A Hybrid Evolution Algorithm with Application Based on Chaos Genetic Algorithm and Particle Swarm Optimization

Transcription

1 Natonal Conference on Informaton Technology and Computer Scence (CITCS ) A Hybrd Evoluton Algorthm wth Applcaton Baed on Chao Genetc Algorthm and Partcle Swarm Optmzaton Fu Yu School of Computer & Informaton technology, Northeat Petroleum Unverty, Daqng, 6338 Chna Wang Bng* School of Computer & Informaton technology, Northeat Petroleum Unverty, Daqng, 6338 Chna Xu Shao-Hua School of Computer & Informaton technology, Northeat Petroleum Unverty, Daqng, 6338 Chna Abtract Amng at the complex functon extreme value and non-lnear ytem model parameter adjut, a hybrd optmzaton algorthm baed on chao GA combned wth PSO propoed n the paper. Wth applcaton of applyng experence of PSO, harng nformaton of GA, and traverng pathway of chao, the adaptve wtchng of two algorthm are mplemented through etmatng the ftne and optmzaton effcency, whch may qucly obtan the global optmal oluton. The propoed algorthm appled to the functon extreme optmzng and the parameter adjutng of fuzzy controller, and the expermental reult how that the optmzaton ablty of propoed algorthm obvouly uperor to the ngle one, and that the ntegraton of ome ntellgent optmzaton algorthm a potental reearch drecton. Key Word-chaotc genetc algorthm, partcle warm optmzaton, hybrd evoluton algorthm, algorthm degn, contnuou optmzaton I. INTRODUCTION In recent year, the optmzaton technque baed on evolutonary computaton are wdely ued to olve the optmal oluton of varou engneerng problem, whch play an mportant role [-5] n the feld of mult-objectve optmzaton, expermental degn and analy, ytem dentfcaton and control. Snce the prncple and mechanm of ngle evolutonary algorthm generally propoed by a certan charactertc n the evoluton of the mulated bologcal communte, and dfferent algorthm conder the ue from dfferent angle, ngle algorthm how the performance advantage n a certan apect and the dadvantage of prncple and tratege n other certan apect [6, 7]. For example, be eay to fall nto local optmum, cannot earch n the global oluton pace, fal to meet the requrement of mult-objectve contrant, etc. Chao genetc algorthm (CGA) an optmzaton algorthm that combne evolutonary mechanm of genetc algorthm wth chao earch trategy, and ha properte of group earch and trac traverng, but there are defect that the degree of global nformaton harng low [8,9]. Partcle warm optmzaton (PSO) an evolutonary computaton technque baed on warm ntellgence theory, to et up the mulaton of bologcal predaton phenomenon n nature baed on of the evoluton of computng technology whch mulate bologcal predaton phenomenon n nature. It olve optmzaton problem through ndvdual cooperaton and competton n the populaton, whch can remember the bet partcle poton and hare nformaton between the partcle, but the rate of convergence low []. Therefore, If can fnd a hybrd algorthm combned CGA wth PSO, the ablty of complex problem olvng and adaptablty can be mproved. Amng at the problem of complex functon calculaton and parameter optmzaton of nonlnear ytem, a Hybrd Evoluton Algorthm baed on Chao Genetc Algorthm (CGA) and Partcle Swarm Optmzaton (PSO) propoed n the paper. The algorthm combne chaotc varable wth parameter to be optmzed and et the traverng range of chaotc moton n the feable oluton pace of optmzaton varable, whch buld the adaptve adjutment mechanm baed on ftne aement and effcency analy to wtch both algorthm of CGA and PSO to olve Global optmzaton oluton n the feable oluton pace of problem. The hybrd optmzaton trategy and detaled algorthm tep of CGA-PSO are gven n the paper. The example of functon extremum olvng and parameter adjutment of fuzzy controller are ued a experment, and the reult how that the method of CGA-PSO better than that of GA or PSO. II. CHAOTIC GENETIC ALGORITHM AND PARTICLE SWARM OPTIMIZATION A Chaotc Search Chao a nonlnear phenomenon common n nature, whch ha properte of ntrnc random, orbt ergodcty and mplct rule. Chaotc earch that chaotc tate are ntroduced to the optmzaton varable, whch can travere all tate repeatedly accordng to the law of the ytem telf wthn a certan range. The method ha good adaptablty n mechanm to determne the global optmal oluton n the feable oluton pace of problem. Conder a chaotc earch trategy baed on the nect populaton model, of whch logtc map a chaotc equence generator [], and chaotc tate ntroduced to the optmzaton varable. The Iteratve equaton a follow: 45. The author - Publhed by Atlant Pre

2 j u ( ) j j where u a chaotc attractor. Whenu 4 (), the ytem become nto a chaotc tate, a chao varable of j emerged, whch change n the nterval of [,]. B Chaotc Genetc Algorthm Chao Genetc Algorthm baed on orbt ergodcty of chaotc varable movement evolutonary mechanm of Genetc Algorthm, combne chaotc earch properte wth parameter to be optmzed, and encode the chaotc varable, whch are repreented a chromoome and are placed n the envronment of the problem to elect, copy, chaotc cro and chaotc mutaton accordng to the prncple of urvval of the fttet. Accordng to the evolvng of evolutonary teraton repeatedly, the optmal oluton obtaned, whch converged to the ndvdual on the mot utable envronment fnally. C The bac PSO algorthm The bac PSO algorthm [] can be decrbed a follow: Set that there a populaton compoed of m partcle n n-dmenonal pace, the locaton and the peed of the th partcle X and V, the local optmal locaton of P are X ( x, x,, xn) and V ( v, v,, vn ), and the global optmum poton of Pg are P ( p, p,, pn ) and Pg ( pg, pg,, pgn ). The update tratege of partcle tate are a follow: V t ) wv ( t) c r ( P X ( t)) c r ( P X ( )) ( g t () X ( t ) X ( t) V ( t ) (3) Where,,, m, w the nerta factor, c and c are contant, r and r are random number n the nterval of [,]. Loop terate each partcle of the populaton nto Eq. () and Eq. (3), the whole populaton can approach to the global optmal oluton gradually. III. THE HYBRID ALGORITHM OF CGA AND PSO The hybrd optmzaton trategy of Chao genetc and partcle warm to combne the advantage of PSO wth thoe of CGA, whch et ftne aement and analy rule of algorthm effcency to realze adaptve alternatng teraton of PSO and CGA n control gudelne and acheve the purpoe of Nature complement each other and global optmzaton. A The rule of hybrd optmzaton algorthm wtchng Combned the change of objectve functon value wth operatng effcency of algorthm, two elf-adaptve wtchng rule are propoed a follow: Set the wtchng threhold, the algebrac nterval G teraton of, the ncrement value of objectve functon after F G tme F. If G, wtch the algorthm. Accordng to the above rule, the algorthm wll not be wtched untl atfyng the condton of meetng the optmzaton precon or the maxmum evoluton tme. B The mplementaton tep of Hybrd optmzaton algorthm Frtly, the algorthm realze evoluton teraton of PSO or CGA wth a certan populaton ze and chec the ftne and the effcency of the algorthm at the ame tme. When the termnaton condton atfed, chooe the partcle whoe ftne better a the object of next round and chooe other partcle randomly a upplement populaton. When reachng the gven ze, the other algorthm choen to terate contnually. The mplementaton tep of Hybrd optmzaton algorthm are decrbed a follow: Step Determne the populaton ze N.Generate the ntal populaton G randomly, and encode the chromoome wth decmal number, on whch the number of gene the number of varable to be optmzed. Set the wtchng threhold, the algebrac nterval G. Step Buld the ftne functon. For the functon mnmum optmzaton problem of F, the ftne functon F choen a ft e. Step 3 Implement of the PSO algorthm () PSO ntalzaton. () Iterate Eq. () and Eq. (3) G tme, and calculate the change F of the objectve functon. F (3) If, turn to Eq. (4). Otherwe, turn to Eq. G (). (4) If atfe the termnaton condton, ave and top. Otherwe, chooe the partcle whoe ftne better than other and other partcle a upplement populaton untl reachng the gven ze of N, a new populaton of G generated. Turn to tep 4 and wtch to CGA. Step 4 Implement CGA earchng () Iterate G tme a the followng tep, and calculate the change F of the objectve functon. electon operaton:chooe chromoome by runner rule, of whch the electon probablty proportonal to t ftne. Chaotc cro: Two chromoome are combned a follow: WW( ) W, W W ( ) W, where (, ) are chaotc 46

3 varable. At frt, defne a cro-ampltude of, then determne accordng to Eq. (4). In order to how the bdrectonalty, the chaotc varable of determned accordng to Eq. (5). j j are (4) j j j 8 ( ) (5) Mutaton operaton: Set the mutated gene ' U followng a w w ( w w ) or w ' L w ( w w ), where U w w, the the upper L bound, w the lower bound, and the chaotc varable that change n the nterval of (,). Mutaton operaton need to defne varaton ampltude of ~ at frt, and then chao varable are ntroduced. For m ndvdual elected to be varated, ort n acendng order of ftne. For the th ndvdual, varaton ampltude of ~ can be ~ choen a Eq. (6), where the parameter that control the dturbance ze, and earche n the nterval of ~ ~ [, ]. ~ ~ exp(( m ) / m) (6) If atfe the termnaton condton, ave the optmal oluton and top. Otherwe, elect the partcle whoe adaptaton degree before 5%, upply the other to the populaton n the feable oluton pace randomly, mae the populaton reach the gven ze of N, and generate a new populaton G. Go to Step 3. F () If, turn to Eq. (3). Otherwe, turn to Eq. G (). (3) If atfe the termnaton condton, ave and top. Otherwe, chooe the partcle whoe ftne better than other and other partcle a upplement populaton untl reachng the gven ze of N, a new populaton of G generated. Turn to tep 3, and wtch to PSO. Wth applcaton of harng nformaton and traverng pathway of chao from the hybrd algorthm of CGA and PSO, the advantage of both algorthm are hown and the optmzaton effcency mproved. IV. ANALYSIS OF EXPERIMENT RESULTS A Functon global optmzaton Ue the followng four tandard tet functon and verfy the performance of the algorthm propoed n the paper. () Roenbroc functon n ( ) f x [( x x ) ( x ) ], x [ 3,3] () Ratrgn functon n f( x) n ( x co( x )), x [ 5., (3) Grewan functon n n x x f3( x) co( ), x [ 6, 4 (4) Acley functon n x n co( x ) (7) 5.] (8) 6] 5 n n f4( x) e e e, x [ 3, 3] () An average of the global mnmum of the above four functon. When the dmenon of n, populaton ze of GA and PSO are taen, and the total optmzaton tme are. When the dmenon of n, populaton ze of GA and PSO are taen 4, and the total optmzaton tme are 5. Set the algebrac nterval G and the wtchng threhold 3. In order to reflect the effcency of CGA-PSO, contrat wth the GA and PSO n the paper, of whch parameter are the ame a thoe of CGA-PSO. Each algorthm run tme, and the optmzaton reult are hown n Table. The average wtchng tme are hown n Table. TAB. COMPARISON OF OPTIMIZATION RESULTS AMONG CGA-PSO, GA AND PSO functon Dmenon Roenbroc Ratrgn Grewan Acley CGA-PSO GA PSO average reult (9) average average average average average tme reult tme reult tme

4 TAB. CGA-PSO ALGORITHM SWITCHING TIMES Roenbroc Ratrgn Grewan Acley We can ee form the optmzaton reult n table that CGA-PSO better than GA or PSO. We can ee form the average tme n table that CGA-PSO better than GA but wore than PSO. The above reult can be explaned a follow:for optmzaton reult, nce CGA-PSO n the optmzaton proce acheved the adaptve wtchng of both algorthm to complement advantage of each other when an algorthm lghtly tagnant mmedately wtch to the other algorthm. For average tme, nce the number of teraton of the three model the ame, the run-tme of CGA-PSO approxmate to the weghted average of that of each algorthm, and the calculaton of chao earch of CGA-PSO mall, the average tme of CGA-PSO between that of each algorthm. In fact, CGA-PSO to ncreae the runnng tme of PSO for the prce, to exchange for the optmzaton of the performance mprovement. B parameter optmzaton of Fuzzy controller In the degn of fuzzy controller, the control acton ofu determned by the error and the change of the error. In order to atfy requrement of dfferent controlled object, an adjutment factor of ntroduced. We can get the fuzzy control rule decrbed by the adjutment factor a follow: u E ( ) EC (, ) () By adjutng the ze of, we can change the weghted degree of the error and the change of the error. In the degn of fuzzy controller, nce relyng on a fxed weghted factor uually dffcult to meet the requrement, we conder that ntroducng dfferent weghted factor n dfferent error level to adaptve the adjutment of fuzzy control rule. Set a econd-order ytem of for the controlled object, the nput a tep ( )(4 ) gnal, the error, the change of the error, the doman of controller a { E} { EC} { u } { 3,,,,,, 3},and the control rule a u E ( ) EC, where (, ). Conder that the fuzzy control ytem n dfferent tate ha dfferent requrement n the control rule of rule, are dvded nto three level E ( ) EC u E ( ) EC 3E ( 3) EC E, E E 3 () Therefore, the x fuzzy controller parameter that need optmzng at the ame tme are e c u, where e and c are the quantzaton factor of the error 3 and the change of the error, u the cale factor of the output of the controller. Ue the ITAE ntegral performance to degn evaluaton functon of, where J (ITAE) = a J (ITAE) t e( t) dt. In order to mae the denomnator not zero, et a a a mall potve number. Obvouly, when the tracng error maller, the value of evaluaton functon greater. Baed on the experence, the range of the x controller parameter to be optmzed determned a follow: e c u [, ] ;.4] ; [, [.4,.8] ; 3 [.8,.]. Th experment wll alo contrat CGA-PSO wth GA and PSO. Set the populaton ze of CGA-PSO, GA and PSO are taen, the total optmzaton tme of CGA-PSO are, the total optmzaton tme of GA and PSO are 5, the algebrac nterval G and the wtchng threhold. 5. Table the optmzaton reult comparon of the three algorthm. The reult comparon of the correpondng tep repone curve hown n Fgure, the evoluton curve comparon of the evaluaton functon value hown n Fgure. Fg. Tracng Repone Comparon Curve of Optmzaton Reult Fg. Index Comparon Curve n Optmzaton Proce 48

5 TAB.3 PARAMETER OPTIMIZATION COMPARISON OF FUZZY CONTROLLERS AMONG CGA-PSO, GA AND PSO Algorthm 3 e c u J (ITAE) CGA-PSO PSO GA Fgure hown that there lttle dfference wth the performance of three controller. After CGA-PSO optmzaton, the peed of the controller fater and the overhoot maller. However, conder the optmzaton tme of GA and PSO fve tme of thoe of CGA-PSO, CGA-PSO ha tronger earchng capablty and the convergence peed and optmzaton performance of CGA-PSO gnfcantly better than that of GA and PSO, whch how that there greater value of CGA-PSO to promote. Fgure hown that: For CGA-PSO, after CGA optmzaton G tme, we can get ITAE / G Contnue to ue CGA, after CGA optmzaton G tme, we can get ITAE / G Contnue to ue CGA, after CGA optmzaton G tme, we can get ITAE / G.5. Swtch to PSO, ue PSO, after PSO optmzaton G tme, we can get ITAE / G.39. Swtch to PSO, Contnue to ue PSO, after PSO optmzaton G tme, top the optmzaton. We can ee form the above reult: Early n the algorthm run, t relatvely eay to optmze, when the ITAE ndex value drop gnfcantly, whch reult n the algorthm can not wtch n the frt two round, enter nto the rregular urface area to ncreae the dffculty of earchng optmzaton, top n the thrd round, and wtch the algorthm at lat. V. CONCLUSIONS A hybrd optmzaton algorthm baed on chao GA combned wth PSO propoed n the paper. The experment reult how that the optmzaton ablty of propoed algorthm obvouly uperor to the ngle one. However, nce the algorthm combne the chaotc mechanm, the algorthm traverng capablte are mproved, but t depend on the ntal value at the ame tme. How to mprove the robutne of the algorthm, the next reearch we need to tudy. REFERENCES [] Ma Ruxn, Lu Yu, QnZheng, Wang Xao. Momentum partcle warm optmzer for contraned optmzaton [J]. Journal of Sytem Smulaton,, (): [] Feng Zhenpng,L Jun,Shen Zyda. Applcaton of Genetc Algorthm To Degn For Turbne machnery [J].Ga Turbne Technology, 997,():3- [3] L Jun, Feng Zhenpng. Aerodynamc Optmum Degn of Tranonc Turbne Cacade Ung Genetc Algorthm [J]. Journal of Thermal Scence,997,6(): [4] Tong Tong, Feng Zhen png, L Jun. Applcaton of Genetc Algorthm To Mult-objectve Optmzaton Degn For Turbne Cacade [J]. Proceedng of t he CSEE,999,9 (6):74-76 [5] Mao Mngfe, Zhang Yonglang, Ma Jmng. Mult-objectve Evolutonary Optmzaton of Large Dfferental Surge Chamber [J]. Journal of hydroelectrc engneerng,, 9 () :57-6. [6] Gong Maoguo, Jao Lcheng, Yang Dongdong, Ma WenPng. Reearch on Evolutonary Mult-Objectve Optmzaton Algorthm [J]. Journal of Software, 9, () :7-89. [7] KONG We-jan, DING Jn-lang, CHAI Tan-you. Survey on large-dmenonal mult-objectve evolutonary algorthm [J]. Control and Decon,,5 (3) :3-35. [8] Chen Bngru, Yang Chengxang. Self-Adaptng Chao-Genetc Hybrd Algorthm and Sentvty Analy of It Parameter [J]. Journal of Northeatern Unverty, 6,7 (6) : [9] L Bng, Jang Weun. Chao Optmzaton Method and It Applcaton [J]. CONTROL THEORY AND APPLICATIONS, 997, 4(4): [] SU Shou-bao, WANG J-wen, FANG Je. Overvew Applcaton and Reearch on Partcle Swarm Optmzaton Algorthm [J]. COMPUTER TECHNOLOGY AND DEVELOPMENT, 7,7(5): [] WU Te-bn,CHENG Yun, ZHOU Tao-yun,YUE Zhou. Optm zaton Control of PID Baed on ChaoGenetc Algorthm [J]. Computer Smulaton, 9,6(5):-5 [] Ca X.J.,Cu Z.H.,Zeng J.C., et al. Partcle Swarm Optmzaton wth Self-adjutng Cogntve Selecton Strategy [J]. Internatonal Journal of Innovatve Computng, Informaton and Control, 8, 4(4):