Detailed Description

constraint handler for (partitioning/packing) orbitope constraints w.r.t. the full symmetric group

Author: Timo Berthold; Marc Pfetsch

This constraint handler can be used to handle symmetries in certain 0/1-programs. The principle structure is that some variables can be ordered in matrix form, such that permuting columns does not change the validity and objective function value of a solution. That is, the symmetry group of the program contains the full symmetric group obtained by permuting the columns of this matrix. The variables in each row have to be contained in set packing or partitioning constraints.

In more mathematical terms the structure has to be as follows: There are 0/1-variables $x_{ij}$ , $i \in \{1, \dots, p\}$ , $j \in \{1, \dots, q\}$ . The variables are coupled through set packing or partitioning constraints:

$\sum_{j = 1}^q x_{ij} \leq 1 \quad \mbox{or} \quad \sum_{j = 1}^q x_{ij} = 1 \quad \mbox{for all }i = 1, \ldots, p.$

Permuting columns of $x$ does not change the validity and objective function value of any feasible solution.

Definition in file cons_orbitope.h.

#include "scip/scip.h"

Go to the source code of this file.

Functions
SCIP_RETCODE	SCIPincludeConshdlrOrbitope (SCIP *scip)

SCIP_RETCODE	SCIPcreateConsOrbitope (SCIP scip, SCIP_CONS cons, const char name, SCIP_VAR ***vars, SCIP_Bool ispart, int nspcons, int nblocks, SCIP_Bool resolveprop, SCIP_Bool initial, SCIP_Bool separate, SCIP_Bool enforce, SCIP_Bool check, SCIP_Bool propagate, SCIP_Bool local, SCIP_Bool modifiable, SCIP_Bool dynamic, SCIP_Bool removable, SCIP_Bool stickingatnode)

SCIP_RETCODE	SCIPcreateConsBasicOrbitope (SCIP scip, SCIP_CONS cons, const char name, SCIP_VAR ***vars, SCIP_Bool ispart, int nspcons, int nblocks, SCIP_Bool resolveprop)

Function Documentation

SCIP_RETCODE SCIPincludeConshdlrOrbitope ( SCIP * scip )

creates the handler for orbitope constraints and includes it in SCIP

Parameters

scip	SCIP data structure

SCIP_RETCODE SCIPcreateConsOrbitope	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		SCIP_VAR ***	vars,
		SCIP_Bool	ispart,
		int	nspcons,
		int	nblocks,
		SCIP_Bool	resolveprop,
		SCIP_Bool	initial,
		SCIP_Bool	separate,
		SCIP_Bool	enforce,
		SCIP_Bool	check,
		SCIP_Bool	propagate,
		SCIP_Bool	local,
		SCIP_Bool	modifiable,
		SCIP_Bool	dynamic,
		SCIP_Bool	removable,
		SCIP_Bool	stickingatnode
	)

creates and captures a orbitope constraint

Note: the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()

Parameters

scip	SCIP data structure
cons	pointer to hold the created constraint
name	name of constraint
vars	matrix of variables on which the symmetry acts
ispart	whether we deal with the partitioning case (packing otherwise)
nspcons	number of set partitioning/packing constraints <=> p
nblocks	number of symmetric variable blocks <=> q
resolveprop	should propagation be resolved?
initial	should the LP relaxation of constraint be in the initial LP? Usually set to TRUE. Set to FALSE for 'lazy constraints'.
separate	should the constraint be separated during LP processing? Usually set to TRUE.
enforce	should the constraint be enforced during node processing? TRUE for model constraints, FALSE for additional, redundant constraints.
check	should the constraint be checked for feasibility? TRUE for model constraints, FALSE for additional, redundant constraints.
propagate	should the constraint be propagated during node processing? Usually set to TRUE.
local	is constraint only valid locally? Usually set to FALSE. Has to be set to TRUE, e.g., for branching constraints.
modifiable	is constraint modifiable (subject to column generation)? Usually set to FALSE. In column generation applications, set to TRUE if pricing adds coefficients to this constraint.
dynamic	is constraint subject to aging? Usually set to FALSE. Set to TRUE for own cuts which are separated as constraints.
removable	should the relaxation be removed from the LP due to aging or cleanup? Usually set to FALSE. Set to TRUE for 'lazy constraints' and 'user cuts'.
stickingatnode	should the constraint always be kept at the node where it was added, even if it may be moved to a more global node? Usually set to FALSE. Set to TRUE to for constraints that represent node data.

SCIP_RETCODE SCIPcreateConsBasicOrbitope	(	SCIP *	scip,
		SCIP_CONS **	cons,
		const char *	name,
		SCIP_VAR ***	vars,
		SCIP_Bool	ispart,
		int	nspcons,
		int	nblocks,
		SCIP_Bool	resolveprop
	)

creates and captures an orbitope constraint in its most basic variant, i. e., with all constraint flags set to their default values, which can be set afterwards using SCIPsetConsFLAGNAME() in scip.h

See also: SCIPcreateConsOrbitope() for the default constraint flag configuration

Note: the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()

Parameters

scip	SCIP data structure
cons	pointer to hold the created constraint
name	name of constraint
vars	matrix of variables on which the symmetry acts
ispart	whether we deal with the partitioning case (packing otherwise)
nspcons	number of set partitioning/packing constraints <=> p
nblocks	number of symmetric variable blocks <=> q
resolveprop	should propagation be resolved?

SCIP

Detailed Description

Functions

Function Documentation