Particle Swarm Optimization

Transcription

1 Paricle Swarm Opimizaion Speaker: Jeng-Shyang Pan Deparmen of Elecronic Engineering, Kaohsiung Universiy of Applied Science, Taiwan 7/26/2004 ppso 1

2 Wha is he Paricle Swarm Opimizaion (PSO)? PSO is a recenly proposed algorihm, moivaed from he simulaion of social behavior. PSO is based on he evoluionary compuaion echnique. 7/26/2004 ppso 2

3 Wha is he Paricle Swarm Opimizaion (PSO)? A swarm of objecs moving in space and hus objecs are said o possess posiion and velociy and are influenced by he ohers in he swarm. PSO process he search scheme using populaions of paricles which correspond o he use of individuals in GAs. 7/26/2004 ppso 3

4 Wha is he Paricle Swarm Opimizaion (PSO)? Each paricle (individual) adjuss is flying (adjus velociy) according o is own flying experience and is companions flying experience. Each paricle is equivalen o a candidae soluion of a problem. 7/26/2004 ppso 4

5 Definiion The ih paricle posiion a he h ieraion can be represened as: X i = i i ( x (1), x (2), L, x ( D)). i 7/26/2004 ppso 5

6 Definiion The bes previous posiion (he posiion giving he bes finess value) of he ih paricle from he firs ieraion o he h ieraion is represened as: P i = i i ( p (1), p (2), L, p ( D)). i 7/26/2004 ppso 6

7 Definiion The bes posiion amongs all paricles from he firs ieraion o he h ieraion can be defined as: G = ( X (1), X (2), L, X ( D)). 7/26/2004 ppso 7

8 Definiion The rae of posiion change (velociy) for he ih paricle is recorded as: V i = i i ( v (1), v (2), L, v ( D)). i 7/26/2004 ppso 8

9 Definiion The paricles are manipulaed according o he following equaion: V + 1 i = W Vi + C1 r1 ( Pi X i ) + C2 r2 ( G X i ) (a) i = X i + Vi Where and are wo posiive consans, r 2 X C1 2 and are wo random funcions in he range [0,1]. W is he ineria weigh. C 1 (b) 7/26/2004 ppso 9 r

10 Applicaions Y. Fukuyama and H. Yoshida (2001), A paricle swarm opimizaion for reacive power and volage conrol in elecric power sysems. B. R. Secres and G. B. Lamon (2001), Communicaion in paricle swarm opimizaion illusraed by he raveling salesman problem. 7/26/2004 ppso 10

11 Applicaions V. Tandon (2000), Closing he gap beween CAD/CAM and opimized CNC end milling. H. Yoshida, K. Kawaa, Y. Fukuyama (1999) and Y. Nakanishi, A paricle swarm opimizaion for reacive power and volage conrol considering volage sabiliy. 7/26/2004 ppso 11

12 Applicaions R. Eberhar and X. Hu (1999), Human remor analysis using paricle swarm opimizaion. R. C. Eberhar and Y. Shi (1998), Evolving arificial neural neworks. 7/26/2004 ppso 12

13 Drawback of PSO Paricle swarm opimizaion algorihm and is relaed improved mehods are effecive for parameers of soluions which are independen or are loosely correlaed. However, i is no effecive when parameers of soluions are highly correlaed. (as shown in previous work by Shi & Eberhar (2001)) 7/26/2004 ppso 13

14 Why We Propose Parallel PSO algorihm? In 1987, Cohoon proposed he parallel geneic algorihms ha worked by dividing he populaion ino several groups and running he same algorihm over each group using differen processors. In order o achieve lower overall compuaion and ge beer soluions, a level of communicaion beween he groups is performed every fixed number of generaions. 7/26/2004 ppso 14

15 Why We Propose Parallel PSO algorihm? The parallel geneic algorihm periodically selecs promising individuals from each subpopulaion and migraes hem o differen subpopulaions. Wih his migraion, each subpopulaion will receive some new and promising chromosomes o replace he poorer chromosomes in a subpopulaion. This sraegy helps o avoid premaure convergence. 7/26/2004 ppso 15

16 Why We Propose Parallel PSO algorihm? The spiri of he daa parallelism mehod is uilized o creae a parallel paricle swarm opimizaion algorihm. PPSO is presened ogeher wih hree communicaion sraegies which can be used according o he independence of he daa. 7/26/2004 ppso 16

17 Communicaion Sraegies ( ) The firs sraegy is based on he observaion ha if parameers are independen or are only loosely correlaed. If we une he value of one parameer o ge a beer soluion cos by keeping he oher parameers consan, he value of his parameer is always near o he value of his parameer of he bes soluion. 7/26/2004 ppso 17

18 The Firs Sraegy Muliple copies of he bes paricles for all groups are muaed and hose muaed paricles migrae and replace he poorer paricles in he oher R 1 G groups every ieraions. 7/26/2004 ppso 18

19 f 2 2 1, x2) = ( x1 1) + ( x2 2) ( x x Global opimum 1 x 1 7/26/2004 ppso 19

20 Communicaion Sraegies ( ) The second sraegy is based on self-adjusmen in each group ha if he parameers of a soluion are srongly correlaed. In fac, he beer soluions spread among all he search space. We need o keep he parameers be divergen o all possible searching space. I is beer he communicaion only for he neighbourhood in order o keep he divergence. 7/26/2004 ppso 20

21 The Second Sraegy The bes paricle in G j each group is migraed o is neighbour groups o replace some of he more poorly performing paricles every ieraions. R 2 7/26/2004 ppso 21

22 f , x2) = ( x2 2) ( x1 + 3) + ( x2 5) ( x x 2 1 x1 = 3, x2 = 2 x 2 x = 0, x2 1 = 5 x 1 7/26/2004 ppso 22

23 Communicaion Sraegies ( ) If he properies of he parameers are unknown, we may apply he communicaion sraegy 3 which is he hybrid version of he communicaion sraegy 1 and 2. 7/26/2004 ppso 23

24 The Third Sraegy The hybrid sraegy separaes he groups ino wo equal sized subgroups wih he firs subgroup applying he firs R 1 sraegy every ieraions and all groups applying he second sraegy every ieraions. R 2 7/26/2004 ppso 24

25 PPSO wih Three Communicaion Sraegies 1. Iniializaion: Generae paricles for he jh group, i=0, N j -1, j=0,.s-1, S is he number of groups, is he paricle size for he N j jh group and is he ieraion number. Se =1. 2. Evaluaion: The value of f ) for every paricle N j in each group is evaluaed. ( X i, j X i, j 7/26/2004 ppso 25

26 PPSO wih hree communicaion sraegies 3. Updae: Updae he velociy and paricle posiions using equaions (a) and (b). 4. Communicaion: Three possible communicaion sraegies are adoped. 7/26/2004 ppso 26

27 PPSO wih hree communicaion sraegies 5. Terminaion: Sep 2 o 5 are repeaed unil he predefined value of he funcion or some maximum number of ieraions has been reached. Record he bes value of he funcion f ( G ) and he bes paricle posiion among all paricles G. 7/26/2004 ppso 27

28 Experimens For comparison, hree benchmark funcion repored in Shi & Eberhar (1999) are used. The firs funcion is he Rosenbrock funcion: n f1 ( X ) = (100( xi+ 1 xi ) + ( xi 1) ) i= /26/2004 ppso 28

29 Experimens The second funcion is he generalized Rasrigrin funcion: n 2 f 2 ( X ) = ( x i 10 cos(2π xi ) + 10) i= 1 The las funcion is he generalized Griewank funcion : 1 n n 2 xi f 3 ( X ) = xi cos( ) i= 1 i= 1 i 7/26/2004 ppso 29

30 Experimens Percenage of cos f 1 ( X ) Migraion PSO PPSO(2,80) PPSO(4,40) PPSO(8,20) None % % % % Performance comparison of PSO & PPSO wih he firs communicaion sraegy for Rosenbrock funcion 7/26/2004 ppso 30

31 Experimens Percenage of cos f 2 ( X ) Migraion PSO PPSO(2,80) PPSO(4,40) PPSO(8,20) None % % % % Performance comparison of PSO & PPSO wih he firs communicaion sraegy for Rasrigrin funcion 7/26/2004 ppso 31

32 Experimens Number of cos f 3 ( X ) Migraion PSO PPSO(2,80) PPSO(4,40) PPSO(8,20) None Performance comparison of PSO & PPSO wih he second communicaion sraegy for Griewank funcion 7/26/2004 ppso 32

33 Experimens Funcion cos PSO PPSO(4,40) PPSO(8,20) Rosenbrock Rasrigrin Griewank Performance comparison of PSO & PPSO wih he hird communicaion sraegy 7/26/2004 ppso 33

34 T H A N K Y O U!