Performance Assessment of Search Management Agent under Asymmetrical Problems and Control Design Applications

Transcription

1 Performance Aement of Search Management Agent under Ammetrical Problem and Control Deign Application Jukkrit Kluabwang Deacha Puangdownreong and Sarawut Sujitjorn * School of Electrical Engineering, Intitute of Engineering Suranaree Univerit of Technolog Nakhon Ratchaima, Thailand Department of Electrical Engineering, Facult of Engineering South-Eat Aia Univerit Bangkok, Thailand * correponding author: arawut@ut.ac.th Abtract: - The article preent the performance evaluation of the management agent (MA) containing the adaptive tabu earch (ATS) a it earch core. In particular, ammetrical urface optimization problem have been conidered. It ha been found that mmetrical propert of the problem ha a ignificant effect on earch performance of the ATS, but MA(ATS). A an average, the MA(ATS) i about time fater than the ATS under both mmetrical and ammetrical problem. The article alo give review on the ATS and the MA(ATS) algorithm. An application on controller deign for a coupled tem with three-degree-of-freedom i alo elaborated. Ke-Word: - ammetrical urface optimization problem, adaptive tabu earch, management agent Introduction In recent ear, intelligent earch technique have become major approache for olving variou optimization problem. Among thoe, tabu earch (TS) ha been widel applied for combinatorial optimization problem [,]. The TS conit of two main trategie: intenification and diverification [,]. Since the TS i ver fleible to ue for variou problem, Sujitjorn et. al. [,6] have launched a modified verion of the TS namel adaptive tabu earch (ATS). The ATS poee the backtracking (BT) and adaptive radiu (AR) mechanim. The former i regarded a a diverification trateg, while the later a an intenification one. The convergence proof and performance aement of the ATS can be found in [,6]. Reader can find ATS application, uch a electrical tem protection in [7], tem identification in [8,9], control nthei in [,], and acoutic ignal proceing in []. In 8, the author propoed a management agent for earch algorithm called hortl a MA ( ). ( ) can be replaced b an earch algorithm uch a ATS, imulated annealing, genetic algorithm, etc. The MA contain three major mechanim: partitioning mechanim (PM), dicarding mechanim (DM), and equencing mechanim (SM). Thi article report our computing reult in order to ae the effect of mmetr of the problem on earch performance of the MA(ATS), i.e. the MA having the ATS a it earch core. Section of the paper review the ATS and the MA. Section and preent our problem formulation, reult and dicuion, repectivel. An application on control tem deign appear in ection. Concluion i in ection 6. Review of Algorithm. Adaptive Tabu Search (ATS) The ATS [,6] preerve the main earch mechanim of the generic TS [,]. Regarding thi, the tabu lit (TL), the apiration criteria (AC), and the termination criteria (TC) are effective. The additional mechanim are the backtracking (BT), and the adaptive earch radiu (AR), repectivel. The BT i for ecaping the lock b local olution via looking backward the TL for ome previou olution and adopting them for generating new earch direction. The AR ubequentl reduce the earch radii in earch of a high fidelit olution. The proof elaborated in [,6] confirm the ATS rapid ISSN: Iue, Volume 8, April 9

2 earch performance, and convergence. The following decription ummarize the algorithm. STEP Initialization: earch radiu R, TL, count, count ma, TC, BT, and AR. STEP Random an initial olution S. Set S a a local olution. Generate the neighbourhood of radiu R around S. Keep N olution of the neighbourhood in the et X. STEP Evaluate the cot, C, of each olution belonging to X. The olution having the minimum cot i deignated a S. If C(S ) < C(S ), move S into TL and aign S = S, otherwie move S into TL. Start STEP If the olution ccling occur, invoke the BT mechanim. STEP Eit with S a the bet olution if the TC are met. STEP If the current olution S in the vicinit of the local or the global minimum, invoke the AR mechanim. Update count, and goto STEP. Intereted reader can find the ueful recommendation with eample for the benefit of emploing the algorithm from [-]. MA Initialization : - Preet variable(count, Re, n_ccling, Tabu lit) in all ATS to be zero or empt. - Set proper value for thee variable, count ma, Re ma, N. Load a urface optimization problem, from eq.() -(), including it earch pace. Chooe number of path for MA. Activate PM to genetate ub-earch-pace for generating initial olution. After obtaining all initial olution in each ub-earch-pace, then, replace all ub-earch-pace with the original earch pace to all ATS. ATS # ATS # Sequencing thee ub-earch-pace on the bai of time haring. ATS # n Stop earching and report reult e TC met? Stop no DC met? no e Activate DM - etinguih k ATS earch path - n = n - k, k >= n -, n min = Fig. Flow diagram of the MA. [,] ISSN: Iue, Volume 8, April 9

3 . Management Agent for Search Recentl, the author have launched the earch management agent (MA) fleible enough to be ued with an earch algorithm, particularl the metaheuritic one [,]. The MA doe not intrude the main algorithm ued a the earch core unit. So, the convergence propert of the earch core i alwa preerved. The MA conited of main trategie namel the partitioning, the equencing, and the dicarding mechanim (PM, SM, and DM), repectivel. The PM erve to plit an entire earch pace into man ub-earch-pace. It alo initiate earche correpondingl to thoe ub-earchpace. After the earch initiation, the earch boundarie, once arien from the PM, are immediatel removed. The earch pace i then the original one containing everal to man earch path. The PM concept i not new, and ha been applied to data fuion [] and genetic algorithm [6], for intance. The SM on a ingle CPU platform i crucial becaue it organize the earch unit to perform earche in a equential manner without a conflict. The SM can be regarded a a time-haring trateg. A oon a all earch path finih their earche at the k th round, the DM interrupt all earch path, and interrogate them for the current olution with aociated cot value. The DM, apparentl behave imilarl to the location management algorithm [7,8], i an important tactic to accelerate the earch. It determine the chance of ucce of each earch path, and eliminate thoe conidered to have le chance. For intance, ome earch path that are locked b local minima are rapidl deleted from the earch plateau. The DM i activated upon the dicarding criteria (DC). The DC i impl the meaurement of error between the cot of the global olution and that of the current one. The concept of MA become clearer with the flow diagram reproduced from [,] and illutrated in Fig.. Referring to the flow diagram, the earch core implemented i the ATS. In addition to thi, the algorithm MA(ATS) can be ummarized a follow: STEP Define earch pace and earch path. Generate initial olution (random or well-educated gue). Activate PM. STEP Invoke SM and ATS of multiple path (or other earch algorithm). STEP Eit with the bet olution if the TC are met, otherwie invoke DM. STEP Update counter and goto STEP. Performance Evaluation Our evaluation wa conducted againt the Shekel Fohole function (ee Fig. and ) epreed b equation (). The global olution it on (-,-) coordinate. It cot value i. Fig. how the top view location of the global olution for the mmetrical and ammetrical problem. Table ummarrize the correponding earch pace. Our MATLAB TM code were run on a Pentium IV. GHz 6 Mbte of SD-RAM (-,-) i the global olution with objective value equal one in which Global olution, (-,-) in a mmetrical earch pace [8 8;-7-7] Fig. Shekel Fohole urface under mmetrical problem -D and -D. f (, ) = j= j i= 6 ( ) i a ij - (), a =. ij 6... Our tet were alo conducted againt the Bohachevk, and the Ratrigin function. The ISSN: Iue, Volume 8, April 9

4 WSEAS TRANSACTIONS on COMPUTERS are repreented b the epreion () and (), repectivel, with their correponding urface plot hown in Fig. and 6. For ammetrical problem, the global olution are eccentric in the imilar manner to what hown in Fig., otherwie mmetrical. earch pace earch pace global olution global olution f (, ) =. co(π). co(π).7 (), f (, ) = co( π) co( π ) (). Fig. Top view location of the global olution mmetrical and ammetrical problem. Table Correponding earch pace. earch pace Tpe BF & RF SF Sm. [ ;- -] [8 8;-7-7] Am. [ ;- -] [ ;- -] f(,) (,,) i the global olution (-,-) i the global olution.. (,) i the global olution (-,-) i the global olution Fig. Bohachevk urface under ammetrical problem -D and -D. Fig. Shekel Fohole urface under ammetrical problem -D and -D. ISSN: Iue, Volume 8, April 9

5 WSEAS TRANSACTIONS on COMPUTERS 6 # begin ATS# f(,) # end f(,) ATS# # begin ATS# # begin # end # end. Global olution (,,) # end. ATS#.. # begin (,,) i the global olution ATS# ATS# ATS#. ATS# f(,). (,) i the global olution Global olution at (,,) Fig. 6 Ratrigin urface under ammetrical problem -D and -D. Fig. 7 Search trajectorie ( path) on Ratrigin urface bird ee view and front view. Reult and Dicuion Referring to the average earch time in econd ummarized b table, the earch time conumed b the ATS i longer than that ued b the MA(ATS) for each cae. Under ammetrical problem, the ATS conume longer earch time than that ued under mmetrical problem. For the MA(ATS), the following detail are clarified. With the BF, 66.67% of MA(ATS), i.e.,, 6, and 6 path, reach the global olution fater under mmetrical problem than under ammetrical one. Similar ituation occur with the RF and the SF. 8.% of MA(ATS), i.e.,, 8, 6, and 6 path, perform fater earche with the mmetrical RF. % of MA(ATS), i.e., 6, and 6 path, perform fater earche with the mmetrical SF. Fig. 7 demontrate the cae of earch trajectorie on the Ratrigin urface. The ATS# and # are dicarded on the th iteration, ubequentl ATS# on the th iteration. The ATS# pent.8 econd to hit the global optimum b the 7nd iteration and at (.8-6, -.7-6), with the cot value of Moreover, Fig.8- illutrate the trace of earch trajectorie (6 path) on the three contour of both mmetrical and ammetrical problem. Table Average earch time. average earch time (econd) Tet function ATS BF RF SF # # MA(ATS) #6 # #6 Sm Am Sm Am Sm Am ISSN: 9-7 peed up ratio = average earch time b ATS () average earch time b MA(ATS) The peed up ratio according to () are calculated and ummarized b the bar graph hown in Fig.. 69 Iue, Volume 8, April 9

6 . #7 #6 # # # # Path trike # #9 # # # # # # #6. # # # # # # #9 #9 # #7 # # #6 #9 #7 #7 #6 # # # -. # # # # # #6 #7 # - # # # # # # #9 -. #7 #6 # #6 #6 #6 #6 #6. #7 #6 # # # # Path trike # #9 # # # # # # #6. # # # # # # #9 #7 #6 #7 #9 # # #. # #9 #6 #7 #6 # # #7 # # # # # # # # # # # # #9 -. #6 #7 # #6 #6 #6 #6 #6 Fig. 8 Trace of earch path (6 path) on Bohachevk contour mmetrical cae and ammetrical cae. 6 ISSN: Iue, Volume 8, April 9

7 WSEAS TRANSACTIONS on COMPUTERS #6 # # # #7. # Path trike # : tart : between : top # #9 # # # # #6 # # # #9 # # # #7. #6 #9 #7 # # # # #9 # #6 #7 -. # # # # # # # - #6 #7 #6 # # # # # # #9 # -. #7 #6 # #6 # #6. #6. #6 #7 # # # # # : tart : between : top Path trike. # #9 # # # # # # # #6 #9 # # # #7. #6 # # #9 # #7 # # #6 #7 #9 # # #. # # # # # #6 #7 #6 # # # # # # # #6 #7 #6 #9 -. #6. #6 #6.. Fig. 9 Trace of earch path (6 path) on Ratrigin contour mmetrical cae and ammetrical cae. ISSN: Iue, Volume 8, April 9

8 # # : tart : between : top Path trike # #9 # #6 #7 # #7 # #6 # # # #6 #7 #9 # # # #9 # # #7 # # # # #6 # # #9 # # #6 # #9 # # # # # #6 #6 #6 # #7 # # #6 #7 # # # #9 #6 # # #7 #6 #9 # # # # # # # # Path trike # : tart : between : top # # # #6 - # # # #6 #9 # # # # #9 #7 #9 # #7 # #7 # - # # #6 # # #6 #9 # # #9 # - # #6 #6 #7 #6 #6 # Fig. Trace of earch path (6 path) on Shekel fohole contour mmetrical cae and ammetrical cae. #6 # # # #7 # # 8 ISSN: Iue, Volume 8, April 9

9 Speed up ratio (time) Speed up ratio(time) # # # # #. #.7 #6.8 #6 #. #. #6.6 # Sm. Bohachevk' BF function Am. # # # # #. #.9 #6.9 #6 #.8 #.6 #6. # are ummarized b table. The figure indicate that the MA(ATS) of 6 path provide the fatet earch. Table Average peed up ratio. no. of path average peed up ratio (time) Application Control engineering application are dicued herein. The problem i to fine tune an eiting control tem uch that optimall eeked controller could be obtained. The control tem of the Illinoi Roadwa Simulator (IRS) tem [9,] in which the aw rate control (ee Fig. ) i of prime objective. Speed up ratio (time) #. #. #.6 Sm..7 Sm. #6.7 Ratrigin' RFfunction #.8 #6.8 #. #. #. Shekel' fohole SF function Am..6 Am. #6.79 #. Fig. Speed up ratio of the MA(ATS). #6. The top window of Fig. how the reult of the MA(ATS) earching through the Bohachevk urface. The numeric figure embedded in each bar, for intance, (#,.) mean that it i of the cae ingle path ATS, thu having the peed up ratio equal to. A another eample, conider the ammetrical cae appearing in the ame window, the bar with (,.) mean the cae of 8-path ATS having the peed up ratio of. time that of the ingle path ATS. The imilar eplanation i applied to the ret of the reult. Noticeabl, the peed up ratio of the mmetrical and the ammetrical problem bear ver imilar figure. Thi mean that the mmetrical propert of the problem doe not greatl affect the earch performance of the MA(ATS). To give an average figure, the MA(ATS) perform earch in equential manner about.7 time fater than the ATS doe. Average peed up ratio of,,...,6 path Fig. Car reference frame. The tem can be repreented b the block diagram hown in Fig.. Referring to Fig., two -polnomial ratio namel G and G repreent the d vehicle dnamic, and epreed b Fig. Block diagram repreenting the aw rate control..8.6 G = () (6). G d = ISSN: Iue, Volume 8, April 9

10 The control tem ha three degree-offreedom, and poee the following controller: 9 8 Rie time =. ec Final value = 8.66 rad/ec Settling time =. ec G = dc (7) G = (8) ff Yaw Rate (rad/ec) G = (9). fb. The tranfer functiong ir Y ( ) = R( ).7 9. V ( ) = G = ir can be written a (). Fig. how the imulation reult of the original control tem. The aw rate repone due to unit-tep input i quite mooth and contain a dela time of. ec. It i noticed that the tem ha the DC-gain of rad/ec Time (ec) Fig. Yaw rate repone of the original tem [9,]. function J=obj(r,r,r,r,,,,,t,t,t,a,a,a,a,a,a6, b, b, b,b,b,b6) % Declaration G=tf([.8e.7e],[ e.8e.66e]); Gd=tf([.8e 6.7e],[..9.9e.698e.67e]); Gdc=tf([b b b b b b6],[a a a a a a6]) ; Gff=tf([t t t],[r r r r]); Gfb=tf([ ],[r r r r]); Gir=(GdG*GdcG*Gff)/(G*Gfb); a=real(pole(gir)); % Pole of overall Cloedloop Stem. if a< % Onl Stable Stem allowed come in. [,t]=tep(gir); % Step repone data recorded. if (length())>8.66 & (length())<8.67 % Onl ame DC gain. i=find(>.*((length())-())&<.9*((length())-())); tr=t(i(length(i)))-t(i()); trj=(tr*)/.96979; % Find trj. Mpj=*(ma()-(length()))/(length()); % Find Mpj. for i=:length() % Find tj. (length())=(length()); d(i)=(i)-(i); end i=find(~(d<e-)); t=t(i(length(i)))-t(i()); tj=(t*)/(.96979*); if trj< % Contraint, trj mut be le than. trj=trj; % Contraint, otherwie trj =,. ele trj=; end if Mpj< % Contraint, Mpj mut be le than. Mpj=; % Contraint, then Mpj =. ele % Contraint, otherwie Mpj =,. Mpj=; end if tj<*trj % Contraint, tj mut be < *trj. tj=; % Contraint, then tj =. ele % Contraint, otherwie tj =,. tj=; end J=trjMpjtj; % Objective function, J. ele J=; end ele J=; end return % Note that the original tem ha the objective function J =. Fig. Objective function coding. ISSN: Iue, Volume 8, April 9

11 To obtain controller that render an optimum repone i not a trivial tak. In conventional practice, the controller have to be deigned one-b-one with an epectation of having a atifactor repone of the complete tem. Snthei all the controller imultaneoul i poible via an intelligent earch method. Thi control nthei can be formulated a a combinatorial optimization problem to minimize J, where J i a combined objective function namel t rj, J t M t = (). rj M pj and t j in the equation () are normalized, hence unitle, and tand for rie time, overhoot and ettling time, repectivel. In our oftware implementation, the penalt concept of uing, a a magnification factor i applied to t r, M p and t in order to obtain a fine qualit olution. The tep performance pecfication are t r <. ec, M p < %, and t defined a the firt time the repone top ocillating completel. Moreover, it i mandated that the tem maintain the DC-gain. Defining uch performance pecification, the MA(ATS) i epected to produce three polnomial controller optimall rendering a better repone than that of the original. Fig. provide the code lit of the objective function, J. Our control problem aume the nominal plant model whoe parameter are fied. The three controller namel G dc, G ff and G fb are rewritten a follow: b b b b b b = () G 6 dc a a a a a a6 p p p = () r G ff r r r G fb r r r q q q = () r whoe parameter r, q, p, a and b are to be earched. Regarding to the original deign, thee parameter are ummarized in table. Some initial trial referred to a pre-earch proce were carried out in order to etablih earch range of all influential parameter. The TC for the pre-earch pj j proce wa either J< or count ma =. The parameter were earched one-b-one. During the pre-earch, one parameter wa earched while the other were kept contant a their original value in order to invetigate it influence on the tem timedomain performance, tabilit a well a ma-min range for earch. Referring to the table, the parameter hown in bold character are thoe influencing the performance while being tabilit inenitive. Some hown in ordinar character do not have much influence on the performance, but the are tabilit enitive. Table alo how the ma-min range of the parameter obtained from the pre-earch. Thee range are further ued a earch pace for the correponding parameter. Fig. 6 depict the influential parameter affecting the tem performance in term of the percent reduction in rie time. Thee parameter printed in bold in the table are to be tuned via our MA(ATS). Percent of reduction in rie time (%) 6.7 Reult of Pre-Search proce b ATS to all parameter t The number of path in the MA(ATS) can be nd obtained from here, according to the number rd of the activel tuned parameter, o we get path to do the net tep. th th th th th th th th th 6 th r b b a a t b r r t b the b b a a b r t r r tret Influential parameter Fig. 6 Reult of the pre-earch proce. The earch for thee parameter are ditributed among ATS path with the correponding earch pace hown b bold character in the table. At the beginning, all ATS path emplo different initial olution and the following heuriticall et earch parameter: N_neighbour =, R=., AR -if J<9 then R=.R, AR -if J<8 then R=.R, k th _backward=, N_re_ma =, ma_count =, TC if J<7 or ma_count hit, DM -at th iteration reduce to 7 path, DM -at th iteration reduce 7 to path and DM -at th iteration reduce to path. Referring to the table, ATS path perform a mied tpe of multiple point ingle trateg (MPSS) and ingle point ingle trateg (SPSS) earche. The PM of the MA(ATS) deignate the earch in the following manner: - within the t neighbourhood, ATS# to # perform independentl earch for the individual parameter r, r, r, q, q, p, p, a, a, b, b, b, and ISSN: Iue, Volume 8, April 9

12 Table Summar of controller parameter and correponding earch pace. no. parameter of original controller parameter obtained from MA(ATS) ma-min range of parameter ATS (at PM) r r r r q q q q p p p a a a a a a6 b b b b b b [.] [..] [ ] [.7.7 ] [ ] [ ] [ ] [.8.8 ] [ -] [ ] [ ] [.66 ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [-. -. ] [ ] ATS# ATS# ATS# ATS# ATS# ATS#6 ATS#7 ATS ATS#9 ATS# ATS# ATS# ATS# Objective value; J Objective value; J At PM time, an earch unit ma have ver high objective value uch a ATS# and # DM t tage eliminated ATS#, #, #,, #9 and # from earch proce. DM nd tage eliminated ATS#, #6, # and # from earch proce. Onl ATS# i left in the earch proce. DM rd tage eliminated ATS# and ATS#7 from earch proce iteration Convergence curve of MA(ATS) Objective value; J ATS# hit the global olution. J=69.89 (J<7,TC) iteration Three tage of DM reduced a number of earch path from to 7 at th iteration in t tage, and net tage, th iteration reduced from 7 to and the lat tage, th iteration there i onl from to continue. ATS# hit the global olution within 7. econd at iteration th with the objective value, J= iteration Fig. 7 Convergence curve of the control deign problem. ISSN: Iue, Volume 8, April 9

13 b, repectivel; during thi earch tage, the parameter not being ubjected to the earch are kept contant a the original value; each ATS path would obtain it bet olution to be ued a an initial olution for a new earch generation; - after finihing the t neighbourhood earch, all ATS path with their correponding initial olution for the parameter are releaed to earch freel for all parameter. The cot value monitored are preented a the convergence curve in Fig. 7. Among the ATS path, the th path ucceeded in reaching the olution with J=69.89, and within 7. ec. The parameter obtained from earch are hown in bold character in the table. The reult in the following controller * G = dc () * G ff = (6) * G fb = (7). The overall tranfer function of the tem having the controller in ()-(7) i epreed b * G = ir Yaw Rate (rad/ec) Overhoot =. % Final value = 8.66 Rie time =.6 ec Rie time =. ec Settling time =.79 ec. Settling time =. ec (8). Original output Tuned output Searched controller provide.% and.% reduction in rie time and ettling time, repectivel, while the overhoot i kept below % Time (ec) Fig. 8 Comparion of time-domain performance. Fig. 8 how the time-domain performance of the original and the propoed tem for comparion. It can be noticed that the new controller provide much better performance in term of.% and.% reduction in rie time and ettling time, repectivel, while the overhoot of.% i acceptable. 6 Concluion The performance aement of the management agent for earch, in particular MA(ATS), ha been preented. Computing eperiment were conducted againt mmetrical and ammetrical problem. In thi contet, a mmetrical problem ha it global olution ituated at the center of the earch pace, while that of an ammetrical problem i eccentric. Surface optimization problem have been utilized baed on the Bohachevk, Ratrigin, and Shekel Fohole function, repectivel. The derived peedup ratio indicated that (i) the MA(ATS) under mmetrical problem i.-.6 time fater than the ATS, and (ii) under ammetrical problem the MA(ATS) i.8-. time fater than the ATS. A an average, the MA(ATS) i about.7 time fater than the ATS. The MA(ATS) of 6 path ha the mot rapid performance, i.e.. time the ATS, on urface optimization problem. From the peed up ratio of both cae, we can conclude that the MA(ATS) perform etremel well under mmetrical and ammetrical problem, it i uperior to the ATS, and the mmetrical propert of the problem doe not have a ignificant effect on earch performance ISSN: Iue, Volume 8, April 9

14 of the MA(ATS). The method ha been uccefull applied for a control deign problem that require three controller. The MA(ATS) with ATS path pent 7. ec. on a Pentium IV platform to finih the earch. The control tem having the new controller obtained from earch ha better tep repone than the original a elaborated in ection of thi paper. Opportunitie open for further invetigation of the earch performance of having different earch algorithm a the earch core of the MA ( ). Acknowledgement The author epre their thank to At. Prof. Dr. Arthit Srikeaw, School of Eletrical Engineering, Suranaree Univerit of Technolog for hi valuable uggetion on the mmetrical propert of earch problem. Financial upport from Rajamangala Univerit of Technolog Lanna, Tak Campu, and Suranaree Univerit of Technolog are ver much appreciated. Reference: [] F. Glover and M. Laguna, Tabu Search, Kluwer Academic Publiher, 997. [] F. Glover, Parametric tabu earch for mied integer program, Computer and Operation Reearch, Vol., No.9, 6, pp [] F. Glover, Tabu earch-part I, ORSA Journal on Computing, Vol., No., 989, pp [] F. Glover, Tabu earch-part II, ORSA Journal on Computing, Vol., No., 99, pp. -. [] S. Sujitjorn, T. Kulworawanichpong and D. Puangdownreong and K-N Areerak, Adaptive tabu earch and application in engineering deign, Book Chapter in Integrated Intelligent Stem for Engineering Deign (ed. X. F. Zha and R.J.Howlett), IOS Pre, The Netherland, 6, pp. -7. [6] D. Puangdownreong, T. Kulworawanichpong and S. Sujitjorn, Finite convergence and performance evaluation of adaptive tabu earch, Lecture Note in Computer Science, Springer- Verlag Heidelberg,. (online) [7] K-N. Areerak, T. Kulworawanichpong and S. Sujitjorn, Moving toward a new era of intelligent protection through digital relaing in tem, Lecture Note in Computer Science, Springer-Verlag Heidelberg,. (online) [8] T. Kulworawanichpong, K-L. Areerak, K-N. Areerak and S. Sujitjorn, Harmonic identification for active power filter via adaptive tabu earch, Lecture Note in Computer Science, Springer-Verlag Heidelberg,. (online) [9] D. Puangdownreong and S. Sujitjorn, Image approach to tem identification, WSEAS Tranaction on Stem, Vol., No.9, 6, pp [] D. Puangdownreong and S. Sujitjorn, Optaining an optimum PID controller uing adaptive tabu earch, Lecture Note in Computer Science, Springer-Verlag Heidelberg, 7. (online) [] D. Puangdownreong, T. Kulworawanichpong and S. Sujitjorn, Input weighting optimization for PID controller baed on the adaptive tabu earch, Proc. IEEE TENCON, Vol.,, pp. -. [] N. Sriingong, and K. Attakitmongcol, Wavelet-baed audio watermarking uing adaptive tabu earch, Proc. Wirele Pervaive Computing, 6 t International Smpoium on, pp. -. [] J. Kluabwang, D. Puangdownreong and S. Sujitjorn, Management agent for earch algorithm with urface optimization application, WSEAS Tranaction on Computer, Vol.7, No.6, 8, pp [] J. Kluabwang, D. Puangdownreong and S. Sujitjorn, Management agent for earch algorithm, In Proc. th WSEAS Int. Conf. on- Computer, Vol., No., 8, pp.7-8. [] X. Haidong and L. Jianhua, Partition of computing granularit of ecurit data fuion under high performance computing environment WSEAS Tranaction on Computer, Vol., No., 6, pp [6] L. Phillip and R. Bart, Problem partitioning in hbrid genetic algorithm, WSEAS Tranaction on Stem, Vol.6, No., 7, pp [7] R-B. Patel, M. Niko and K. Garq, Mobile agent location management in global network, WSEAS Tranaction on Computer, Vol., No.7,, pp [8] R.B. Patel, and M. Niko, Locating mobile agent in a wide ditributed tem: a dnamic approach, WSEAS Tranaction on Mathematic, Vol., No.,, pp [9] S. Brennan, and A. Allene, The Illinoi roadwa imulator: a mechatronic tetbed for vehicle dnamic and control, IEEE/ASME Tranaction on Mechatronic, Vol., No.,, pp.9-9. [] S. Brennan, and A. Allene, Uing a caled tetbed: controller deign and evaluation, IEEE Control Stem Magazine, Vol., No.,, pp.-6. ISSN: Iue, Volume 8, April 9