Anytime Local Search for Multi-Objective Combinatorial Optimization

239 Pages·2014·14.65 MB·English

UNIVERSITÉLIBREDEBRUXELLES
EcolePolytechniquedeBruxelles
IRIDIA-InstitutdeRecherchesInterdisciplinaires
etdeDéveloppementsenIntelligenceArtificielle
Anytime Local Search for Multi-Objective
Combinatorial Optimization: Design,
Analysis and Automatic Configuration
Jérémie DUBOIS–LACOSTE
PromoteurdeThèse:
Dr. Thomas Stützle
Co-promoteursdeThèse:
Dr. Mauro Birattari
Dr. Manuel López-Ibáñez
Thèseprésentéeenvuedel’obtentiondutitredeDocteurenSciencesdel’Ingénieur
AnnéeAcadémique2013/2014
ii
Abstract
Our world is becoming increasingly complex and many systems are key to the well-
functioning of our modern society. They can be any sort of technological systems,
processes, logistical organization in the industry, distribution of goods, planning and
schedulingoftrainsandplanes,designofacityroadmap,controloftrafficsignals,and
soon.
In all these situations, the decisions taken have a strong impact on efficiency, be it
a matter of time, resources, or any other element to be optimized. Once the problems
havebeenfullyidentifiedandtheobjectivehasbeenclearlyestablished,theactualtask
of finding a good (or the optimal) solution is typically very hard for humans. In fact,
even assisted by computers an entire class of problems remains very hard to solve to
NP
optimality(problemsthatintheoreticalComputerSciencehavebeenidentifiedas -
hard). Inthiscase,thepracticalgoaltobeachievedisoftentofindsatisfactorysolutions
in reasonable time. Algorithms designed for this task are called heuristic optimization
algorithms.
Atthebeginningofthealgorithmicoptimizationfield, mostoftheresearchefforts
were devoted to problems with a single objective to be optimized. However, many
problemsinrealsituationscanbeconsideredashavingseveralobjectives. Forinstance
thescheduleofpublictransportscanaimat(i)minimizingthetimerequiredforusers
to reach their destination, or (ii) minimizing the cost of the transportation system so
that it remains economically profitable or at least feasible. In this example, as in most
real-worldproblems,theobjectivesthatarerelevantareconflictingwitheachotherso
that optimizing one is likely to worsen another. Therefore, research in multi-objective
optimization aims at finding efficient methods and algorithms that take into account
severalobjectives,andreturnasetofsolutionsthataretrade-offsbetweenobjectives. In
thisthesis,weareinterestedinthedesignandstudyofheuristicalgorithmsformulti-
objectiveoptimization.
Twoaspectsarekeytoourworkandmakeitnovelinthemulti-objectiveoptimiza-
tion field: the use of automatic configuration techniques, and the consideration of the
anytime behavior. Automatic configuration techniques free the human designer from
the time-consuming task of setting parameter, and have already been successfully ap-
pliedtosingle-objectivealgorithms. Asweshowinthisthesis,theyarebothapplicable
anddesirableformulti-objectivealgorithmsaswell. Theanytimebehaviorofanalgo-
rithm is its ability to return as high-quality solutions as possible at any moment of its
execution. Having algorithms that have a good anytime behavior is highly desirable
insituationswherethecomputationtimeisunknownaprioriorwhenitchangeseach
time the algorithm is launched. The optimization literature is mostly focused on the
quality reached by an algorithm after a given time defined a priori, and the outcomes
ofsuchstudiesmaypoorlyextendtosituationswheretheanytimebehaviorisrelevant.
Inthisthesis,besidesstudyingtheanytimebehaviorofmulti-objectivealgorithms,we
alsotesttheapplicationofautomaticconfigurationtechniquesinordertoobtainauto-
maticallygood“anytime”algorithms.
All algorithms are evaluated on well-known combinatorial problems by means of
statistical and graphical tools. Our results, published in several international journals
andconferences,improveoverthestate-of-the-artforrelevantandwidelystudiedprob-
lems,intermsofanytimebehaviorandalsointermsoffinalquality.
Acknowledgments
FirstofallIwouldliketoexpressmygratitudetoDr. ThomasStützleforitsoutstanding
supervisionduringtheseyears. Itwasagreatpleasureformetosharehispassionand
knowledge. I also wish to deeply thank Dr. Manuel López-Ibáñez with whom I had
manyinterestingdiscussionsandjointworks.
IRIDIAisawonderfulplaceandIfeeltrulyhonoredtobeapartofit. Thislaboratory
isuniquebyallthepeoplethatmadeandmakesit. Iwasluckytomeetallthosewhom
Imet,someheretodayandsomethatleftlongagoalready. Youhavevastlybroadened
myhorizon. IamprofoundlygratefultoallIridiansforthis,andforallthenicemoments
together.
Additionally to Thomas, I want to thank the “backbone” of IRIDIA for maintaining
a nice environment and high-quality standards of teaching and research: Dr. Mauro
Birattari,Pr. HuguesBersiniandPr. MarcoDorigo.
DuringmyPhD,IreceivedsupportfromtheEuropeanCommissionthroughtheproject
MIBISOC.Iamgratefultoallpeoplewhomanagedthisproject,inparticularPr. Oscar
Cordónwhodidanamazingjobwithatrulycommunicativeenthusiasm. Idonotthink
Ineedtoexpressmywarmsentimenttomyfellowmibisockers,Iwillmakesuretotravel
wherevertheyaretoremindthemfromtimetotime.
Rossella, thank you for your patience and for sharing me so much with “my algo-
rithms”. Somehow,wemadeittogether.
A mes parents: merci pour votre confiance depuis toujours. Sans elle et la liberté qui
vaavec,cettethèsen’auraitpasvulejour.
Jérémie
ThisworkhasbeenmainlyfundedbytheEuropeanCommissionundertheMIBISOC
project(GrantAgreement: 238819),withintheactionMarieCurieInitialTrainingNet-
workoftheSeventhFrameworkProgram(7FP).
IalsoacknowledgesupportfromtheMETA-Xproject,anActiondeRechercheConcertée
fundedbytheScientificResearchDirectorateoftheFrenchCommunityofBelgium.
“ÀAnneetVincent,
Camille,Christiane,Jacques,Jacques”
viii
Contents
1 Introduction 1
1.1 GoalsofthisThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 ContributionsofthisThesis . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 StructureofthisThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Background 11
2.1 CombinatorialProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 TheTravelingSalesmanProblem . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 LocalSearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 NeighborhoodOperators: anExamplefortheTravelingSalesman
Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.2 PivotRule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Metaheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.1 IteratedLocalSearch . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.2 SimulatedAnnealing . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.3 TabuSearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.4 GreedyRandomizedAdaptiveSearchProcedures . . . . . . . . . 19
2.4.5 Population-BasedMetaheuristics . . . . . . . . . . . . . . . . . . . 21
2.5 Multi-objectiveOptimization . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.1 RelationsbetweenSolutions . . . . . . . . . . . . . . . . . . . . . . 23
2.5.2 RelationsbetweenSetsofSolutions . . . . . . . . . . . . . . . . . 24
2.6 PerformanceAssessmentofMulti-objectiveAlgorithms . . . . . . . . . . 25
2.6.1 HypervolumeIndicator . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6.2 GraphicalQualityAssessment: EmpiricalAttainmentFunction . 27
ix
2.7 LocalSearchApproachestoMulti-objectiveOptimization . . . . . . . . . 29
2.7.1 ScalarizationofMulti-objectiveProblems . . . . . . . . . . . . . . 29
2.7.2 AScalarization-basedAlgorithm: Two-phaseLocalSearch . . . . 32
2.7.3 Scalarization-BasedParadigm: LiteratureReview . . . . . . . . . 34
2.7.4 ParetoDominanceApproachforMulti-objectiveOptimization . . 36
2.7.5 ADominance-basedAlgorithm: ParetoLocalSearch . . . . . . . 36
2.7.6 Dominance-basedParadigm: LiteratureReview . . . . . . . . . . 38
2.7.7 HybridizationofthetwoParadigms: LiteratureReview . . . . . . 40
2.8 AutomaticConfigurationofAlgorithms . . . . . . . . . . . . . . . . . . . 44
2.8.1 TheiraceSoftwareforOfflineAutomaticConfiguration . . . . . 46
2.9 AnytimeBehaviorofAlgorithms . . . . . . . . . . . . . . . . . . . . . . . 47
2.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3 AnytimeTwo-phaseLocalSearch 51
3.1 ThePermutationFlow-ShopSchedulingProblem . . . . . . . . . . . . . . 52
3.2 AGeneralizedViewofTwo-phaseLocalSearch . . . . . . . . . . . . . . . 54
3.3 RegularAnytimeTPLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.1 RegularAnytimeStrategy . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.2 ExperimentalAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4 AdaptiveTPLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4.1 AdaptiveAnytimeStrategy . . . . . . . . . . . . . . . . . . . . . . 65
3.4.2 ExperimentalEvaluationofAdaptiveAnytimeTPLSonBi-objective
TravelingSalesmanProblemInstances . . . . . . . . . . . . . . . . 68
3.4.3 ExperimentalEvaluationofAdaptiveAnytimeTPLSonBi-objective
PermutationFlowshopSchedulingProblem . . . . . . . . . . . . 68
3.4.4 FurtherAnalysisofAN-TPLS-1seedandAN-TPLS-2seed . . . . . 71
3.4.5 AdaptiveFocusTPLS . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4.6 Experimental Evaluation of Adaptive Focus on Bi-objective Per-
mutationFlowshopSchedulingProblem . . . . . . . . . . . . . . 74
3.5 StatisticalAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.5.1 ResultsontheBi-objectiveTravelingSalesmanProblem . . . . . . 76
3.5.2 ResultsontheBi-objectivePermutationFlowshopSchedulingProb-
lem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.6 OptimisticHypervolumeContributionasSelectionCriterion . . . . . . . 78
x