# SCIP

Solving Constraint Integer Programs

branch_distribution.c File Reference

## Detailed Description

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

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 "scip/branch_distribution.h"
#include "scip/pub_branch.h"
#include "scip/pub_event.h"
#include "scip/pub_lp.h"
#include "scip/pub_message.h"
#include "scip/pub_misc.h"
#include "scip/pub_var.h"
#include "scip/scip_branch.h"
#include "scip/scip_event.h"
#include "scip/scip_general.h"
#include "scip/scip_lp.h"
#include "scip/scip_message.h"
#include "scip/scip_mem.h"
#include "scip/scip_numerics.h"
#include "scip/scip_param.h"
#include "scip/scip_pricer.h"
#include "scip/scip_prob.h"
#include "scip/scip_probing.h"
#include <string.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 void branchruledataFreeArrays (SCIP *scip, SCIP_BRANCHRULEDATA *branchruledata)

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

static SCIP_VARbranchruledataPopBoundChangeVar (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)

## ◆ BRANCHRULE_NAME

 #define BRANCHRULE_NAME   "distribution"

Definition at line 81 of file branch_distribution.c.

## ◆ BRANCHRULE_DESC

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

Definition at line 82 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

## ◆ BRANCHRULE_PRIORITY

 #define BRANCHRULE_PRIORITY   0

Definition at line 83 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

## ◆ BRANCHRULE_MAXDEPTH

 #define BRANCHRULE_MAXDEPTH   -1

Definition at line 84 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

## ◆ BRANCHRULE_MAXBOUNDDIST

 #define BRANCHRULE_MAXBOUNDDIST   1.0

Definition at line 85 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

## ◆ SCOREPARAM_VALUES

 #define SCOREPARAM_VALUES   "dhlvw"

Definition at line 87 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

## ◆ DEFAULT_SCOREPARAM

 #define DEFAULT_SCOREPARAM   'v'

Definition at line 88 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

## ◆ DEFAULT_PRIORITY

 #define DEFAULT_PRIORITY   2.0

Definition at line 89 of file branch_distribution.c.

Referenced by SCIP_DECL_BRANCHEXECLP().

## ◆ SQRTOFTWO

 #define SQRTOFTWO   1.4142136

Definition at line 90 of file branch_distribution.c.

Referenced by SCIPcalcCumulativeDistribution().

## ◆ SQUARED

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

Definition at line 91 of file branch_distribution.c.

## ◆ DEFAULT_ONLYACTIVEROWS

 #define DEFAULT_ONLYACTIVEROWS   FALSE

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

Definition at line 92 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 93 of file branch_distribution.c.

Referenced by SCIPincludeBranchruleDistribution().

## ◆ EVENTHDLR_NAME

 #define EVENTHDLR_NAME   "eventhdlr_distribution"

event handler name

Definition at line 96 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 97 of file branch_distribution.c.

Referenced by branchruledataEnsureArraySize(), and SCIP_DECL_BRANCHEXITSOL().

## ◆ 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 138 of file branch_distribution.c.

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 226 of file branch_distribution.c.

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 427 of file branch_distribution.c.

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 610 of file branch_distribution.c.

Referenced by SCIP_DECL_BRANCHEXECLP().

## ◆ branchruledataFreeArrays()

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

free branchrule data

Parameters
 scip SCIP data structure branchruledata branching rule data

Definition at line 803 of file branch_distribution.c.

References NULL, and SCIPfreeBlockMemoryArray.

Referenced by SCIP_DECL_BRANCHEXITSOL(), and SCIP_DECL_BRANCHFREE().

 static void branchruledataAddBoundChangeVar ( 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
 branchruledata branchrule data var the variable whose bound changes need to be processed

Definition at line 826 of file branch_distribution.c.

References NULL, SCIP_INVALID, and SCIPvarGetProbindex().

Referenced by SCIP_DECL_EVENTEXEC().

## ◆ branchruledataPopBoundChangeVar()

 static SCIP_VAR* branchruledataPopBoundChangeVar ( SCIP_BRANCHRULEDATA * branchruledata )
static

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

Parameters
 branchruledata branchrule data

Definition at line 868 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 897 of file branch_distribution.c.

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 1024 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 1043 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 1054 of file branch_distribution.c.

## ◆ 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 1089 of file branch_distribution.c.

## ◆ SCIP_DECL_BRANCHEXECLP()

 static SCIP_DECL_BRANCHEXECLP ( branchExeclpDistribution )
static

branching execution method for fractional LP solutions

Definition at line 1109 of file branch_distribution.c.

## ◆ 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 1287 of file branch_distribution.c.