Hybrid Evolutionary Algorithms based on PSO-GA for Training ANFIS Structure

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1 IJCSI Internatonal Journal of Computer Scence Issues, Volume, Issue 5, Septemer 05 ISSN (Prnt): ISSN (Onlne): Hyrd Evolutonary Alorthms ased on PSO-GA for Trann ANFIS Structure S.Mlad.Nayyer Saet and MR.Deevand Department of Medcal Physcs and Bomedcal enneern, Shahd Behesht Unversty of Medcal Scences, Tehran, Iran Department of Medcal Physcs and Bomedcal enneern, Faculty of Medcne, Shahd Behesht Unversty of Medcal Scences, Tehran, Iran Astract Ths paper ntroduces a new approach for trann the adaptve network ased fuzzy nference system (ANFIS).In ths study we apply hyrd of Partcle swarm optmzaton wth Genetc Alorthm (PSOGA) n t to the trann the antecedent parameters and the concluson parameters ANFIS structure Fnally the method s appled to the dentfcaton of nonlnear dynamcal system and s compared wth asc BP, GA, PSO and showed qute satsfactory results. The proposed method s appled to dentfcaton of the nonlnear systems and predcton chaos systems Keywords: ANFIS, Genetc Alorthm, Swarm Intellent, Identfcaton, Trann.. Introducton TSK type [] [] s a fuzzy system wth crsp functons n consequent, whch perceved proper for complex applcatons [3].It has een proved that wth convenent numer of rules, a TSK system could approxmate every plant []. The TSK systems are wdely used n the form of a neural-fuzzy system called Adaptve Network-ased Fuzzy Inference System ANFIS [5]. ANFIS s a very effcent modeln method y comnn the attrutes of oth of fuzzy nference system and neural network. The comnaton of fuzzy loc wth archtectural desn of neural network led to creaton of neuro- fuzzy systems whch enft from feed forward calculaton of output and ack propaaton learnn capalty of neural networks, whle keepn nterpretalty of a fuzzy system [3].ANFIS has ood alty and performance n system dentfcaton, predcton and control and has een appled n many dfferent systems. The ANFIS has the advantae of ood applcalty as t can e nterpreted as local lnearzaton modeln and conventonal lnear technques for state estmaton and control are drectly applcale. The updatn and trann of ANFIS parameters that consst of the antecedent and concluson parameters s one of the man prolems. The trann ANFIS, n the antecedent parameters s more dffcult than the concluson parameters. Varous methods have een used to optmze the fuzzy memershp functons n recent years. These methods can e dvded nto two types ncludn dervatve ased and heurstc alorthms n eneral []. Shoorehdel et al [6-] proposed hyrd methods composed partcle swarm optmzaton (PSO) and et al [7] [8] used recursve least square (RLS) and extended Kalman flter (EKL) et al [9] for trann. In dfferent studes, they proposed forettn factor recursve least square for trann the concluson parameters and Lyapunov stalty theory to study the stalty of used alorthm [6]. In addton to these, they used NSGA-II the trann of all parameters of ANFIS structure []. Zaneneh et al [3] proposed a new type of trann ANFIS s applyn complex type (DE/current-toest/+/n & DE/rand//n) on predctn of Mackeylass tme seres. In ths paper, we propose trann ANFIS y usn hyrd evolutonary Alorthms ased on PSO-GA alorthm. The proposed method s appled to predcton of Mackey-lass tme seres and dentfcaton of a nonlnear dynamc system revealn the effcency of proposed structure. Ths paper s oranzed nto sx sectons. In the next secton, we revew ANFIS. In secton 3, we dscuss learnn alorthms for ANFIS structure. In secton, the trann ANFIS usn PSOGA s explaned. In secton 5, the smulaton results are ven.fnally, secton 6 presents our concludn.. The Concept of ANFIS ANFIS technque was ornally presented y Jan []. It comnes the advantaes of fuzzy loc and neural networks. The ANFIS s composed of two approaches neural network and fuzzy. If we compose these two ntellent approaches, t wll e acheve ood reasonn n qualty and quantty. In other words we have fuzzy reasonn and network calculaton. ANFIS s structure oranzes two parts. The frst part conssts of antecedent 05 Internatonal Journal of Computer Scence Issues

2 IJCSI Internatonal Journal of Computer Scence Issues, Volume, Issue 5, Septemer 05 ISSN (Prnt): ISSN (Onlne): part and the second part conssts of concluson part. Antecedent part and concluson part are connected to each other y the fuzzy rules n network form. The updatn and trann of ANFIS depends on these parts. An adaptve network s a multlayer feed-forward network n whch each node performs a node functon on the ncomn snal as well as a set of parameters pertann to ths node of whch ts output depends. These parameters can e fxed or varale, and t s throuh the chane of the last ones that the network s tuned. ANFIS has nodes wth varale parameters, called square nodes whch wll represent the memershp functons of the antecedents, and the lnear functons for TSK-type consequent. The nodes n the ntermedate layers connect the antecedent wth the consequent. Ther parameters are fxed and they are called crcular nodes. Moreover, the network otaned ths way would not reman a lack ox, snce ths network would have fuzzy nference system capaltes to nterpret n terms of lnustc varales [5].The ANFIS structure s demonstrated n fve layers. It can e descred as a mult-layered neural network as shown n F.. Layer : The frst layer s called Fuzzfcaton layer. The parameters n ths layer are referred to as premse parameters. In fact, any dfferentale functon such as ell and tranular-shaped memershp functons (MFs) are vald for the nodes n ths layer. Every node n ths layer s a square node wth a node functon. Usually MFs are used as Gaussan wth maxmum equal to and mnmum equal to 0 such as: A (x) x c [( ) ] a B (x) x c [( ) ] a Where a,,c are the parameters of MFS whch are affected n shape of MFs. The parameters n ths layer are called the antecedent parameters. Layer : Ths layer s called rule layer. The rule layer represents the frn strenth for each rule en enerated n fuzzfcaton layer. They are crcular nodes wth a node functon: R O O, R O O, R O O, R O O (3) Layer 3: Ths layer s called normalzaton layer. rmalze layer calculates the normalzed frn strenth for each of the nputs. Ths normalzaton s the rato of the frn strenth of the th rule to the total of all frn strenths as ven (). R R ' R R R R 3 Layer : Ths layer s called defuzzfcaton layer. Every node n ths layer s a square node wth a node functon: F (x, x ) x x (5) 0 F (x, x ) R R R R R 3 (6) Layer 5: Ths layer s called sum layer. The snle node n ths layer computes the overall output as the sum of all ncomn snals. F (x, x ) R 3 O(x, x ) R R R R 3 F(x) (x ) A O (x, x ) (8) (x ) X X A A B B A O R R' Π N O Π Π Π R F.. The ANFIS network wth nputs and MF for an nput ANFIS approxmaton alty wll depend on the resoluton of the nput space parttonn whch s determned y the numer of MFs n ANFIS and the numer of layers. 3. Learnn Alorthms The susequent to the development of ANFIS approach, a numer of methods have een proposed for learnn the parameters and for otann an optmal numer of MFs. Jan [6] s ntroduced four methods to update the parameters of ANFIS structure, as lsted elow accordn to ther computaton complextes: N N N R' R'3 R' F F F3 F () (7) 05 Internatonal Journal of Computer Scence Issues

3 IJCSI Internatonal Journal of Computer Scence Issues, Volume, Issue 5, Septemer 05 ISSN (Prnt): ISSN (Onlne): All parameters are updated y the radent descent. After the network parameters are set wth ther ntal values, the consequent part parameters s adjusted throuh the LSE whch t s appled only once at the very ennn. Then, the radent decent updates all parameters. The hyrd learnn comnn radent descent and LSE. Usn extended kalman flter to update all parameters. In ths paper we used a hyrd method whch has less complexty and fast converence 3. Genetc alorthms Genetc alorthms (GAS) are a famly of computatonal models developed y Holland who s nspred y evoluton. [7] [8]. These alorthms encode a potental soluton to a specfc prolem on a smple chromosome lke data structure and apply recomnaton operators to these structures so as to preserve crtcal nformaton. GAS are often vewed as functon optmzers, althouh the rane of prolems to whch GAS have een appled s qute road. Ths GA procedure s sketched n Alorthm. Alorthm (Pseudo code verson of the GA alorthm): {Intalzaton} 0 /* : eneraton counter */ for = to M do /* M: populaton sze*/ Intalze ndvduals x to random values F f (x ) /* f: ftness functon */ Pop {x, x... x M} F {F, F,..., F M} {Man Loop} whle (not termnaton condton) do {Genetc Operators} Pop Selecton (Pop, F) Pop Crossover (Pop, p c) /*pc: proalty of crossover*/ Pop Mutaton (Pop, p m)/* pm: proalty of mutaton */ {Evaluaton Loop} for = to M do F f (x) F {F, F,..., F M} + end whle In GA populatons are formulated as astract representatons (called chromosomes) of canddate solutons (called ndvduals or phenotypes) to an optmzaton prolem. Typcally, the alorthm mantans a populaton of M ndvduals Pop () ={x (),..., x M()} for each teraton (also called eneraton), where each ndvdual represents a potental soluton of the prolem. The alorthm s an teratve process n whch new populatons are otaned usn a selecton process ased on ndvdual adaptaton and some enetc operators (crossover and mutaton). In each eneraton, the ftness (a measure of the qualty of the represented soluton) of every ndvdual n the populaton s evaluated. The ndvduals wth the est adaptaton measure have more chance of reproducn and eneratn new ndvduals y crossn and mutn. The selecton process s repeated several tmes and the selected ndvduals form a tentatve new populaton for further enetc operator actons. After selecton some of the memers of the new tentatve populaton undero transformatons. A crossover operator creates two new ndvduals (off sprns) y comnn parts from two randomly selected ndvduals of the populaton. In GA the crossover operator s randomly appled wth a specfc proalty, p c. A ood GA performance requres the choce of a hh crossover proalty. Mutaton s a untary transformaton whch creates, wth certan proalty, pm, a new ndvdual y a small chane n a snle ndvdual. In ths case, a ood alorthm performance requres the choce of a low mutaton proalty (nversely proportonal to the populaton sze).the mutaton operator uarantees that all the search space has a nonzero proalty of en explored. Usn these enetc operators, the eneral structure of the alorthm s sketched n Alorthm. Ths procedure s repeated several tmes (thus yeldn successve eneratons) untl a termnaton condton has een reached. Common termnatn crtera are that a soluton s found that satsfes a lower threshold value, or that a fxed numer of eneratons has een reached, or that successve teratons no loner produce etter results. Ideally, the alorthm s expected to evolve over tme toward etter solutons, althouh converence to loal optma cannot e enerally assured. 3. Partcle swarm optmzaton Partcle swarm optmzaton (PSO) s also an evolutonary computatonal model whch s ased on swarm ntellence. PSO s developed y Kennedy and Eerhart who have een nspred y the research of the artfcal lfe [8]. Smlar to GA, PSO s also an optmzer ased on populaton. The PSO does not possess the crossover and mutaton processes adopted n GA. It fnds the optmum soluton y swarms follown the est partcle. Compared to GA, the PSO has much more profound ntellent ackround and could e performed more easly. In PSO alorthm, the soluton of each prolem s 05 Internatonal Journal of Computer Scence Issues

4 IJCSI Internatonal Journal of Computer Scence Issues, Volume, Issue 5, Septemer 05 ISSN (Prnt): ISSN (Onlne): a rd n the search space called partcle. Every partcle has a ftness value whch s otann y ftness functon. The rd whch s closer to food has more ftness value. PSO starts wth a roup of random answers (partcles), and then t searches for fndn optmal answer n prolem space y updatn partcles poston. Every multdmensonal partcle (dependn on the prolem nature) s specfed y P d and V d whch denote the locaton poston and speed of dmenson d th of partcle. In every phase of swarm movement, poston of each partcle s updated y two est values. The frst value s the est answer accordn to ftness whch s otaned for each partcle separately untl now and s called P. Another value s the est value that s otaned y all of partcles throuh total swarms untl now and s called P. If a nehorhood s defned for every partcle, ths value s computed n that nehorhood. In ths case, ths value s called P. In every teratons of the alorthm, the new speed and poston of each partcle are updated y (9) and (0), after fndn and [9]: V ( s ) wv ( s) R [ P ( s) P( s)] R [ P ( s) P( s )] (9) d P ( s ) P ( s) V ( s ) (0) d d Where P d(s) and V d(s) are respectvely the poston and the velocty of partcle at tme s, w s called nerta weht and decde how much the old velocty wll affect the new one and coeffcents _and _ are constant values called learnn factors, whch decde the deree of affecton of P and P. In partcular, _ s a weht that accounts for the socal component, whle _ represents the contve component, accountn for the memory of an ndvdual partcle alon the tme. Two random numers, R and R, wth unform dstruton on [0, ], are ncluded to enrch the searchn space. Fnally, a ftness functon must e ven to evaluate the qualty of a poston. Ths PSO procedure s sketched n Alorthm. Alorthm (pseudo code verson of the PSO alorthm): {Intalzaton} s 0 /* s: tme varale*/ for = to N do /* N: sze of the swarm */ Intalze vectors V and P to random values P P P est { P ; =... N} /* ntal loal est */ {Man Loop} whle (not termnaton condton) do {Evaluaton Loop} for = to N do f f( P ) s etter than f ( P ) then P /* f: ftness functon*/ P /* partcle s est poston */ end f f f ( P ) s etter than f ( P ) then P P /* swarm s est poston */ end f {Update Loop} for = to N do V w.v +γ.r(0,).(p -P )+γ.r (0,).(P -P ) P P + V s s + end whle Ths procedure s repeated several tmes (thus yeldn successve eneratons) untl a termnaton condton s reached. Common termnatn crtera are that a soluton s found that satsfes a lower threshold value, or that a fxed numer of eneratons has een reached, or that successve teratons no loner produce etter results. 3.3 Hyrdzaton of GA and PSO The drawack of PSO s that stochastc approaches have prolem-dependent performance. Ths dependency usually results from the parameter settns n each alorthm. In eneral, no snle parameter settn can e appled to all prolems. Increasn the nerta weht (w) wll ncrease the speed of the partcles resultn n more exploraton (loal search) and less explotaton (local search). Thus fndn the est value for the parameter s not an easy task and t may dffer from one prolem to another. A further drawack s that the swarm may prematurely convere. Therefore, from the aove, t can e concluded that the PSO performance s prolem-dependent. The prolemdependent performance can e addressed throuh hyrd mechansm. It comnes dfferent approaches to e enefted from the advantaes of each approach. To overcome the lmtatons of PSO, hyrd alorthms wth GA are proposed. The ass ehnd ths s that such a hyrd approach s expected to have merts of PSO wth those of GA. One advantae of PSO over GA s ts alorthmc smplcty [0]. Ths smplcty wll result n the ncrease of speed calculatons and the reachn to the desred answer wth low volume of memory.another clear dfference etween PSO and GA s the alty to control converence. Crossover and mutaton rates can sutly affect the converence of GA, ut these cannot e analoous to the level of control acheved throuh 05 Internatonal Journal of Computer Scence Issues

5 IJCSI Internatonal Journal of Computer Scence Issues, Volume, Issue 5, Septemer 05 ISSN (Prnt): ISSN (Onlne): manpulatn of the nerta weht. In fact, the decrease of nerta weht dramatcally ncreases the swarm's converence. The man prolem wth PSO s that t prematurely converes to stale pont, whch s not necessarly maxmum. To prevent the occurrence, poston update of the loal est partcles s chaned. The poston update s done throuh some hyrd mechansm of GA. By applyn crossover operaton, nformaton can e swapped etween two partcles to have the alty to fly to the new search area. The purpose of applyn mutaton to PSO s to ncrease the dversty of the populaton and the alty to have the PSO to avod the local maxma. There are three dfferent hyrd approaches are proposed n [0].n ths paper used PSO-GA-seres hyrd evolutonary alorthm (PSOGA). The PSO-GA performs N PSO s populatons smultaneously at frst. After M teratons the est partcles n each populaton are selected to encode nto chromosomes to consttute an N- ndvdual-populaton for GA operatons. Then the populaton should e run usn GA-operators. After M teratons the est soluton of GA should e transmtted ack to PSO populatons. We defne ap-pso, ap-ga and ap as the teraton numers of PSO susystem, GA su-system, and whole system, respectvely; M, M and GAP-MAX the correspondn permssle maxmum teraton numers, respectvely[].the flow chart of the PSO-GA s shown n F.. Learnn y PSOGA In ths secton, the trann and updatn of ANFIS parameters usn PSO-GA s explaned. The ANFIS has two types of parameters whch need trann, the antecedent part parameters and the concluson part parameters. The memershp functons are assumed Gaussan as n equaton (, ), and ther parameters are a,,c, where a s the varance of memershp functons and c s the center of MFs. Also s usually equal to. The parameters of concluson part are traned and here are represented wth p,q,r. There are 3 sets of tranale parameters n antecedent part, each of these parameters has N enes. Where, N represents the numer of MFs. The concluson parts parameters also are traned durn optmzaton alorthm. Each chromosome n concluson part has (I +) R enes that R s equal to Numer of rules and I denotes dmenson of data nputs. The ftness s defned as RMSE [9]. Parameters are ntalzed randomly n frst step and then are en updated usn PSO-GA alorthms. In each teraton, one of the parameters set are en updated..e. n frst teraton for example a s are updated then n second teraton are updated and then after updatn all parameters aan the frst parameter update s consdered and so on. Intalzaton of N PSO populaton Set ap=0 Set ap_pso=0 Do PSO operators for each populaton=0 Termnaton crteron met? If ap_pso=m? Gap_PSO++ Intalzaton of GA populaton Set ap_ga=0 DO GA operators Termnaton crteron met? If ap_ga=m? Gap_GA++ If ap>=gap_max? Best ndvdual=>pso populatons Gap++ Fnal soluton F.. Flow chart of PSO-GA 05 Internatonal Journal of Computer Scence Issues

6 IJCSI Internatonal Journal of Computer Scence Issues, Volume, Issue 5, Septemer 05 ISSN (Prnt): ISSN (Onlne): Smulaton Results Ths secton presents the smulaton results of ANFIS trann usn ack propaaton (BP), enetc alorthm (GA), partcle swarm optmzaton (PSO) and PSOGA alorthm. In ths secton, we use two dfferent types of trann data set: a snle-nput and snle-output trann data set, four-nput and snle-output trann data set. A. Example (nlnear Functon Modeln) In ths applcaton, a snle-nput and snle-output trann data set s used defned y (). Defnn rane of x s [-, ], the system produces 5 roups of nput and output data. y 0.6sn( x) 0.3sn( x) 0.sn(5 x) () The parameters for trann the ANFIS y PSO-GA lsted n Tale. Tale: parameters PSOGA for trann ANFIS Swarm sze (populaton sze) 0 Num.of epochs 00 Crossover percentae(pc) 0.8 Mutaton percentae(pm) 0.3 Mutaton rate(µ) 0.0 Gamma(γ) 0. Selecton pressure(β) 8 Constrcton coeffcents(φ).05 The results are ven n Tale.Ths Tale shows tran, test RMSE and STD (standard devatons) for dfferent types of trann ANFIS structure. The RMSE of PSOGA s 0.0 for 0 rules, as ven n Tale. The comparsons wth ANFIS valdate the performance of the PSOGA. Num. rule Tale : Test, Tran RMSE and STD for Example Tran y Tran. Test. Tran. Test. RMSE RMSE STD STD BP PSO GA PSO- 8 GA B. Example (Predctn Chaos Dynamcs) The data s enerated from the Mackey-Glass tme-delay dfferental equaton whch s defned y: 0. x(t ) x 0 x t 0. x(t) () When x (0) =. and τ = 7, we have a non-perodc and non-converent tme seres that s very senstve to ntal condtons. (We assume x (t) = 0 when t < 0.) ANFIS structure has nputs and one output. We use 807/36 data as trann/test. F.3- s depcted predctn of Mackey-Glass tme seres usn PSOGA, GA, BP, and PSO to tran parameters n ANFIS structure. Ths raphc shows tran, test data for tarets and outputs and RMSE for errors usn y dfferent types of trann ANFIS structure. The numers of teratons of ths alorthm and populaton sze s 000 and 00 respectvely, we used 0 rules and other parameters s accordn Tale. 05 Internatonal Journal of Computer Scence Issues

7 IJCSI Internatonal Journal of Computer Scence Issues, Volume, Issue 5, Septemer 05 ISSN (Prnt): ISSN (Onlne): F3.The ANFIS traned y GA for Tran data and RMSE F6. The ANFIS traned y PSO for Test data and RMSE F. The ANFIS traned y GA for Test data and RMSE F7.The ANFIS traned y BP for Tran Data and RMSE F5. The ANFIS traned y PSO for Tran data and RMSE F8.The ANFIS traned y BP for Test Data and RMSE 05 Internatonal Journal of Computer Scence Issues

8 IJCSI Internatonal Journal of Computer Scence Issues, Volume, Issue 5, Septemer 05 ISSN (Prnt): ISSN (Onlne): Conclusons F9.The ANFIS traned y PSOGA for Tran Data and RMSE In ths paper, we proposed a novel method for trann the parameters of ANFIS structure. In our novel method we used PSOGA for updatn the parameters. The smulaton results show that PSOGA s successful for trann ANFIS for complex nonlnear systems and predcton chaos systems. Snce ths alorthm s free of dervaton whch s very dffcult to calculate for trann of antecedent and concluson part parameters complexty of ths new approach s less than other trann alorthms lke BP,GA and PSO. Also, the local mnmum prolem n BP alorthm for trann n ths novel approach s solved. The effectveness of the proposed PSOGA method was shown y applyn t to dentfcaton of nonlnear model. Acknowledments Ths work s part of my master s thess. Authors are ndeted to the Department of Medcal Physcs and Bomedcal enneern of Shahd Behesht Unversty for the support provded durn ths study. F0.The ANFIS traned y PSOGA for test Data and RMSE F.The RMSE-Iteraton ANFIS usn y PSOGA The smulatons results showed PSOGA optmzes ANFIS parameters etter than GA, BP and PSO for test and tran data. References [] M.Sueno and G. T. Kan, Structure dentfcaton of fuzzy model, Fuzzy sets and systems, pp.5-33, 998. [] T. Taka and M. Sueno, Fuzzy dentfcaton of systems and ts applcaton to modeln and control, IEEE Trans. Sys., Man& Cyernetcs, pp.6-3, 985. [3] R. Alcala, J. Casllas, O. Cordon and F. Herrera, Learnn TSK rule ased system from approxmate ones y mean of MAGUL methodoloy. Granada unversty of Span, Oct.000. [] M. Mannle, FSTM: Fast Taka-Sueno fuzzy modeln. Unversty of Karsruhe, 999. [5] Jyh-Shn Roer Jan, ANFIS: Adaptve Network Based Fuzzy Inference System, IEEE Trans. Sys., Man & Cyernetcs, vol.3, no.3, May-June 993. [6] M. A. Shoorehdel, M. Teshnehla and A. Sedh, "Trann ANFIS as an dentfer wth ntellent hyrd stale learnn alorthm ased on partcle swarm optmzaton and extended Kalman flter," Fuzzy Sets and Systems, vol. 60, pp. 9-98, 009. [7] M. A. Shoorehdel, M. Teshnehla and A. Sedh, "A novel trann alorthm n ANFIS structure," n Amercan Control Conference, IEEE, June 006. [8] M. A. Shoorehdel, M. Teshnehla and A. Sedh, Identfcaton usn ANFIS wth ntellent hyrd stale learnn alorthm approaches, Neural computn & applcatons, vol. 8(), pp. 57-7, 009. [9] M. A. Shoorehdel, M. Teshnehla and A. Sedh, vel hyrd learnn alorthms for tunn ANFIS parameters 05 Internatonal Journal of Computer Scence Issues

9 IJCSI Internatonal Journal of Computer Scence Issues, Volume, Issue 5, Septemer 05 ISSN (Prnt): ISSN (Onlne): usn adaptve wehted PSO, In Fuzzy Systems Conference, fuzzy-ieee 007, IEEE Internatonal, pp. -6, 007. [0] M. A. Shoorehdel, M. Teshnehla, A. K. Sedh and M. A. Khanesar, Identfcaton usn ANFIS wth ntellent hyrd stale learnn alorthm approaches and stalty analyss of trann methods, Appled Soft Computn, vol. 9(), pp , 009. [] V. S. Ghomsheh, M. A. Shoorehdel, M. Teshnehla, Trann ANFIS structure wth modfed PSO alorthm, In Control & Automaton, MED'07. Medterranean Conference on IEEE, pp. -6, June 007. [] A. Chatterjee and K. Watanae, An optmzed Taka- Sueno type neuro-fuzzy system for modeln root manpulators, Neural Computn & Applcatons, vol. 5(), pp. 55-6, 006. [3] A. Z. Zaneneh, M. Mansour, M. Teshnehla and A. K. Sedh, Trann ANFIS system wth DE alorthm, In Advanced Computatonal Intellence (IWACI), IEEE 0 Fourth Internatonal Workshop on, pp , Octoer 0. [] J. S. Jan, "ANFIS: Adaptve-network-ased fuzzy nference system," Systems, Man and Cyernetcs, IEEE Transactons on 3.3, pp , 993. [5] M. Kumar and P. G. Devendra, Intellent Learnn of Fuzzy Loc Controllers va Neural Network and Genetc Alorthm, Proceedns of 00 JUSFA 00 Japan-USA Symposum on Flexle Automaton Denver, Colorado, 00. [6] Jyh-Shn Roer Jan, ANFIS: Adaptve-Network-Based Fuzzy Inference System, IEEE Trans. Sys.Man and Cyernetcs. Vol. 3,.3, May/June 993. [7] J.H. Holland, Adaptaton n Natural and Artfcal System, the Unversty of Mchan Press, Ann Aror, 975. [8] D.E.Golder, Genetc Alorthms n Search, Optmzaton & Machne Learnn. Readn, MA: Addson Wesley, 989. [9] J. Kennedy, R.C. Eerhart, "Partcle swarm optmzaton", Proceedns of IEEE Internatonal Conference on Neural Networks, vol., 995. [0] K. Premalatha and A.M. Natarajan, "Hyrd PSO and GA for Gloal Maxmzaton", Int. J. Open Prolems Compt. Math., Vol.,., pp , Decemer 009. [] Sh, X.H.; Lu, Y.H.; Zhou, C.G.; Lee, H.P.; Ln, W.Z.; Lan, Y.C., "Hyrd evolutonary alorthms ased on PSO and GA," n Evolutonary Computaton, 003. CEC '03. The 003 Conress on, vol., no., pp Vol., 8- Dec MR.Deevand receved the B.Sc. deree from the shahd ahonar Kerman, Tehran, Iran, the M.Sc. deree from the Isfahan Unversty of Medcal Scence, Tehran, Iran, and the Ph.D. deree from Tarat Modaress Unversty, Tehran, Iran, n 998, all n medcal physc.from 0, he was a Faculty Memer at the Shahd Behesht Unversty of Medcal Scences and Health Servces, Tehran, Iran. He s currently an Assocate Professor wth the Faculty Medcal Physcs and Bomedcal enneern Department of Medcal Physcs and Bomedcal enneern. Hs nterest nterests nclude medcal mae processn, computatonal ntellence, ntellent optmzaton and radaton protecton. S. Mlad. Nayyer Saet was orn n Rasht, Iran, n 986. He receved the B.Sc. deree from the Unversty of Rasht, Iran, n electrcal enneern snce 008.and the M.Sc. deree from the Shahd Behesht Unversty of Medcal Scences and Health Servces, Tehran, Iran n omedcal enneern. He has een workn toward the M.Sc. deree n omedcal enneern at the Shahd Behesht Unversty. Hs man research nterests nclude o rootc, snal processn& medcal mae processn, computatonal ntellence, ntellent optmzaton, and mult ojectve optmzaton. He s currently don research n the feld of control o rootc systems, as M.Sc. thess. 05 Internatonal Journal of Computer Scence Issues