Detailed Description

optimization-based bound tightening propagator

Author: Stefan Weltge

Definition in file prop_obbt.c.

#include <assert.h>
#include <string.h>
#include "scip/prop_obbt.h"
#include "scip/prop_genvbounds.h"
#include "scip/debug.h"

Go to the source code of this file.

Macros
#define	PROP_NAME "obbt"

#define	PROP_DESC "optimization-based bound tightening propagator"

#define	PROP_TIMING SCIP_PROPTIMING_AFTERLPLOOP

#define	PROP_PRIORITY -1000000

#define	PROP_FREQ 0

#define	PROP_DELAY TRUE

#define	DEFAULT_CREATE_GENVBOUNDS TRUE

#define	DEFAULT_FILTERING_NORM TRUE

#define	DEFAULT_APPLY_FILTERROUNDS FALSE

#define	DEFAULT_DUALFEASTOL 1e-9

#define	DEFAULT_CONDITIONLIMIT -1.0

#define	DEFAULT_FILTERING_MIN 2

#define	DEFAULT_ITLIMITFACTOR 5.0

#define	DEFAULT_MAXLOOKAHEAD 3

#define	OBBT_SCOREBASE 5

#define	GENVBOUND_PROP_NAME "genvbounds"

Typedefs
typedef struct Bound	BOUND

typedef struct BoundGroup	BOUNDGROUP

Functions
static SCIP_RETCODE	solveLP (SCIP scip, int itlimit, SCIP_Bool error, SCIP_Bool *optimal)

static SCIP_RETCODE	addObjCutoff (SCIP scip, SCIP_PROPDATA propdata)

static SCIP_Bool	varIsFixedLocal (SCIP scip, SCIP_VAR var)

static int	getIterationsLeft (SCIP *scip, SCIP_Longint nolditerations, SCIP_Longint itlimit)

static SCIP_Real	getFilterCoef (SCIP scip, SCIP_PROPDATA propdata, SCIP_VAR *var, SCIP_BOUNDTYPE boundtype)

static SCIP_RETCODE	filterExistingLP (SCIP scip, SCIP_PROPDATA propdata, int *nfiltered)

static SCIP_RETCODE	filterRound (SCIP scip, SCIP_PROPDATA propdata, int itlimit, int *nfiltered)

static SCIP_RETCODE	filterBounds (SCIP scip, SCIP_PROPDATA propdata, SCIP_Longint itlimit)

static SCIP_RETCODE	applyBoundChgs (SCIP scip, SCIP_PROPDATA propdata, SCIP_RESULT *result)

static SCIP_RETCODE	tightenBoundDive (SCIP scip, BOUND bound, SCIP_Real newval, SCIP_Bool *tightened)

static SCIP_RETCODE	createGenVBound (SCIP scip, SCIP_PROPDATA propdata, BOUND *bound)

static SCIP_RETCODE	findNewBounds (SCIP scip, SCIP_PROPDATA propdata, SCIP_Longint itlimit)

static SCIP_RETCODE	applyObbt (SCIP scip, SCIP_PROPDATA propdata, SCIP_Longint itlimit, SCIP_RESULT *result)

static unsigned int	getScore (SCIP scip, BOUND bound, int nlcount, int maxnlcount)

static	SCIP_DECL_SORTPTRCOMP (compBounds)

static SCIP_RETCODE	createGroups (SCIP_PROPDATA *propdata)

static SCIP_Bool	varIsInteresting (SCIP scip, SCIP_VAR var, int nlcount)

static SCIP_RETCODE	initBounds (SCIP scip, SCIP_PROPDATA propdata)

static	SCIP_DECL_PROPINITSOL (propInitsolObbt)

static	SCIP_DECL_PROPEXEC (propExecObbt)

static	SCIP_DECL_PROPRESPROP (propRespropObbt)

static	SCIP_DECL_PROPEXITSOL (propExitsolObbt)

static	SCIP_DECL_PROPFREE (propFreeObbt)

SCIP_RETCODE	SCIPincludePropObbt (SCIP *scip)

Macro Definition Documentation

#define PROP_NAME "obbt"

Definition at line 44 of file prop_obbt.c.

#define PROP_DESC "optimization-based bound tightening propagator"

Definition at line 45 of file prop_obbt.c.

#define PROP_TIMING SCIP_PROPTIMING_AFTERLPLOOP

Definition at line 46 of file prop_obbt.c.

#define PROP_PRIORITY -1000000

propagator priority

Definition at line 47 of file prop_obbt.c.

#define PROP_FREQ 0

propagator frequency

Definition at line 48 of file prop_obbt.c.

#define PROP_DELAY TRUE

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

Definition at line 49 of file prop_obbt.c.

#define DEFAULT_CREATE_GENVBOUNDS TRUE

should obbt try to provide genvbounds if possible?

Definition at line 52 of file prop_obbt.c.

#define DEFAULT_FILTERING_NORM TRUE

should coefficients in filtering be normalized w.r.t. the domains sizes?

Definition at line 53 of file prop_obbt.c.

#define DEFAULT_APPLY_FILTERROUNDS FALSE

try to filter bounds in so-called filter rounds by solving auxiliary LPs?

Definition at line 56 of file prop_obbt.c.

#define DEFAULT_DUALFEASTOL 1e-9

feasibility tolerance for reduced costs used in obbt; this value is used if SCIP's dual feastol is greater

Definition at line 59 of file prop_obbt.c.

#define DEFAULT_CONDITIONLIMIT -1.0

maximum condition limit used in LP solver (-1.0: no limit)

Definition at line 62 of file prop_obbt.c.

#define DEFAULT_FILTERING_MIN 2

minimal number of filtered bounds to apply another filter round

Definition at line 63 of file prop_obbt.c.

#define DEFAULT_ITLIMITFACTOR 5.0

multiple of root node LP iterations used as total LP iteration limit for obbt (<= 0: no limit )

Definition at line 66 of file prop_obbt.c.

#define DEFAULT_MAXLOOKAHEAD 3

maximal number of bounds evaluated without success per group (-1: no limit)

Definition at line 69 of file prop_obbt.c.

#define OBBT_SCOREBASE 5

base that is used to calculate a bounds score value

Definition at line 73 of file prop_obbt.c.

#define GENVBOUND_PROP_NAME "genvbounds"

Definition at line 74 of file prop_obbt.c.

Typedef Documentation

typedef struct Bound BOUND

Definition at line 91 of file prop_obbt.c.

typedef struct BoundGroup BOUNDGROUP

Definition at line 99 of file prop_obbt.c.

Function Documentation

static SCIP_RETCODE solveLP	(	SCIP *	scip,
		int	itlimit,
		SCIP_Bool *	error,
		SCIP_Bool *	optimal
	)

static

solves the LP and handles errors

Parameters

scip	SCIP data structure
itlimit	maximal number of LP iterations to perform, or -1 for no limit
error	pointer to store whether an unresolved LP error occurred
optimal	was the LP solved to optimalilty?

Definition at line 132 of file prop_obbt.c.

static SCIP_RETCODE addObjCutoff	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata
	)

static

adds the objective cutoff to the LP; must be in diving mode

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator

Definition at line 203 of file prop_obbt.c.

static SCIP_Bool varIsFixedLocal	(	SCIP *	scip,
		SCIP_VAR *	var
	)

static

determines, whether a variable is already locally fixed

Parameters

scip	SCIP data structure
var	variable to check

Definition at line 253 of file prop_obbt.c.

References SCIP_Longint.

static int getIterationsLeft	(	SCIP *	scip,
		SCIP_Longint	nolditerations,
		SCIP_Longint	itlimit
	)

static

returns number of LP iterations left (-1: no limit )

Parameters

scip	SCIP data structure
nolditerations	iterations count at the beginning of the corresponding function
itlimit	LP iteration limit (-1: no limit)

Definition at line 263 of file prop_obbt.c.

static SCIP_Real getFilterCoef	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata,
		SCIP_VAR *	var,
		SCIP_BOUNDTYPE	boundtype
	)

static

returns the objective coefficient for a variable's bound that will be chosen during filtering

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
var	variable
boundtype	boundtype to be filtered?

Definition at line 293 of file prop_obbt.c.

static SCIP_RETCODE filterExistingLP	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata,
		int *	nfiltered
	)

static

trying to filter some bounds using the existing LP solution

Parameters

scip	original SCIP data structure
propdata	data of the obbt propagator
nfiltered	how many bounds were filtered this round?

Definition at line 338 of file prop_obbt.c.

static SCIP_RETCODE filterRound	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata,
		int	itlimit,
		int *	nfiltered
	)

static

enforces one round of filtering

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
itlimit	LP iteration limit (-1: no limit)
nfiltered	how many bounds were filtered this round

Definition at line 392 of file prop_obbt.c.

static SCIP_RETCODE filterBounds	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata,
		SCIP_Longint	itlimit
	)

static

filter some bounds that are not improvable by solving auxiliary LPs

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
itlimit	LP iteration limit (-1: no limit)

Definition at line 475 of file prop_obbt.c.

static SCIP_RETCODE applyBoundChgs	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata,
		SCIP_RESULT *	result
	)

static

applies possible bound changes that were found

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
result	result pointer

Definition at line 564 of file prop_obbt.c.

static SCIP_RETCODE tightenBoundDive	(	SCIP *	scip,
		BOUND *	bound,
		SCIP_Real	newval,
		SCIP_Bool *	tightened
	)

static

tries to tighten a bound in diving mode

Parameters

scip	SCIP data structure
bound	bound that could be tightened
newval	new bound value
tightened	was tightening successful?

Definition at line 627 of file prop_obbt.c.

static SCIP_RETCODE createGenVBound	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata,
		BOUND *	bound
	)

static

creates a genvbound if the dual LP solution provides such information

Consider the problem

min { +/- x_i : obj * x <= z, lb <= Ax <= ub, l <= x <= u },

where z is the current cutoff bound. Let (mu, nu, gamma, alpha, beta) >= 0 be the optimal solution of the dual of problem (P), where the variables correspond to the primal inequalities in the following way:

     Ax >=  lb    <->   mu
    -Ax >= -ub    <->   nu

-obj * x >= -z <-> gamma x >= l <-> alpha -x >= -u <-> beta

Fixing these multipliers, by weak duality, we obtain the inequality

+/- x_i >= lb*mu - ub*nu - z*gamma + l*alpha - u*beta

that holds for all primal feasible points x with objective value at least z. Setting

c = lb*mu - ub*nu, redcost_k = alpha_k - beta_k

we obtain the inequality

+/- x_i >= sum ( redcost_k * x_k ) + (-gamma) * cutoff_bound + c,

that holds for all primal feasible points with objective value at least cutoff_bound. Therefore, the latter inequality can be added as a generalized variable bound.

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
bound	bound of x_i

Definition at line 717 of file prop_obbt.c.

static SCIP_RETCODE findNewBounds	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata,
		SCIP_Longint	itlimit
	)

static

tries to find tighter values for bounds and stores them in the bound data structure

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
itlimit	LP iteration limit (-1: no limit)

Definition at line 857 of file prop_obbt.c.

static SCIP_RETCODE applyObbt	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata,
		SCIP_Longint	itlimit,
		SCIP_RESULT *	result
	)

static

main function of obbt

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
itlimit	LP iteration limit (-1: no limit)
result	result pointer

Definition at line 1016 of file prop_obbt.c.

static unsigned int getScore	(	SCIP *	scip,
		BOUND *	bound,
		int	nlcount,
		int	maxnlcount
	)

static

computes the score of a bound

Parameters

scip	SCIP data structure
bound	pointer of bound
nlcount	number of nonlinear constraints containing the bounds variable
maxnlcount	maximal number of nonlinear constraints a variable appears in

Definition at line 1115 of file prop_obbt.c.

static SCIP_DECL_SORTPTRCOMP ( compBounds )

static

comparison method for two bounds w.r.t. their scores

Definition at line 1158 of file prop_obbt.c.

References Bound::boundtype, NULL, SCIP_BOUNDTYPE_LOWER, SCIPdebugPrintf, SCIPvarGetName(), Bound::score, and Bound::var.

static SCIP_RETCODE createGroups ( SCIP_PROPDATA * propdata )

static

creates groups for the bounds array

Parameters

propdata data of the obbt propagator

Definition at line 1205 of file prop_obbt.c.

static SCIP_Bool varIsInteresting	(	SCIP *	scip,
		SCIP_VAR *	var,
		int	nlcount
	)

static

determines whether a variable is interesting

Parameters

scip	SCIP data structure
var	variable to check
nlcount	number of nonlinear constraints containing the variable

Definition at line 1263 of file prop_obbt.c.

static SCIP_RETCODE initBounds	(	SCIP *	scip,
		SCIP_PROPDATA *	propdata
	)

static

initializes interesting bounds

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator

Definition at line 1276 of file prop_obbt.c.

static SCIP_DECL_PROPINITSOL ( propInitsolObbt )

static

solving process initialization method of propagator (called when branch and bound process is about to begin)

Definition at line 1390 of file prop_obbt.c.

static SCIP_DECL_PROPEXEC ( propExecObbt )

static

execution method of propagator

Definition at line 1419 of file prop_obbt.c.

References SCIP_OKAY, and SCIPdebugMessage.

static SCIP_DECL_PROPRESPROP ( propRespropObbt )

static

propagation conflict resolving method of propagator

Definition at line 1507 of file prop_obbt.c.

References NULL.

static SCIP_DECL_PROPEXITSOL ( propExitsolObbt )

static

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

Definition at line 1516 of file prop_obbt.c.

static SCIP_DECL_PROPFREE ( propFreeObbt )

static

destructor of propagator to free user data (called when SCIP is exiting)

Definition at line 1554 of file prop_obbt.c.

SCIP_RETCODE SCIPincludePropObbt ( SCIP * scip )

creates the obbt propagator and includes it in SCIP

Parameters

scip	SCIP data structure

Definition at line 1577 of file prop_obbt.c.

Referenced by SCIPincludeDefaultPlugins().

SCIP

Detailed Description

Macros

Typedefs

Functions

Macro Definition Documentation

Typedef Documentation

Function Documentation