Optimization by GRASP: Greedy Randomized Adaptive Search Procedures PDF
Preview Optimization by GRASP: Greedy Randomized Adaptive Search Procedures
Mauricio G.C. Resende Celso C. Ribeiro Optimization by GRASP Greedy Randomized Adaptive Search Procedures Optimization by GRASP Mauricio G.C. Resende • Celso C. Ribeiro Optimization by GRASP Greedy Randomized Adaptive Search Procedures 123 MauricioG.C.Resende CelsoC.Ribeiro ModelingandOptimizationGroup(MOP) InstitutodeCieˆnciadaComputac¸a˜o Amazon.com,Inc. UniversidadeFederalFluminense Seattle,WA,USA Nitero´i,RiodeJaneiro,Brazil ISBN978-1-4939-6528-1 ISBN978-1-4939-6530-4 (eBook) DOI10.1007/978-1-4939-6530-4 LibraryofCongressControlNumber:2016948721 ©SpringerScience+BusinessMediaNewYork2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerScience+BusinessMediaLLC Theregisteredcompanyaddressis:233SpringStreet,NewYork,NY10013,U.S.A In memoryof David StiflerJohnson Foreword In recent years, advances in metaheuristics have given practitioners a powerful frameworkformakingkeydecisionsinproblemsasdiverseastelecommunications networkdesignandsupplychainplanningtoschedulingintransportationsystems. GRASPisametaheuristicthathasenjoyedwidesuccessinpractice,withanextraor- dinarily broadrange of applicationsto real-world optimizationproblems. Starting from the seminal 1989 paper by Feo and Resende, over the past 25 years, a large bodyofworkongreedyrandomizedadaptivesearchprocedureshasemerged.Avast arrayofpapersonGRASPhavebeenpublishedintheopenliterature,andnumer- ous MSc and PhD theses have been written on the subject. This book is a timely and welcome addition to the metaheuristicsliterature, bringingtogether this body ofworkinasinglevolume. TheaccountofGRASPinthisbookisespeciallycommendableforitsreadabil- ity,coveringmanyfacetsofthismetaheuristic,suchassolutionconstruction,local search, hybridizations,and extensions. It is organizedinto four main sections: in- troduction to combinatorial optimization, fundamentals of heuristic search, basic GRASP, and advanced topics. The book can be used as an introductory text, not onlytoGRASPbutalsotocombinatorialoptimization,localsearch,path-relinking, andmetaheuristicsingeneral.Forthemoreadvancedreader,chaptersonhybridiza- tionwithpath-relinkingandparallelandcontinuousGRASPpresentthesetopicsin aclearandconcisefashion.Thebookadditionallyoffersaverycompleteannotated bibliographyofGRASPandcombinatorialoptimization. Forthepractitionerwhoneedstosolvecombinatorialoptimizationproblems,the bookprovidesimplementabletemplatesforallalgorithmscoveredinthetext. Thisbook,with itsexcellentoverviewofthestate oftheartofGRASP, should appeal to researchers and practitioners of combinatorial optimization who have a needtofindoptimalornear-optimalsolutionstohardoptimizationproblems. Boulder,CO,USA FredGlover May2016 vii Preface Greedy randomized adaptive search procedures, or GRASP, were introduced by T. Feo and M. Resende in 1989 as a probabilistic heuristic for solving hard set coveringproblems.Soonafteritsintroduction,itwasrecognizedasageneralpur- posemetaheuristicandwasappliedtoanumberofothercombinatorialoptimization problems, including scheduling problems, the quadratic assignment problem, the satisfiability problem, and graph planarization. At the Spring 1991 ORSA/TIMS meetinginNashville,T.FeoandM.ResendepresentedthefirsttutorialonGRASP asametaheuristic,whichwasfollowedbytheirtutorialpublishedintheJournalof GlobalOptimizationin1995.Sincethen,GRASPhasgainedwideacceptanceasan effectiveand easy-to-implementmetaheuristicfor findingoptimalor near-optimal solutionstocombinatorialoptimizationproblems. Thisbookhasbeenmanyyearsinplanning.Thoughmanybookshavebeenwrit- tenaboutothermetaheuristics,includinggeneticalgorithms,tabusearch,simulated annealing,andantcolonyoptimization,abookonGRASPhadyettobepublished. Sincethesubjecthashad25yearstomature,wefeelthatthisistherighttimefor suchabook.AfterSpringeragreedtopublishthisbook,webeganthetaskofwriting itin2010. WehavebeencollaboratingonthedesignandimplementationofGRASPheuris- ticssince1994whenwedecided,attheTIMSXXXIIInternationalMeetinginAn- chorage, Alaska, to partner in designing a GRASP for graph planarization. Since then,we haveworkedtogetherona numberof papersonGRASP, includingthree highlycitedsurveys. Thisbookisaimedatstudents,engineers,scientists,operationsresearchers,ap- plicationdevelopers,andotherspecialistswhoarelookingforthemostappropriate andrecentGRASP-basedoptimizationtoolstosolveparticularproblems.Itfocuses on algorithmic and computational aspects of applied optimization with GRASP. Emphasis is given to the end user, providing sufficient information on the broad spectrumofadvancesinappliedoptimizationwithGRASP. The bookgrew fromtalksand shortcoursesthatwe gaveatmanyuniversities, companies, and conferences. Optimization by GRASP turned out to be not only a bookon GRASP butalso a pedagogicalbookonheuristics, metaheuristicsandits ix x Preface basics, foundations, extensions, and applications. We motivate the subject with a numberofhardcombinatorialoptimizationproblemsexpressedin simpledescrip- tions in the first chapter. This is followed by an overview of complexity theory thatmakesthecaseforheuristicsandmetaheuristicsasveryeffectivestrategiesfor solving hard or large instances of the so-called intractable NP-hard optimization problems. In our view, most metaheuristics share a number of common building blocksthat are combinedfollowingdifferentstrategiesto overcomeprematurelo- cal optimality. Such building blocks are explored, for example, in the chapters or sectionsongreedyalgorithms,randomization,localsearch,costupdatesandcandi- datelists,solutionperturbationsandejectionchains,adaptivememoryandelitesets, path-relinking,runtimedistributionsandprobabilisticanalysistools,parallelization strategies,andimplementationtricks,amongothertopics.Assuch,preliminaryver- sionsofthistexthavebeenusedinthelastthreeyearsasatextbookforthecourse onmetaheuristicsatthegraduateprogramincomputerscienceatUniversidadeFed- eral Fluminense, Brazil, complementedwith specific reading material aboutother metaheuristics,whereithasmaturedandwasexposedtocriticismsandsuggestions frommanystudentsandcolleagues. ThebookbeginsinChapter1withanintroductiontooptimizationandadiscus- sion about solution methods for discrete optimization, such as exact and approxi- matemethods,includingheuristicsandmetaheuristics. We then provide in Chapter 2 a short tour of combinatorial optimization and computationalcomplexity,inwhichweintroducemetaheuristicsasaveryeffective toolforapproximatelysolvinghardoptimizationproblems. This is followed in Chapter 3 with solution construction methods, including greedyalgorithmsandtheirrelationtomatroids,adaptivegreedyandsemi-greedy algorithms,andsolutionrepairprocedures. Chapter 4 focuses on local search. We discuss solution representation, neigh- borhoods, and the solution space graph. We then focus on local search methods, coveringneighborhoodsearch strategies, cost function updates, and candidate list strategies. Ejection chains and perturbations as well as other strategies to escape fromlocaloptimaarediscussed. Chapter 5 introduces the basic GRASP as a semi-greedy multistart procedure withlocalsearch.Techniquesforacceleratingthebasicprocedurearepointedout. ProbabilisticstoppingcriteriaforGRASParealsodiscussed.Thechapterconcludes withashortintroductiontotheapplicationofGRASPasaheuristicformultiobjec- tiveoptimization. Chapter6focusesontime-to-targetplots(orruntimedistributions)forcompar- ing exponentially distributed runtimes, such as those for GRASP heuristics, and runtimeswithgeneraldistributions,suchasthoseforGRASPwithpath-relinking. Runtime distribution will be extensively used throughout this book to assess the performanceofstochasticsearchalgorithms. ExtendedGRASPconstructionheuristicsarecoveredinChapter7.Thechapter beginswithreactiveGRASPandthencoverstopicssuchasprobabilisticchoiceof theconstructionparameter,randomplusgreedyandsampledgreedyconstructions, construction by cost perturbation, and the use of bias functions in construction. Preface xi Thechaptercontinueswiththeuseofmemory,learning,andtheproximateoptimal- ityprincipleinconstruction,pattern-basedconstruction,andLagrangeanGRASP. Path-relinking is introduced in Chapter 8. The chapter provides a template for path-relinking and discusses its mechanics and implementation strategies. Other topicsrelatedtopath-relinkingarealsodiscussedinthischapter.Thisincludeshow todealwithinfeasibilitiesinpath-relinking,howtorandomizepath-relinking,and externalpath-relinkinganditsrelationtodiversification. The hybridizationof GRASP with path-relinkingis covered in Chapter 9. The chapterbeginsbyprovidingmotivationforhybridizingpath-relinkingwithGRASP toprovideGRASPwithamemorymechanism.Itthengoesontodiscusselitesets andhowtheycanbeusedasawaytoconnectGRASPandpath-relinking.Thechap- terendswithadiscussionofevolutionarypath-relinkingandrestartmechanismsfor GRASPwithpath-relinkingheuristics. The implementation of GRASP on parallel machines is the topic of Chap- ter10.Thechapterintroducestwotypesofstrategiesforparallelimplementationof GRASP: multiple-walk independent-thread and multiple-walk cooperative-thread strategies.Itthengoesontoillustratetheseimplementationstrategieswiththreeex- amples:thethree-indexassignmentproblem,thejobshopschedulingproblem,and the2-pathnetworkdesignproblem. Continuous GRASP extends GRASP heuristics from discrete optimization to continuous global optimization. This is the topic of Chapter 11. After establish- ing the similarities and differencesbetween GRASP for discrete optimizationand continuousGRASP (or simply C-GRASP), the chapter describes the construction andlocalsearchphasesofC-GRASPandconcludeswith severalexamplesapply- ingC-GRASPtomultimodalbox-constrainedoptimization. ThebookconcludeswithChapter12wherefourimplementationsofGRASPand GRASPwithpath-relinkingaredescribedindetail.Theseimplementationsarefor the 2-path network design problem, the graph planarization problem, the unsplit- tablenetworkflowproblem,andthemaximumcutproblem. Eachchapterconcludeswithbibliographicalnotes. Writing this book was certainly a long and arduoustask, but most of all it has beenanamazingexperience.ThemanytripsbetweenHolmdel,Seattle,andRiode Janeiroandtheperiodstheauthorsspentvisitingeachotheralongthelastsixyears havebeengratifyingand contributedmuchto fortifyan alreadystrongfriendship. Wehadalotoffunandweareveryhappywiththeoutcomeofthisproject.Wewill beevenhappierifthereadersappreciatereadingandusingthisbookasmuchaswe enjoyedwritingit. Seattle,WA,USA MauricioG.C.Resende RiodeJaneiro,RJ,Brazil CelsoC.Ribeiro May2016 Acknowledgments Overtheyears,wehavecollaboratedwithmanypeopleonresearchrelatedtotopics covered in this book. We make an attempt to acknowledge all of them below, in alphabeticalorder,andapologizeincasesomeonewasomittedfromthislonglist: James Abello, Vaneet Aggarwal,Renata Aiex, Daniel Aloise, Dario Aloise, Adri- anaAlvim,DiogoAndrade,AlexandreAndreatta,DavidApplegate,Alete´iaArau´jo, AaronArcher,SilvioBinato,ErnestoBirgin,IsabelleBloch,MariaClaudiaBoeres, MariaCristinaBoeres,JullianyBranda˜o,LucianaBuriol,VicenteCampos,Suzana Canuto, Sergio Carvalho, W.A. Chaovalitwongse, Bruno Chiarini, Clayton Com- mander, Abraham Duarte, Alexandre Duarte, Christophe Duhamel, Sandra Duni- Ekis¸og˜lu, Joa˜o Lauro Faco´, Djalma Falca˜o, Haroldo Faria Jr., Tom Feo, Eraldo Fernandes, Daniele Ferone, Paola Festa, Rafael Frinhani, Micael Gallego, Fred Glover,FernandoCarvalho-Gomes,Jose´FernandoGonc¸alves,Jose´LuisGonza´lez- Velarde,EricoGozzi,AllisonGuedes,WilliamHery,MichaelHirsch,Rube´nInte- rian, David Johnson,HowardKarloff,Yong Li, X. Liu, David Loewenstern,Irene Loiseau, Abilio Lucena, Rafael Mart´ı, Cristian Mart´ınez, Simone Martins, Ger- aldo Mateus, Thelma Mavridou, Marcelo Medeiros, Rafael Melo, Claudio Mene- ses, Renato Moraes, Luis Mora´n-Mirabal, Leonardo Musmanno, Fernanda Naka- mura, Maria´ Nascimento, Thiago Noronha, Carlos Oliveira, Panos Pardalos, Lu- ciana Pessoa, AlexandrePlastino, LeonidasPitsoulis, Marcelo Prais, Fa´bio Protti, Tianbing Qian, Michelle Ragle, Sanguthevar Rajasekaran, Martin Ravetti, Vinod Rebello,LuciaResende,AlbertoReyes,CarolineRocha,NoemiRodriguez,Isabel Rosseti, Jesus Sa´nchez-Oro, Andre´a dos Santos, Ricardo Silva, Stuart Smith, Cid de Souza, Mauricio de Souza, Reinaldo Souza, Fernando Stefanello, Sandra Su- darksy,FranklinaToledo,GiorgiodeTomi,GerardoToraldo,MarcoTsitselis, Ed- uardo Uchoa, Osman Ulular, Sebastia´n Urrutia, Reinaldo Vallejos, A´lvaro Veiga, AnaViana,DalessandroVianna,CarlosEduardoVieira,EugeneVinod,andRenato Werneck. TheauthorsareparticularlyindebtedtoSimoneMartinsforhercarefulrevision ofthismanuscript.WearealsoverythankfultoFredGloverforkindlyagreeingto writetheforewordofthisbook. xiii
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