MULTI-OBJECTIVE REAL EVOLUTION PROGRAMMING AND GRAPH THEORY FOR DISTRIBUTION NETWORK RECONFIGURATION

Transcription

1 74 MULTI-OBJECTIVE REAL EVOLUTION PROGRAMMING AND GRAPH THEORY FOR DISTRIBUTION NETWORK RECONFIGURATION Mohammad SOLAIMONI,, Malh M. FARSANGI, Hossn NEZAMABADI-POUR. Elctrcal Engnrng Dpartmnt, Krman Unvrsty, Krman, Iran. South Krman Elctrc Powr Dstrbuton Company, Krman, IRAN Kywords: Evolutonary programmng, gntc algorthm, dstrbuton systms, rconfguraton, load balancng, loss rducton, graph thory. Abstract: Ths papr nvstgats th ablty of Evolutonary programmng (EP) n coopraton wth graph thory for ntwork rconfguraton to balanc th load, rduc th powr loss and nhancmnt of voltag profl of dstrbuton systm. A numrcal rsult of a dstrbuton systm s prsntd whch llustrat th fasblty of th proposd mthod by EP usng th graph thory. To valdat th obtand rsults, Gntc Algorthm (GA) usng graph thory s also appld and s compard wth th proposd EP combnd wth graph thory.. INTRODUCTION Fdr rconfguraton s a vry mportant and usabl opraton to rduc dstrbuton fdr losss and mprov systm scurty. Dstrbuton fdrs hav two typs of swtchs: sctonalzng swtchs and t swtchs. Sctonalzng swtchs nstalld on th ln and normally ar closd. To hlp rstor powr to customrs followng a fault, most fdrs hav svral ntrconnctng t swtchs to nghborng fdrs. By changng th opn and closd status of th fdr swtchs, load currnts can b transfrrd from fdr to fdr. Dstrbuton systms ar radally structurd to smplfy ovrcurrnt protcton. Ntwork rconfguraton n a dstrbuton systm s ralzd by changng th status of sctonalzng swtchs and t s usually don for loss rducton or for load balancng n th systm []-[]. Snc, thr s numrous numbrs of swtchs n a dstrbuton systm, and th numbr of possbl swtchng opratons s trmndous, thrfor, ntwork rconfguraton bcoms a vry complx dcson-makng problm. On th othr hand, radallty constrant and th dscrt natur of th swtch valus prvnt th us of classcal optmzaton tchnqus to solv th rconfguraton problm. Thrfor, most of th algorthms n th ltratur ar basd on hurstc algorthms [3]-[0]. Also, dffrnt approachs usng graph thory ar rportd n []-[] for ntwork rconfguraton. Th volutonary algorthm usng graph thory was proposd n [3]. Also, th authors n [4] usd th concpts of graph thory along wth Guarantd Convrgnc Partcl Swarm Optmzaton (GCPSO) for loss rducton. In ths papr, a nw approach by usng EP combnd wth graph thory s proposd to fnd th optmal confguraton. To mplmnt EP n coopraton wth graph thory, two dffrnt obctv functons ar consdrd by dfnng a pnalty functon. Th pnalty functon s usd n th cas of xstng mshs or solatng som loads n th solutons found by th algorthms. It hlps th algorthms to convrg fastr, rsultng n a shortr runnng tm. Also, to valdat th rsults obtand by EP usng graph thory, GA usng graph thory s appld.

2 M. SOLAIMONI, M. M. FARSANGI, H. NEZAMABADI-POUR Mult-Obctv Ral Evoluton Programmng And Graph Thory For Dstrbuton Ntwork Rconfguraton 75. EVOLUTIONARY PROGRAMMING AND GENETIC ALGORITHM A. Evolutonary programmng Evolutonary programmng (EP) s a tchnqu n th fld of volutonary computaton. It sks th optmal soluton by volvng a populaton of canddat solutons ovr a numbr of gnratons or tratons. Durng ach traton, a scond nw populaton s formd from an xstng populaton through th us of a mutaton oprator. Ths oprator producs a nw soluton by prturbng ach componnt of an xstng soluton by a random amount. Th dgr of optmalty of ach of th canddat solutons or ndvduals s masurd by thr ftnss (obctv functon). Through th us of a comptton schm, th ndvduals n ach populaton compt wth ach othr. Th wnnng ndvduals form a rsultant populaton, whch s rgardd as th nxt gnraton. For optmzaton to occur, th comptton schm must b such that th mor optmal solutons hav a gratr chanc of survval than th poorr solutons. Through ths th populaton volvs towards th global optmal pont. Th Evolutonary programmng tchnqu s tratv and th procss s trmnatd by a stoppng rul. Thrfor, optmzaton by EP can b summarzd nto two maor stps: a) Mutat th solutons n th currnt populaton; b) Slct th nxt gnraton from th mutatd and th currnt solutons. Th gnral prncpl of EP s as follows [8]: Stp ) Gnrat th ntal populaton of µ ndvduals. Each ndvdual s takn as a par of ralvalud vctors, ( x, η {,..., µ }, whr x s ar obctv varabls and η s ar standard dvatons for Gaussan mutatons. Stp ) Evaluat th ftnss scor for ach ndvdual basd on th obctv functon. Stp 3) Each parnt ( x, η =,..., µ, crats a sngl offsprng ( x, η ) by: for =,..., n. dstrbutd on-dmnsonal random numbr wth man zro and standard dvaton on. N ( 0,) ndcats that th random numbr s gnratd anw for ach valu of. Th factors τ and τ ar commonly st to n and ( n ). Stp 4) Calculat th ftnss of ach offsprng ( x, η {,..., µ }. Stp 5) Conduct parws comparson ovr th unon of parnts ( x, η ) and offsprng ( x, η {,..., µ }. For ach ndvdual, q opponnts ar chosn unformly at random from all th parnts and offsprng. For ach comparson, f th ndvdual s ftnss s no smallr than th opponnt s, t rcvs a wn. Stp 6) Slct th µ ndvduals out of ( x, η ) and ( x, η {,..., µ }, that hav th most wns to b parnts of th nxt gnraton. Stp 7) Stop f th stoppng crtron s satsfd; othrws, go to Stp 3. B. Gntc Algorthm Th GA s a sarch algorthm basd on th mchansm of gntc and natural slcton. Th GA starts wth random gnraton of ntal populaton and thn th slcton, crossovr and mutaton opratons ar prcdd untl th ftnss functon convrgs to a maxmum or th maxmal numbr of gnratons s rachd. A typcal smpl gntc algorthm s dscrbd n dtal n [5]. GA can b mplmntd through bnary GA (BGA) and ral GA (RGA). Th frst stp n th soluton of an optmzaton problm usng BGA s th ncodng of th varabls. Th most usual approach s to rprsnt ths varabls as strngs of 0s and s. A collcton of such strngs s calld populaton. Thn, slcton, crossovr and mutaton ar appld on th ncodd varabls. On th othr hand, RGA uss th ral cods and th slcton, crossovr and mutaton ar appld to th varabl drctly. x ( ) = x ( ) + η( ) N ( 0,) () η ( ) = η( ) xp( τ N( 0,) + τn ( 0,) ) () whr x ( ), x ( ), η ( ) and η ( ) dnot th th componnt of th vctors x, x, η and η, rspctvly. N ( 0,) dnots a normally 3. GRAPH THEORY In graph thory, a graph s mad up of dots connctd by lns whr two dots can only b connctd by on ln [6]. In graph thory, a dot s known as vrtx and a ln known as dg.

3 76 UNIVERSITY OF PITESTI ELECTRONICS AND COMPUTERS SCIENCE, SCIENTIFIC BULLETIN, No. 8, Vol., 008 Thrfor, a graph s a par G = ( V, E) of sts whr th lmnts of V ( V = { v } =, K, l ) ar th vrtcs or nods or ponts of th graph G and th lmnts of E ( E = { } =, K, m ) ar ts dgs or lns. A graph wth vrtx st V s sad to b a graph on V. Th vrtx st of a graph G s rfrrd to as V (G) and ts dg st as E (G). Th dgr of a vrtx n a graph s th numbr of th dgs that touch t and t s dfnd by th followng quaton: dg( V ) = E (3) Th sz of a graph s th numbr of vrtcs that t has. A path s a rout that can b travld along dgs and through vrtcs n a graph. All of th vrtcs and dgs n a path ar connctd to on anothr. A cycl s a path that bgns and nds on th sam vrtx, whch somtms calld a crcut. Th numbr of dgs n a path or a cycl s calld th lngth of th path. A graph s dfnd a conncton graph f thr s at last on ln or dg btwn ach two nods and thr s no any vrtx connctd to tslf through an dg drctly. Fgs. - show a conncton graph and a graph whch s not a conncton graph. A B Fg.. A conncton graph. A B 3 E D C Fg.. A graph whch s not a conncton graph. Consdr a graph G wth l vrtcs. Ths graph can b dfnd by a squar matrx such as A l known as adacncy matrx, whr shows th l connctons btwn th l vrtcs of th graph. If any two of ts vrtcs ar lnkd togthr drctly by a path n G, th lmnt of th matrx s qual to on, othrws s qual to zro. 4 5 E 3 D C A = 0 whn th vrtx lnkd to drctly for (4) othrws A graph that s a conncton graph and s not contanng any cycls s calld a tr graph. In a tr graph wth V vrtcs and E dgs, th followng quaton s satsfd: V = E (5) Th numbr of cycls n a graph s gvn by th followng quaton: cycl = ( E + ) V (6) Thrfor, f only on rgon s mad by a graph, th graph wll b a tr graph. 4. DISTRIBUTION SYSTEMS AND GRAPH THEORY Dstrbuton systms ar radally structurd. If all swtchs ar closd n a dstrbuton systm, thrfor a mshd ntwork wll b xstd. For a ntwork wth k mshs, th k swtchs must b opnd to rtan a radal ntwork structur; whr only on swtch s opnd n ach msh. Thrfor, confguraton s prformd by changng th status of ntwork swtchs such a way that radallty s always rstablshd and no fdr scton can b lft out of srvc. To fnd th bst confguraton of a dstrbuton systm usng EP, graph thory can b usd to chck whthr radallty s rtand as wll as all loads bng n srvc. For ths purpos, th followng procdur can b usd: Fnd th adacncy matrx for th obtand soluton whr shows th connctons btwn th l vrtcs of th graph (ncludng th conncton btwn th fdrs and buss). Th xstng matrx s namd AK. Thn by lmnatng th rpatd lmnts, th matrx AK wll b obtand. Now th non-zro lmnts of th matrx AK s compard wth th numbr of buss and on of th two followng condtons wll b obtand: - Th numbrs of non-zro lmnts of th matrx AK s not qual wth th numbr of buss: t mans that th graph s not a conncton graph and w hav som solatd loads. Th

4 M. SOLAIMONI, M. M. FARSANGI, H. NEZAMABADI-POUR Mult-Obctv Ral Evoluton Programmng And Graph Thory For Dstrbuton Ntwork Rconfguraton 77 numbrs of solatd loads ar qual to th dffrncs btwn th non-zro lmnts of th matrx AK and th numbr of buss. Th numbrs of non-zro lmnts of th matrx AK s not qual wth th numbr of buss: by rturnng to matrx AK and lmnatng th frst column of th matrx. If a row wth zros lmnts s ncountrd thn t mans that thr ar som solatd buss. Ths buss ar thos buss whch ar connctd to th fdrs. If thr ar no solatd loads n th graph, thn th numbrs of cycls (loops) ar calculatd by quaton (6). If th numbr of cycls s qual to zro t mans that th graph s tr. In th othr word th dstrbuton systm s a radal wth all loads n srvc. Th abov procdur s shown n Fg. 3. whr k s th numbr of xstng mshs, p s th numbr of solatd loads, A and B ar constant paramtrs known as wghts. 5. STUDY SYSTEM AND PROBLEM FORMULATION Th study systm s a dstrbuton systm whch conssts of 8 sctonalzng swtchs and 5 t swtchs as shown n Fg. 4. Th systm data can b found n [7]. To fnd th bst confguraton of th ntworks, two dffrnt mult-obctv scnaros ar usd. In th frst on th problm formulaton s how to rconfgur th ntwork to mnmz th total powr losss as wll as mprovng th voltag profl: N mn F = mn w ( PT, Loss ) + w V + C (7) = whr, P T, s th total ral powr loss of th Loss systm, and V s th voltag of th th bus, w and w ar th wghts. Snc, two dffrnt typs of varabls (losss and voltags) ar consdrd smultanously n (7 a balancng factor should b ncludd (by w and w ) to wght ths varabls. Aftr rconfguraton of th ntwork, th radal charactrstcs of th ntwork should b kpt and all loads hav to b n srvc. In vw of ths, C s dfnd as th pnalty factor for th xstng msh(s) or n th cas of solatng som loads by th followng quaton : C = A k + B p (8) Fg. 3. Graph thory for chckng th radallty and bng all loads n srvc for a dstrbuton systm. Th scond mult-obctv functon s formulatd to optmz th load balancng as wll as mprovng th voltag profl. Th obctv functon can b xprssd as follows: nl I N mn F = mn w L + w V + C (9) R = I = whr, I s th currnt of th R branch, I s th nomnal currnt, L s th lngth of th th th branch, V s th voltag of th bus, w and w ar th wghts and C s th pnalty functon.

5 78 UNIVERSITY OF PITESTI ELECTRONICS AND COMPUTERS SCIENCE, SCIENTIFIC BULLETIN, No. 8, Vol., 008 Fg. 4. Th study systm: 33-bus dstrbuton systm. Also, n both scnaros th magntud of th voltag at ach bus must b mantand wthn ts lmts. Th currnt on ach branch has to l wthn ts capacty ratng. Ths constrants ar xprssd as: V V (0) whr, mn V max I I,max V V max and mn () V ar th magntud of th voltag of th th bus, th mnmum and maxmum voltag lmts, rspctvly. I and I ar th magntud of th currnt and th,max maxmum currnt lmt of th th branch. 6. IMPLEMENTATION OF EP, BGA AND RGA USING GRAPH THEORY EP and GA ncorporatng th graph thory ar usd for ntwork rconfguraton n ordr to hav mnmum losss, optmz th load balancng n th ntwork as wll as mprovng th voltag profl. Th mplmntaton of BGA, RGA and EP s prsntd blow: Usng RGA and BGA, a confguraton s consdrd wth fv gns (th numbr of mshs). Th numbr of chromosoms for a populaton s st to b 50. Th chromosoms volv through succssv tratons, calld gnratons. Durng ach gnraton, th chromosoms ar valuatd wth som masur of ftnss, whch s calculatd from th obctv functon ((7) or (9)). Movng to a nw gnraton s don from th rsults obtand for th old gnraton. A basd roultt whl s cratd from th obtand valus of th obctv functon of th currnt populaton. To crat th nxt gnraton, nw chromosoms, calld offsprngs, ar formd usng a crossovr oprator and a mutaton oprator. In ths papr, on pont crossovr s appld wth th crossovr probablty p c = 0. 9 and th mutaton probablty s slctd to b p m = Also, th numbr of traton s consdrd to b 50. Basd on Scton II, EP s appld. Th numbr of chromosoms for a populaton s st to b 50 and q=0. Owng to th randomnss of th hurstc algorthms, thr prformanc cannot b udgd by th rsult of a sngl run. Thus, to fnd th bst rconfguraton for th two ntworks, sutabl swtchs to b opnd ar slctd basd on 0 ndpndnt runs, undr dffrnt random sds. Th obtand rsults by EP and GA ar gvn n Tabl I for two dffrnt obctv functons ((7) and (9)) n whch BGA and EP algorthms convrg to th sam soluton but RGA fald to fnd th soluton. avrag bst so-far EP BGA RGA traton Fg. 5. Convrgnc charactrstcs of EP, BGA and RGA on th avrag bst-so-far n fndng th soluton for th study systm basd on Equ. (9). Tabl, shows that, consdrng th swtchs 7, 9, 4, 8 and 3 as t swtchs, th dstrbuton systm rconfgurs to a ntwork wth a bttr Load balanc ndx (Lb mnmum losss and a bttr bus voltag magntud profl. Th avrag bst-so-far of ach run of thr algorthms ar rcordd and avragd ovr 0 ndpndnt runs. To hav a bttr clarty, th convrgnc charactrstcs n fndng th bst

6 M. SOLAIMONI, M. M. FARSANGI, H. NEZAMABADI-POUR Mult-Obctv Ral Evoluton Programmng And Graph Thory For Dstrbuton Ntwork Rconfguraton 79 confguraton for th ntwork ar gvn n Fg. 5. Ths fgur dtrmns th convrgnc rat and th qucknss of th algorthms to fnd th soluton whch th RGA dosn t convrg to th sam soluton as EP and GA. Although, EP prforms bttr than BGA but th bst found soluton s th sam for both. Also, bus voltag magntud profl of th orgnal systm and rconfgurd systm basd on Equ. (9) ar shown n Fg. 6. bfor rcon. aftr rcon. voltag of bus (p.u) numbr of bus Fg.6. Bus voltag magntud profl of th systm bfor and aftr rconfguraton by EP basd on Equ. (9). Tabl : Th obtand rsults BY EP, BGA and RGA for th study systm Ntwork confguraton Orgnal confguraton Ftnss functon - T swtchs 33, 34, 35, 36, 37 Powr loss (KW) or Load balanc ndx (Lb) Powr loss: 0.8 Lb: , Improvmnt % - Mn. Voltag magntud (Pu) (bus 8) Aftr rconfguraton F 7, 9, 4, 8, (bus 3) EP & BGA F 7, 9, 4, 8, (bus 3) Aftr rconfguraton F 0, 7, 3, 33, (bus 3) RGA F 6, 9, 4, 7, (bus 3) 7. CONCLUSION In ths papr, EP, RGA and BGA usng graph thory ar appld to confgur a dstrbuton ntwork to mnmz losss, optmz th load balancng and nhancmnt of voltag profl. Th suggstd mthod usng graph thory and pnalty functon hlp EP, RGA and BGA to fnd th radal confguraton for dstrbuton ntwork asly. Th obtand rsults show that EP has a bttr convrgnc rat. Also, EP and BGA found th optmum soluton whl RGA fald to fnd t. REFERENCES [] S. Cvanlar, J. J. Grangr, H. Yn, and S. S. H. L, Dstrbuton fdr rconfguraton for loss rducton, IEEE Transactons on Powr Dlvry, Vol. 3, No.3, Jul. 988, pp [] M.E. Baran and F.F. Wu, Ntwork rconfguraton n dstrbuton systms for loss rducton and load balancng. IEEE Transactons on Powr Dlvry, Vol. 4, No., Apr. 989, pp [3] K. Nara, A. Shos, M. Ktagawa and T. Ishhara; Implmntaton of gntc algorthm for dstrbuton systms loss mnmum rconfguraton, IEEE Transactons on Powr Systms, Vol. 7, No. 3, Aug. 99, pp [4] S.K. Goswam and S. K. Basu, A nw algorthm for th rconfguraton of dstrbuton fdrs for loss mnmzaton, IEEE Transactons on Powr Dlvry, Vol. 7, No. 3, Jul. 989, pp [5] D. Shrmohammad and H. W. Hong, Rconfguraton of lctrc dstrbuton ntworks for rsstv ln loss rducton, IEEE Transactons on Powr Dlvry, Vol. 4, No., Apr. 989, pp [6] T.P. Wagnr, A.Y. Chkhan, and R. Hackam, Fdr rconfguraton for loss rducton: an applcaton of dstrbuton automaton, IEEE Transactons on Powr Dlvry, Vol. 6, No. 4, Oct. 99, pp [7] E. Ramos, A.G. Exposto, J.R. Santos and F.L. Iborra, Path-basd dstrbuton ntwork

7 80 UNIVERSITY OF PITESTI ELECTRONICS AND COMPUTERS SCIENCE, SCIENTIFIC BULLETIN, No. 8, Vol., 008 modlng: applcaton to rconfguraton for loss rducton, IEEE Transactons on Powr Systms, Vol. 0, No., May 005, pp [8] Y. Yu and J. Wu, Loads combnaton mthod basd cor schma gntc shortst-path algorthm for dstrbuton ntwork rconfguraton, n Proc. 00 IEEE Int. Conf. Powr Systm Tchnology, Vol. 3, Oct. 00, pp [9] K. Nara and M. Ktagawa, Dstrbuton systms loss mnmum r-confguraton by smulatd annalng mthod, n Proc. 99 IEEE Int. Conf. Advancs Powr Systm Control n Opraton and Managmnt, Vol., Nov. 99, pp [0] M.A. Matos, P. Mlo, Multobctv rconfguraton for loss rducton and srvc rstoraton usng smulatd annalng, n Proc. 999 IEEE Int. Conf. Elctrc Powr Engnrng, Aug.999, pp [] Y.H. Song, G.S. Wang, A.T. Johns and P.Y. Wang, Evolutonary approach to dstrbuton ntwork rconfguraton for nrgy savng, n Proc. 997 IEEE Int. Conf. Elctrcty Dstrbuton, Vol.5, No., Jun 997, pp. 33/- 33/8. [] H. Mor and Y. Ogta, A paralll tabu sarch mthod for rconfguratons of dstrbuton systms, n Proc. 000 IEEE Int. Conf. Powr Engnrng Socty Summr Mtng, Vol., July 000, pp [3] J.P. Chou, C.f. Chang and C.T. Su, Varabl scalng hybrd dffrntal voluton for solvng ntwork rconfguraton of dstrbuton systm, IEEE Transactons on Powr Systms, Vol. 0, No., May. 005, pp [4] X. Jn, J. Zhao, Y. Sun, K. L and B. Zhang, Dstrbuton ntwork rconfguraton for load balancng usng bnary partcl swarm optmzaton, n Proc. 004 IEEE Int. Conf. Powr Systm Tchnology, Vol., Nov. 004, pp [5] M. Assadan, M.M. Farsang and H. Nzamabadpour, Dstrbuton ntwork rconfguraton for loss rducton usng partcl swarm optmzaton, n Proc. Intrnatonal confrnc on physcal and tchncal problms n powr systm (TPE Ankara, Turky, 006. [6] Y. Lu and X. Gu, Sklton-Ntwork Rconfguraton Basd on Topologcal Charactrstcs of Scal-Fr Ntworks and Dscrt Partcl Swarm Optmzaton, IEEE Transactons on Powr Systms, Vol., No. 3, Aug. 007, pp [7] C. Zhang, J. Zhang and X. Gu, Th Applcaton of Hybrd Gntc Partcl Swarm Optmzaton Algorthm n th Dstrbuton Ntwork Rconfguratons Mult-Obctv Optmzaton, n Proc. Intrnatonal Confrnc on Natural Computaton ( ICNC , pp [8] W. Cu-Ru and Zhang Y.E., Dstrbuton Ntwork Rconfguraton Basd on Modfd Partcl Swarm Optmzaton Algorthm, n Proc. Intrnatonal Confrnc on Machn Larnng and Cybrntcs, 006, pp [9] A. Ahua, S. Das and A. Pahwa, An AIS-ACO Hybrd Approach for Mult-Obctv Dstrbuton Systm Rconfguraton, IEEE Transactons on Powr Systms, Vol., No. 3, Aug. 007, pp. 0-. [0] H. Salazar, R. Gallgo and R. Romro, Artfcal nural ntworks and clustrng tchnqus appld n th rconfguraton of dstrbuton systms, IEEE Transactons on Powr Dlvry, Vol., No. 3, July 007, pp [] D. E. Bouchard, D.E., M.M.A Salama, A.Y. Chkhan, Algorthms for dstrbuton fdr rconfguraton, n Proc. Canadan Confrnc on Elctrcal and Computr Engnrng, Vol, May 996, pp [] C. N. Macqun, M. R. Irvng, An algorthm for th allocaton of dstrbuton systm dmand and nrgy losss, IEEE Transactons on Powr Systms, Vol., No., Fb. 996, pp [3] A.C.B. Dlbm, A.C.Pd.L.F. d Carvalho and N.G. Brtas, Man chan rprsntaton for volutonary algorthms appld to dstrbuton systm rconfguraton, IEEE Transactons on Powr Systms, Vol. 0, No., Fb. 005, pp [4] M. Assadan, M.M. Farsang and H. Nzamabadpour, Dstrbuton Ntwork Rconfguraton Basd on GCPSO and graph thory, Frst Jont Confrnc on Fuzzy and Intllgnt Systms, Mashhad, Iran, Aug [5] D.E. Goldbrg, Gntc Algorthms n Sarch, Optmzaton, and Machn Larnng, Addson- Wsly: Nw York, 989. [6] J.A. Bondy and U.S.R. Murty, Graph thory wth applcaton, Canada, 976. [7] F.V. Goms, S. Carnro, J.L.R. Prra, M.P. Vnagr, P.A.N. Garca and L.R. Arauo, A nw hurstc rconfguraton algorthm for larg dstrbuton systms, IEEE Transactons on Powr Systms, Vol. 0, No. 3, Aug. 005, pp [8] D.B. Fogl, "An ntroducton to smulatd volutonary optmzaton", IEEE Trans. Nural Ntworks, vol. 5, Jan. 994, pp. 3-4.