Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing PDF
Preview Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing
HimeAguiareOliveiraJunior,LesterIngber,AntonioPetraglia, MarianeRemboldPetraglia,andMariaAugustaSoaresMachado StochasticGlobalOptimizationandItsApplicationswithFuzzyAdaptive SimulatedAnnealing IntelligentSystemsReferenceLibrary,Volume35 Editors-in-Chief Prof.JanuszKacprzyk Prof.LakhmiC.Jain SystemsResearchInstitute UniversityofSouthAustralia PolishAcademyofSciences Adelaide ul.Newelska6 MawsonLakesCampus 01-447Warsaw SouthAustralia5095 Poland Australia E-mail:[email protected] E-mail:[email protected] Furthervolumesofthisseriescanbefoundonourhomepage: springer.com Vol.11.SamuliNiiranenandAndreRibeiro(Eds.) Vol.24.DawnE.HolmesandLakhmiC.Jain(Eds.) InformationProcessingandBiologicalSystems,2011 DataMining:FoundationsandIntelligentParadigms,2011 ISBN978-3-642-19620-1 ISBN978-3-642-23240-4 Vol.12.FlorinGorunescu Vol.25.DawnE.HolmesandLakhmiC.Jain(Eds.) 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StochasticGlobalOptimizationandItsApplicationswith DataMining:FoundationsandIntelligentParadigms,2011 FuzzyAdaptiveSimulatedAnnealing,2012 ISBN978-3-642-23165-0 ISBN978-3-642-27478-7 Hime Aguiar e Oliveira Junior, Lester Ingber, Antonio Petraglia, Mariane Rembold Petraglia, and Maria Augusta Soares Machado Stochastic Global Optimization and Its Applications with Fuzzy Adaptive Simulated Annealing 123 Authors Dr.HimeAguiareOliveiraJunior Prof.MarianeRemboldPetraglia RiodeJaneiro UniversidadeFederaldoRiodeJaneiro Brazil RiodeJaneiro Brazil Prof.LesterIngber LesterIngberResearch Prof.MariaAugustaSoaresMachado Ashland IBMEC-RJ USA RiodeJaneiro Brazil Prof.AntonioPetraglia UniversidadeFederaldoRiodeJaneiro RiodeJaneiro Brazil ISSN1868-4394 e-ISSN1868-4408 ISBN978-3-642-27478-7 e-ISBN978-3-642-27479-4 DOI10.1007/978-3-642-27479-4 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2011945156 (cid:2)c Springer-VerlagBerlinHeidelberg2012 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpub- lication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforany errorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespect tothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Global optimization is a very important subject. It finds applications in Biology, Statistics, Engineering, Mathematics itself, Medicine, Management Science, Eco- nomicsandinvirtuallyeverythingyoucanimagine.Althoughmanyexcellentmeth- ods have been developed so far, several of them assume certain conditions about functionstobeprocessed,asconvexityordifferentiability,and,inpractice,weoften getintosituationsinwhichobjectivefunctionstobeoptimized(minimizedormax- imized)arenotdifferentiable,convexorevencontinuous.Insuchsettings,gradient- basedmethodsarenotofmuchhelpanditisnecessaryto findmoregeneralways togetgoodresults.Duringthelastdecadesanexpressivenumberofnewglobalop- timizationmethodswereidealized,aimingtoreachthatmoregeneralobjectiveand substantialpartofthembelongtothecategoryofmetaheuristicmethods,beingalso known generically as metaheuristics. Their majority are of a probabilistic nature, thatistosay,useprobabilitytheoryresultstogettotheirtarget,consequentlybeing classified asstochasticmethodsaswell. Knowledgeofthe capabilitiesandlimita- tionsofthesealgorithmsleadstoabetterunderstandingoftheirreachovervarious applicationsandpointsusthewaytofutureresearchonimprovingandextendingal- gorithms’theoreticalfoundationsandrespectiveimplementations.Ourgoalinthis book is to present a description of some techniques for solving stochastic global optimizationproblemsandto detailone,in particular-FuzzyAdaptiveSimulated Annealing(FuzzyASA).Bypresentingseveral,detailedexamplesofitsapplication we will try to stimulate the reader’sintuitionand makethe use of FuzzyASA (or ASA)easiertoallwishingtosolvetheirproblemswiththistool. Itisimportanttonotethat,inthisbook,allexampleprogramcodesarepresented inthehopethattheywillbeusefulinthelearningprocess,butwithoutanywarranty - withouteven the implied warrantyof fitness for a particularpurpose.Besides, it isadvisableto highlightthatthearchitectureoftheexampleroutinesisnotneces- sarilythemostefficientincomputationalterms,takingintoaccountthattheywere constructedforpedagogicalreasonsonly. Formal mathematical requirements are kept to a minimum and our focus will be on continuousproblems,although ASA is able to handle discrete optimization tasks as well. This book could be used in courses related to optimization as well VI Preface asbyresearchersandpractitionersinEngineeringandindustry,andisadequatefor self-study,also. Prerequisitesforreadingthisbookincludesome knowledgeof LinearAlgebra, introductoryNumericAnalysisandbasicProbabilityTheory. Theworkisdividedinthreeparts: • Anintroductorysetofchapters,exposingbasicfactsaboutsomeimportantglobal optimizationmethodsandtheiroverallstructure; • A secondpartcontaininga detaileddescriptionofAdaptiveSimulatedAnneal- ing(ASA)anditsfuzzycontrolledversion,howtomakeconstrainedanduncon- strainedoptimizationwiththemandseveralillustrativeexamplesthat,wehope, willbehelpfultothereader; • AfinalpartcontainingchaptersthatdescribeapplicationsofFuzzyASAtosev- eralareasofknowledgelikesignalprocessing,statisticalestimation,fuzzymod- elingandnonlinearequationsolving. Tocomplementthematerialcontainedinthetextandmakethelearningtimeshorter, weinvitethereadertotrydoingsomeglobaloptimizationtasksbyhimorherself. It suffices to download the publicly available code at www.ingber.com and start coding.Incaseofdoubts,suggestionsoranythingelse,please,feelfreetocontact us.Wehopeyouenjoythebookandthatitwillbeusefulinyourwork. RiodeJaneiro,BRAZIL HimeAguiareOliveiraJunior Ashland,USA LesterIngber AntonioPetraglia October2011 MarianeRemboldPetraglia MariaAugustaSoaresMachado Acknowledgements We would like to thank Dr. Leontina Di Cecco (Publishing Editor), Mr. Hol- ger Scha¨pe (Engineering Editorial) and all staff of Springer-Verlag for their kind support. This page intentionally left blank Contents PartI Fundamentals 1 Introduction.................................................. 3 1.1 WhytoOptimize?......................................... 3 1.2 KindsofOptimizationProblems............................. 5 1.3 HowtoOptimize?......................................... 6 References.................................................... 10 2 GlobalOptimizationandItsApplications........................ 11 2.1 Introduction .............................................. 11 2.2 StochasticorDeterministic? ................................ 12 2.3 ConsiderationsaboutGeneralGlobalOptimizationTasks ........ 13 2.4 SomePopularApproachesandFinalComments................ 18 References.................................................... 20 3 MetaheuristicMethods ........................................ 21 3.1 Introduction .............................................. 21 3.2 GeneticAlgorithms........................................ 23 3.3 ParticleSwarmOptimization................................ 24 3.4 DifferentialEvolution...................................... 25 3.5 Cross-EntropyMethod ..................................... 26 3.6 SimulatedAnnealing....................................... 27 References.................................................... 30 PartII ASA,FuzzyASAandTheirCharacteristics 4 AdaptiveSimulatedAnnealing.................................. 33 4.1 Introduction .............................................. 33 4.1.1 LICENSEandContributions ......................... 34 4.1.2 OrganizationofChapter ............................ 34 4.2 TheoreticalFoundationsofAdaptiveSimulatedAnnealing(ASA). 35
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