硕士论文-进化策略在数值计算中的一些应用研究

广西民族大学硕士学位论文进化策略在数值计算中的一些应用研究姓名：夏慧明申请学位级别：硕士专业：计算数学指导教师：周永权20080401I19IIAPPLICATIONRESEARCHONNUMERICALMETHODSBASEDONEVOLUTIONSTRATEGYABSTRACTEvolutioncomputingisanauto-adaptedglobaloptimizesearchalgorithmswhichsimulatesthegeneticandformsofthenaturalenvironment.Themethodisdifferentfromthetraditionalnumericalmethod.Peoplehaverealizedincreasinglythattheresearchaboutsoftcomputingareveryimportantandtakeittobeanovelmethodwhichsettlestheproblemsthismethodstudiestheindividualsbyreorganization,mutation,selectionintheevolutionprocessandapproachestotheoptimalsolution.Thenumericalmethodisamathematicsbranch,whoseobjectofstudyistosolvethenumericalmethodsofeachmathematicsquestionsbyusingthecomputer.Thecontentincludesdigitalapproximation(interpolationandfitting),numericalintegrationandnumericaldifferentiation,numericalsolutionoflinearequation(group)function,numericalsolutionofordinarydifferentialequationgroupandpartialdifferentialequationgroupandsoon.Theyhadbeenproposedin1990s,evenearlier.Themoderncomputershavecreatedconditionsforlargescalenumericalcomputing,itisurgentandnecessarytoresearchassemblyandsystematicwhichsuitcomputernumericalmethod.InthisobjectusesEvolutionStrategytoresearchnumericalcomputing,inordertosettlethenumericalcomputingproblemstransferthenumericalcomputingproblemstofunctionaloptimizationproblemsandproposednewhybridalgorithmbycombiningthethreeintelligentalgorithms:EvolutionStrategy,DifferentialEvolutionAlgorithmandFunctionalNetworksatthesametime.Usingthemethodtosolvethematrix’seigenvaluesandeigenvectors;balancechemicalequations;computethecomplexfunctionsandsoon.TheseproblemscanbesettledbythetraditionalnumericalmethodbutthereexistsomedisadvantagesuchasIIIselectoftheinitialvaluesensitively,thespeedconvergentslowly,theaccuracylowly,evennotconvergentandsoon.Inviewofquestionsabouttraditionalnumericalmethods,primetaskofthisarticleusesthecharacteristicsofEvolutionStrategy,suchas,parallelsearch,globalconvergenceandrobustnessandsoon,tosolvetheproblemsoftraditionalnumericalmethods.LetthethreemethodsEvolutionStrategy,DifferentialEvolutionAlgorithmandFunctionalNetworksbecombinedwitheachotherandexerteachadvantages,itcanobtainbestanswerwhendealwithsomeproblems.So,researchingnumericalcomputingbyEvolutionStrategy,DifferentialEvolutionAlgorithmandFunctionalNetworkshavehighertheoryvalueandpracticalsignificance.KEYWORDS:numericalcomputing;intelligencealgorithm;evolutionstrategyalgorithm;differentialevolutionalgorithm;functionalnetworks;improvedevolutionstrategy;hybridevolutionstrategy;mutationoperator111.1]1[Lanczos]1[Davidson]2[1993C.Bischof]3[1999]4[2002MichaelGrantExcel]5[2004]6[2006]7[2007[8][910]−1999[11]2001WORD[12]2001[13]2003[14]2007[15]21999[16]2001LarsKindermann[17]2001[18]2002[19]2004[20]1997RainerS[21]1998Hyun-KyoJung[22]2006[23]2006[24]2007[25][2628]−(ANN)[2931]−1989HornikK[32]1997AhmedMoatazA[33]1997JeanGabrielAttali3[31]2000[34]2000[35]2005[36]1.2(1)(2)(3)1.31.4(1)(2)(3)41.552()()2.1(1)(2)(TravelingSalesmanProblemTSP)(SchedulingProblem)01(KnapsackProblem)(BinPackingProblem)()62.22.2.12.2.1.12060I.RechenbergH.P.Schwefel(EvolutionStrategies,ES)[3738]−ESES2.2.1.21ES−+)11(1963I.RechenbergES−+)11(),0(1σNXXtt+=+(2.1)tX——t),0(σN0σ〉〈σ,X1+tXtX),0(σNES−+)11(2ES−+)1(µ(1+1)—ESI.RechenbergES−+)1(µµ)1(µµ)),,,(),,,,((),()),,,(),,,,((),(222212222122112111121111nnnnxxxXxxxXσσσσσσσσ==(2.2))),,,(),,,,((),(21212121nnqnqqqnqqxxxXσσσσ=(2.3)71=iq2ni,,2,1=σES−+)11(µµES−+)1(µES−+)11(3ES−+)(λµES−),(λµ1975H.P.SchwefelES−+)(λµES−),(λµµλES−+)(λµµλ(λµ+)µES−),(λµλµµλ“+”)11(+)1(+µ)(λµ+),(λµES−),(λµ2.2.22.2.2.1()2.2.2.21Xσn)),,,,,(),,,,,,((),(2121ninixxxxXσσσσσ=(2.4)Xσ⋅+=⋅+⋅⋅=)1,0())1,0()1,0('exp(''iiiiiiiNxxNrNrσσσ(2.5)),(iixσi),(''iixσi)1,0(N8)1,0(iNi'r1)2(−n1r1)2(−n12µ),(σXnixiσ))0(),0((σXµ0.3)0(=σ344.1)(2.2)(2.3)µ(2.2))))2)(,,2)(,2)((),2)(,,2)(,2)(((),(21221221112122122111nnnnxxxxxxXσσσσσσσ++++++=4.2)(2.5)4.3)4.4)),(λµ542.2Gen0µjλλ)(λµ+λµ92.1Fig.2.1Theprocessofevolutionstrategy2.2.3(1)λ)(λµ+µ(2)(3)n2.32.3.1RainerStornKennethPrice[3940]−1996[4142]−(ICEO)[43]2.3.22.3.2.110,2.3.2.21.()N)1,0[∈cP))0(,),0(),0(()0(21NXXXX=)0(X)0(bestX0:=t)0(iXn2.())(tX)(tXi2.1)]()([)]()([)()(12tXtXtXtXtXtVrribestii−+−+=βλTntVtVtV))(,),(),((21∆1r2r],1[Nλβ,∆2.2],1[NmkcpkLp==}{),1[NLTniuuutU),,,()(21=Nj,,2,1=nnnLmmmj−++=1,,1,jjVu=jijtXu)]([=n•n2.3))(())((tXJtUJii)()1(tUtXii=+)()1(tXtXii=+3.()2))1(,),1(),1(()1(21+++=+tXtXtXtXN)1(+tX)1(+tXbest)1(+tXbest1:=t22.3.32.4112.4.1[44]1998E.Castillo(Fourier)2.4.22.4.2.12.4.2.2(1)(2)(3)s),,,(21sxxxkkjFj,,2,1,=kjxxxFysjj,,2,1),,,,(21==jFjF(4)2.22.2Fig.2.2Thetopologyconfigurationofthefunctionalnetwork122.4.3(SigmoidRBF)F()2.51333.1]1[Lanczos]1[Davidson]2[A3.2[45]Ann×XnAXY=nλXXAXλ=AXXT=)(XXλXλXA(eigenpair)X,λλX2.1Ann×nnλλλ,,,21),,2,1(nii=λ2.2λAVVAVλ=VAλ(1)λV(2)λrrrVVV,,,21143.33.3.1(1)Xσ2)),(),,((),(2121σσσxxX=(2)µ),(σX20.3)0(=σ(3))det(AIe−=λ)1/(12ef+=110f1εε(4)(5)5.1)-5.4)5.1)5.2)))1,0()1,0(exp(''iiiNrNr⋅+⋅⋅=σσ)1,0('iiiiNxx⋅+=σ2,1=ir'r15.3)f5.4)),(λµ(6)(5)3.3.213.3.3)1/(12ef+=ef1),(λµ1407,20=∗==µλµ19999999999.0