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31 6 Vol.31,No.62005 11 ACTAAUTOMATICASINICANovember,2005 1) (!#$%&’#()*310027)(E-mail:xiaozhao9912@sina.com)+,-./0123456789:;=(?LELS)@01ABC56789:;=(?DELS)7DEFGH7IJ:KLMNOPQRSTUVNH7KLMWXYZ[GH7\]^@0_^‘:;7abcEdef9[VNH\]^7g9hijklm0_^7ngopq3Brstuvwx/yz{|7}~RU ‘uv -./DELS 7 o‘ c q8 8 U \xyz{| 7 f9 @ 7}~ U cDELS7 o¡¢£89:;=U23456UABC56ULELSDELSNOPQRST⁄¥ƒ§¤TP273;TP30ConvergenceandEscapeCapacityResearchofEvolutionLearningStrategiesYANLingJIANGJing-Ping(CollegeofElectricalEngineering,ZhejiangUniversity,Hangzhou310027)(E-mail:xiaozhao9912@sina.com)AbstractTheLamarckianevolutionlearningstrategy(LELS)andDarwinianevolutionlearningstrategy(DELS)arediscussedintermsoftheirsimilaritiesanddifferencesinlearn-ingimplementation.Theformerisbasedoninheritanceofacquiredcharacter,i.e.,bothphenotypeandgenotypecanbeoptimizedthroughlearningwhilethelateronlyoptimizesphenotypebasedonDarwinianselection.TheconvergenceofELSisprovedusingMarkovchaintheory.AndwealsotheoreticallydemonstratethatDELShasstrongerescapingcapac-ity.Thesealgorithmsareappliedto8standardtestfunctions.SimulationresultsshowthatLELSandDELSyieldfasterconvergenceandbetterglobaloptimizationabilitythanstan-dardevolutionstrategies;moreover,DELSalsoleadstobetterescapingcapacity.Finally,limitationsoftheworkaswellasthefuturestudyarediscussed.KeywordsELS,Lamarckian,Darwinian,LELS,DELS,inheritanceofacquiredcharacter1'“«‹›fifl –(EvolutionStrategy)†‡· fl¶•‚„”»…‰ ¿ `´ˆ˜¯˘˙‚¨ ˚¸ [1]˝˛‡¶•†ˇ— •‚„”» ˇ— •fi »1) Æ #ª (60405012) SupportedbyNationalNaturalScienceFoundationofP.R.China(60405012) ŁØ 2004-6-28 ŒºŁØ 2004-12-28ReceivedJune28,2004;inrevisedformDecember28,2004Copyrightc2005byEditorialOfficeofActaAutomaticaSinica.Allrightsreserved.874W 9: 31 æ ı[2] ł˝ˇ— •øœß ¶ ı[3] ł… » ˛‡ı[4] ł ˛‡¶• ı [5∼7]…˝˛‡¶•† • fl¶•‚„”»fi ‚¨ `´˙ … ø» …˝˘ fifl¶•( ø ! ł •)†#$fifl¶•%& ’()*+ fi ,-» . ¶• / 012 »3456789 ¸:»; …¸¨ =/? @ A `´BBC D EF [8∼10].3GH¸ ß IB (JKL ˚MN Oł), PQ RS T»U VW @4567XNYZ[ `´˙\]fifl – `´X-^T˙ _• ‘aX- b»cd øB a¯œ“ fifl¶•(HybridEA)”, …e fœgSZ Hß hi»j klmœ“fiflß ¶•”;˝fifl –†ß ¶•‚„” »a¯œ“fiflß –”. nopq»e 67 fiflß –(Lamarckianevolutionlearningstrategy,raLELS) PQ fiflß –(Darwinianevolutionlearn-ingstrategy,raDELS) st» _¶• »D45n67 DELSu¸2v wx=/?ıy ł )*z. „{˙2|}~ 2.1 no4 ¨ 1 ˙˘ » D F » u¸ ˛‡ j » fi - ß » - ¡H¢»£8%S/⁄6¥ƒ j §?˙ »…¤ ¡H¢'“ »† j¢«¸‹K ¨ ˙›fifl/ – \]¡H¢¿fi »3†•¥ D j¢g˘‡·n˙ß … ¶ j¢†¡H¢¯• ‚„˙ { 1F”»…‰» ¡H¢D ß FX ¿ j¢»%… ı£8%…PQ »g˝D2.2`F´ˆ5o˙˜1:;¯0_^¯\]^˘˙ Fig.1Therelationshipoflearning,genotype,phenotypeandfitnesscd fifl¶•… fifl¨E ˘ w rˇ ˚»M«¸pq ß ¸ ˙j »Dfifl¶•F ˝ I˛ˇß —`»%¸ /De n æ / 01˙2.2 Æ y ˘ ª˜%…“ ˛‡”, “ fi ” »yŁ6ØŒº F89:;=}~R@ 7 875‘ + %…“ æ”: æ # ı łøæœ ß »ı » »3g˘˜ ˛‡»j % , ı ˘ »#¨˘ ˘ fifl»ı % ¿ ˙h ¿ »%… D ß F ¡H¢ m ( æ ı D F ), ¿ j¢ m »fi3 fifl PQ ] ¸ KSt » fœ…K›fiD ø D æ ¨EF» ¸ s ¸ »¸ ı »¸ »˝K ¸ S g s… “ ”.! #ı æ $#%&’()* +, -./0 %&123 4 56789:; =?@A B(CD 1EFGHIJKL0 3MNOPCQR5STUV ,6WD CXY75ST678 Z[\TR0] TU^_‘a ! Fb_:; cd/ Fe6G fg 0h ijkPlCQRNO mlWnopqrs’( tku Y7(CQR D FvwIxC),y_%z{|e-. %&1 ! M}~ u Y7 )M o [11].b20 z0 b_:;q] FT o x 23 W! [x %zFT =X ¡T f¢ £⁄NO¥ƒ §z2%z¤'“YNNO«‹{›T⁄#fi fl@W –†‡zx 9· – ¤¶• ‚„”c»…¤x F‰,NO 2 ¿ ` z´ˆ ¤fl@0˜ ¯˘¥ƒW3˙¨ ˚¸ ˝˛3.1ˇ— (DELS) ¯˘IÆ 9 UH ª †‡dμ9λt ¤(μ,λ)-LELS,ŁØŒ/º1) Oº ‰ μUUH æ1 GH Æ WeI\UUH UH u s W2)78º\UÆ UH bı 78o ‰λ/μU łø‰ λU UHWœλU UH eßb Æ UHF #§ W3)qrºλU UHßbN qrW5T %z d qr¯˘ – d # ˘Wqro( UH tku O X{| ! uM@‰7OW4):;º\UUH [Z 1 stkP ‰ X 9opqr ø WλUUHI#‰ μUUH ¤/T Æ UHWŒ a ¯˘ W 2).FN VT # u 78 /T tkuFœ cdWFDELS¯˘I u tku!#_ #$ u% UH tkuT %&tku% UH uT %W3.2ˇ—’() (LELS)*+1.FLELS¯˘I tku, [ uWT-0] u tku . #$ ¤/0 ! [LELS¯˘ dx tku Y1M }~ u Y1 œ2» . 3ª#$ 456 W –¤ 7 FLELS¯˘I tku, [ u zœ0Hk“op’(1 ” 89W876:;=31?LELSFqr978@c DELS#§ Wqro( UH tku O X{|W [ dx zABC3.2,§z u2 S OWλUUHItku % X | μUUH ¤/T Æ WDEF‚ FÆ UH bı /T G HI opqrI’( u(tku) Y7W4JKLMNOPQRSTUVWXY4.1 Z[\]^ _§‘ NOqr«‹(ELS),HILELS9DELS¯˘WBCELSFæt(t0) 6G¤X(t)=(xt,1,xt,2,···,xt,N),xt,l∈S, {X(t)}t0 TUaK. b= eEcd.¤E=SN,t∈Z−=(0,1,···,n,···). [V6GX(t+1)ezT6fgmh¶i[jk6GX(t), œ l={X(t)}t0 TUmK.n %opWq 1.Z[ELSr ªs O¥ƒtC b7uT=min{t∈Z−:Ft=f∗}t v¢wIxyzs9n.tŒ P{T∞}=1{ 6G #t |ELSzfg1F#}.~ ¥ xyzs9W3ªsf∗=f(x∗)+∞|¤TUxyz4sj{ej∀x∈S⇒f(x)6f(x∗) t |¤TUxyz4s9[12].*+2.F\TNO t,ZÆ 6GX(t) 78¯ cdT¢o( no 6GX(t)zA ‚ny∈S,Œ y6∈X(t), -Fp(t)0,B(y∈X(t)nfgp(t).5UBC FNOn\T It\TUUH%zz 4[0nfgnT¢78 ¤ d.Ie ‚TUUHWZ[ 4*ª t´BC nWq 2. ª O¥ƒ(Continuousparameteroptimizationproblem),l d.¤ dn hd.RnIn# S=nYt=1[ai,bi],eIaibi,i=1,2,···,n. S1¤xyz49 d.tS2¤ xyz49 d.tj{ejS1∩S2=Φ,S1∪S2=