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ժ  Ҫ  ڸcaz㷨мPowellmڲ΢ȫփĻz㷨?w㷨{Ŵ㷨ľֲ?@z㷨ȫֽĸֻúֵϢ㷨һN΢Ͳ΢ȫփ}ͨ÷

PI~  ȫ㷨z㷨Powell

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1 

΢ǾԺ}ЏVĹ̺͑ñYOӋʹýYСwYOOСminmax}ԔMвȡС^ֵʄtʧMⷽоԽԽܵ˂ҕõ㷨ģʽμηPowell@ЩǾֲYcֵP

HollandоȻFc˹ϵymОrb̭Mcz˼z㷨һN^Ч󲻿΢ǾԺȫķz㷨M㷨lչܿڸN}cչFcՓA߀Փ͑ϱ¶T಻ȱՔٶҴՔ}[1,2]˷@һ}1989GoldbergϷĿ[2]GAcy֪RĆlʽgYƻz㷨ľֲʹz㷨x_ՔB^mӽȫīI[3][4]ڿYаlչɹĻAָz㷨Ĵ󷶇cՔľֲYϘµȫփĿǰдоĆ}֮һ@NϲԿԏĸz㷨ӋīI[5]ţDRɭz㷨Ms̆}īI[6]½cz㷨YρBm΢}ȡõӋЧDzmڲ΢}

Powell븡caz㷨Powellcx׃ƽеһmⲻ΢}Ļz㷨ԓ^ýQz㷨Ք}ֵϷЧMC

2  z㷨

    az㷨еҪ}cMƾa^ڸcaz㷨оȸڴgăccaԽԽܵҕ[7]?Ƿ[ЈA΢ӇI?/span>(1)ʽ ׃  քeǵ ׃ ½ϽPowellǶ뵽caz㷨õ↖}(1)»z㷨

             min            (1)

    step1 oz㷨xֵ@ЩNȺҎģm׃npc׃pmMPowellĸpPowellzӋST

       Step2 SCaʼȺwӋmֵȵiwmֵȡfi=fmax - fifiǵiwĿ˺ֵfmax鮔ǰNȺɆTĿ˺ֵi=1,2,,mGoldbergԱ׃Qģ[2] ʽ(2)M

fi= afi+b fi  ³ 0                      (2)

    step3 бxMx

    step4 gMнxăɂĸw gaăɂӴ  [01]ϵSC1 , 

    step5 ո зǾ׃[8]w Ԫ x׃ t׃Y  

                              (3)

                               (4)

؅^g[ , ]һֵʹ 0ĸS Ӷ@һ|ʹڳʼAξgںAηdzֲ [ , ]֮gSC  QǾȵϵy

    step6 ÿwոpPowellMPowellw xMPowellt ʼcPowell  tӋY Ӵ t ȡ =  ȡ = 1 

    step7 Ӌむwmֵw

    step8 ДǷKֹӋlMtDstep3MtݔӋY

os}һNֱӷPowellӋ^݆Mÿһ݆֪nһcȻر݆ijʼccԓcBM@һAεcȡǰn֮һ_ʼһAεĵ˱㷨nǾԟoPC㷨ՔQҎtMиMڻϷӋ㲽Estep6в[9]еĸMPowell^£

    (1) ׃xֵ nԟoPn , ,, S`>0k=1

    (2)  lط , ,, һSõc , ,, ָmʹ - =max { - }  tPowellӋYt(3)

    (3) ʹ =min  = =  tPowellӋYc t(4)

    (4)  t ( )Ȼ D(2)

3 

    T  [-500,500] 


D1 f(x)ʾD

f(x)ஔĘOСc,ȫ֘OСc =-420.97 =1,2,, ֵ-837.97c ={( , ,, ) =-420.97, , =302.52} =1,2,, ΃ֵ-719.53׃n=2rf(x) D1ʾƺ\ЭhFortran Power Station 4.0SCɃȲSCaڱv133΢C\

øMPowellӋ100ֵڅ^g[-500,500]SCaֻ6ΣԸ0.06ȫӋɹĸʘO

HollandĘ˜ʣ򺆆Σz㷨cǶMƾaـ݆x񷽷SC䌦һcȺwSͬĂwȡNȺҎģm=30pc=0.95׃pm=0.05MT=1000ÿ׃ôLL=16ĶMӴʾMƾaȸcaz㷨Ӌ㾫ȵژ˜z㷨Ŀ˺С-800ɹ˜z㷨\100ȡMT=200r40ΣԸ0.40ȫƽӋrg0.51ȡT=500r51ΣԸ0.51ȫƽӋrg1.13

ñĻϷӋȡm=30 pc=0.85pm=0.2T=100MPowellĸpPowellȡֵͬϷ\100ӋYҊ1@жOֵӋpPowell=0.3rϷȫȫĜʴ_ֵǴ˕rϷӋrgs˜z㷨ȡT=500rӋrg4/5ĸcaz㷨ȡm=30pc=0.85pm=0.2T=100\10082ΣԸ0.82ȫ1PPowell =0ʾӋrgs˜z㷨ȡT=500rӋrg1/8ȫĸʅshhژ˜z㷨

1  pPowellȡֵͬrϷӋY

PPowell

0.0

0.02

0.05

0.1

0.2

0.3

ĴΔ

82

85

89

94

98

100

ĸ

0.82

0.85

0.89

0.94

0.98

1.00

ƽӋrg/

0.14

0.20

0.31

0.47

0.68

0.87

4  YZ

ᘌ΢ȫփ}һNPowellccaz㷨YϵĻz㷨ԓ㷨z㷨ȫփăݺPowellֲ^cȫֽĸӋYϷz㷨PowellԿɿжֲOֵĺ}ȫֽӋֻõֵϢĻϷHmڲ΢}ҲmϿ΢ȫփ}

 

īI

[1]  O֣z㷨ԭ[M]I1999

[2]  Goldberg D E. Genetic algorithms in search, optimization and machine learning[M]. Reading, Ma: Addison Wesley,1989

[3]  ϑcZlPGenetic㷨оìF[J]AW199535(5)4448

[4]  ԕܼoɣz㷨ՓоC[J]cQ200015(3)263268

[5]  Lin WDelgado-Frias J GHybrid Newton-Raphson genetic algorithm for traveling salesman problem[J]. Cybernetics and systems, 199526(5)387-412

[6]  wBm΢ȫփĻz㷨[J] cQ199712(5)589592

[7]  Goldberg D EReal-Code Genetic Algorithm,Virtual Alphabets and Blocking[J]. Complex Systems19915139-167

[8]  Michalewicz ZA modified genetic algorithm for optimal control problems[J]Computers math. Application1992231283-94

[9]  ꐌ֣Փc㷨[M]AW1989

[10]    t÷ȫ^ϵyCϷо[D]BWʿWλՓ1998

Hybrid approach for global optima of indifferentiable nonlinear function

WANG Denggang,  LIU Yingxi,  LI Shouju

 ( Dept. of Eng. Mechanics., Dalian Univ. of Technol. Dalian, 116024)

Abstract  A hybrid computational intellective algorithm for locating the global optima of indifferentiable nonlinear function was put forward by setting the Powell algorithm in real-code genetic algorithm. The hybrid approach improved the local searching ability of the genetic algorithm and promoted the probability for the global optima greatly. Because only the objective values are used, the hybrid approach is a generalized genetic algorithm for global optima of differentiable and indifferentiable nonlinear functions.

Key words  global optimahybrid approachgenetic algorithmsPowell algorithm

       T   -500:2:500       (9)

 


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