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1、TimeComplexityofEvolutionaryAlgorithmsforCombinatorialOptimization：ADecadeofResultsInternationalJournalofAutomationandComputingTimeComplexity一一ofEvolutionary04(3),July2007,281-293DOI:10.1007/s11633-007-0281-3AlgorithmsforOptimization:ADecadeofResultsPietroS.OlivetoJunHeXi
2、nYaoTheCenterofExcellenceforResearchinComputationalIntelligenceandApplications(CERCIA),SchoolofComputerScienceUniversityofBirmingham,Edgbaston,BirminghamBI52TT,UKAbstract:Computationaltimecornplexityanalyzesofevolutionaryalgorithms(EAs)havebeenperformedsincethemid-ninetie
3、s.Thefirstresultswererelatedtoverysimplealgorithms,suchasthe(1+1)-EA,ontoyproblems.TheseeffortsproducedadeeperunderstandingofhowEAsperformondifierentkindsoffitrIesslandscapesandgeneralmathematicaltoolsthatmaybeextendedtotheanalysisofmorecomplicatedEAsonmorerealisticproble
4、ms.Infact,inrecentyears,ithasbeenpossibletoanalyzethe(1+1)-EAoncombinatorialoptimizationproblemswithpracticalapplicationsandmorerealisticpopulation-basedEAsonstructuredtoyproblems.Thispaperpresentsasurveyoftheresultsobtainedinthelastdecadealongthesetworesearchlines.Themos
5、tcommonmathematicaltechniquesareintroduced,thebasicideasbehindthemarediscussedandtheirelectiveapplicationsarehighlighted.Solvedproblemsthatwerestillopenareenumeratedasarethosestillawaitingforasolution.Newquestionsandproblemsariseninthemeantimearealsoconsidered.Keywords:Ev
6、olutionaryalgorithms,computationalcomplexity,combinatorialoptimization,evolutionarycomputationtheory1IntroductionEvolutionaryalgorithms(EAs)areawideclassofran.domizedproblemsolversbasedonprinciplesofbiologicalevolution.Theyhavebeenused.oftensuccessfully.inmanycomputationa
7、lareassuchasOptimization,Learning,Adap-tationandotherst.Hence.therearelotsofavailableex.perimentalresultsconcerningthisclassofalgorithms,butcomparedtothatamount,thetheoreticalknowledgeofhowtheyperformlagswaybehind.Indeed,thelargestpartoftheavailableresearchstudiesareofemp
8、iricalnature.How.ever,sincetheeightieswhenEAsstartedtobecomepopu-lar,therehavealwaysbeentheoreti
