改进的混沌粒子群算法(总结)

•qÆÒµ2013210040󰀃󰀂ÆÒµ2013210047

2014c4󰀆12F

Á‡µ󰀂éDÚ󰀇IOâf+Ž{£standardparticleswarmalgorithm))SPSO¤@Ù!´€\\ÛÜ•`󰀇\"€§ò·bK\\󰀅IOâf+Ž{¥§|^·b$Ä󰀇H{5!‘Å59éЊ󰀇¯a5󰀈A:§ÀJÜ·󰀇·bN󰀃J󰀂SPSOЩ«+§¦âfþ!©Ù3)˜m.󰀃SPSO€\\@Ùž§U?󰀇·bâf+Ž{£GCPSO¤3•`)±Œ󰀇«•S?1·b|¢§󰀂“󰀂5«+¥󰀇Ü©âf§‘+«+aÑÛÜ•`§?˜ÚJp󰀂OŽ°ÝÚÂñ„ݧ±9󰀄ÛÏ`Uå.3dÄ:þ§òGCPSOA^󰀅°edÎ󰀇´‚5y¯K§ò´‚5y¯K=z¤‘k^‡󰀄å󰀇•`z¯K?1¦).

˜!U?󰀇·bâf+Ž{£GCPSO¤󰀇gŽ1.IO󰀇âf+`zŽ{

âf+`zŽ{´KennedyÚEberhartu1995cJÑ󰀇˜«œU`zŽ{.âf+Ž{£SPSO¤󰀃uéj+Ú~+󰀈+N$Ä1•󰀇ïħÏd§Ú¬+Ž{˜󰀃Ñk+œU󰀇A:.du§{ü§Âñ„ݯ§¿…é8I¼ê‡¦󰀄󰀂£~XÃIFÝ&E¤󰀈A:§®²¤•˜«-‡󰀇󰀄Û`zóä.

3SPSO󰀇󰀂.¥§`z¯K󰀇z‡)éA|¢˜m«󰀇˜•j§¤•âf§z‡âfk˜‡„Ýû½§œ‹󰀇••Úål.SPSOЩz•˜+‘Åâf§,󰀂âfm©J‘󰀃c󰀇•`âf$ħ†󰀅3󰀃‡)˜m¥|¢󰀅•`)•Ž.3zgS“¥§âfÏLJlü‡4Š5•#gCµ˜‡´âfgC8cé󰀅󰀇•`)§¡•‡N4Špi;,˜‡´󰀃‡âf8cé󰀅󰀇•`)§¡•󰀄Û4Špg.b󰀄˜‡d‘8I|¢˜mS§dN‡âf|¤˜‡«+§xi=(xi1,xi2,...,xid)L«1i‡âf§§î8²{󰀇•Ð ˜L«pi=(pi1,pi2,...,pid),󰀂󰀃‡«+8c²{󰀇󰀇•Ð ˜L«pg=(pg1,pg2,...,pgd)§âfi󰀇„Ývi=(vi1,vi2,...,vid).UJ‘󰀃c•`âf󰀇󰀂n§âfiòUeªUC„ÝÚ ˜§=µ

1

£1¤

vij(t+1)=ω(t)vij(t)+c1r1(pij(t)−xij(t))+c2r2(pgj(t)−xij(t))£2¤

xij(t+1)=xij(t)+vij(t+1)

Ù¥t•󰀃c󰀇?z“ê§c1,c2•ÆSÏf§r1,r2•0u(0,1)ƒm󰀇‘Åê§ω•.5󰀃-§ïÄL²󰀄Œ󰀇ωk|uaÑÛÜ4󰀂:§󰀄Û|¢Uå󰀄r¶󰀄󰀂󰀇ωk|uŽ{󰀇ÂñÚJp)󰀇°Ý§ÛÜ|¢Uå󰀄r.

SPSOáuk󰀄•.󰀇‘Å5éuªŽ{§3¦)E,•`z¯Kž§zg¦)(JŒUØÓ§•ŒUéØ󰀅󰀄Û•`)§•3´€\\ÛÜ•`:§Ñy@ÙÂñ󰀇\":.

2.·bA5

8cé·bÿÃî‚󰀇½Â§˜„d(½5•§󰀆󰀅󰀇äk‘Å5󰀇$ÄG󰀂¡•·b§¥y·bG󰀂󰀇Cþ¡•·bCþ.8c󰀇·b󰀂.kéõ§'󰀄ˆ‡󰀂.󰀇A:§LogisticN󰀃¼êk󰀄Ð󰀇5Ÿ§Ù󰀂.µ

£3¤

zn+1=ηzn(1−zn)

N󰀃󰀇½Â••[1,1]§…Ø•\"§η=4§dN󰀃'󰀄{ü…´uOŽÅOŽ.

·bXÚ•,mq‘ŧ󰀂§.¾´d(½•§󰀄Ñ󰀇§ÏdäkAÏ󰀇$Ä5Ƨ̇Ly•‘Å5!H{5ÚéЊ󰀇¯a5.

‘Å5µ§©ªÛ•3k•«•…;,[Ø-E.

H{5µlnØþ§²L󰀄•žm󰀇S“±󰀂U󰀂H{«mS󰀇¤kŠ.‘Xžm󰀇í£§·b$Ä󰀇;,ýØÏ33,˜G󰀂§󰀂´H{«•˜m¥z˜:§|^dA5Œ±?1`z|¢.

éЊ󰀇¯a5µÏL¢󰀂L²§ØÓ󰀇ЊÀ󰀂§‘Xžm󰀇í£§LyшgÕá󰀇žmüz.

3.âf+Ž{@Ùy–󰀇󰀂½

|^«+󰀇󰀇·AÝ•󰀂Ú²þâå5󰀂½«+´ÄÑy@Ùy–.²þâåµ

2

D(t)=

NL

󰀆N󰀅N󰀅󰀂1󰀂󰀄(p

i=1

d=1

id

−pd)2

L•|¢˜mé󰀃•Œ•Ý§N•«+5󰀂Œ󰀂§pdL«¤kâf1d‘‹IþŠ.²þâåD(t)Lˆ󰀂«+ˆ‡Nƒpƒm󰀇©ÙlѧÝ.D(t)󰀅󰀂§L««+󰀅8¥¶D(t)󰀅Œ§L««+󰀅©Ñ.

·AÝ•󰀂µ

‘X«+󰀇Øä?z§‡Nƒm󰀇󰀂É󰀅5󰀅󰀂§󰀂‡N ˜û½X‡N󰀇·AÝ£8I¼êŠ¤Œ󰀂.

N󰀂fi−favg2

)σ=(2

i=1

f

f•8˜z½IÏf§ÙŠ^´•›·AÝ•󰀂σ2󰀇Œ󰀂§f󰀇󰀂Šæ󰀂Xeúªµ󰀃max|fi−favg|>1§f=max1≤i≤N|fi−favg|¶󰀃max|fi−favg|>1•Ù¦Š§f=1.+N·AÝ•󰀂σ2‡N󰀇´«+¥‡N/à8§Ý.σ2󰀅󰀂§«+¥‡N󰀇à8§Ý󰀅Œ¶‡ƒ§à8§Ý󰀅󰀂.

«+󰀇·AÝ•󰀂l¼êŠ•¡‡Nâf©Ùœ¹§󰀂²þâål˜m󰀃݇Nˆ‡‡Nƒpƒm󰀇©ÙlѧÝ.Ïd§Óžæ^ü«üÑ5󰀂äŽ{´Ä€\\Ê¢.

4.·bâf+`zŽ{£CPSO¤

󰀃âf?\\@Ùž§|^·b|¢5aÑÛÜ•`.·b|¢󰀇̇gŽ¶󰀃âf€\\ÛÜ•`:ž§Äk󰀃)˜Ð©·bCþ§,󰀂|^LogisticN󰀃¼ê󰀃)·bS󰀄§¿rz‘󰀇󰀇·bCþC†󰀅`zCþ󰀇󰀂Š«m§P¹|¢󰀅󰀇•`Š§†󰀅ˆ󰀅·b|¢󰀇•Œ“꧕󰀂2‘Å󰀂“˜‡âf§±O\\Ùõ󰀃5.

·bâf+`zŽ{󰀇äNgŽ´µÄk$1âf+Ž{󰀇Ä󰀃öŠ§†󰀅âf€\\@ÙG󰀂§,󰀂2?1·b|¢§l󰀂Ú󰀄âf¯„aÑÛÜ•`\\¯Âñ.

Ž{󰀇äN6§Xeµ

step1.Щzëê.󰀄½ÆSÏfc1,c2∈(0.5,2.5)§•Œ.5󰀃-ωmaxÚ•󰀂.5󰀃-ωmin§•Œ?z“êkmax§„Ýþ•vmax±9·b|¢S“gêM.

step2.Щz˜+âf§󰀃)‘Å ˜Ú„Ý.

step3.µdz‡âf󰀇·AÝŠ£=8I¼êŠ¤§•#‡N4ŠpiÚ󰀄Û4Špg.step4.OŽâf󰀇²þâåD(t)Ú·AÝ•󰀂σ2.XJD(t)<α½σ2<β£α,β•ýk‰½󰀇KŠ¤§KÑy@Ùy–§?1·b|¢=step5¶ÄK=step6.

3

step5.·b|¢.‘Å󰀃)˜·bCþY0§2|^£3¤ª󰀃)·bS󰀄Yn§¿|^

󰀄§†󰀅·bS“gên>M,2^·b|£4¤ªòÙC†󰀅`zCþ󰀇󰀂Š«m󰀆󰀅Yn

¢󰀅󰀇•Ð󰀇Œ1:Y∗‘Å󰀂“˜‡âf§,󰀂=step6.

‘ÅЩŠY0=(y0,1,y0,2,...,yo,d),…z˜‘‰Œ3[1,1]§£4¤

󰀄

y0j=

bj−aj

pgj,j=1,2,...,d2

󰀄,y󰀄,...,y󰀄)§Ù¥a,b•1j‘`zCþ󰀇󰀂Š‰Œ.󰀆󰀅Y0󰀄=(y0jj.10.20.d

step6.|^£1¤ªÚ£2¤ª•#âf󰀇 ˜Ú„Ý.Ù¥

ωmax−ωmin

kmax

ω(t)=ωmax−t

step7.󰀂äÂñ^‡.e÷v§K=step8¶ÄK§=step3.step8.?zL§(姈£󰀄Û•`).5.U?󰀇·bâf+Ž{£GCPSO¤

U?󰀇·bâf+Ž{£GCPSO¤󰀇Ä󰀃gŽµ3󰀂kŽ{󰀇Ä:þ§é.5󰀃-ÚÆSÏf?1N󰀃µ-#½ÂÆSÏf§é.5󰀃-\\\\š‚5σ§?󰀂¦󰀆U?󰀂󰀇·bâf+Ž{•¯Âñ§Ž{°(Ý?˜ÚJp.

\\\\š‚5σ󰀇.5󰀃-ω

kkmax

ω=(ωmax−ωmin)(1−

)m+ωmin

ëêm∈[2,∞]§•Œ.5󰀃-ωmax§•󰀂.5󰀃-ωmin§•Œ?z“êkmax§󰀃c?z“êk.󰀃m󰀄󰀂§ω󰀇CzÇ󰀄Œ§dž·ÜåÐ󰀂󰀃󰀇󰀄Û|¢¶󰀃m󰀄Œ§ω󰀇CzÇ󰀄󰀂§ù󰀃󰀂󰀇CzÇéuE,󰀇•`z¯K±9󰀂ÏS“󰀇ÛÜ|¢§󰀃JwÍ.Ïd§\\\\š‚5σ󰀇.5󰀃-ω§Jp󰀂Ž{󰀇„Ý.

-#½Â󰀇ÆSÏfc1,c2∈(0.5,2.5)

kkmaxkkmax

c1=c1c+(c1m−c1c)(1−

)

c2=c2c+(c2m−c2c)(1−

)

c1c,c2c,c1m,c2m‰½󰀇ëê.-#½Â󰀇ÆSÏf§Ø2´󰀃½ØC󰀇ê§󰀂´‘kCz󰀇§ù󰀃?˜ÚJp󰀂Ž{󰀇󰀄Û|¢U姕¯󰀇|󰀅󰀄Û•`).

4

äNÚ½6§µÓ·bâf+Ž{Ú½£æ^\\\\š‚5σ󰀇.5󰀃-Ú-#½Â󰀇ÆSÏf¤.

ÏLnر9ꊢ󰀂󰀇󰀂y§U?󰀇·bâf+Ž{£GCPSO¤²w`uIO󰀇âf+Ž{§Âñ•¯§OŽ°Ý•p.

󰀃!GCPSO󰀇A^))°edÎ󰀇´‚5y

Ye󰀂Ï󰀇´‚5y´󰀃cïÄ9:§8󰀇´•󰀂¼󰀆{'󰀇•á´‚§Ù¦)•{kµä|¢•{£treesearchalgorithm¤§TŽ{Âñú§´€\\ÛÜ•`§Ø´ˆ󰀅ýÏ󰀃J.󰀂|^GCPSO¦)•á´‚󰀃J•`.

¦)gŽµ

A.n‘˜mpïá󰀂[󰀇°.//§=˜m êd=3.B.z‡dÎwŠâfi(i=1,2,...,N).C.•á´‚•8I¼êf=min•`§=‡N4Š§lpipi+1=󰀇ål.

D.•(󰀂Ê1´‚󰀇S󰀄§I÷vS󰀄5^‡µa.z‡âf󰀇󰀅ÝHi≥S󰀄Ê1󰀇•󰀂󰀅ÝHmax.b.Ê1´‚ØU†°.ƒ󰀂§=z‡âf󰀇󰀅ÝŒu¤3°.󰀇󰀅ݧâfƒm󰀇ë‚ØU†°.ƒ󰀂.

E.󰀄½Ð©:Q0=(x0,y0,z0)Ú8I:Qn=(xn,yn,zn)§òQ0QnŠn󰀈©§…ŠR†x¶󰀇n‡²¡£3󰀈©:?¤.z‡âf󰀇Щ ˜ÚЩ„ݑʼn½.

F.Щâf+¥󰀇z‡âf󰀇󰀅݇pu¤3°. ˜󰀇󰀅ݧÄK¿ïT:§†󰀅¤kЩâf󰀇󰀅ÝÑpu¤3°. ˜󰀇󰀅Ý.

G.ë󰀅ü‡ƒ󰀅󰀇âf§󰀂äz‡©ãlpipi+1´ÄÚ°.ƒ󰀂§XJƒ󰀂§K¦ü‡âf󰀇z‹I󰀇ŠO\\1‡ü •Ý§?󰀂UY󰀂ä´Äƒ󰀂§XJ„´ƒ󰀂§KUYO\\ü •Ý§†󰀅©ã؆°.ƒ󰀂.

H.|^GCPSOOŽz‡©ãlpipi+1§?󰀂OŽÑ¼êŠf§=âf󰀇·AÝŒ•§•󰀂S“^|§󰀄½„Ýþ•vmax†e•vmin,󰀃„Ývi(t+1)>vmax§vi(t+1)=vmax¶󰀃„Ývi(t+1)G.󰀂ä´Ä÷vÂñ^‡§XJ÷vKÊŽ§é󰀅•á´‚¶XJØ÷v§KUYS“.

ÏLꊢ󰀂󰀇󰀂[§Œ±󰀆ѧ|^GCPSO¦)󰀇󰀃JéЧ󰀆󰀅󰀇•á´‚•{'Œ‚.

5

󰀃

󰀁N−1

i=0

lpipi+1,pi=(xi,yi,zi)L«âfiî8é󰀅󰀇

(xi+1−xi)2+(yi+1−yi)2+(zi+1−zi)2´pi,pi+1ü: