fixVariableZeroNode (SCIP *scip, SCIP_VAR *var, SCIP_NODE *node, SCIP_Bool *infeasible)
static SCIP_RETCODE	fixVariableZero (SCIP *scip, SCIP_VAR *var, SCIP_Bool *infeasible, SCIP_Bool *tightened)
static SCIP_RETCODE	lockVariableCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var, SCIP_VAR *indvar)
static SCIP_RETCODE	unlockVariableCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var, SCIP_VAR *indvar)
static SCIP_RETCODE	consdataEnsurevarsSizeCardinality (SCIP *scip, SCIP_CONSDATA *consdata, int num, SCIP_Bool reserveweights)
static SCIP_RETCODE	handleNewVariableCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_CONSDATA *consdata, SCIP_CONSHDLRDATA *conshdlrdata, SCIP_VAR *var, SCIP_VAR *indvar, int pos, SCIP_Bool transformed, SCIP_EVENTDATA **eventdata)
static SCIP_RETCODE	addVarCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_CONSHDLRDATA *conshdlrdata, SCIP_VAR *var, SCIP_VAR *indvar, SCIP_Real weight)
static SCIP_RETCODE	appendVarCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_CONSHDLRDATA *conshdlrdata, SCIP_VAR *var, SCIP_VAR *indvar)
static SCIP_RETCODE	deleteVarCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_CONSDATA *consdata, SCIP_EVENTHDLR *eventhdlr, int pos)
static SCIP_RETCODE	polishPrimalSolution (SCIP *scip, SCIP_CONS **conss, int nconss, SCIP_SOL *sol, SCIP_SOL *primsol)
static SCIP_RETCODE	consdataUnmarkEventdataVars (SCIP_CONSDATA *consdata)
static SCIP_RETCODE	presolRoundCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_CONSDATA *consdata, SCIP_EVENTHDLR *eventhdlr, SCIP_Bool *cutoff, SCIP_Bool *success, int *ndelconss, int *nupgdconss, int *nfixedvars, int *nremovedvars)
static SCIP_RETCODE	propCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_CONSDATA *consdata, SCIP_Bool *cutoff, int *nchgdomain)
static SCIP_RETCODE	branchUnbalancedCardinality (SCIP *scip, SCIP_SOL *sol, SCIP_CONS *branchcons, SCIP_VAR **vars, SCIP_VAR **indvars, int nvars, int cardval, int branchnnonzero, int branchpos)
static SCIP_RETCODE	branchBalancedCardinality (SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_SOL *sol, SCIP_CONS *branchcons, SCIP_VAR **vars, SCIP_VAR **indvars, int nvars, int cardval, int branchnnonzero, int branchpos, SCIP_Real balancedcutoff)
static SCIP_RETCODE	enforceCardinality (SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_SOL *sol, int nconss, SCIP_CONS **conss, SCIP_RESULT *result)
static SCIP_RETCODE	generateRowCardinality (SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_CONS *cons, SCIP_Bool local, SCIP_ROW **rowlb, SCIP_ROW **rowub)
static SCIP_RETCODE	initsepaBoundInequalityFromCardinality (SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_CONS **conss, int nconss, SCIP_SOL *sol, SCIP_Bool solvedinitlp, int *ngen, SCIP_Bool *cutoff)
static SCIP_RETCODE	separateCardinality (SCIP *scip, SCIP_CONSHDLR *conshdlr, SCIP_SOL *sol, int nconss, SCIP_CONS **conss, SCIP_RESULT *result)
static	SCIP_DECL_CONSHDLRCOPY (conshdlrCopyCardinality)
static	SCIP_DECL_CONSFREE (consFreeCardinality)
static	SCIP_DECL_CONSEXITSOL (consExitsolCardinality)
static	SCIP_DECL_CONSDELETE (consDeleteCardinality)
static	SCIP_DECL_CONSTRANS (consTransCardinality)
static	SCIP_DECL_CONSPRESOL (consPresolCardinality)
static	SCIP_DECL_CONSINITLP (consInitlpCardinality)
static	SCIP_DECL_CONSSEPALP (consSepalpCardinality)
static	SCIP_DECL_CONSSEPASOL (consSepasolCardinality)
static	SCIP_DECL_CONSENFOLP (consEnfolpCardinality)
static	SCIP_DECL_CONSENFORELAX (consEnforelaxCardinality)
static	SCIP_DECL_CONSENFOPS (consEnfopsCardinality)
static	SCIP_DECL_CONSCHECK (consCheckCardinality)
static	SCIP_DECL_CONSPROP (consPropCardinality)
static	SCIP_DECL_CONSLOCK (consLockCardinality)
static	SCIP_DECL_CONSPRINT (consPrintCardinality)
static	SCIP_DECL_CONSCOPY (consCopyCardinality)
static	SCIP_DECL_CONSPARSE (consParseCardinality)
static	SCIP_DECL_CONSGETVARS (consGetVarsCardinality)
static	SCIP_DECL_CONSGETNVARS (consGetNVarsCardinality)
static	SCIP_DECL_EVENTEXEC (eventExecCardinality)
SCIP_RETCODE	SCIPincludeConshdlrCardinality (SCIP *scip)
SCIP_RETCODE	SCIPcreateConsCardinality (SCIP *scip, SCIP_CONS **cons, const char *name, int nvars, SCIP_VAR **vars, int cardval, SCIP_VAR **indvars, 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	SCIPcreateConsBasicCardinality (SCIP *scip, SCIP_CONS **cons, const char *name, int nvars, SCIP_VAR **vars, int cardval, SCIP_VAR **indvars, SCIP_Real *weights)
SCIP_RETCODE	SCIPchgCardvalCardinality (SCIP *scip, SCIP_CONS *cons, int cardval)
SCIP_RETCODE	SCIPaddVarCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var, SCIP_VAR *indvar, SCIP_Real weight)
SCIP_RETCODE	SCIPappendVarCardinality (SCIP *scip, SCIP_CONS *cons, SCIP_VAR *var, SCIP_VAR *indvar)
int	SCIPgetNVarsCardinality (SCIP *scip, SCIP_CONS *cons)
SCIP_VAR **	SCIPgetVarsCardinality (SCIP *scip, SCIP_CONS *cons)
int	SCIPgetCardvalCardinality (SCIP *scip, SCIP_CONS *cons)
SCIP_Real *	SCIPgetWeightsCardinality (SCIP *scip, SCIP_CONS *cons)

Macro Definition Documentation

CONSHDLR_NAME

#define CONSHDLR_NAME   "cardinality"

Definition at line 45 of file cons_cardinality.c.

Referenced by SCIPaddVarCardinality(), SCIPappendVarCardinality(), SCIPchgCardvalCardinality(), SCIPcreateConsCardinality(), SCIPgetCardvalCardinality(), SCIPgetNVarsCardinality(), SCIPgetVarsCardinality(), SCIPgetWeightsCardinality(), and SCIPincludeConshdlrCardinality().

CONSHDLR_DESC

#define CONSHDLR_DESC   "cardinality constraint handler"

Definition at line 46 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_SEPAPRIORITY

#define CONSHDLR_SEPAPRIORITY   10

priority of the constraint handler for separation

Definition at line 47 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_ENFOPRIORITY

#define CONSHDLR_ENFOPRIORITY   100

priority of the constraint handler for constraint enforcing

Definition at line 48 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_CHECKPRIORITY

#define CONSHDLR_CHECKPRIORITY   -10

priority of the constraint handler for checking feasibility

Definition at line 49 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_SEPAFREQ

#define CONSHDLR_SEPAFREQ   10

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

Definition at line 50 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_PROPFREQ

#define CONSHDLR_PROPFREQ   1

frequency for propagating domains; zero means only preprocessing propagation

Definition at line 51 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

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 52 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_MAXPREROUNDS

#define CONSHDLR_MAXPREROUNDS   -1

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

Definition at line 55 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_DELAYSEPA

#define CONSHDLR_DELAYSEPA   FALSE

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

Definition at line 58 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_DELAYPROP

#define CONSHDLR_DELAYPROP   FALSE

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

Definition at line 59 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_NEEDSCONS

#define CONSHDLR_NEEDSCONS   TRUE

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

Definition at line 60 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_PROP_TIMING

#define CONSHDLR_PROP_TIMING   SCIP_PROPTIMING_BEFORELP

Definition at line 62 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

CONSHDLR_PRESOLTIMING

#define CONSHDLR_PRESOLTIMING   SCIP_PRESOLTIMING_FAST

Definition at line 63 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

DEFAULT_BRANCHBALANCED

#define DEFAULT_BRANCHBALANCED   FALSE

whether to use balanced instead of unbalanced branching

Definition at line 66 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

DEFAULT_BALANCEDDEPTH

#define DEFAULT_BALANCEDDEPTH   20

maximum depth for using balanced branching (-1: no limit)

Definition at line 67 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

DEFAULT_BALANCEDCUTOFF

#define DEFAULT_BALANCEDCUTOFF   2.0

determines that balanced branching is only used if the branching cut off value w.r.t. the current LP solution is greater than a given value

Definition at line 68 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

EVENTHDLR_NAME

#define EVENTHDLR_NAME   "cardinality"

Definition at line 73 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

EVENTHDLR_DESC

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

Definition at line 74 of file cons_cardinality.c.

Referenced by SCIPincludeConshdlrCardinality().

Function Documentation

catchVarEventCardinality()

static SCIP_RETCODE catchVarEventCardinality ( SCIP *  scip, SCIP_EVENTHDLR *  eventhdlr, SCIP_CONSDATA *  consdata, SCIP_VAR *  var, SCIP_VAR *  indvar, int  pos, SCIP_EVENTDATA **  eventdata  )

static

catches bound change events for a variable and its indicator variable

Parameters

scip	SCIP data structure
eventhdlr	event handler for bound change events
consdata	constraint data
var	implied variable
indvar	indicator variable
pos	position in constraint
eventdata	pointer to store event data for bound change events

Definition at line 122 of file cons_cardinality.c.

References dropVarEventCardinality(), FALSE, SCIP_CALL, SCIP_EVENTTYPE_BOUNDCHANGED, SCIP_OKAY, SCIPallocBlockMemory, and SCIPcatchVarEvent().

Referenced by handleNewVariableCardinality(), and presolRoundCardinality().

dropVarEventCardinality()

static SCIP_RETCODE dropVarEventCardinality ( SCIP *  scip, SCIP_EVENTHDLR *  eventhdlr, SCIP_CONSDATA *  consdata, SCIP_VAR *  var, SCIP_VAR *  indvar, SCIP_EVENTDATA **  eventdata  )

static

drops bound change events for a variable and its indicator variable

Parameters

scip	SCIP data structure
eventhdlr	event handler for bound change events
consdata	constraint data
var	implied variable
indvar	indicator variable
eventdata	pointer of event data for bound change events

Definition at line 157 of file cons_cardinality.c.

References fixVariableZeroNode(), SCIP_CALL, SCIP_EVENTTYPE_BOUNDCHANGED, SCIP_OKAY, SCIPdropVarEvent(), and SCIPfreeBlockMemory.

Referenced by catchVarEventCardinality(), deleteVarCardinality(), and presolRoundCardinality().

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

scip	SCIP pointer
var	variable to be fixed to 0
node	node
infeasible	pointer to store if fixing is infeasible

Definition at line 188 of file cons_cardinality.c.

References FALSE, fixVariableZero(), 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 branchBalancedCardinality(), branchUnbalancedCardinality(), dropVarEventCardinality(), and enforceCardinality().

fixVariableZero()

static SCIP_RETCODE fixVariableZero ( SCIP *  scip, SCIP_VAR *  var, SCIP_Bool *  infeasible, SCIP_Bool *  tightened  )

static

try to fix variable to 0

Try to treat fixing by special consideration of multiaggregated variables. For a multi-aggregation

\[ x = \sum_{i=1}^n \alpha_i x_i + c, \]

we can express the fixing \(x = 0\) by fixing all \(x_i\) to 0 if \(c = 0\) and the lower bounds of \(x_i\) are nonnegative if \(\alpha_i > 0\) or the upper bounds are nonpositive if \(\alpha_i < 0\).

Parameters

scip	SCIP pointer
var	variable to be fixed to 0
infeasible	if fixing is infeasible
tightened	if fixing was performed

Definition at line 247 of file cons_cardinality.c.

References FALSE, lockVariableCardinality(), SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIP_VARSTATUS_MULTAGGR, SCIPfixVar(), SCIPflattenVarAggregationGraph(), SCIPisNegative(), SCIPisPositive(), SCIPisZero(), SCIPvarGetLbLocal(), SCIPvarGetMultaggrConstant(), SCIPvarGetMultaggrNVars(), SCIPvarGetMultaggrScalars(), SCIPvarGetMultaggrVars(), SCIPvarGetStatus(), SCIPvarGetUbLocal(), and TRUE.

Referenced by fixVariableZeroNode(), and propCardinality().

lockVariableCardinality()

static SCIP_RETCODE lockVariableCardinality ( SCIP *  scip, SCIP_CONS *  cons, SCIP_VAR *  var, SCIP_VAR *  indvar  )

static

add lock on variable

Parameters

scip	SCIP data structure
cons	constraint
var	variable
indvar	indicator variable

Definition at line 316 of file cons_cardinality.c.

References SCIP_CALL, SCIP_OKAY, SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPlockVarCons(), SCIPvarGetLbLocal(), SCIPvarGetUbLocal(), TRUE, and unlockVariableCardinality().

Referenced by fixVariableZero(), handleNewVariableCardinality(), and presolRoundCardinality().

unlockVariableCardinality()

static SCIP_RETCODE unlockVariableCardinality ( SCIP *  scip, SCIP_CONS *  cons, SCIP_VAR *  var, SCIP_VAR *  indvar  )

static

Parameters

scip	SCIP data structure
cons	constraint
var	variable
indvar	indicator variable

Definition at line 337 of file cons_cardinality.c.

References consdataEnsurevarsSizeCardinality(), SCIP_CALL, SCIP_OKAY, SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPunlockVarCons(), SCIPvarGetLbLocal(), SCIPvarGetUbLocal(), and TRUE.

Referenced by deleteVarCardinality(), lockVariableCardinality(), and presolRoundCardinality().

consdataEnsurevarsSizeCardinality()

static SCIP_RETCODE consdataEnsurevarsSizeCardinality ( 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

scip	SCIP data structure
consdata	constraint data
num	minimum number of entries to store
reserveweights	whether the weights array is handled

Definition at line 358 of file cons_cardinality.c.

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

Referenced by addVarCardinality(), appendVarCardinality(), and unlockVariableCardinality().

handleNewVariableCardinality()

static SCIP_RETCODE handleNewVariableCardinality ( SCIP *  scip, SCIP_CONS *  cons, SCIP_CONSDATA *  consdata, SCIP_CONSHDLRDATA *  conshdlrdata, SCIP_VAR *  var, SCIP_VAR *  indvar, int  pos, SCIP_Bool  transformed, SCIP_EVENTDATA **  eventdata  )

static

handle new variable that was added to the constraint

We perform the following steps:

• catch bound change events of variable.
• update rounding locks of variable.
• don't allow multiaggregation of variable, since this cannot be handled by branching in the current implementation
• update lower and upper bound row, i.e., the linear representations of the cardinality constraints

Parameters

scip	SCIP data structure
cons	constraint
consdata	constraint data
conshdlrdata	constraint handler data
var	variable
indvar	indicator variable to indicate whether variable may be treated as nonzero in cardinality constraint
pos	position in constraint
transformed	whether original variable was transformed
eventdata	pointer to store event data for bound change events

Definition at line 400 of file cons_cardinality.c.

References addVarCardinality(), catchVarEventCardinality(), lockVariableCardinality(), SCIP_CALL, SCIP_OKAY, SCIPaddVarToRow(), SCIPisFeasEQ(), SCIPisInfinity(), SCIPisZero(), SCIPmarkDoNotMultaggrVar(), SCIPvarGetLbGlobal(), SCIPvarGetLbLocal(), and SCIPvarGetUbGlobal().

Referenced by addVarCardinality(), appendVarCardinality(), consdataEnsurevarsSizeCardinality(), and SCIPcreateConsCardinality().

addVarCardinality()

static SCIP_RETCODE addVarCardinality ( SCIP *  scip, SCIP_CONS *  cons, SCIP_CONSHDLRDATA *  conshdlrdata, SCIP_VAR *  var, SCIP_VAR *  indvar, SCIP_Real  weight  )

static

adds a variable to a cardinality constraint, at position given by weight - ascending order

Parameters

scip	SCIP data structure
cons	constraint
conshdlrdata	constraint handler data
var	variable to add to the constraint
indvar	indicator variable to indicate whether variable may be treated as nonzero in cardinality constraint (or NULL)
weight	weight to determine position

Definition at line 457 of file cons_cardinality.c.

References appendVarCardinality(), consdataEnsurevarsSizeCardinality(), FALSE, handleNewVariableCardinality(), SCIP_Bool, SCIP_CALL, SCIP_INVALIDCALL, SCIP_MAXSTRLEN, SCIP_OKAY, SCIP_VARTYPE_BINARY, SCIPaddVar(), SCIPblkmem(), SCIPconsGetData(), SCIPconsGetName(), SCIPconsIsTransformed(), SCIPcreateVar(), SCIPerrorMessage, SCIPgetNTotalVars(), SCIPgetTransformedVar(), SCIPhashmapCreate(), SCIPhashmapExists(), SCIPhashmapGetImage(), SCIPhashmapInsert(), SCIPreleaseVar(), SCIPsnprintf(), SCIPvarGetName(), SCIPvarIsBinary(), SCIPvarIsTransformed(), and TRUE.

Referenced by handleNewVariableCardinality(), and SCIPaddVarCardinality().

appendVarCardinality()

static SCIP_RETCODE appendVarCardinality ( SCIP *  scip, SCIP_CONS *  cons, SCIP_CONSHDLRDATA *  conshdlrdata, SCIP_VAR *  var, SCIP_VAR *  indvar  )

static

appends a variable to a cardinality constraint

Parameters

scip	SCIP data structure
cons	constraint
conshdlrdata	constraint handler data
var	variable to add to the constraint
indvar	indicator variable to indicate whether variable may be treated as nonzero in cardinality constraint

Definition at line 584 of file cons_cardinality.c.

References consdataEnsurevarsSizeCardinality(), deleteVarCardinality(), FALSE, handleNewVariableCardinality(), SCIP_Bool, SCIP_CALL, SCIP_MAXSTRLEN, SCIP_OKAY, SCIP_VARTYPE_BINARY, SCIPaddVar(), SCIPblkmem(), SCIPconsGetData(), SCIPconsIsTransformed(), SCIPcreateVar(), SCIPgetNTotalVars(), SCIPgetTransformedVar(), SCIPhashmapCreate(), SCIPhashmapExists(), SCIPhashmapGetImage(), SCIPhashmapInsert(), SCIPreleaseVar(), SCIPsnprintf(), SCIPvarGetName(), SCIPvarIsBinary(), and SCIPvarIsTransformed().

Referenced by addVarCardinality(), and SCIPappendVarCardinality().

deleteVarCardinality()

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

static

deletes a variable from a cardinality constraint

Parameters

scip	SCIP data structure
cons	constraint
consdata	constraint data
eventhdlr	corresponding event handler
pos	position of variable in array

Definition at line 685 of file cons_cardinality.c.

References dropVarEventCardinality(), polishPrimalSolution(), SCIP_CALL, SCIP_OKAY, SCIPisFeasEQ(), SCIPvarGetLbLocal(), and unlockVariableCardinality().

Referenced by appendVarCardinality(), and presolRoundCardinality().

polishPrimalSolution()

static SCIP_RETCODE polishPrimalSolution ( SCIP *  scip, SCIP_CONS **  conss, int  nconss, SCIP_SOL *  sol, SCIP_SOL *  primsol  )

static

for each indicator variable sets solution to 1.0 if the solution value of the implied variable is nonzero

Parameters

scip	SCIP pointer
conss	constraints
nconss	number of constraints
sol	solution to be enforced (or NULL)
primsol	primal solution

Definition at line 726 of file cons_cardinality.c.

References consdataUnmarkEventdataVars(), SCIP_CALL, SCIP_OKAY, SCIPconsGetData(), SCIPgetSolVal(), SCIPisFeasZero(), and SCIPsetSolVal().

Referenced by deleteVarCardinality(), and enforceCardinality().

consdataUnmarkEventdataVars()

static SCIP_RETCODE consdataUnmarkEventdataVars ( SCIP_CONSDATA *  consdata )

static

unmark variables that are marked for propagation

Parameters

consdata

constraint data

Definition at line 773 of file cons_cardinality.c.

References FALSE, presolRoundCardinality(), and SCIP_OKAY.

Referenced by polishPrimalSolution(), and presolRoundCardinality().

presolRoundCardinality()

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

static

perform one presolving round

We perform the following presolving steps:

• If the bounds of some variable force it to be nonzero, we can fix all other variables to zero and remove the cardinality constraints that contain it.
• If a variable is fixed to zero, we can remove the variable.
• If a variable appears twice, it can be fixed to 0.
• We substitute appregated variables.

Parameters

scip	SCIP pointer
cons	constraint
consdata	constraint data
eventhdlr	event handler
cutoff	whether a cutoff happened
success	whether we performed a successful reduction
ndelconss	number of deleted constraints
nupgdconss	number of upgraded constraints
nfixedvars	number of fixed variables
nremovedvars	number of variables removed

Definition at line 809 of file cons_cardinality.c.

References catchVarEventCardinality(), consdataUnmarkEventdataVars(), deleteVarCardinality(), dropVarEventCardinality(), FALSE, lockVariableCardinality(), propCardinality(), SCIP_Bool, SCIP_CALL, SCIP_INVALIDDATA, SCIP_Longint, SCIP_OKAY, SCIP_Real, SCIPaddCons(), SCIPallocBufferArray, SCIPconsGetName(), SCIPconsIsChecked(), SCIPconsIsDynamic(), SCIPconsIsEnforced(), SCIPconsIsInitial(), SCIPconsIsLocal(), SCIPconsIsModifiable(), SCIPconsIsPropagated(), SCIPconsIsRemovable(), SCIPconsIsSeparated(), SCIPconsIsStickingAtNode(), SCIPcreateConsKnapsack(), SCIPdebugMsg, SCIPdelCons(), SCIPfixVar(), SCIPfreeBufferArray, SCIPgetProbvarSum(), SCIPisFeasEQ(), SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPisFeasZero(), SCIPisZero(), SCIPreleaseCons(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetUbLocal(), SCIPvarIsBinary(), TRUE, and unlockVariableCardinality().

Referenced by consdataUnmarkEventdataVars().

propCardinality()

static SCIP_RETCODE propCardinality ( SCIP *  scip, SCIP_CONS *  cons, SCIP_CONSDATA *  consdata, SCIP_Bool *  cutoff, int *  nchgdomain  )

static

propagates a cardinality constraint and its variables

The number 'ntreatnonzeros' that is assigned to the constraint data returns the number of variables that are either known to be nonzero or can be treated as nonzero. We say that a variable is known to be nonzero, if zero is outside the domain of this variable. A variable can be treated as nonzero, if its corresponding indicator variable 'indvar' is fixed to 1.0, e.g., by branching.

We perform the following propagation steps:

• if the number 'ntreatnonzeros' is greater than the cardinality value of the constraint, then the current subproblem is marked as infeasible.
• if the cardinality constraint is saturated, i.e., the number 'ntreatnonzeros' is equal to the cardinality value of the constraint, then fix all the other variables of the constraint to zero.
• remove the cardinality constraint locally if all variables are either fixed to zero or can be treated as nonzero.
• if a (binary) indicator variable is fixed to zero, then fix the corresponding implied variable to zero.
• if zero is outside of the domain of an implied variable, then fix the corresponding indicator variable to one.

Parameters

scip	SCIP pointer
cons	constraint
consdata	constraint data
cutoff	whether a cutoff happened
nchgdomain	number of domain changes

Definition at line 1096 of file cons_cardinality.c.

References branchUnbalancedCardinality(), FALSE, fixVariableZero(), SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIPchgVarLb(), SCIPconsGetName(), SCIPconsIsModifiable(), SCIPdebugMsg, SCIPdelConsLocal(), SCIPisFeasEQ(), SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPisFeasZero(), SCIPresetConsAge(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetUbLocal(), SCIPvarIsBinary(), and TRUE.

Referenced by enforceCardinality(), and presolRoundCardinality().

branchUnbalancedCardinality()

static SCIP_RETCODE branchUnbalancedCardinality ( SCIP *  scip, SCIP_SOL *  sol, SCIP_CONS *  branchcons, SCIP_VAR **  vars, SCIP_VAR **  indvars, int  nvars, int  cardval, int  branchnnonzero, int  branchpos  )

static

apply unbalanced branching (see the function enforceCardinality() for further information)

Parameters

scip	SCIP pointer
sol	solution to be enforced (or NULL)
branchcons	cardinality constraint
vars	variables of constraint
indvars	indicator variables
nvars	number of variables of constraint
cardval	cardinality value of constraint
branchnnonzero	number of variables that are fixed to be nonzero
branchpos	position in array 'vars'

Definition at line 1307 of file cons_cardinality.c.

References branchBalancedCardinality(), fixVariableZeroNode(), SCIP_Bool, SCIP_BRANCHDIR_DOWNWARDS, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIPcalcChildEstimate(), SCIPcalcNodeselPriority(), SCIPchgVarLbNode(), SCIPconsGetName(), SCIPcreateChild(), SCIPdebugMsg, SCIPgetLocalTransEstimate(), SCIPgetSolVal(), SCIPisFeasEQ(), SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPisFeasZero(), SCIPvarGetLbLocal(), SCIPvarGetName(), and SCIPvarGetUbLocal().

Referenced by branchBalancedCardinality(), enforceCardinality(), and propCardinality().

branchBalancedCardinality()

static SCIP_RETCODE branchBalancedCardinality ( SCIP *  scip, SCIP_CONSHDLR *  conshdlr, SCIP_SOL *  sol, SCIP_CONS *  branchcons, SCIP_VAR **  vars, SCIP_VAR **  indvars, int  nvars, int  cardval, int  branchnnonzero, int  branchpos, SCIP_Real  balancedcutoff  )

static

apply balanced branching (see the function enforceCardinality() for further information)

Parameters

scip	SCIP pointer
conshdlr	constraint handler
sol	solution to be enforced (or NULL)
branchcons	cardinality constraint
vars	variables of constraint
indvars	indicator variables
nvars	number of variables of constraint
cardval	cardinality value of constraint
branchnnonzero	number of variables that are fixed to be nonzero
branchpos	position in array 'vars'
balancedcutoff	cut off value for deciding whether to apply balanced branching

Definition at line 1410 of file cons_cardinality.c.

References branchUnbalancedCardinality(), enforceCardinality(), FALSE, fixVariableZeroNode(), MAX, REALABS, SCIP_Bool, SCIP_BRANCHDIR_DOWNWARDS, SCIP_CALL, SCIP_MAXSTRLEN, SCIP_OKAY, SCIP_PARAMETERWRONGVAL, SCIP_Real, SCIPaddConsNode(), SCIPallocBufferArray, SCIPcalcChildEstimate(), SCIPcalcNodeselPriority(), SCIPconsGetName(), SCIPconshdlrGetSepaFreq(), SCIPcreateChild(), SCIPcreateConsCardinality(), SCIPdebugMsg, SCIPerrorMessage, SCIPfloor(), SCIPfreeBufferArray, SCIPgetLocalTransEstimate(), SCIPgetNNodes(), SCIPgetSolVal(), SCIPisFeasLT(), SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPisFeasZero(), SCIPreleaseCons(), SCIPsnprintf(), SCIPvarGetLbLocal(), SCIPvarGetUbLocal(), and TRUE.

Referenced by branchUnbalancedCardinality(), and enforceCardinality().

enforceCardinality()

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

static

enforcement method

We check whether the current solution is feasible. If not, the cardinality constraints can be enforced by different branching rules:

• Unbalanced branching: Branch on the neighborhood of a single variable \(i\), i.e., in one branch \(x_i\) is fixed to zero and in the other we modify cardinality constraints \(|\mbox{supp}(x)| \leq k\) with \(i\in D\) to \(|\mbox{supp}(x_{D\setminus i}) \leq k-1\)
• Balanced branching: First, choose a cardinality constraint \(|\mbox{supp}(x_D) \leq k\) that is violated by the current LP solution. Then, we compute \(W = \sum_{j=1}^n |x_i|\) and \(w = \sum_{j=1}^n j\, |x_i|\). Next, search for the index \(r\) that satisfies

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

  Choose a number \(s\) with \(0\leq s < \min\{k, r\}\). The branches are then

  \[ |\mbox{supp}(x_{d_1}, \ldots, x_{d_r})| \leq s \qquad \mbox{and}\qquad |\mbox{supp}(x_{d_{r+1}}, \ldots, x_{d_{n}})| \leq k-s-1, \]

  where \(d_1, \ldots, d_n\) are the elements of the set \(D\).

The branching constraint is chosen by the largest sum of variable values.

Parameters

scip	SCIP pointer
conshdlr	constraint handler
sol	solution to be enforced (or NULL)
nconss	number of constraints
conss	indicator constraints
result	result

Definition at line 1701 of file cons_cardinality.c.

References branchBalancedCardinality(), branchUnbalancedCardinality(), FALSE, fixVariableZeroNode(), generateRowCardinality(), polishPrimalSolution(), propCardinality(), REALABS, SCIP_Bool, SCIP_BRANCHED, SCIP_CALL, SCIP_CUTOFF, SCIP_FEASIBLE, SCIP_OKAY, SCIP_Real, SCIP_REAL_MAX, SCIP_REDUCEDDOM, SCIP_VARSTATUS_MULTAGGR, SCIPconsGetData(), SCIPconsGetName(), SCIPconshdlrGetData(), SCIPconshdlrGetName(), SCIPcreateSolCopy(), SCIPdebugMsg, SCIPfreeSol(), SCIPgetCurrentNode(), SCIPgetDepth(), SCIPgetSolVal(), SCIPinfinity(), SCIPisFeasEQ(), SCIPisFeasGT(), SCIPisFeasNegative(), SCIPisFeasPositive(), SCIPisFeasZero(), SCIPresetConsAge(), SCIPtrySol(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetStatus(), SCIPvarGetUbLocal(), and TRUE.

Referenced by branchBalancedCardinality().

generateRowCardinality()

static SCIP_RETCODE generateRowCardinality ( SCIP *  scip, SCIP_CONSHDLR *  conshdlr, SCIP_CONS *  cons, SCIP_Bool  local, SCIP_ROW **  rowlb, SCIP_ROW **  rowub  )

static

Generate row

We generate the row corresponding to the following simple valid inequalities:

\[ \frac{x_1}{u_1} + \ldots + \frac{x_n}{u_n} \leq k\qquad\mbox{and}\qquad \frac{x_1}{\ell_1} + \ldots + \frac{x_n}{\ell_1} \leq k, \]

where \(\ell_1, \ldots, \ell_n\) and \(u_1, \ldots, u_n\) are the nonzero and finite lower and upper bounds of the variables \(x_1, \ldots, x_n\) and k is the right hand side of the cardinality constraint. If at least k upper bounds < 0 or a lower bounds > 0, the constraint itself is redundant, so the cut is not applied (lower bounds > 0 and upper bounds < 0 are usually detected in presolving or propagation). Infinite bounds and zero are skipped. Thus \(\ell_1, \ldots, \ell_n\) are all negative, which results in the \(\leq\) inequality.

Note that in fact, any mixture of nonzero finite lower and upper bounds would lead to a valid inequality as above. However, usually either the lower or upper bound is nonzero. Thus, the above inequalities are the most interesting.

Parameters

scip	SCIP pointer
conshdlr	constraint handler
cons	constraint
local	produce local cut?
rowlb	output: row for lower bounds (or NULL if not needed)
rowub	output: row for upper bounds (or NULL if not needed)

Definition at line 1970 of file cons_cardinality.c.

References FALSE, initsepaBoundInequalityFromCardinality(), SCIP_CALL, SCIP_MAXSTRLEN, SCIP_OKAY, SCIP_Real, SCIPaddVarsToRow(), SCIPallocBufferArray, SCIPconsGetData(), SCIPconsGetName(), SCIPcreateEmptyRowCons(), SCIPdebug, SCIPfreeBufferArray, SCIPinfinity(), SCIPisFeasEQ(), SCIPisInfinity(), SCIPisNegative(), SCIPisPositive(), SCIPisZero(), SCIPprintRow(), SCIPsnprintf(), SCIPvarGetLbGlobal(), SCIPvarGetLbLocal(), SCIPvarGetUbGlobal(), and TRUE.

Referenced by enforceCardinality(), and initsepaBoundInequalityFromCardinality().

initsepaBoundInequalityFromCardinality()

static SCIP_RETCODE initsepaBoundInequalityFromCardinality ( SCIP *  scip, SCIP_CONSHDLR *  conshdlr, SCIP_CONS **  conss, int  nconss, SCIP_SOL *  sol, SCIP_Bool  solvedinitlp, int *  ngen, SCIP_Bool *  cutoff  )

static

initialize or separate bound inequalities from cardinality constraints (see the function generateRowCardinality() for an explanation of bound inequalities)

Parameters

scip	SCIP pointer
conshdlr	constraint handler
conss	cardinality constraints
nconss	number of cardinality constraints
sol	LP solution to be separated (or NULL)
solvedinitlp	TRUE if initial LP relaxation at a node is solved
ngen	pointer to store number of cuts generated (or NULL)
cutoff	pointer to store whether a cutoff occurred

Definition at line 2095 of file cons_cardinality.c.

References FALSE, generateRowCardinality(), SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIPaddRow(), SCIPconsGetData(), SCIPconsGetName(), SCIPconsIsLocal(), SCIPdebug, SCIPdebugMsg, SCIPisCutEfficacious(), SCIPisInfinity(), SCIPisLE(), SCIPprintRow(), SCIPreleaseRow(), SCIPresetConsAge(), SCIProwGetLhs(), SCIProwGetRhs(), SCIProwIsInLP(), separateCardinality(), and TRUE.

Referenced by generateRowCardinality(), and separateCardinality().

separateCardinality()

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

static

separates cardinality constraints for arbitrary solutions

Parameters

scip	SCIP pointer
conshdlr	constraint handler
sol	solution to be separated (or NULL)
nconss	number of constraints
conss	cardinality constraints
result	result

Definition at line 2208 of file cons_cardinality.c.

References initsepaBoundInequalityFromCardinality(), SCIP_Bool, SCIP_CALL, SCIP_CUTOFF, SCIP_DECL_CONSHDLRCOPY(), SCIP_DIDNOTFIND, SCIP_DIDNOTRUN, SCIP_OKAY, SCIP_SEPARATED, SCIPdebugMsg, SCIPisStopped(), and TRUE.

Referenced by initsepaBoundInequalityFromCardinality().

SCIP_DECL_CONSHDLRCOPY()

static SCIP_DECL_CONSHDLRCOPY ( conshdlrCopyCardinality  )

static

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

Definition at line 2256 of file cons_cardinality.c.

Referenced by separateCardinality().

SCIP_DECL_CONSFREE()

static SCIP_DECL_CONSFREE ( consFreeCardinality  )

static

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

Definition at line 2272 of file cons_cardinality.c.

SCIP_DECL_CONSEXITSOL()

static SCIP_DECL_CONSEXITSOL ( consExitsolCardinality  )

static

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

Definition at line 2296 of file cons_cardinality.c.

SCIP_DECL_CONSDELETE()

static SCIP_DECL_CONSDELETE ( consDeleteCardinality  )

static

frees specific constraint data

Definition at line 2342 of file cons_cardinality.c.

SCIP_DECL_CONSTRANS()

static SCIP_DECL_CONSTRANS ( consTransCardinality  )

static

transforms constraint data into data belonging to the transformed problem

Definition at line 2400 of file cons_cardinality.c.

SCIP_DECL_CONSPRESOL()

static SCIP_DECL_CONSPRESOL ( consPresolCardinality  )

static

presolving method of constraint handler

Definition at line 2498 of file cons_cardinality.c.

SCIP_DECL_CONSINITLP()

static SCIP_DECL_CONSINITLP ( consInitlpCardinality  )

static

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

Definition at line 2577 of file cons_cardinality.c.

SCIP_DECL_CONSSEPALP()

static SCIP_DECL_CONSSEPALP ( consSepalpCardinality  )

static

separation method of constraint handler for LP solutions

Definition at line 2593 of file cons_cardinality.c.

SCIP_DECL_CONSSEPASOL()

static SCIP_DECL_CONSSEPASOL ( consSepasolCardinality  )

static

separation method of constraint handler for arbitrary primal solutions

Definition at line 2607 of file cons_cardinality.c.

SCIP_DECL_CONSENFOLP()

static SCIP_DECL_CONSENFOLP ( consEnfolpCardinality  )

static

constraint enforcing method of constraint handler for LP solutions

Definition at line 2621 of file cons_cardinality.c.

SCIP_DECL_CONSENFORELAX()

static SCIP_DECL_CONSENFORELAX ( consEnforelaxCardinality  )

static

constraint enforcing method of constraint handler for relaxation solutions

Definition at line 2636 of file cons_cardinality.c.

SCIP_DECL_CONSENFOPS()

static SCIP_DECL_CONSENFOPS ( consEnfopsCardinality  )

static

constraint enforcing method of constraint handler for pseudo solutions

Definition at line 2651 of file cons_cardinality.c.

SCIP_DECL_CONSCHECK()

static SCIP_DECL_CONSCHECK ( consCheckCardinality  )

static

feasibility check method of constraint handler for integral solutions

We simply check whether more variables than allowed are nonzero in the given solution.

Definition at line 2669 of file cons_cardinality.c.

SCIP_DECL_CONSPROP()

static SCIP_DECL_CONSPROP ( consPropCardinality  )

static

domain propagation method of constraint handler

Definition at line 2740 of file cons_cardinality.c.

SCIP_DECL_CONSLOCK()

static SCIP_DECL_CONSLOCK ( consLockCardinality  )

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 rhs of the constraint can be updated and the variable can be removed from the constraint. Thus, 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 2796 of file cons_cardinality.c.

SCIP_DECL_CONSPRINT()

static SCIP_DECL_CONSPRINT ( consPrintCardinality  )

static

constraint display method of constraint handler

Definition at line 2846 of file cons_cardinality.c.

SCIP_DECL_CONSCOPY()

static SCIP_DECL_CONSCOPY ( consCopyCardinality  )

static

constraint copying method of constraint handler

Definition at line 2876 of file cons_cardinality.c.

SCIP_DECL_CONSPARSE()

static SCIP_DECL_CONSPARSE ( consParseCardinality  )

static

constraint parsing method of constraint handler

Definition at line 2955 of file cons_cardinality.c.

SCIP_DECL_CONSGETVARS()

static SCIP_DECL_CONSGETVARS ( consGetVarsCardinality  )

static

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

Definition at line 3040 of file cons_cardinality.c.

SCIP_DECL_CONSGETNVARS()

static SCIP_DECL_CONSGETNVARS ( consGetNVarsCardinality  )

static

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

Definition at line 3062 of file cons_cardinality.c.

SCIP_DECL_EVENTEXEC()

static SCIP_DECL_EVENTEXEC ( eventExecCardinality  )

static

Definition at line 3083 of file cons_cardinality.c.