Optimization by GRASP: Greedy Randomized Adaptive Search Procedures

323 Pages·2016·8.59 MB·English

by  Mauricio G.C. Resende

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
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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.
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