Detailed Description

probability based branching rule based on an article by J. Pryor and J.W. Chinneck

Author: Gregor Hendel

The distribution branching rule selects a variable based on its impact on row activity distributions. More formally, let \( a(x) = a_1 x_1 + \dots + a_n x_n \leq b \) be a row of the LP. Let further \( l_i, u_i \in R\) denote the (finite) lower and upper bound, respectively, of the \( i \)-th variable \(x_i\). Viewing every variable \(x_i \) as (continuously) uniformly distributed within its bounds, we can approximately understand the row activity \(a(x)\) as a Gaussian random variate with mean value \( \mu = E[a(x)] = \sum_i a_i\frac{l_i + u_i}{2}\) and variance \( \sigma^2 = \sum_i a_i^2 \sigma_i^2 \), with \( \sigma_i^2 = \frac{(u_i - l_i)^2}{12}\) for continuous and \( \sigma_i^2 = \frac{(u_i - l_i + 1)^2 - 1}{12}\) for discrete variables. With these two parameters, we can calculate the probability to satisfy the row in terms of the cumulative distribution of the standard normal distribution: \( P(a(x) \leq b) = \Phi(\frac{b - \mu}{\sigma})\).

The impact of a variable on the probability to satisfy a constraint after branching can be estimated by altering the variable contribution to the sums described above. In order to keep the tree size small, variables are preferred which decrease the probability to satisfy a row because it is more likely to create infeasible subproblems.

The selection of the branching variable is subject to the parameter scoreparam. For both branching directions, an individual score is calculated. Available options for scoring methods are:

d: select a branching variable with largest difference in satisfaction probability after branching
l: lowest cumulative probability amongst all variables on all rows (after branching).
h: highest cumulative probability amongst all variables on all rows (after branching).
v: highest number of votes for lowering row probability for all rows a variable appears in.
w: highest number of votes for increasing row probability for all rows a variable appears in.

If the parameter usescipscore is set to TRUE, a single branching score is calculated from the respective up and down scores as defined by the SCIP branching score function (see advanced branching parameter scorefunc), otherwise, the variable with the single highest score is selected, and the maximizing direction is assigned higher branching priority.

The original idea of probability based branching schemes appeared in:

J. Pryor and J.W. Chinneck:
Faster Integer-Feasibility in Mixed-Integer Linear Programs by Branching to Force Change
Computers and Operations Research, vol. 38, 2011, p. 1143–1152
(Paper: PDF).

Definition in file branch_distribution.c.

#include <assert.h>
#include <string.h>
#include "scip/branch_distribution.h"

Go to the source code of this file.

Macros
#define	BRANCHRULE_NAME "distribution"

#define	BRANCHRULE_DESC "branching rule based on variable influence on cumulative normal distribution of row activities"

#define	BRANCHRULE_PRIORITY 0

#define	BRANCHRULE_MAXDEPTH -1

#define	BRANCHRULE_MAXBOUNDDIST 1.0

#define	SCOREPARAM_VALUES "dhlvw"

#define	DEFAULT_SCOREPARAM 'v'

#define	DEFAULT_PRIORITY 2.0

#define	SQRTOFTWO 1.4142136

#define	SQUARED(x) ((x) * (x))

#define	DEFAULT_ONLYACTIVEROWS FALSE

#define	DEFAULT_USEWEIGHTEDSCORE FALSE

#define	EVENTHDLR_NAME "eventhdlr_distribution"

#define	EVENT_DISTRIBUTION SCIP_EVENTTYPE_BOUNDCHANGED

Functions
static SCIP_RETCODE	branchruledataEnsureArraySize (SCIP scip, SCIP_BRANCHRULEDATA branchruledata, int maxindex)

static void	branchruledataUpdateCurrentBounds (SCIP scip, SCIP_BRANCHRULEDATA branchruledata, SCIP_VAR *var)

void	SCIPvarCalcDistributionParameters (SCIP scip, SCIP_Real varlb, SCIP_Real varub, SCIP_VARTYPE vartype, SCIP_Real mean, SCIP_Real *variance)

SCIP_Real	SCIPcalcCumulativeDistribution (SCIP *scip, SCIP_Real mean, SCIP_Real variance, SCIP_Real value)

SCIP_Real	SCIProwCalcProbability (SCIP scip, SCIP_ROW row, SCIP_Real mu, SCIP_Real sigma2, int rowinfinitiesdown, int rowinfinitiesup)

static void	rowCalculateGauss (SCIP scip, SCIP_BRANCHRULEDATA branchruledata, SCIP_ROW row, SCIP_Real mu, SCIP_Real sigma2, int rowinfinitiesdown, int *rowinfinitiesup)

SCIP_RETCODE	SCIPupdateDistributionScore (SCIP scip, SCIP_Real currentprob, SCIP_Real newprobup, SCIP_Real newprobdown, SCIP_Real upscore, SCIP_Real *downscore, char scoreparam)

static SCIP_RETCODE	calcBranchScore (SCIP scip, SCIP_BRANCHRULEDATA branchruledata, SCIP_VAR var, SCIP_Real lpsolval, SCIP_Real upscore, SCIP_Real *downscore, char scoreparam)

static SCIP_RETCODE	branchruledataFreeArrays (SCIP scip, SCIP_BRANCHRULEDATA branchruledata)

static void	branchruledataAddBoundChangeVar (SCIP scip, SCIP_BRANCHRULEDATA branchruledata, SCIP_VAR *var)

static SCIP_VAR *	branchruledataPopBoundChangeVar (SCIP scip, SCIP_BRANCHRULEDATA branchruledata)

static SCIP_RETCODE	varProcessBoundChanges (SCIP scip, SCIP_BRANCHRULEDATA branchruledata, SCIP_VAR *var)

static	SCIP_DECL_EVENTFREE (eventFreeDistribution)

static	SCIP_DECL_BRANCHCOPY (branchCopyDistribution)

static	SCIP_DECL_BRANCHEXITSOL (branchExitsolDistribution)

static	SCIP_DECL_BRANCHFREE (branchFreeDistribution)

static	SCIP_DECL_BRANCHEXECLP (branchExeclpDistribution)

static	SCIP_DECL_EVENTEXEC (eventExecDistribution)

SCIP_RETCODE	SCIPincludeBranchruleDistribution (SCIP *scip)

Macro Definition Documentation

◆ BRANCHRULE_NAME

#define BRANCHRULE_NAME "distribution"

Definition at line 64 of file branch_distribution.c.

Referenced by SCIP_DECL_BRANCHEXECLP(), SCIP_DECL_BRANCHEXITSOL(), SCIP_DECL_BRANCHFREE(), and SCIPincludeBranchruleDistribution().

◆ BRANCHRULE_DESC

#define BRANCHRULE_DESC "branching rule based on variable influence on cumulative normal distribution of row activities"

Definition at line 65 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

◆ BRANCHRULE_PRIORITY

#define BRANCHRULE_PRIORITY 0

Definition at line 66 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

◆ BRANCHRULE_MAXDEPTH

#define BRANCHRULE_MAXDEPTH -1

Definition at line 67 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

◆ BRANCHRULE_MAXBOUNDDIST

#define BRANCHRULE_MAXBOUNDDIST 1.0

Definition at line 68 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

◆ SCOREPARAM_VALUES

#define SCOREPARAM_VALUES "dhlvw"

Definition at line 70 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

◆ DEFAULT_SCOREPARAM

#define DEFAULT_SCOREPARAM 'v'

Definition at line 71 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

◆ DEFAULT_PRIORITY

#define DEFAULT_PRIORITY 2.0

Definition at line 72 of file branch_distribution.c.

Referenced by SCIP_DECL_BRANCHEXECLP().

◆ SQRTOFTWO

#define SQRTOFTWO 1.4142136

Definition at line 73 of file branch_distribution.c.

Referenced by SCIPcalcCumulativeDistribution().

◆ SQUARED

#define SQUARED ( x ) ((x) * (x))

Definition at line 74 of file branch_distribution.c.

Referenced by calcBranchScore(), rowCalculateGauss(), SCIPvarCalcDistributionParameters(), and varProcessBoundChanges().

◆ DEFAULT_ONLYACTIVEROWS

#define DEFAULT_ONLYACTIVEROWS FALSE

should only rows which are active at the current node be considered?

Definition at line 75 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

◆ DEFAULT_USEWEIGHTEDSCORE

#define DEFAULT_USEWEIGHTEDSCORE FALSE

should the branching score weigh up- and down-scores of a variable

Definition at line 76 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

◆ EVENTHDLR_NAME

#define EVENTHDLR_NAME "eventhdlr_distribution"

event handler name

Definition at line 79 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

◆ EVENT_DISTRIBUTION

#define EVENT_DISTRIBUTION SCIP_EVENTTYPE_BOUNDCHANGED

the event tyoe to be handled by this event handler

Definition at line 80 of file branch_distribution.c.

Referenced by branchruledataEnsureArraySize(), and SCIP_DECL_BRANCHEXITSOL().

Function Documentation

◆ branchruledataEnsureArraySize()

static SCIP_RETCODE branchruledataEnsureArraySize	(	SCIP *	scip,
		SCIP_BRANCHRULEDATA *	branchruledata,
		int	maxindex
	)

static

ensure that maxindex + 1 rows can be represented in data arrays; memory gets reallocated with 10% extra space to save some time for future allocations

Parameters

scip	SCIP data structure
branchruledata	branchruledata
maxindex	row index at hand (size must be at least this large)

Definition at line 121 of file branch_distribution.c.

References EVENT_DISTRIBUTION, NULL, SCIP_CALL, SCIP_INVALID, SCIP_OKAY, SCIP_STAGE_SOLVING, SCIPallocBlockMemoryArray, SCIPcatchVarEvent(), SCIPfeasCeil(), SCIPgetNVars(), SCIPgetStage(), SCIPgetVars(), SCIPreallocBlockMemoryArray, SCIPvarGetProbindex(), and SCIPvarIsActive().

Referenced by calcBranchScore(), SCIP_DECL_BRANCHEXECLP(), and varProcessBoundChanges().

◆ branchruledataUpdateCurrentBounds()

static void branchruledataUpdateCurrentBounds	(	SCIP *	scip,
		SCIP_BRANCHRULEDATA *	branchruledata,
		SCIP_VAR *	var
	)

static

Parameters

scip	SCIP data structure
branchruledata	branchrule data
var	the variable to update current bounds

Definition at line 210 of file branch_distribution.c.

References NULL, SCIP_Real, SCIPisFeasLE(), SCIPvarGetLbLocal(), SCIPvarGetProbindex(), and SCIPvarGetUbLocal().

Referenced by rowCalculateGauss(), SCIP_DECL_BRANCHEXECLP(), and varProcessBoundChanges().

◆ rowCalculateGauss()

static void rowCalculateGauss	(	SCIP *	scip,
		SCIP_BRANCHRULEDATA *	branchruledata,
		SCIP_ROW *	row,
		SCIP_Real *	mu,
		SCIP_Real *	sigma2,
		int *	rowinfinitiesdown,
		int *	rowinfinitiesup
	)

static

calculates the initial mean and variance of the row activity normal distribution.

The mean value \( \mu \) is given by \( \mu = \sum_i=1^n c_i * (lb_i +ub_i) / 2 \) where \(n \) is the number of variables, and \( c_i, lb_i, ub_i \) are the variable coefficient and bounds, respectively. With the same notation, the variance \( \sigma^2 \) is given by \( \sigma^2 = \sum_i=1^n c_i^2 * \sigma^2_i \), with the variance being \( \sigma^2_i = ((ub_i - lb_i + 1)^2 - 1) / 12 \) for integer variables and \( \sigma^2_i = (ub_i - lb_i)^2 / 12 \) for continuous variables.

Parameters

scip	SCIP data structure
branchruledata	the branching rule data
row	the row for which the gaussian normal distribution has to be calculated
mu	pointer to store the mean value of the gaussian normal distribution
sigma2	pointer to store the variance value of the gaussian normal distribution
rowinfinitiesdown	pointer to store the number of variables with infinite bounds to DECREASE activity
rowinfinitiesup	pointer to store the number of variables with infinite bounds to INCREASE activity

Definition at line 411 of file branch_distribution.c.

References branchruledataUpdateCurrentBounds(), NULL, SCIP_INVALID, SCIP_Real, SCIPcolGetVar(), SCIPdebug, SCIPdebugMsg, SCIPisFeasLE(), SCIPisFeasNegative(), SCIPisInfinity(), SCIPprintRow(), SCIProwGetCols(), SCIProwGetConstant(), SCIProwGetName(), SCIProwGetNNonz(), SCIProwGetVals(), SCIPvarCalcDistributionParameters(), SCIPvarGetLbLocal(), SCIPvarGetProbindex(), SCIPvarGetType(), SCIPvarGetUbLocal(), and SQUARED.

Referenced by calcBranchScore().

◆ calcBranchScore()

static SCIP_RETCODE calcBranchScore	(	SCIP *	scip,
		SCIP_BRANCHRULEDATA *	branchruledata,
		SCIP_VAR *	var,
		SCIP_Real	lpsolval,
		SCIP_Real *	upscore,
		SCIP_Real *	downscore,
		char	scoreparam
	)

static

calculate the branching score of a variable, depending on the chosen score parameter

Parameters

scip	current SCIP
branchruledata	branch rule data
var	candidate variable
lpsolval	current fractional LP-relaxation solution value
upscore	pointer to store the variable score when branching on it in upward direction
downscore	pointer to store the variable score when branching on it in downward direction
scoreparam	the score parameter of this branching rule

Definition at line 594 of file branch_distribution.c.

References branchruledataEnsureArraySize(), MAX, NULL, rowCalculateGauss(), SCIP_Bool, SCIP_CALL, SCIP_INVALID, SCIP_OKAY, SCIP_Real, SCIP_VARSTATUS_COLUMN, SCIPcolGetNNonz(), SCIPcolGetRows(), SCIPcolGetVals(), SCIPdebugMsg, SCIPfeasCeil(), SCIPfeasFloor(), SCIPgetRowLPFeasibility(), SCIPisFeasLT(), SCIPisInfinity(), SCIPisIntegral(), SCIPisNegative(), SCIPisSumPositive(), SCIProwCalcProbability(), SCIProwGetIndex(), SCIProwGetName(), SCIPupdateDistributionScore(), SCIPvarCalcDistributionParameters(), SCIPvarGetCol(), SCIPvarGetLbLocal(), SCIPvarGetName(), SCIPvarGetStatus(), SCIPvarGetType(), SCIPvarGetUbLocal(), and SQUARED.

Referenced by SCIP_DECL_BRANCHEXECLP().

◆ branchruledataFreeArrays()

static SCIP_RETCODE branchruledataFreeArrays	(	SCIP *	scip,
		SCIP_BRANCHRULEDATA *	branchruledata
	)

static

free branchrule data

Parameters

scip	SCIP data structure
branchruledata	branching rule data

Definition at line 787 of file branch_distribution.c.

References NULL, SCIP_OKAY, and SCIPfreeBlockMemoryArray.

Referenced by SCIP_DECL_BRANCHEXITSOL(), and SCIP_DECL_BRANCHFREE().

◆ branchruledataAddBoundChangeVar()

static void branchruledataAddBoundChangeVar	(	SCIP *	scip,
		SCIP_BRANCHRULEDATA *	branchruledata,
		SCIP_VAR *	var
	)

static

add variable to the bound change event queue; skipped if variable is already in there, or if variable has no row currently watched

Parameters

scip	SCIP data structure
branchruledata	branchrule data
var	the variable whose bound changes need to be processed

Definition at line 812 of file branch_distribution.c.

References NULL, SCIP_INVALID, and SCIPvarGetProbindex().

Referenced by SCIP_DECL_EVENTEXEC().

◆ branchruledataPopBoundChangeVar()

static SCIP_VAR* branchruledataPopBoundChangeVar	(	SCIP *	scip,
		SCIP_BRANCHRULEDATA *	branchruledata
	)

static

returns the next unprocessed variable (last in, first out) with pending bound changes, or NULL

Parameters

scip	SCIP data structure
branchruledata	branchrule data

Definition at line 855 of file branch_distribution.c.

References NULL, and SCIPvarGetProbindex().

Referenced by SCIP_DECL_BRANCHEXECLP().

◆ varProcessBoundChanges()

static SCIP_RETCODE varProcessBoundChanges	(	SCIP *	scip,
		SCIP_BRANCHRULEDATA *	branchruledata,
		SCIP_VAR *	var
	)

static

process a variable from the queue of changed variables

Parameters

scip	SCIP data structure
branchruledata	branchrule data
var	the variable whose bound changes need to be processed

Definition at line 885 of file branch_distribution.c.

References branchruledataEnsureArraySize(), branchruledataUpdateCurrentBounds(), MAX, NULL, SCIP_CALL, SCIP_INVALID, SCIP_OKAY, SCIP_Real, SCIPcolGetNNonz(), SCIPcolGetRows(), SCIPcolGetVals(), SCIPinProbing(), SCIPisFeasEQ(), SCIPisFeasGE(), SCIPisInfinity(), SCIProwGetIndex(), SCIPvarCalcDistributionParameters(), SCIPvarGetCol(), SCIPvarGetLbLocal(), SCIPvarGetProbindex(), SCIPvarGetType(), SCIPvarGetUbLocal(), and SQUARED.

Referenced by SCIP_DECL_BRANCHEXECLP().

◆ SCIP_DECL_EVENTFREE()

static SCIP_DECL_EVENTFREE ( eventFreeDistribution )

static

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

Definition at line 1011 of file branch_distribution.c.

References NULL, SCIP_OKAY, SCIPeventhdlrGetData(), SCIPeventhdlrSetData(), and SCIPfreeBlockMemory.

◆ SCIP_DECL_BRANCHCOPY()

static SCIP_DECL_BRANCHCOPY ( branchCopyDistribution )

static

copy method for branchrule plugins (called when SCIP copies plugins)

Definition at line 1030 of file branch_distribution.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPincludeBranchruleDistribution().

◆ SCIP_DECL_BRANCHEXITSOL()

static SCIP_DECL_BRANCHEXITSOL ( branchExitsolDistribution )

static

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

Definition at line 1041 of file branch_distribution.c.

References BRANCHRULE_NAME, branchruledataFreeArrays(), EVENT_DISTRIBUTION, NULL, SCIP_CALL, SCIP_OKAY, SCIPbranchruleGetData(), SCIPbranchruleGetName(), SCIPdropVarEvent(), SCIPfreeBlockMemoryArray, SCIPgetNVars(), and SCIPgetVars().

◆ SCIP_DECL_BRANCHFREE()

static SCIP_DECL_BRANCHFREE ( branchFreeDistribution )

static

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

Definition at line 1076 of file branch_distribution.c.

References BRANCHRULE_NAME, branchruledataFreeArrays(), NULL, SCIP_CALL, SCIP_OKAY, SCIPbranchruleGetData(), SCIPbranchruleGetName(), SCIPbranchruleSetData(), and SCIPfreeBlockMemory.

◆ SCIP_DECL_BRANCHEXECLP()

static SCIP_DECL_BRANCHEXECLP ( branchExeclpDistribution )

static

branching execution method for fractional LP solutions

Definition at line 1096 of file branch_distribution.c.

References BRANCHRULE_NAME, branchruledataEnsureArraySize(), branchruledataPopBoundChangeVar(), branchruledataUpdateCurrentBounds(), calcBranchScore(), DEFAULT_PRIORITY, NULL, SCIP_BRANCHDIR_AUTO, SCIP_BRANCHDIR_DOWNWARDS, SCIP_BRANCHDIR_UPWARDS, SCIP_BRANCHED, SCIP_CALL, SCIP_DIDNOTRUN, SCIP_INVALID, SCIP_OKAY, SCIP_Real, SCIPbranchruleGetData(), SCIPbranchruleGetName(), SCIPbranchVar(), SCIPchgChildPrio(), SCIPdebugMsg, SCIPgetBranchScore(), SCIPgetLPBranchCands(), SCIPgetNActivePricers(), SCIPgetNLPRows(), SCIPisFeasEQ(), SCIPisFeasIntegral(), SCIPisFeasLE(), SCIPvarGetLbLocal(), SCIPvarGetLPSol(), SCIPvarGetName(), SCIPvarGetProbindex(), SCIPvarGetSol(), SCIPvarGetUbLocal(), TRUE, and varProcessBoundChanges().

◆ SCIP_DECL_EVENTEXEC()

static SCIP_DECL_EVENTEXEC ( eventExecDistribution )

static

event execution method of distribution branching which handles bound change events of variables

Definition at line 1273 of file branch_distribution.c.

References branchruledataAddBoundChangeVar(), NULL, SCIP_OKAY, SCIPeventGetVar(), and SCIPeventhdlrGetData().

SCIP

Detailed Description

Macros

Functions

Macro Definition Documentation

◆ BRANCHRULE_NAME

◆ BRANCHRULE_DESC

◆ BRANCHRULE_PRIORITY

◆ BRANCHRULE_MAXDEPTH

◆ BRANCHRULE_MAXBOUNDDIST

◆ SCOREPARAM_VALUES

◆ DEFAULT_SCOREPARAM

◆ DEFAULT_PRIORITY

◆ SQRTOFTWO

◆ SQUARED

◆ DEFAULT_ONLYACTIVEROWS

◆ DEFAULT_USEWEIGHTEDSCORE

◆ EVENTHDLR_NAME

◆ EVENT_DISTRIBUTION

Function Documentation

◆ branchruledataEnsureArraySize()

◆ branchruledataUpdateCurrentBounds()

◆ rowCalculateGauss()

◆ calcBranchScore()

◆ branchruledataFreeArrays()

◆ branchruledataAddBoundChangeVar()

◆ branchruledataPopBoundChangeVar()

◆ varProcessBoundChanges()

◆ SCIP_DECL_EVENTFREE()

◆ SCIP_DECL_BRANCHCOPY()

◆ SCIP_DECL_BRANCHEXITSOL()

◆ SCIP_DECL_BRANCHFREE()

◆ SCIP_DECL_BRANCHEXECLP()

◆ SCIP_DECL_EVENTEXEC()