prop_obbt.c File Reference

Detailed Description

optimization-based bound tightening propagator

Author

Stefan Weltge

Benjamin Mueller

Definition in file prop_obbt.c.

#include <assert.h>
#include <string.h>
#include "scip/cons_linear.h"
#include "scip/cons_nonlinear.h"
#include "scip/nlhdlr_bilinear.h"
#include "scip/prop_genvbounds.h"
#include "scip/prop_obbt.h"
#include "scip/pub_cons.h"
#include "scip/pub_lp.h"
#include "scip/pub_message.h"
#include "scip/pub_misc.h"
#include "scip/pub_misc_sort.h"
#include "scip/pub_nlp.h"
#include "scip/pub_prop.h"
#include "scip/pub_tree.h"
#include "scip/pub_var.h"
#include "scip/scip_cons.h"
#include "scip/scip_copy.h"
#include "scip/scip_cut.h"
#include "scip/scip_general.h"
#include "scip/scip_lp.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_nlp.h"
#include "scip/scip_numerics.h"
#include "scip/scip_param.h"
#include "scip/scip_prob.h"
#include "scip/scip_probing.h"
#include "scip/scip_prop.h"
#include "scip/scip_randnumgen.h"
#include "scip/scip_solvingstats.h"
#include "scip/scip_tree.h"
#include "scip/scip_var.h"

Go to the source code of this file.

Data Structures
struct	Bound
struct	BilinBound

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_APPLY_TRIVIALFITLERING   TRUE
#define	DEFAULT_GENVBDSDURINGFILTER   TRUE
#define	DEFAULT_DUALFEASTOL   1e-9
#define	DEFAULT_CONDITIONLIMIT   -1.0
#define	DEFAULT_BOUNDSTREPS   0.001
#define	DEFAULT_FILTERING_MIN   2
#define	DEFAULT_ITLIMITFACTOR   10.0
#define	DEFAULT_MINITLIMIT   5000L
#define	DEFAULT_ONLYNONCONVEXVARS   TRUE
#define	DEFAULT_TIGHTINTBOUNDSPROBING   TRUE
#define	DEFAULT_TIGHTCONTBOUNDSPROBING   FALSE
#define	DEFAULT_ORDERINGALGO   1
#define	OBBT_SCOREBASE   5
#define	GENVBOUND_PROP_NAME   "genvbounds"
#define	DEFAULT_SEPARATESOL   FALSE
#define	DEFAULT_SEPAMINITER   0
#define	DEFAULT_SEPAMAXITER   10
#define	DEFAULT_GENVBDSDURINGSEPA   TRUE
#define	DEFAULT_PROPAGATEFREQ   0
#define	DEFAULT_CREATE_BILININEQS   TRUE
#define	DEFAULT_CREATE_LINCONS   FALSE
#define	DEFAULT_ITLIMITFAC_BILININEQS   3.0
#define	DEFAULT_MINNONCONVEXITY   1e-1
#define	DEFAULT_RANDSEED   149

Typedefs
typedef struct Bound	BOUND
typedef enum Corner	CORNER
typedef struct BilinBound	BILINBOUND

Enumerations
enum	Corner {   LEFTBOTTOM = 1,   RIGHTBOTTOM = 2,   RIGHTTOP = 4,   LEFTTOP = 8,   FILTERED = 15 }

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 SCIP_RETCODE	setObjProbing (SCIP *scip, SCIP_PROPDATA *propdata, BOUND *bound, SCIP_Real coef)
static SCIP_Bool	includeVarGenVBound (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	createGenVBound (SCIP *scip, SCIP_PROPDATA *propdata, BOUND *bound, SCIP_Bool *found)
static void	exchangeBounds (SCIP_PROPDATA *propdata, int i)
static void	getCorner (SCIP_VAR *x, SCIP_VAR *y, CORNER corner, SCIP_Real *px, SCIP_Real *py)
static void	getCorners (SCIP_VAR *x, SCIP_VAR *y, CORNER corner, SCIP_Real *xs, SCIP_Real *ys, SCIP_Real *xt, SCIP_Real *yt)
static SCIP_VAR *	bilinboundGetX (BILINBOUND *bilinbound)
static SCIP_VAR *	bilinboundGetY (BILINBOUND *bilinbound)
static int	bilinboundGetLocksNeg (BILINBOUND *bilinbound)
static int	bilinboundGetLocksPos (BILINBOUND *bilinbound)
static SCIP_Real	bilinboundGetScore (SCIP *scip, SCIP_RANDNUMGEN *randnumgen, BILINBOUND *bilinbound)
static SCIP_RETCODE	filterExistingLP (SCIP *scip, SCIP_PROPDATA *propdata, int *nfiltered, BOUND *currbound)
static SCIP_RETCODE	filterRound (SCIP *scip, SCIP_PROPDATA *propdata, int itlimit, int *nfiltered, SCIP_Real *objcoefs, int *objcoefsinds, int nobjcoefs)
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	tightenBoundProbing (SCIP *scip, BOUND *bound, SCIP_Real newval, SCIP_Bool *tightened)
static	SCIP_DECL_SORTPTRCOMP (compBoundsScore)
static	SCIP_DECL_SORTPTRCOMP (compBilinboundsScore)
static	SCIP_DECL_SORTPTRCOMP (compBoundsBoundtype)
static SCIP_RETCODE	sortBounds (SCIP *scip, SCIP_PROPDATA *propdata)
static SCIP_Real	evalBound (SCIP *scip, BOUND *bound)
static int	nextBound (SCIP *scip, SCIP_PROPDATA *propdata, SCIP_Bool convexphase)
static SCIP_RETCODE	applySeparation (SCIP *scip, SCIP_PROPDATA *propdata, BOUND *currbound, SCIP_Longint *nleftiterations, SCIP_Bool *success)
static SCIP_RETCODE	findNewBounds (SCIP *scip, SCIP_PROPDATA *propdata, SCIP_Longint *nleftiterations, SCIP_Bool convexphase)
static SCIP_RETCODE	applyObbt (SCIP *scip, SCIP_PROPDATA *propdata, SCIP_Longint itlimit, SCIP_RESULT *result)
static SCIP_RETCODE	solveBilinearLP (SCIP *scip, SCIP_VAR *x, SCIP_VAR *y, SCIP_Real xs, SCIP_Real ys, SCIP_Real xt, SCIP_Real yt, SCIP_Real *xcoef, SCIP_Real *ycoef, SCIP_Real *constant, SCIP_Longint iterlim, int *nnonzduals)
static SCIP_RETCODE	applyObbtBilinear (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_RETCODE	getNLPVarsNonConvexity (SCIP *scip, unsigned int *nccounts)
static SCIP_Bool	varIsInteresting (SCIP *scip, SCIP_VAR *var, int nlcount)
static SCIP_RETCODE	initBounds (SCIP *scip, SCIP_PROPDATA *propdata)
static	SCIP_DECL_PROPCOPY (propCopyObbt)
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

PROP_NAME

#define PROP_NAME   "obbt"

Definition at line 82 of file prop_obbt.c.

Referenced by SCIP_DECL_PROPCOPY().

PROP_DESC

#define PROP_DESC   "optimization-based bound tightening propagator"

Definition at line 83 of file prop_obbt.c.

PROP_TIMING

#define PROP_TIMING   SCIP_PROPTIMING_AFTERLPLOOP

Definition at line 84 of file prop_obbt.c.

PROP_PRIORITY

#define PROP_PRIORITY   -1000000

propagator priority

Definition at line 85 of file prop_obbt.c.

PROP_FREQ

#define PROP_FREQ   0

propagator frequency

Definition at line 86 of file prop_obbt.c.

PROP_DELAY

#define PROP_DELAY   TRUE

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

Definition at line 87 of file prop_obbt.c.

DEFAULT_CREATE_GENVBOUNDS

#define DEFAULT_CREATE_GENVBOUNDS   TRUE

should obbt try to provide genvbounds if possible?

Definition at line 91 of file prop_obbt.c.

DEFAULT_FILTERING_NORM

#define DEFAULT_FILTERING_NORM   TRUE

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

Definition at line 92 of file prop_obbt.c.

DEFAULT_APPLY_FILTERROUNDS

#define DEFAULT_APPLY_FILTERROUNDS   FALSE

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

Definition at line 95 of file prop_obbt.c.

DEFAULT_APPLY_TRIVIALFITLERING

#define DEFAULT_APPLY_TRIVIALFITLERING   TRUE

should obbt try to use the LP solution to filter some bounds?

Definition at line 98 of file prop_obbt.c.

DEFAULT_GENVBDSDURINGFILTER

#define DEFAULT_GENVBDSDURINGFILTER   TRUE

try to genrate genvbounds during trivial and aggressive filtering?

Definition at line 99 of file prop_obbt.c.

DEFAULT_DUALFEASTOL

#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 100 of file prop_obbt.c.

DEFAULT_CONDITIONLIMIT

#define DEFAULT_CONDITIONLIMIT   -1.0

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

Definition at line 103 of file prop_obbt.c.

DEFAULT_BOUNDSTREPS

#define DEFAULT_BOUNDSTREPS   0.001

minimal relative improve for strengthening bounds

Definition at line 104 of file prop_obbt.c.

DEFAULT_FILTERING_MIN

#define DEFAULT_FILTERING_MIN   2

minimal number of filtered bounds to apply another filter round

Definition at line 105 of file prop_obbt.c.

DEFAULT_ITLIMITFACTOR

#define DEFAULT_ITLIMITFACTOR   10.0

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

Definition at line 108 of file prop_obbt.c.

DEFAULT_MINITLIMIT

#define DEFAULT_MINITLIMIT   5000L

minimum LP iteration limit

Definition at line 111 of file prop_obbt.c.

DEFAULT_ONLYNONCONVEXVARS

#define DEFAULT_ONLYNONCONVEXVARS   TRUE

only apply obbt on non-convex variables

Definition at line 112 of file prop_obbt.c.

DEFAULT_TIGHTINTBOUNDSPROBING

#define DEFAULT_TIGHTINTBOUNDSPROBING   TRUE

should bounds of integral variables be tightened during the probing mode?

Definition at line 113 of file prop_obbt.c.

DEFAULT_TIGHTCONTBOUNDSPROBING

#define DEFAULT_TIGHTCONTBOUNDSPROBING   FALSE

should bounds of continuous variables be tightened during the probing mode?

Definition at line 116 of file prop_obbt.c.

DEFAULT_ORDERINGALGO

#define DEFAULT_ORDERINGALGO   1

which type of ordering algorithm should we use? (0: no, 1: greedy, 2: greedy reverse)

Definition at line 119 of file prop_obbt.c.

OBBT_SCOREBASE

#define OBBT_SCOREBASE   5

base that is used to calculate a bounds score value

Definition at line 122 of file prop_obbt.c.

GENVBOUND_PROP_NAME

#define GENVBOUND_PROP_NAME   "genvbounds"

Definition at line 123 of file prop_obbt.c.

DEFAULT_SEPARATESOL

#define DEFAULT_SEPARATESOL   FALSE

should the obbt LP solution be separated? note that that by separating solution OBBT will apply all bound tightenings immediatly

Definition at line 125 of file prop_obbt.c.

DEFAULT_SEPAMINITER

#define DEFAULT_SEPAMINITER   0

minimum number of iteration spend to separate an obbt LP solution

Definition at line 130 of file prop_obbt.c.

DEFAULT_SEPAMAXITER

#define DEFAULT_SEPAMAXITER   10

maximum number of iteration spend to separate an obbt LP solution

Definition at line 131 of file prop_obbt.c.

DEFAULT_GENVBDSDURINGSEPA

#define DEFAULT_GENVBDSDURINGSEPA   TRUE

try to create genvbounds during separation process?

Definition at line 132 of file prop_obbt.c.

DEFAULT_PROPAGATEFREQ

#define DEFAULT_PROPAGATEFREQ   0

trigger a propagation round after that many bound tightenings (0: no propagation)

Definition at line 133 of file prop_obbt.c.

DEFAULT_CREATE_BILININEQS

#define DEFAULT_CREATE_BILININEQS   TRUE

solve auxiliary LPs in order to find valid inequalities for bilinear terms?

Definition at line 136 of file prop_obbt.c.

DEFAULT_CREATE_LINCONS

#define DEFAULT_CREATE_LINCONS   FALSE

create linear constraints from inequalities for bilinear terms?

Definition at line 137 of file prop_obbt.c.

DEFAULT_ITLIMITFAC_BILININEQS

#define DEFAULT_ITLIMITFAC_BILININEQS   3.0

multiple of OBBT LP limit used as total LP iteration limit for solving bilinear inequality LPs (< 0 for no limit)

Definition at line 138 of file prop_obbt.c.

DEFAULT_MINNONCONVEXITY

#define DEFAULT_MINNONCONVEXITY   1e-1

minimum nonconvexity for choosing a bilinear term

Definition at line 139 of file prop_obbt.c.

DEFAULT_RANDSEED

#define DEFAULT_RANDSEED   149

initial random seed

Definition at line 140 of file prop_obbt.c.

Typedef Documentation

BOUND

typedef struct Bound BOUND

Definition at line 159 of file prop_obbt.c.

CORNER

typedef enum Corner CORNER

Definition at line 170 of file prop_obbt.c.

BILINBOUND

typedef struct BilinBound BILINBOUND

Definition at line 180 of file prop_obbt.c.

Enumeration Type Documentation

Corner

enum Corner

Enumerator
LEFTBOTTOM
RIGHTBOTTOM
RIGHTTOP
LEFTTOP
FILTERED

Definition at line 162 of file prop_obbt.c.

Function Documentation

solveLP()

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 252 of file prop_obbt.c.

Referenced by filterExistingLP().

addObjCutoff()

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

static

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

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator

Definition at line 324 of file prop_obbt.c.

varIsFixedLocal()

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 374 of file prop_obbt.c.

setObjProbing()

static SCIP_RETCODE setObjProbing ( SCIP *  scip, SCIP_PROPDATA *  propdata, BOUND *  bound, SCIP_Real  coef  )

static

sets objective to minimize or maximize a single variable

Definition at line 384 of file prop_obbt.c.

Referenced by filterExistingLP().

includeVarGenVBound()

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

static

determines whether variable should be included in the right-hand side of the generalized variable bound

Parameters

scip	SCIP data structure
var	variable to check

Definition at line 431 of file prop_obbt.c.

getIterationsLeft()

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 458 of file prop_obbt.c.

References Bound::boundtype, getFilterCoef(), MAX, NULL, SCIP_Real, SCIPdebugMsg, and SCIPgetNLPIterations().

getFilterCoef()

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 488 of file prop_obbt.c.

Referenced by getIterationsLeft().

createGenVBound()

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

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
found	pointer to store if we have found a non-trivial genvbound

Definition at line 562 of file prop_obbt.c.

Referenced by filterExistingLP().

exchangeBounds()

static void exchangeBounds ( SCIP_PROPDATA *  propdata, int  i  )

static

exchange a bound which has been processed and updates the last undone and unfiltered bound index NOTE: this method has to be called after filtering or processing a bound

Parameters

propdata	propagator data
i	bound that was filtered or processed

Definition at line 748 of file prop_obbt.c.

References NULL.

Referenced by filterExistingLP().

getCorner()

static void getCorner ( SCIP_VAR *  x, SCIP_VAR *  y, CORNER  corner, SCIP_Real *  px, SCIP_Real *  py  )

static

helper function to return a corner of the domain of two variables

Parameters

x	first variable
y	second variable
corner	corner
px	buffer to store point for x
py	buffer to store point for y

Definition at line 771 of file prop_obbt.c.

References FILTERED, getCorners(), LEFTBOTTOM, LEFTTOP, NULL, RIGHTBOTTOM, RIGHTTOP, SCIP_Real, SCIPABORT, SCIPvarGetLbGlobal(), and SCIPvarGetUbGlobal().

Referenced by filterExistingLP().

getCorners()

static void getCorners ( SCIP_VAR *  x, SCIP_VAR *  y, CORNER  corner, SCIP_Real *  xs, SCIP_Real *  ys, SCIP_Real *  xt, SCIP_Real *  yt  )

static

helper function to return the two end points of a diagonal

Parameters

x	first variable
y	second variable
corner	corner
xs	buffer to store start point for x
ys	buffer to store start point for y
xt	buffer to store end point for x
yt	buffer to store end point for y

Definition at line 809 of file prop_obbt.c.

Referenced by getCorner().

bilinboundGetX()

static SCIP_VAR* bilinboundGetX ( BILINBOUND *  bilinbound )

static

returns the first variable of a bilinear bound

Parameters

bilinbound

bilinear bound

Definition at line 851 of file prop_obbt.c.

References BilinBound::expr, NULL, SCIPexprGetChildren(), SCIPexprGetNChildren(), and SCIPgetExprAuxVarNonlinear().

Referenced by bilinboundGetLocksPos(), and filterExistingLP().

bilinboundGetY()

static SCIP_VAR* bilinboundGetY ( BILINBOUND *  bilinbound )

static

returns the second variable of a bilinear bound

Parameters

bilinbound

bilinear bound

Definition at line 863 of file prop_obbt.c.

References bilinboundGetLocksPos(), BilinBound::expr, NULL, and SCIPgetExprNLocksNegNonlinear().

Referenced by bilinboundGetLocksPos(), and filterExistingLP().

bilinboundGetLocksNeg()

static int bilinboundGetLocksNeg ( BILINBOUND *  bilinbound )

static

returns the negative locks of the expression in a bilinear bound

Parameters

bilinbound

bilinear bound

Definition at line 875 of file prop_obbt.c.

References bilinboundGetScore(), BilinBound::expr, NULL, SCIP_Real, and SCIPgetExprNLocksPosNonlinear().

bilinboundGetLocksPos()

static int bilinboundGetLocksPos ( BILINBOUND *  bilinbound )

static

returns the positive locks of the expression in a bilinear bound

Parameters

bilinbound

bilinear bound

Definition at line 886 of file prop_obbt.c.

References bilinboundGetX(), bilinboundGetY(), SCIP_Real, SCIPvarGetLbLocal(), and SCIPvarGetUbLocal().

Referenced by bilinboundGetY().

bilinboundGetScore()

static SCIP_Real bilinboundGetScore ( SCIP *  scip, SCIP_RANDNUMGEN *  randnumgen, BILINBOUND *  bilinbound  )

static

computes the score of a bilinear term bound

Parameters

scip	SCIP data structure
randnumgen	random number generator
bilinbound	bilinear bound

Definition at line 897 of file prop_obbt.c.

Referenced by bilinboundGetLocksNeg().

filterExistingLP()

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

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?
currbound	bound for which OBBT LP was solved (Note: might be NULL)

Definition at line 943 of file prop_obbt.c.

References bilinboundGetX(), bilinboundGetY(), bound, Bound::boundtype, createGenVBound(), Bound::done, BilinBound::done, exchangeBounds(), Bound::filtered, FILTERED, BilinBound::filtered, filterRound(), Bound::found, getCorner(), LEFTBOTTOM, LEFTTOP, NULL, REALABS, RIGHTBOTTOM, RIGHTTOP, SCIP_BASESTAT_BASIC, SCIP_Bool, SCIP_BOUNDTYPE_LOWER, SCIP_BOUNDTYPE_UPPER, SCIP_CALL, SCIP_INVALID, SCIP_OKAY, SCIP_Real, SCIPchgVarObjProbing(), SCIPcolGetBasisStatus(), SCIPdebug, SCIPdebugMessage, SCIPdebugMsg, SCIPgetDepth(), SCIPgetNLPIterations(), SCIPgetNVars(), SCIPgetVarObjProbing(), SCIPgetVars(), SCIPinProbing(), SCIPisFeasEQ(), SCIPisFeasGE(), SCIPisFeasLE(), SCIPisInfinity(), SCIPisZero(), SCIPvarGetCol(), SCIPvarGetLbGlobal(), SCIPvarGetLbLocal(), SCIPvarGetLPSol(), SCIPvarGetName(), SCIPvarGetUbGlobal(), SCIPvarGetUbLocal(), setObjProbing(), solveLP(), TRUE, and Bound::var.

filterRound()

static SCIP_RETCODE filterRound ( SCIP *  scip, SCIP_PROPDATA *  propdata, int  itlimit, int *  nfiltered, SCIP_Real *  objcoefs, int *  objcoefsinds, int  nobjcoefs  )

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
objcoefs	array to store the nontrivial objective coefficients
objcoefsinds	array to store bound indices for which their corresponding variables has a nontrivial objective coefficient
nobjcoefs	number of nontrivial objective coefficients

Definition at line 1116 of file prop_obbt.c.

Referenced by filterExistingLP().

filterBounds()

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 1276 of file prop_obbt.c.

applyBoundChgs()

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 1420 of file prop_obbt.c.

tightenBoundProbing()

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

static

tries to tighten a bound in probing mode

Parameters

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

Definition at line 1487 of file prop_obbt.c.

SCIP_DECL_SORTPTRCOMP() [1/3]

static SCIP_DECL_SORTPTRCOMP ( compBoundsScore  )

static

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

Definition at line 1548 of file prop_obbt.c.

SCIP_DECL_SORTPTRCOMP() [2/3]

static SCIP_DECL_SORTPTRCOMP ( compBilinboundsScore  )

static

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

Definition at line 1558 of file prop_obbt.c.

SCIP_DECL_SORTPTRCOMP() [3/3]

static SCIP_DECL_SORTPTRCOMP ( compBoundsBoundtype  )

static

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

Definition at line 1568 of file prop_obbt.c.

References NULL, SCIP_OKAY, SCIPdebugMsg, and SCIPsortDownPtr().

sortBounds()

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

static

sort the propdata->bounds array with their distance or their boundtype key

Parameters

scip	SCIP data structure
propdata	propagator data

Definition at line 1594 of file prop_obbt.c.

References Bound::boundtype, NULL, REALABS, SCIP_BOUNDTYPE_LOWER, SCIPvarGetLbLocal(), SCIPvarGetLPSol(), SCIPvarGetUbLocal(), and Bound::var.

evalBound()

static SCIP_Real evalBound ( SCIP *  scip, BOUND *  bound  )

static

evaluates a bound for the current LP solution

Definition at line 1610 of file prop_obbt.c.

References NULL, and SCIP_Real.

nextBound()

static int nextBound ( SCIP *  scip, SCIP_PROPDATA *  propdata, SCIP_Bool  convexphase  )

static

returns the index of the next undone and unfiltered bound with the smallest distance

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
convexphase	consider only convex variables?

Definition at line 1626 of file prop_obbt.c.

applySeparation()

static SCIP_RETCODE applySeparation ( SCIP *  scip, SCIP_PROPDATA *  propdata, BOUND *  currbound, SCIP_Longint *  nleftiterations, SCIP_Bool *  success  )

static

try to separate the solution of the last OBBT LP in order to learn better variable bounds; we apply additional separation rounds as long as the routine finds better bounds; because of dual degeneracy we apply a minimum number of separation rounds

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
currbound	current bound
nleftiterations	number of left iterations (-1 for no limit)
success	pointer to store if we have found a better bound

Definition at line 1678 of file prop_obbt.c.

findNewBounds()

static SCIP_RETCODE findNewBounds ( SCIP *  scip, SCIP_PROPDATA *  propdata, SCIP_Longint *  nleftiterations, SCIP_Bool  convexphase  )

static

finds new variable bounds until no iterations left or all bounds have been checked

Parameters

scip	SCIP data structure
propdata	data of the obbt propagator
nleftiterations	pointer to store the number of left iterations
convexphase	consider only convex variables?

Definition at line 1760 of file prop_obbt.c.

applyObbt()

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 1999 of file prop_obbt.c.

Referenced by SCIP_DECL_PROPEXEC().

solveBilinearLP()

static SCIP_RETCODE solveBilinearLP ( SCIP *  scip, SCIP_VAR *  x, SCIP_VAR *  y, SCIP_Real  xs, SCIP_Real  ys, SCIP_Real  xt, SCIP_Real  yt, SCIP_Real *  xcoef, SCIP_Real *  ycoef, SCIP_Real *  constant, SCIP_Longint  iterlim, int *  nnonzduals  )

static

computes a valid inequality from the current LP relaxation for a bilinear term xy only involving x and y; the inequality is found by optimizing along the line connecting the points (xs,ys) and (xt,yt) over the currently given linear relaxation of the problem; this optimization problem is an LP

max lambda s.t. Ax <= b (x,y) = (xs,ys) + lambda ((xt,yt) - (xs,ys)) lambda in [0,1]

which is equivalent to

max x s.t. (1) Ax <= b (2) (x - xs) / (xt - xs) = (y - ys) / (yt - ys)

Let x* be the optimal primal and (mu,theta) be the optimal dual solution of this LP. The KKT conditions imply that the aggregation of the linear constraints mu*Ax <= mu*b can be written as

x * (1 - theta) / (xt - xs) + y * theta / (yt - ys) = mu * Ax <= mu * b

<=> alpha * x + beta * y <= mu * b = alpha * (x*) + beta * (y*)

which is a valid inequality in the (x,y)-space; in order to avoid numerical difficulties when (xs,ys) is too close to (xt,yt), we scale constraint (1) by max{1,|xt-xs|,|yt-ys|} beforehand

Parameters

scip	SCIP data structure
x	first variable
y	second variable
xs	x-coordinate of the first point
ys	y-coordinate of the first point
xt	x-coordinate of the second point
yt	y-coordinate of the second point
xcoef	pointer to store the coefficient of x
ycoef	pointer to store the coefficient of y
constant	pointer to store the constant
iterlim	iteration limit (-1: for no limit)
nnonzduals	buffer to store the number of non-zero dual multipliers except for the auxiliary row (NULL if not needed)

Definition at line 2253 of file prop_obbt.c.

References applyObbtBilinear(), FALSE, NULL, r, REALABS, SCIP_Bool, SCIP_CALL, SCIP_INVALID, SCIP_Longint, SCIP_LPSOLSTAT_OPTIMAL, SCIP_OKAY, SCIP_Real, SCIPaddRowProbing(), SCIPaddVarToRow(), SCIPbacktrackProbing(), SCIPchgVarObjProbing(), SCIPcreateEmptyRowUnspec(), SCIPdebugMsg, SCIPgetLPRows(), SCIPgetLPSolstat(), SCIPgetNLPRows(), SCIPinProbing(), SCIPisFeasEQ(), SCIPisFeasZero(), SCIPisHugeValue(), SCIPisZero(), SCIPnewProbingNode(), SCIPreleaseRow(), SCIProwGetDualsol(), SCIPsolveProbingLP(), SCIPvarGetLPSol(), SCIPvarGetName(), SCIPwarningMessage(), and TRUE.

applyObbtBilinear()

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

static

Parameters

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

Definition at line 2401 of file prop_obbt.c.

Referenced by SCIP_DECL_PROPEXEC(), and solveBilinearLP().

getScore()

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 2596 of file prop_obbt.c.

getNLPVarsNonConvexity()

static SCIP_RETCODE getNLPVarsNonConvexity ( SCIP *  scip, unsigned int *  nccounts  )

static

count how often each variable is used in a nonconvex term

Parameters

scip	SCIP data structure
nccounts	store the number each variable appears in a non-convex term

Definition at line 2639 of file prop_obbt.c.

varIsInteresting()

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 or number of non-convex terms containing the variable (depends on propdata->onlynonconvexvars)

Definition at line 2698 of file prop_obbt.c.

initBounds()

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 2714 of file prop_obbt.c.

Referenced by SCIP_DECL_PROPEXEC().

SCIP_DECL_PROPCOPY()

static SCIP_DECL_PROPCOPY ( propCopyObbt  )

static

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

Note

The UG framework assumes that all default plug-ins of SCIP implement a copy callback. We check SCIPgetSubscipDepth() in PROPEXEC to prevent the propagator to run in a sub-SCIP.

Definition at line 2906 of file prop_obbt.c.

References NULL, PROP_NAME, SCIPpropGetData(), and SCIPpropGetName().

SCIP_DECL_PROPINITSOL()

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 2920 of file prop_obbt.c.

SCIP_DECL_PROPEXEC()

static SCIP_DECL_PROPEXEC ( propExecObbt  )

static

execution method of propagator

Definition at line 2951 of file prop_obbt.c.

References applyObbt(), applyObbtBilinear(), initBounds(), MAX, NULL, SCIP_CALL, SCIP_DECL_PROPEXITSOL(), SCIP_DECL_PROPRESPROP(), SCIP_DIDNOTFIND, SCIP_DIDNOTRUN, SCIP_Longint, SCIP_LPSOLSTAT_OPTIMAL, SCIP_LPSOLSTAT_UNBOUNDEDRAY, SCIP_OKAY, SCIPallColsInLP(), SCIPdebugMsg, SCIPgetCurrentNode(), SCIPgetDepth(), SCIPgetLPSolstat(), SCIPgetNRootLPIterations(), SCIPgetProbName(), SCIPinProbing(), SCIPnodeGetNumber(), and SCIPpropGetData().

SCIP_DECL_PROPRESPROP()

static SCIP_DECL_PROPRESPROP ( propRespropObbt  )

static

propagation conflict resolving method of propagator

Definition at line 3064 of file prop_obbt.c.

Referenced by SCIP_DECL_PROPEXEC().

SCIP_DECL_PROPEXITSOL()

static SCIP_DECL_PROPEXITSOL ( propExitsolObbt  )

static

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

Definition at line 3073 of file prop_obbt.c.

Referenced by SCIP_DECL_PROPEXEC().

SCIP_DECL_PROPFREE()

static SCIP_DECL_PROPFREE ( propFreeObbt  )

static

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

Definition at line 3136 of file prop_obbt.c.