circlepacking.c File Reference

Detailed Description

Packing circles in a rectangle of minimal size.

Author

Jose Salmeron

Stefan Vigerske

This example shows how to setup quadratic constraints in SCIP when using SCIP as callable library. The example implements a model for the computation of a smallest rectangle that contains a number of given circles in the plane or the computation of the maximal number of circles that can be placed into a given rectangle.

Suppose that n circles with radii \(r_i\) are given. The task is to find coordinates \((x_i, y_i)\) for the circle midpoints and a rectangle of width \(W \geq 0\) and height \(H \geq 0\), such that

• every circle is placed within the rectangle ( \(r_i \leq x_i \leq W-r_i\), \(r_i \leq y_i \leq H-r_i\)),
• circles are not overlapping \(\left((x_i-x_j)^2 + (y_i-y_j)^2 \geq (r_i + r_j)^2\right)\), and
• the area of the rectangle is minimal.

Alternatively, one may fix the size of the rectangle and maximize the number of circles that can be fit into the rectangle without being overlapping.

Definition in file circlepacking.c.

#include <stdio.h>
#include <string.h>
#include <math.h>
#include "scip/scip.h"
#include "scip/scipdefplugins.h"

Go to the source code of this file.

Functions
static void	visualizeSolutionMatplotlib (SCIP *scip, SCIP_SOL *sol)
static void	visualizeSolutionGnuplot (SCIP *scip, SCIP_SOL *sol)
static SCIP_RETCODE	visualizeSolutionAscii (SCIP *scip, SCIP_SOL *sol)
static	SCIP_DECL_EVENTINIT (eventInitDispsol)
static	SCIP_DECL_EVENTEXIT (eventExitDispsol)
static	SCIP_DECL_EVENTEXEC (eventExecDispsol)
static SCIP_RETCODE	includeEventHdlrDispsol (SCIP *scip)
static SCIP_RETCODE	setupProblem (SCIP *scip, SCIP_Real fixwidth, SCIP_Real fixheight)
static SCIP_RETCODE	runPacking (SCIP_Real fixwidth, SCIP_Real fixheight, SCIP_Bool dognuplot, SCIP_Bool domatplotlib)
int	main (int argc, char **argv)

Variables
int	ncircles = 0
SCIP_Real *	r = NULL
int	rsize = 0
SCIP_VAR **	x
SCIP_VAR **	y
SCIP_VAR **	b
SCIP_VAR *	a
SCIP_VAR *	w
SCIP_VAR *	h
SCIP_Bool	minarea

Function Documentation

visualizeSolutionMatplotlib()

static void visualizeSolutionMatplotlib ( SCIP *  scip, SCIP_SOL *  sol  )

static

plots solution by use of Python/Matplotlib

Parameters

scip	SCIP data structure
sol	solution to plot

Definition at line 74 of file circlepacking.c.

References a, b, h, minarea, ncircles, NULL, r, SCIPerrorMessage, SCIPgetSolOrigObj(), SCIPgetSolVal(), SCIPinfoMessage(), SCIPround(), w, x, and y.

Referenced by runPacking().

visualizeSolutionGnuplot()

static void visualizeSolutionGnuplot ( SCIP *  scip, SCIP_SOL *  sol  )

static

plots solution by use of gnuplot

Parameters

scip	SCIP data structure
sol	solution to plot

Definition at line 136 of file circlepacking.c.

References a, b, h, MAX, minarea, ncircles, NULL, r, SCIP_Real, SCIPerrorMessage, SCIPgetSolOrigObj(), SCIPgetSolVal(), SCIPinfoMessage(), SCIPround(), w, x, and y.

Referenced by runPacking().

visualizeSolutionAscii()

static SCIP_RETCODE visualizeSolutionAscii ( SCIP *  scip, SCIP_SOL *  sol  )

static

plots solution by use of ascii graphics

Parameters

scip	SCIP data structure
sol	solution to plot

Definition at line 194 of file circlepacking.c.

References b, h, minarea, ncircles, NULL, phi(), r, SCIP_CALL, SCIP_OKAY, SCIP_Real, SCIPallocBufferArray, SCIPceil(), SCIPfreeBufferArray, SCIPgetIntParam(), SCIPgetSolOrigObj(), SCIPgetSolVal(), SCIPinfoMessage(), SCIPround(), SCIPsnprintf(), w, x, and y.

Referenced by SCIP_DECL_EVENTEXEC().

SCIP_DECL_EVENTINIT()

static SCIP_DECL_EVENTINIT ( eventInitDispsol  )

static

initialization method of event handler (called after problem was transformed)

Definition at line 286 of file circlepacking.c.

References NULL, SCIP_CALL, SCIP_EVENTTYPE_BESTSOLFOUND, SCIP_OKAY, and SCIPcatchEvent().

SCIP_DECL_EVENTEXIT()

static SCIP_DECL_EVENTEXIT ( eventExitDispsol  )

static

deinitialization method of event handler (called before transformed problem is freed)

Definition at line 295 of file circlepacking.c.

References NULL, SCIP_CALL, SCIP_EVENTTYPE_BESTSOLFOUND, SCIP_OKAY, and SCIPdropEvent().

SCIP_DECL_EVENTEXEC()

static SCIP_DECL_EVENTEXEC ( eventExecDispsol  )

static

execution method of event handler

Definition at line 304 of file circlepacking.c.

References NULL, SCIP_CALL, SCIP_EVENTTYPE_BESTSOLFOUND, SCIP_OKAY, SCIPeventGetSol(), SCIPeventGetType(), and visualizeSolutionAscii().

includeEventHdlrDispsol()

static SCIP_RETCODE includeEventHdlrDispsol ( SCIP *  scip )

static

creates event handler for dispsol event

Parameters

scip	SCIP data structure

Definition at line 320 of file circlepacking.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPincludeEventhdlrBasic(), SCIPsetEventhdlrExit(), and SCIPsetEventhdlrInit().

Referenced by runPacking().

setupProblem()

static SCIP_RETCODE setupProblem ( SCIP *  scip, SCIP_Real  fixwidth, SCIP_Real  fixheight  )

static

create problem in given SCIP and add all variables and constraints to model the circle packing problem

Parameters

scip	SCIP data structure
fixwidth	a given fixed width for the rectangle, or SCIP_INVALID if not fixed
fixheight	a given fixed height for the rectangle, or SCIP_INVALID if not fixed

Definition at line 339 of file circlepacking.c.

References a, b, FALSE, h, MIN, minarea, ncircles, NULL, r, SCIP_Bool, SCIP_CALL, SCIP_INVALID, SCIP_MAXSTRLEN, SCIP_OBJSENSE_MAXIMIZE, SCIP_OKAY, SCIP_Real, SCIP_VARTYPE_BINARY, SCIP_VARTYPE_CONTINUOUS, SCIPaddCoefLinear(), SCIPaddCons(), SCIPaddVar(), SCIPallocMemoryArray, SCIPcreateConsBasicLinear(), SCIPcreateConsQuadraticNonlinear(), SCIPcreateProbBasic(), SCIPcreateVarBasic(), SCIPfixVar(), SCIPinfinity(), SCIPisLT(), SCIPreleaseCons(), SCIPsetObjsense(), SCIPsnprintf(), SQR, TRUE, w, x, and y.

Referenced by runPacking().

runPacking()

static SCIP_RETCODE runPacking ( SCIP_Real  fixwidth, SCIP_Real  fixheight, SCIP_Bool  dognuplot, SCIP_Bool  domatplotlib  )

static

run circle packing example

Sets up SCIP and the SCIP problem, solves the problem, and shows the solution.

Parameters

fixwidth	a given fixed width for the rectangle, or SCIP_INVALID if not fixed
fixheight	a given fixed height for the rectangle, or SCIP_INVALID if not fixed
dognuplot	whether to draw best solution with gnuplot
domatplotlib	whether to draw best solution with python/matplotlib

Definition at line 554 of file circlepacking.c.

References a, b, FALSE, h, includeEventHdlrDispsol(), minarea, ncircles, NULL, r, SCIP_CALL, SCIP_OKAY, SCIPcreate(), SCIPfree(), SCIPfreeMemoryArray, SCIPgetBestSol(), SCIPgetNSols(), SCIPincludeDefaultPlugins(), SCIPinfoMessage(), SCIPprintOrigProblem(), SCIPprintSol(), SCIPreleaseVar(), SCIPsetRealParam(), SCIPsolve(), setupProblem(), visualizeSolutionGnuplot(), visualizeSolutionMatplotlib(), w, x, and y.

Referenced by main().

main()

int main	(	int	argc,
		char **	argv
	)

main method starting SCIP

Parameters

argc	number of arguments from the shell
argv	array of shell arguments

Definition at line 629 of file circlepacking.c.

References BMSallocMemoryArray, BMSreallocMemoryArray, FALSE, ncircles, r, rsize, runPacking(), SCIP_ALLOC_ABORT, SCIP_Bool, SCIP_INVALID, SCIP_OKAY, SCIP_Real, SCIPprintError(), and TRUE.

Variable Documentation

ncircles

int ncircles = 0

Number of possible circles

Definition at line 56 of file circlepacking.c.

Referenced by getNCircles(), main(), runPacking(), setupProblem(), solvePricingMINLP(), visualizeSolutionAscii(), visualizeSolutionGnuplot(), and visualizeSolutionMatplotlib().

r

SCIP_Real* r = NULL

Radii

Definition at line 59 of file circlepacking.c.

Referenced by addFlowrowToCommodity(), addFracCounter(), addLocalRows(), addOrbitopesDynamic(), addRangeInfo(), addRelaxation(), allRowsInLP(), applyCompression(), branchruledataEnsureArraySize(), checkCons(), cleanupNetwork(), computeAndConstraintInfos(), computeVarRatio(), consdataCreate(), consdataFreeRows(), constructCompression(), createCGMIPprimalsols(), createRelaxation(), createSubscip(), cutsSubstituteMIR(), cutsSubstituteStrongCG(), deleteCommodity(), detectParallelCols(), displayReaders(), enforceExprNlhdlr(), ensureRngrowmapMem(), evaluateLiftingFunction(), extractCapacities(), extractCapacityRows(), extractFlow(), extractFlowRows(), extractNodes(), fillRelationTables(), findUncapacitatedArcs(), forkAddLP(), generateAverageRay(), generateClusterCuts(), generateDisjCutSOS1(), getAlphaAndBeta(), getDualBranchscore(), getFlowrowFit(), getIncidentNodes(), getJobs(), getNActiveConsScore(), getNextFlowrow(), getNodeSimilarityScore(), getResourcesCapacities(), getResourcesNames(), getSimplexCoefficients(), getVarRank(), heurdataEnsureArraySize(), identifySourcesTargets(), improvePoint(), invertCommodity(), lpCleanupRows(), lpDelRowset(), lpFlushAddRows(), lpLexDualSimplex(), lpRemoveObsoleteRows(), main(), markRelaxsUnsolved(), markRowsXj(), mcfnetworkFill(), parseDetails(), ObjPricerVRP::pricing(), profilesFindEarliestFeasibleStart(), profilesFindLatestFeasibleStart(), propagateStaticOrbitope(), propVariables(), pseudoforkAddLP(), relaxVar(), runPacking(), SCIP_DECL_COMPREXIT(), SCIP_DECL_CONSGETNVARS(), SCIP_DECL_CONSGETVARS(), SCIP_DECL_HEUREXEC(), SCIP_DECL_NLHDLRENFO(), SCIP_DECL_PRESOLEXEC(), SCIP_DECL_READERREAD(), SCIPapplyLockFixings(), SCIPcolPrint(), SCIPconflictAnalyzeLP(), SCIPcreateSchedulingProblem(), SCIPexprintHessianSparsity(), SCIPfreeRepresentation(), SCIPgetDualProof(), SCIPgetFarkasProof(), SCIPgetLPBInvARow(), SCIPgetLPBInvRow(), SCIPgetRandomSubset(), SCIPgetReadingTime(), SCIPinitRepresentation(), SCIPlpEndDive(), SCIPlpGetBInvARow(), SCIPlpGetBInvRow(), SCIPlpGetDualDegeneracy(), SCIPlpGetDualfarkas(), SCIPlpGetSol(), SCIPlpGetUnboundedSol(), SCIPlpiAddRows(), SCIPlpiDelRows(), SCIPlpiDelRowset(), SCIPlpiGetBase(), SCIPlpiGetBasisInd(), SCIPlpiGetBInvACol(), SCIPlpiGetBInvARow(), SCIPlpiGetBInvCol(), SCIPlpiGetBInvRow(), SCIPlpiGetRows(), SCIPlpiGetSol(), SCIPlpiLoadColLP(), SCIPlpiSetBase(), SCIPlpRemoveRedundantRows(), SCIPlpShrinkRows(), SCIPlpStartDive(), SCIPlpSumRows(), SCIPlpUpdateAges(), SCIPmatrixGetParallelCols(), SCIPrandomGetSubset(), SCIPreoptApplyCompression(), SCIPreoptGetNSols(), SCIPreoptMergeVarHistory(), SCIPresetRepresentation(), SCIPrunBoundHeuristic(), SCIPsolAdjustImplicitSolVals(), SCIPsolveProbingRelax(), separateCons(), separateConsBinaryRepresentation(), separateCoverCutsCons(), separateCuts(), separateRltCuts(), setupProblem(), solveBilinearLP(), solveNodeRelax(), solveRowEchelonGF2(), storeCuts(), storeSuitableRows(), strengthenOrbitopeConstraint(), subrootConstructLP(), updateActivities(), updateLoopStatus(), updateSymInfoConflictGraphSST(), varProcessBoundChanges(), visualizeSolutionAscii(), visualizeSolutionGnuplot(), visualizeSolutionMatplotlib(), writeOpbRelevantAnds(), xmlFindNode(), and xmlFindNodeMaxdepth().

rsize

int rsize = 0

Definition at line 60 of file circlepacking.c.

Referenced by main().

x

SCIP_VAR** x

x coordinates

Definition at line 63 of file circlepacking.c.

Referenced by addBilinearTermToCut(), addCut(), addLinearTermToCut(), addProductVars(), applyObbtBilinear(), bilinboundGetScore(), bilinearTermsInsertAll(), bilinearTermsInsertEntry(), checkSystemGF2(), cleanCycle(), computeBilinEnvelope2(), computeConvexEnvelopeFacet(), computeCut(), computeHyperplaneThreePoints(), createSepaData(), detectMinors(), drawScaledImage(), ecaggrAddBilinTerm(), ecaggrAddQuadvar(), errorf(), estimateConvexSecant(), estimateUnivariateQuotient(), eval(), evalFunctionGradient(), evalFunctionValue(), evaluateLiftingFunction(), evaluateLiftingFunctionKnapsack(), extractProducts(), extractVariablesMINLP(), F77_FUNC(), filterExistingLP(), getBestEstimators(), getBilinearBinaryTerms(), getBinaryProductExpr(), getBinaryProductExprDo(), getCorner(), getCorners(), getEigenValues(), getIneqViol(), getMinorVars(), getRelDistance(), getX(), hessLagAddExpr(), hessLagSparsitySetNzFlagForExpr(), initBounds(), isFiniteNonnegativeIntegral(), isPackingCons(), isPointFeasible(), lpiGetBInvVec(), markRowsXj(), negate(), nlrowaggrAddRemBilinTerm(), nlrowaggrCreate(), printRow(), processSolveOutcome(), provedBound(), rbDeleteFixup(), rbRotate(), read_problem(), reversePropBinarySearch(), roundFixingValue(), runBrachistochrone(), runPacking(), SCIP_DECL_EVENTEXEC(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_NLHDLRSOLLINEARIZE(), SCIP_DECL_READERREAD(), SCIPaddIneqBilinear(), SCIPcalcRootNewton(), SCIPcreateConsAbspower(), SCIPcreateConsBasicAbspower(), SCIPcreateConsBasicSignpowerNonlinear(), SCIPerf(), SCIPevalBilinAuxExprNonlinear(), SCIPgetBilinTermIdxNonlinear(), SCIPgetBilinTermNonlinear(), SCIPinsertBilinearTermExistingNonlinear(), SCIPinsertBilinearTermImplicitNonlinear(), SCIPintervalNegateReal(), SCIPintervalQuadBivar(), SCIPintervalQuadUpperBound(), SCIPintervalSquare(), SCIPlapackSolveLinearEquations(), SCIPlpiAddCols(), SCIPlpiAddRows(), SCIPlpiChgBounds(), SCIPlpiChgObj(), SCIPlpiChgSides(), SCIPlpiClearState(), SCIPlpiGetBInvACol(), SCIPlpiGetBInvARow(), SCIPlpiGetBInvCol(), SCIPlpiGetBInvRow(), SCIPlpiGetDualfarkas(), SCIPlpiGetPrimalRay(), SCIPlpiGetSol(), SCIPlpiLoadColLP(), SCIPlpiReadLP(), SCIPlpiScaleCol(), SCIPlpiScaleRow(), SCIPlpiWriteLP(), SCIPnegateReal(), SCIPnlpiOracleEvalConstraintGradient(), SCIPnlpiOracleEvalConstraintValue(), SCIPnlpiOracleEvalConstraintValues(), SCIPnlpiOracleEvalHessianLag(), SCIPnlpiOracleEvalJacobian(), SCIPnlpiOracleEvalObjectiveGradient(), SCIPnlpiOracleEvalObjectiveValue(), SCIPpatternAddElement(), SCIPpatternSetElementPos(), SCIPrbtreeDelete_call(), SCIPrbtreePredecessor_call(), SCIPrbtreeSuccessor_call(), SCIPrealHashCode(), SCIPregressionAddObservation(), SCIPregressionRemoveObservation(), SCIPsolveLinearEquationsIpopt(), sepadataAddMinor(), separateMcCormickImplicit(), separatePoint(), setupProblem(), setupStart(), solveBilinearLP(), solveLinearProb3(), solvePricingMINLP(), solveRowEchelonGF2(), spxSolve(), updateBestCandidate(), updateBilinearRelaxation(), useBilinIneqs(), visualizeSolutionAscii(), visualizeSolutionGnuplot(), and visualizeSolutionMatplotlib().

y

SCIP_VAR** y

y coordinates

Definition at line 64 of file circlepacking.c.

Referenced by addBilinearTermToCut(), addCut(), addProductVars(), applyObbtBilinear(), bilinboundGetScore(), bilinearTermsInsertAll(), bilinearTermsInsertEntry(), computeBilinEnvelope2(), computeCut(), createSepaData(), detectMinors(), drawScaledImage(), ecaggrAddBilinTerm(), errorf(), extractProducts(), extractVariablesMINLP(), filterExistingLP(), getBestEstimators(), getBilinearBinaryTerms(), getBinaryProductExpr(), getBinaryProductExprDo(), getCorner(), getCorners(), getEigenValues(), getIneqViol(), getMinorVars(), getRelDistance(), initBounds(), isPackingCons(), isPointFeasible(), lpiGetBInvVec(), markRowsXj(), nlrowaggrAddRemBilinTerm(), nlrowaggrCreate(), printRow(), provedBound(), rbInsertFixup(), rbRotate(), read_problem(), runBrachistochrone(), runPacking(), SCIP_DECL_EVENTEXEC(), SCIP_DECL_NLHDLRESTIMATE(), SCIP_DECL_READERREAD(), SCIPaddIneqBilinear(), SCIPerf(), SCIPevalBilinAuxExprNonlinear(), SCIPgetBilinTermIdxNonlinear(), SCIPgetBilinTermNonlinear(), SCIPinsertBilinearTermExistingNonlinear(), SCIPinsertBilinearTermImplicitNonlinear(), SCIPintervalQuadBivar(), SCIPintervalSquare(), SCIPlpiGetBInvRow(), SCIPpatternAddElement(), SCIPpatternSetElementPos(), SCIPrbtreeDelete_call(), SCIPrbtreePredecessor_call(), SCIPrbtreeSuccessor_call(), SCIPregressionAddObservation(), SCIPregressionRemoveObservation(), sepadataAddMinor(), separateMcCormickImplicit(), separatePoint(), setupProblem(), solveBilinearLP(), solvePricingMINLP(), updateBestCandidate(), updateBilinearRelaxation(), useBilinIneqs(), visualizeSolutionAscii(), visualizeSolutionGnuplot(), and visualizeSolutionMatplotlib().

b

SCIP_VAR** b

whether circle is placed into rectangle

Definition at line 65 of file circlepacking.c.

Referenced by aggregateConstraints(), alnsFixMoreVariables(), analyseOnoffBounds(), cancelCol(), cancelRow(), checkBlocking(), checkCons(), checkSystemGF2(), collectBinaryVars(), computeModularity(), computeMonoidalQuadCoefs(), computeMonoidalStrengthCoef(), computePosCircleCircle(), computePosRingCircle(), computeRestrictionToLine(), computeRestrictionToRay(), computeRoot(), computeRowEchelonGF2(), consdataCreateBinvars(), consdataLinearize(), createAndSplitProblem(), createCapacityRestriction(), createCoverCutsTimepoint(), createRows(), decompHorizonGetFirstPosBestPotential(), decompHorizonInitialize(), decompHorizonMarkInterval(), detectExpr(), determineVariableFixingsDecomp(), doBinarySearch(), encodeColPair(), encodeRowPair(), estimateBivariateQuotient(), estimateUnivariate(), estimateUnivariateQuotient(), evalPhiAtRay(), findMonoidalQuadRoot(), findNonDominatedVars(), initCurrent(), integerpow(), intEvalQuotient(), isNeighbor(), LNSFixMoreVariables(), lockRounding(), lpiStrongbranch(), optimize(), processRealBoundChg(), projectVbd(), propagateBoundsLinExpr(), propagateBoundsQuadExpr(), provedBound(), removeFixedBinvars(), reoptimize(), reuseSolution(), reversepropQuotient(), roundPartition(), runPacking(), scalePenalties(), SCIP_DECL_CONSCHECK(), SCIP_DECL_CONSINITSOL(), SCIP_DECL_CONSLOCK(), SCIP_DECL_CONSRESPROP(), SCIP_DECL_DIVESETGETSCORE(), SCIP_DECL_HEUREXEC(), SCIP_DECL_NLHDLRINTEVAL(), SCIP_DECL_NLHDLRREVERSEPROP(), SCIP_DECL_PROPRESPROP(), SCIPclassifyConstraintTypesLinear(), SCIPintervalQuadUpperBound(), SCIPintervalSolveBivariateQuadExpressionAllScalar(), SCIPintervalSolveUnivariateQuadExpressionPositiveAllScalar(), SCIPlapackSolveLinearEquations(), SCIPlpiGetBInvCol(), SCIPlpiGetBInvRow(), SCIPrealToRational(), SCIPsolveLinearEquationsIpopt(), SCIPvisualizeConsCumulative(), setupProblem(), solveLinearProb3(), solveRowEchelonGF2(), solveSingleRowLP(), SORTTPL_NAME(), strengthenVarbounds(), tightenedLinkvar(), tryAggregateIntVars(), updateLambda(), visualizeSolutionAscii(), visualizeSolutionGnuplot(), visualizeSolutionMatplotlib(), and xmlFreeAttr().

a

SCIP_VAR* a

area of rectangle

Definition at line 66 of file circlepacking.c.

Referenced by addRowMark(), aggregateConstraints(), applyOptcumulative(), buildVertexPolyhedralSeparationLP(), cancelCol(), cancelRow(), checkBlocking(), cleanCycle(), cleanupNetwork(), computeAndConstraintInfos(), computeMaxBoundaryForBilinearProp(), computeMaxForBilinearProp(), computeMonoidalQuadCoefs(), computeMonoidalStrengthCoef(), computeObjWeightSize(), computePosCircleCircle(), computePosRingCircle(), computeRestrictionToLine(), computeRestrictionToRay(), computeRevPropIntervalSin(), computeRoot(), computeVarRatio(), createEdgesFromRow(), createInitialColumns(), createLP(), detectExpr(), doBinarySearch(), encodeColPair(), encodeRowPair(), estimateBivariateQuotient(), estimateUnivariate(), estimateUnivariateQuotient(), evalPhiAtRay(), F77_FUNC(), findMonoidalQuadRoot(), findNonDominatedVars(), generateClusterCuts(), identifyComponent(), identifySourcesTargets(), integerpow(), intEvalQuotient(), isNeighbor(), markRowsXj(), mcfnetworkFill(), mcfnetworkFree(), nodepairqueueCreate(), nodepartitionIsConnected(), performAggregations(), printNLRow(), propagateBoundsQuadExpr(), provedBound(), reversepropQuotient(), runPacking(), SCIP_DECL_CONSINITSOL(), SCIP_DECL_HEURFREE(), SCIPcallLapackDsyevIpopt(), SCIPintervalQuadUpperBound(), SCIPlapackComputeEigenvalues(), SCIPrealToRational(), SCIPwriteCcg(), setupGradients(), setupProblem(), solveSingleRowLP(), sortArray(), SORTTPL_NAME(), tryAggregateIntVars(), visualizeSolutionGnuplot(), visualizeSolutionMatplotlib(), writeOpbObjective(), writeOpbRelevantAnds(), xmlAddAttr(), xmlFreeAttr(), xmlGetAttrval(), xmlNewAttr(), and xmlShowNode().

w

SCIP_VAR* w

width of rectangle

Definition at line 67 of file circlepacking.c.

Referenced by addNegatedCliques(), branchBalancedCardinality(), cliqueCleanup(), collectBinaryCliqueData(), collectNonBinaryImplicationData(), collectNonBinaryVBoundData(), consdataCreateRedundant(), correctConshdlrdata(), createEdgesFromRow(), deleteRedundantVars(), detectOrbitopalSymmetries(), detectRedundantVars(), dualWeightsTightening(), enforceConssSOS1(), enforceSOS2(), extensionOperatorSOS1(), extractProducts(), extractVariablesMINLP(), getBinaryProductExprDo(), rangedRowPropagation(), rbDeleteFixup(), removeConstraintsDueToNegCliques(), runPacking(), sampleWeighted(), SCIP_DECL_BANDITRESET(), SCIP_DECL_HEUREXEC(), SCIPapplyLockFixings(), SCIPcallLapackDsyevIpopt(), SCIPcliquetableAdd(), SCIPlapackComputeEigenvalues(), SCIPshrinkDisjunctiveVarSet(), SCIPwriteCcg(), separateSolution(), sequentialUpAndDownLifting(), sequentialUpAndDownLiftingGUB(), setupProblem(), simplifyInequalities(), solvePricingMINLP(), sortAndMergeClique(), sortItems(), SYMcheckGraphsAreIdentical(), tarjan(), tightenVarsBoundsSOS1(), tightenWeights(), updateImplicationGraphSOS1(), visualizeSolutionAscii(), visualizeSolutionGnuplot(), visualizeSolutionMatplotlib(), and writeOpbObjective().

h

SCIP_VAR* h

height of rectangle

Definition at line 68 of file circlepacking.c.

Referenced by AMPLProblemHandler::BeginSum(), calcNonZeros(), checkFeasSubtree(), checkParameters(), computePosCircleCircle(), computePosRingCircle(), computeRowEchelonGF2(), conflictAddConflictCons(), createMipCpFormulation(), createMipFormulation(), createPresoldata(), DECL_CURVCHECK(), detectNlhdlr(), enforceConstraints(), evaluateLiftingFunctionKnapsack(), findAndStoreDivesets(), hessLagAddExpr(), includeDivingHeurs(), multihashlistRetrieve(), multihashlistRetrieveNext(), AMPLProblemHandler::OnHeader(), runPacking(), SCIP_DECL_HEUREXEC(), SCIP_DECL_HEURINITSOL(), SCIPdialoghdlrAddHistory(), SCIPfindNlhdlrNonlinear(), SCIPinitConssLP(), SCIPparamsetSetEmphasis(), SCIPpresolve(), SCIPprimalHeuristics(), SCIPprobFree(), SCIPprobTransform(), SCIPreadProb(), SCIPsolCheck(), SCIPsolCheckOrig(), SCIPtransformProb(), setupProblem(), SORTTPL_NAME(), superadditiveUpLifting(), visualizeSolutionAscii(), visualizeSolutionGnuplot(), and visualizeSolutionMatplotlib().

minarea

SCIP_Bool minarea

whether we minimize the area (TRUE) or maximize the number of circles in the rectangle (FALSE)

Definition at line 69 of file circlepacking.c.

Referenced by runPacking(), setupProblem(), visualizeSolutionAscii(), visualizeSolutionGnuplot(), and visualizeSolutionMatplotlib().