comparison between evolutionary programming and particle swarm optimization

7/29/2019 Comparison Between Evolutionary Programming and Particle Swarm Optimization

1/6

C o m p ar i s on b e tw e e n G e n e t ic A l gor it h m s an d P ar t i cl eS w a r m O p t im i za t io nR u s s e l l C . E b e r h a r t a n d Y u h u i S h i

Depa rtment o f Electrical EngineeringIndiana University Purdue University Indianapolis723 W . Michigan St., SL160Indianapolis, IN 4620 2eberhart,[email protected]

A b s t r a c tThis paper compares two evolutionary computation paradigms: genetic algorithms and particleswarm optimization. Th e operators of each paradigm are reviewed, focusing on how each affectssearch behavior in the problem space. The goa ls of the paper are to provide additional insightsinto how each paradigm works, and to suggest ways in which performance might be improvedby incorporating features from one pa radigm into the other.Introduct ionF o u r w e l l - k n o w n p a r ad i g ms cu r r en t l y ex i s t i n ev o l u t i o n a r y co mp u t a t i o n : g en e t i ca lgor i t hms [5 ] , evo lu t iona ry p rog ram m ing [4 ], evo lu t ion s tr a t eg i es [9 ] , and gene t i cp r o g r am mi n g [ 8 ]. A n ew ev o l u t i o n a r y co mp u t a t i o n tech n i q u e , c a l l ed p a r t i c le s w ar mo p t i mi za t i o n ( P S O ) , i n s p i r ed b y s o c i a l b eh av i o r s i mu l a t i o n , w as o r i g i n a l l y d e s i g n edan d d ev e l o p ed b y Eb e r h a r t an d K en n ed y [ 2 ,3,6 ,7 ] . I n P S O , i n s t ead o f u s i n g m o r et r ad i ti ona l gene t i c opera to r s , each par t i c l e ( i nd iv idua l ) ad jus ts i t s " f l y in g" acco rd ing toi ts o w n f l y i n g ex p e r i en ce an d i ts co m p an i o n s ' f l y in g ex p e r i en ce .Th i s p ap e r co mp ar e s g en e t i c a l g o r i t h ms an d p a r t i c l e s w ar m o p t i mi za t i o n . O p e r a t o r st ha t a re u s e d b y e a c h p a r a d i g m a re r e v ie w e d . T h e f o c u s is o n h o w e a c h o p e r a t o r a f f e c tst he p a r a d i g m ' s b e h a v i o r i n t he p r o b l e m s p ac e .T h e r e a r e, o f c o u rs e , m a n y w a y s t o i m p l e m e n t a g e n e t i c a lg o r i th m ( G A ) . R e g a r d l e ss o ft h e s p ec i f ic i mp l eme n t a t io n , i t is g en e r a l l y ag r eed t h a t G A s u t il iz e o n e f o r m o r an o t h e ro f t h r ee o p e r a t o rs : s e l ec ti o n , c ro s s o v e r , an d m u t a ti o n . W e w i l l ex am i n ei mp l em en t a t i o n s o f t h e s e o p e r a t o rs , an d co m p ar e t h em w i t h P S O o p e r a t o rs . I n t h isp ap e r , i t c an b e a s s u m ed t h a t, i n mo s t c a s e s , a b a s ic , b i n a r y v e r s i o n o f a G A i s b e i n gr e f e r r ed t o , s u ch a s t h e " p l a i n v an i l l a " G A i n [2 ] o r th e e l em en t a r y G A 1 -1 i n [ 1 ].Th e au t h o r s r ead i l y co n ced e t h a t f ew ap p l i ca t i o n s u s e t h e s e b a s i c G A co n f i g u r a t i o n s ,an d a n u m b er o f mo d i f i ca t io n s t o t h e s e co n f i g u r a t io n s a r e a l so ex am i n ed . I t s h o u l d b en o t ed th a t i t i s n o t t h e g o a l o f th i s p ap e r t o co m p ar e G A s an d P S O i n o r d e r to d ec l a r eo n e o r t h e o t h e r a s s o m eh o w b e t t er . R a t h e r , t h e g o a l s a r e t o p r o v i d e i n s ig h t s i n t o h o wG A s a n d P S O w o r k , a n d t o su g g e s t w a y s i n w h i c h p e r f o rm a n c e m i g h t b e e n h a n c e d b yi n co r p o r a t in g f ea t u r e s f r o m o n e p a r ad i g m i n to t h e o t h e r .


2/6

612

AnalysisI n P S O , a p a r t i c l e is an a lo g o u s t o a p o p u l a t i o n me m b er ( ch r o m o s o m e) in a G A . L i k e aG A ch r o mo s o me , a p a r t i c l e r ep r e s en t s a can d i d a t e s o l u t i o n t o t h e p r o b l em b e i n gad d r e s s ed . E ach p a r t i c le i s t r e a t ed a s a p o i n t i n th e D - d i m en s i o n a l p r o b l em s p ace . Th ei th par t i c l e i s r ep resen t ed as X~ = (Xil ,Xi2 . . . . X io) . T he b es t p r ev i o u s p o s i t i o n ( t h ep o s i t i o n g i v i n g t h e b e s t f it n e s s v a l u e ) o f t h e i t h p a r t ic l e i s r eco r d ed an d r ep r e s e n t ed a sP 1 = ( P i l , P i2 , . . . . P i D ) . Th e i n d e x o f t h e b e s t p a r ti c l e amo n g a ll t h e p a r t ic l e s i n t h ep o p u l a t i o n is r ep r e s en t ed b y t h e s y m b o l g . Th e r a te o f t h e p o s i ti o n ch an g e ( v e l o c i t y )fo r par t i c l e i i s r ep re sen t ed as VI = (v il , v i2 . . . . V iD). T he p a r t i c l e s a r e man i p u l a t edacco r d i n g t o t h e f o l l o w i n g eq u a t io n s :v i a = w * v i a + c l * r a n d O * ( p i d - x i a ) + c 2 * R a n d O * ( p g a - X i a ) ( I )Xid = Xid + Vid (2 )B y ad d i n g t h e i n e rt ia w e i g h t w i n t o P S O , a n ew v e r s i o n o f P S O i s in t r o d u ce d in [ 1 0] .Th e i n e r t ia w e i g h t w is em p l o y ed to co n t r o l t h e i mp ac t o f t h e p r ev i o u s h i s t o r y o fv e l o c i t ie s o n t h e cu r r en t v e l o c i t y , t h e r eb y i n f lu en c i n g t h e t r ad e - o f f b e t w een g l o b a l( w i d e - r an g i n g ) an d l o ca l ( f in e - g r a i n ed ) ex p l o r a t i o n ab il it ie s o f t h e " f l y i n g p o i n t s . " Al a r g e r i n e r t i a w e i g h t f ac i l i t a t e s g l o b a l ex p l o r a t i o n ( s ea r ch i n g n ew a r ea s ) w h i l e as ma l l e r i n e r t i a w e i g h t t en d s t o f ac i l i t a t e l o ca l ex p l o r a t i o n t o f r ee - t u n e t h e cu r r en ts ea r ch a r ea . S u i tab l e s e l ec t i o n o f t h e in e r t ia w e i g h t p r o v i d es a b a l an ce b e t w e en g l o b a lan d l o ca l ex p l o r a t i o n ab il it ie s an d t h u s r eq u i r e s f ew er i te r a t io n s o n av e r ag e t o f i n d t h eo p t i m u m [ 1 0 ] . ( I n s o m e w a y s , t h e n a m e d a m p i n g w e i g h t m i g h t b e m o r e d e s c ri p ti v e ,b u t t h e t e r m i n e r ti a w e i g h t i s u se d i n t h i s paper . )I n a G A , each o f t h e t h ree m a i n c l a s s e s o f o p e r a t i o n s ( s e lec t i o n , c ro s s o v e r , an dm u t a t i o n ) c a n b e i m p l e m e n t e d i n a n u m b e r o f w a y s . P S O d o e s n o t l a b e l it s o p e r a ti o n si n th e s am e w ay a s G A s , b u t an a l o g i e s ex is t. Th es e an a l o g i e s d ep en d , o f co u r s e , o n t h ei mp l eme n t a t i o n o f th e G A o p e r a t io n . C o m p l i ca ti n g an y c o m p ar i s o n s i s th e f ac t th a t t h ee f f ec t s o f t h e v a r i o u s o p e r a t i o n s o f t en v a r y o v e r th e co u r s e o f a r u n . ( A r u n i s d e f m e das t h e t o ta l n u m b er o f g en e r a t i o n s o f t h e G A p r i o r to t e r mi n a t io n . T e r m i n a t i o n u s u a l l yo ccu r s e i t h e r b ecau s e a p r e s c r i b ed f i t n e s s l ev e l h a s b een ach i ev ed b y a t l e a s t o n em e m b e r o f t h e p o p u l a ti o n , o r b e c a u s e t h e m a x i m u m n u m b e r o f g e n e r a ti o n s a l lo w e dh a s b e e n r e a c h e d .)E f f ec t s o f G A c r o s s o v e r , f o r ex am p l e , u s u a l ly v a r y s i g n i f i can tl y d u ri n g a r u n . A t t h eb eg i n n i n g , t h e p o p u l a t i o n mem b er s a r e u s u a l l y r an d o m i zed , s o t h a t c r o s s o v e r can h av es i g n i fi can t e ff ec t s , m o v i n g a ch r o m o s o m e a r e la t i v e l y l a r g e d is t an ce i n p r o b l e m s p ace .T o w a r d t h e e n d o f a ru n , a p o p u l a t io n h a s o f t e n c o n v e r g e d , m e a n i n g t h a t m a n y , i f n o tmo s t , ch r o m o s o m es h av e s i m i la r s t ru c t u re s . C r o s s o v e r th en u s u a l l y h a s l e s s e f f ec t, an dt h e r e s u lt i n g mo v em en t s a r e r e l a t iv e l y s ma l l e r. A d d i n g an o t h e r l ay e r o f co m p l ex i t y ist h e f ac t t h a t th e p r o b ab i l i t y o f c r o s s o v e r is s o m e t i mes v a r i ed d u r i n g a r u n , o f t ens t a r t ing o u t a t wi th a r e l a t i ve ly l a rge p robab i l i ty , and en d ing w i th a sma l l e r one .P S O d o e s n o t h a v e a c r o s s o v e r op e r a ti o n. H o w e v e r , t h e c o n c e p t o f c r o s s o v e r isr ep r e s en t ed i n P S O b ecau s e each p a r t i c l e i s s t o ch as t i ca l l y acce l e r a t ed t o w ar d i t s o w np r ev i o u s b e s t p o s i ti o n , a s w e l l a s t o w ar d t h e g l o b a l b e s t p o s i t i o n ( o f t h e en t i r e


3/6

6 1 3

p o p u l a t i o n ) o r th e n e i g h b o r h o o d ( l o ca l ) b e s t p o s i ti o n , d ep en d i n g o n t h e v e r s i o n o f P S Ob e i n g u s ed .

Th e c r o s s o v e r co n cep t is a l s o ap p a r en t i n t h e b eh a v i o r o f p a r t i c le s t h a t ap p ea ra p p r o x i m a t e l y m i d w a y b e t w e e n " s w a r m s " o f p a r ti c le s t h a t a r e c l u s te r in g a r o u n d l o c a lb es t p o s i t i o n s , o r , o ccas i o n a l l y , b e t w een s u cces s i v e g l o b a l b e s t p o s i t i o n s . Th es ep a r t i c l e s s eem t o b e ex p l o r i n g ( f o r a s h o r t t i me , an y w ay ) a r eg i o n t h a t r ep r e s en t s t h eg e o m e t r i c m e a n b e t w e e n t w o p r o m i s in g r e g io n s .B e c a u s e o f th e g e o m e t r i c " f e e l " o f w h a t h a p p e n s i n P S O , i t m a y , i n f a ct , b e m o r ean a l o g o u s t o t h e r eco mb i n a t i o n o p e r a t o r i n ev o l u t i o n s t r a t eg i e s [ 9 ] . Th e f ac t t h a tr eco m b i n a t i o n o ccu r s o n a p a r am e t e r - b y - p a r a m e t e r b a s is ( r eco m b i n a t i o n is l i m i t ed top a r am e t e r b o u n d a r i e s ) f u r t h e r s u p p o r t s th i s an a l o g y .Th e e f f ec t o f mu t a t i o n d u r i n g t h e ru n o f a G A t en d s t o b e o p p o s i t e t o th a t o f c r o s s o v e ri n th a t mu t a t i o n t en d s t o h av e l es s i mp ac t n ea r t h e b eg i n n i n g o f a r u n , an d m o r e n ea rt h e en d . T h a t i s b ecau s e t h e i n i ti a l p o p u l a t i o n is r an d o m i zed , s o f l i p p i n g a b i t h e r e an dt h e r e n ea r t h e b eg i n n i n g m ay n o t ch an g e t h i n g s a s d r am a t i ca ll y a s f l ip p i n g b it s n ea r t h een d o f a r u n , w h en t h e p o p u l a t i o n h as co n v e r g ed . I f th e m u t a t i o n r a te i s v a r i ed d u r i n g ar u n , i t i s co mmo n t o u s e a r e l a t i v e l y s ma l l v a l u e i n t h e b eg i n n i n g , an d i n c r ea s e i tt o w ar d t h e en d .I t i s t h eo r e t i ca l l y p o s s i b le f o r a G A ch r o m o s o m e to r each an y p o i n t i n th e p r o b l ems p ace v i a m u t a t io n . I t i s, h o w ev e r , u n l i k e l y , p a r ti cu l a r ly n ea r t h e en d o f a r u n . T h i s i sb e c a u s e a n u m b e r o f m u t a t i o n s m a y b e n e e d e d t o r e a c h a d i st a nt p oi n t. S i n c e m u t a t io nr a te s a r e t y p i ca l l y q u i te l o w ( 0 .1 - 1 .0 p e r ce n t is a co m m o n r an g e ) , s ev e r a l g en e r a t io n so f f a v o r a b le m u t a ti o n s m a y b e n e e d e d . N e a r t h e e n d o f a r u n , h o w e v e r , w h e n t h ep o p u l a t i o n h as co n v e r g ed an d t h e av e r ag e f i t n e s s v a l u e i s h i g h , mu t a t i o n w i l l q u i t el ik e l y r e s u l t in a l o w - f i tn e s s c h r o m o s o m e t h a t d o es n o t s u r v i v e t h e s e l ec t i o n p r o ces s . I nf ac t , t h e p r o b ab i l i t y o f s u r v i v a l d ec r ea s e s g eo me t r i ca l l y w i t h g en e r a t i o n s . S o ev ent h o u g h a n u m b er o f mu t a t io n s w o u l d b r i n g th e ch r o m o s o m e in t o a h i g h - fi tn e s s r eg i o n ,t h e c h r o m o s o m e n e v e r g e ts t h e r e b e c a u s e i t d o e s n ' t s u r v i v e s e l ec t io n .S o , ev en t h o u g h a G A i s t h eo r e t i ca l l y e r g o d i c ( t h e r e ex is t s a n o n - ze r o p r o b a b i l i ty t h a t ach r o m o s o m e can o ccu p y an y s t a te ) , it is n o t e r g o d i c i n a p r ac t ica l s en s e b ecau s e o f t h emu l t i p le s tep s r eq u i red . A n ev o l u t i o n a r y p r o g r am m i n g ( EP ) s y s t em i s tr u l y e r g o d i c ,s i n ce t h e r e i s a f i n i t e p r o b ab i l i t y t h a t an i n d i v i d u a l c an r each an y p o i n t i n p r o b l ems p ace w i t h o n e j u m p ( i n o n e g en e r a t io n ) .T h e b e h a v i o r o f P S O s y s te m s s e e m s t o f a ll s o m e w h e r e b e t w e e n G A a n d E P s y s te m s i nt h is a r ea . I t m ay b e t h a t a P S O p a r t ic l e can n o t r each an y p o i n t in p r o b l em s p ace i n o n ei te r a t io n , a l t h o u g h t h i s m i g h t b e p o s s i b l e a t t h e b eg i n n i n g o f th e r u n , g i v en s u f f i c i en t l yl a rge Vmax. B u t s i n ce p a r t i c l e s s u r v i v e i n t ac t f r o m o n e i t e r a t i o n t o t h e n ex t , an yp a r t ic l e can ev en t u a l l y g o an y w h er e , g i v en en o u g h i te r a ti o n s. A s t r o n g e r ca s e can t h u sb e m a d e f o r th e e r g o d i c i ty o f P S O t h a n f o r G A s .B ec au s e e ach p a r t i c le h a s a v e l o c i t y , P S O mu t a t io n - l i k e b eh av i o r i s d i r ec ti o n a l , w i t h ak i n d o f m o m e n t u m b u i lt i n, e s p e c i a l ly i f usebest i s a c t i v a t ed o n t h e co m m an d l i n e . G A


4/6

614

m u t a t i o n i s g en e r a l l y co n s i d e r ed t o b e o m n i d i r ec t io n a l i n th a t an y b i t i n an i n d i v id u a lcan b e f l i p p ed . ( S o m e G A m u t a t i o n o p e r a to r s , s u ch a s b i t p o s i t i o n - b as ed mu t a t i o n , c ana f f ec t t h e d i r ec t i o n a li ty . ) EP m u t a t i o n i s a l s o o mn i d i rec t i o n a l , an d i n c l u d es c o n t r o l o fm u t a t io n s e v e r it y o n a p a r a m e t e r - b y - p a r a m e t e r ba si s. T h e d i f fe r e n c e b e t w e e n pbestan d t h e p r e s en t l o ca t i o n h as s o m e o f t h is s ame f l av o r , b u t t h e m ax i m u m v e l o c i t y is t h es ame f o r a l l p a r ame t e r s .Th e e f f ec t o f s e l ec t i o n in a G A i s to s u p p o r t th e s u r v i v a l o f t h e f it te s t, a c o n c ep t cen t r a lt o a l l e v o l u ti o n a r y a lg o r it h m s . G A s e l e c ti o n c a n b e i m p l e m e n t e d i n o n e o f a n u m b e r o fw ay s , i n c l u d in g r o u l e t t e w h ee l s e l ec t io n an d t o u r n am en t s e l ec ti o n . R eg a r d l e s s o f th es e l ec t i o n me t h o d u s ed , an elitist s t r a t egy i s o f t en used , wh ich r esu l t s i n t hech r o mo s o me w i t h t h e h i g h es t f i t n e s s v a l u e a l w ay s b e i n g co p i ed i n t o t h e n ex tg en e r a t i o n .P S O d o es n o t u t il iz e s e l ec ti o n . A l l p a r t ic l e s co n t i n u e a s mem b er s o f t h e p o p u l a t i o n f o rt h e d u r a t i o n o f t h e ru n . A p a r t i c l e ' s p a t h d e t e r m i n es i ts an ces t r y . P S O is t h e o n l yev o l u t i o n a r y a l g o r i t h m t h a t d o es n o t i n co r p o r a t e s u r v i v a l o f th e f it te s t, w h i ch f ea t u re st h e r emo v a l o f s o me can d i d a t e p o p u l a t i o n mem b er s ( i n d i v id u a l s w i t h lo w er f it n e s s a rer e m o v e d w i th h i g h e r p r o b a b il it y ).I n t h e ca s e o f a G A , c r o s s o v e r o ccu r s b e t w e en ( u s u a ll y ) r an d o m l y s e l ec t ed p a ren t s .T h e e v o l u t i o n o f a n i n d i v i d u a l c h r o m o s o m e t y p i c a l l y i n v o l v e s e x c h a n g i n g g e n e t i cm a t e r i a l w i t h q u i t e a f ew o t h e r ran d o m l y - s e l ec t ed i n d iv i d u a ls . I n P S O , a p a r ti c l e d o esn o t ex p l i c i t ly ex ch an g e m a t e r i a l w i t h o t h e r p a rt ic l e s , b u t i ts t r a j ec t o r y is i n f l u en c ed b yt h em. A s i g n i f i can t d i f f e r en ce i s t h a t a g i v en p a r t i c l e i s i n f l u en ced o n l y b y i t s o w np r ev i o u s b e s t p o s i ti o n an d t h a t o f th e b e s t p o s i t i o n i n t h e n e i g h b o r h o o d o r i n t h e g l o b a lp o p u l a t i o n . I n th e l o ca l v e r s i o n o f P S O , a p a r ti c l e i s in f l u en ced o n l y b y o n e o f it st o p o l o g i ca l n e ig h b o r s . A n d t h e t o p o l o g i ca l g eo m e t r y o f t h e p a r ti c l e s w ar m r ema i n sc o n s t a n t t h r o u g h o u t th e m n , s o i n fl u e n c e s d o n o t c o m e f r o m " r a n d o m s t ra n g e r s ."R e cen t w o r k w i t h P S O i n d ica t e s t h a t b y p r o p e r l y s e tt in g t h e i n e r t ia w e i g h t w , th e v a l u eo f Vmax c a n b e s e t t o t he d y n a m i c ra n g e o f e a c h p a r a m e t e r, a n d t he g l o b a l m a x i m u mc a n b e f o u n d m o r e q u i ck l y , o n a v e ra g e . E v e n b e t t e r p e r f o r m a n c e c a n b e a c h i e v e d b yr ed u c i n g t h e v a l u e o f w d u r in g a r u n [ 1 1] . Th e i n e r ti a w e i g h t t h u s ap p ea r s t o h av ech a r ac t e r i s t i c s t h a t a r e r emi n i s cen t o f t h e t emp er a t u r e p a r ame t e r i n s i mu l a t edan n ea l in g . A h i g h v a l u e o f w a t t h e b eg i n n i n g o f t h e r u n f ac i l it a te s g l o b a l s ea r ch , w h i l ea s m a l l w t en d s t o l o ca l i ze th e s ea r ch . S i n ce t h is i s " w o r k i n p r o g r e s s , " i t is u n k n o w nh o w u n i v e r s a l th i s ap p r o ac h w i l l b e f o r o th e r p r o b l ems .D i s c u s s i o nA n u m b e r o f i de a s h a v e c o m e o u t o f th is c o m p a r i so n o f G A s a n d P S O . I n fa c t , i t w a st h is k i n d o f t h in k i n g t h a t l ed to t h e d ev e l o p m en t o f th e i n e r t ia w e i g h t w h i ch i s n o w p a r to f P S O an d i s u s ed r o u t i n e l y b y t h e au t h o r s.I t is p o s s ib l e t o co n ce i v e o f s ev e r a l w ay s i n w h i ch t h e e l it is t co n cep t o f G A s co u l d b ei n co r p o r a t ed i n t o P S O . I n o n e s en s e , i t ' s a l r ead y t h e r e , p a r t i cu l a r l y i n t h e g l o b a lv e r s i o n o f P S O . A l s o , t h e r e i s a p a r am e t e r ca l led use-better ( w h i c h c a n b e s e l e c te d a t


5/6

61 5

run t ime in PSO ) tha t causes a par t i c le to con t inue in the d i rec t ion in w hich i t has be engo ing i f the cu r ren t f i tness is h ighe r tha t tha t o f the p rev ious i t e ra t ion . One w ay toexp l ic i t ly implement an e l i t i s t s t ra tegy would be to car ry a "g loba l bes t " par t i c le(perhaps w i th a s tochas t ic ve loc i ty ) in to the nex t i te ra t ion ; som e par t i c le , perhaps theo n e w i t h t h e l o w es t f i tn e s s, co u l d b e e l i m i n a t ed f ro m t h e p o p u l a ti o n .An o t h e r ap p ro ach w o r t h y o f in v es t i g a ti o n i s th e i n co rp o ra ti o n o f a Gau s s i and i s tr i b u ti o n in t o t h e s t o ch as t ic v e l o c i t y ch an g es i n PSO re f l ec t in g t h e w ay m u t a t i o n i sd o n e i n EP . T h e v a r i an ce p a ram e t e r m i g h t t h en p l ay a ro l e s i m i l a r to t h a t o f th e cu r r en tiner ti a we igh t .F i n a l ly , th e a s s i g n m en t o f a m ax i m u m v e l o c i t y o n a p a ram e t e r -b y -p a ram e t e r b a s is i swo r t h y o f co n s id e ra t io n . Th i s is an a l o g o u s t o co n t ro l l in g t h e s ev e r i t y o f m u t a t i o n i nG A o r E P.C o n c l u s i o n sIn t h is p ap e r, w e h a v e a n a l y zed t h e o p e ra t o rs o f GA s an d PSO. I t is h o p ed t h a t th eread e r h a s g a i n ed s o m e i n s i g h t s i n t o h o w t h es e p a rad i g m s wo rk , an d h o w t h ep e r fo rm an ce o f o n e m i g h t b e i m p ro v ed b y i n co rpo ra t in g f ea t u re s o f th e o t h e r.Th e d i s ti n c t io n s b e t ween t h e fo u r m a i n b ran ch es o f ev o l u t io n a ry co m p u t a t i o n co n t i n u et o b l u r. N ew ap p ro ach es co n t in u e to b e d ev e l o p ed . Em p h as i s s h o u l d b e p l aced o n n ewh y b r i d i m p l em en t a t i o n s . S t an d a rd b en ch m ark i n g fu n c t i o n s can b e u s ed t o m ak ecompar i sons , as can p rac t ica l app l ica t ions . I t i s hoped tha t the unders tand ing o f howt h e se p a rad i g m s w o rk wi l l co n t i n u e to b e s t u d ied an d i m p ro v ed .Refere n ces1 . Dav i s , L . , Ed . (1 99 1) , H an d b o o k o f Gen e t i c A l g o r i t h m s , Ne w Y o rk , NY : Va nNo s t r an d R e i n h o l d .2 . Eberhar t , R . C . , Dob b ins , R . W . , and S impson , P . K. (1996) , Co mp uta t iona lIn t e l li g en ce PC To o l s , B o s t o n : Acad em i c P re s s.3 . Eberha r t , R . C ., and K enn edy , J . (1995) , A new o p t imizer us ing par t i c le swarm

t h e o r y , P r oc . S i x th I n te r n a ti o n al S y m p o s i u m o n M i c r o M a c h i n e a n d H u m a nScience (N agoy a , Japan) , IEEE Serv ice Cen ter , P i sca taw ay , NJ , 39-43 .4 . Fog el , L . J . (1994) , E vo lu t ion ary p rog ram m ing in perspec t ive : the top-d ow n v iew ,in Computa t iona l In te l l igence : Imi ta t ing Li fe , J .M. Zurada , R . J . Marks I I , and C.J . Ro b inson , Eds . , IEEE Press , P i sca taw ay , NJ .5 . Go ldberg , D. E . (1989) , G enet ic Algo r i thms in Search , Op t imiza t ion , and M ach in eL e a r n i n g , R e a d i n g M A : A d d i s o n - W e s l e y .6 . K en ned y , J ., and Eberhar t , R . C . (1995), Par t i c le sw arm op t imiza t ion , Proc . IEE EIn t e rn a t i o n a l C o n fe ren ce o n Neu ra l Ne t wo rk s (Pe r t h , Au s t r a l i a ) , IEEE Se rv i ceCen ter , P i sca tawa y , NJ , IV: 1942-1948 .7 . K en n e d y , J. (1 9 9 7) , Th e p a r ti c le s warm : s o c i al ad ap ta t i o n o f k n o wl ed g e , P ro c .IEEE In t e rn a t i o n a l C o n fe ren ce o n Ev o l u t i o n a ry C o m p u t a t i o n ( In d i an ap o l i s ,Ind iana) , IEE E Serv ice Cen ter , P i sca tawa y , NJ , 303-308 .8 . Ko za , J . R . (1 99 2) , G en e t i c P ro g ram m i n g : On t h e P ro g ram m i n g o f C o m p u t e r s b yM ean s o f Na t u ra l Se l ec t io n , C am b r i d g e , M A : M IT P re s s.


6/6

6 16

9. Rec henb erg, I . (1994), Evolut ion s t rategy, in Com putat iona l In tel ligence:Imitat ing Life , J . M. Zurada, R. J . Ma rks II , and C. Robin son, Eds . , IEEE Press ,P i sca taway , NJ .

10. Shi , Y. H. , Eberhart , R. C., (1998), A m odified part ic le swa rm opt imizer , Proc. of1998 IEEE In te rna t iona l Conference on Evo lu t ionary Computa t ion , Anchorage ,AK, in press .11. Shi , Y. H. , Eberhart , R. C. , (1998), Parameter select ion in part ic le swarmoptimizat ion, Proc . EP98: The 7 th Ann. Conf. on Ev olut iona ry Progra mm ing, SanDiego, CA, in press .

comparison between evolutionary programming and particle swarm optimization

Documents