IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 203 Compaave evaluao of Pacle Swam Opmzao Algohms fo Daa Cluseg usg eal wold daa ses R.Kah $, S.Aumugam #, K. Rameshuma @ $ Depame of Compue Scece ad Egeeg, Ama School of Egeeg, Combaoe 641 105, Ida. # Baaamma Educaoal us, Combaoe - 641018 @ Depame of Mechacal Egeeg, Ama School of Egeeg, Combaoe 641 105, Ida. _ah@emada.ama.edu (R.Kah) (coespodg auho) Summay I hs pape, well-ow PSO algohms epoed he leaue fo solvg couous fuco opmzao poblems wee compaavely evaluaed by cosdeg eal wold daa cluseg poblems. Daa cluseg poblems ae solved, by cosdeg hee pefomace cluseg mecs such as TRace Wh cea (TRW), Vaace Rao Cea (VRC) ad Mao Cea (MC). The esuls obaed by he PSO vaas wee compaed wh he basc PSO algohm, Geec algohm ad Dffeeal evoluo algohms. A dealed pefomace aalyss has bee caed ou o sudy he covegece behavo of he PSO algohms usg u legh dsbuo. Key wods: Daa cluseg, Pacle Swam Opmzao, Geec Algohm, Dffeeal Evoluo Algohm, Tace Wh cea, Vaace Rao Cea, Mao Cea. 1. Ioduco Cluseg s a echque ha aemps o ogaze ulabeled daa objecs o cluses o goups of smla objecs. A cluse s a colleco of daa objecs ha ae smla o oe aohe wh he same cluse ad ae dssmla o objecs ohe cluses. Cluseg echques have bee used a vaey of felds le mache leag, afcal ellgece, web mg, mage segmeao, lfe scece ad medce, eah scece, socal scece ad ecoomcs. A compehesve evew of he sae-of-he-a cluseg mehods ca be foud Xu ad Wusch, [1]. I ece yeas, due o he ceasg compuaoal speed of compues, heuscs ae used o solve cluseg poblems. Vaous heusc algohms have aleady bee poposed he leaue such as Geec Algohm (GA), A Coloy Opmzao (ACO), Dffeeal Evoluo (DE) ad Pacle Swam Opmzao (PSO). Cluseg echques based o Evoluoay Compug ad Swam Iellgece algohms have oupefomed may classcal mehods of cluseg. PSO was fs oduced o opmze vaous couous olea fucos by Keedy ad Ebeha [2]. PSO algohms have show o successfully opmze a wde age of couous fucos. May vaas of PSO algohms wee developed ove he yeas ad appled o solve he vaous opmzao poblems. Leaue evew eveals ha oly few aemps has bee made o solve he cluseg poblem usg PSO algohms ad also hee s o coss compaso amog may PSO vaas deved ove he yeas fo solvg cluseg poblems. The pefomace of he well-ow PSO algohms ae suded wh he cosdeao of hee cluseg mecs such as TRace Wh cea (TRW), Vaace Rao Cea (VRC) ad Mao Cea (MC) usg eal wold daa ses. The esuls ae compaed wh he publshed esuls of he basc PSO, GA ad DE fo all he cluseg mecs. A dealed pefomace aalyss of he PSO algohms has bee caed ou based o Ru Legh Dsbuo (RLD). The emag pa of he pape s ogazed as follows: Seco 2 defes he fomal cluseg poblem. I Seco 3, he basc PSO algohm ad s vaas ae dscussed. Seco 4 descbes he PSO algohm fo daa cluseg. Seco 5 peses he bechma daa ses ad paamee segs used fo expemeao. Seco 6 peses he esuls obaed by PSO vaas. A dealed aalyss based o Ru Legh Dsbuo (RLD) s povded. I Seco 7 some coclusos fom hs sudy ae epoed. Mauscp eceved Jauay 5, 2008 Mauscp evsed Jauay 20, 2008
204 IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 2. Daa cluseg poblem fomulao 2.1 Noaos Used: N D he umbe of daa objecs o be cluseed. he dmeso of each of he daa objecs. K he umbe of cluses. O se of N daa objecs o be cluseed, whee, {,,..., 1 2 } N O = O O O. Each daa objec s epeseed as: O = o, o... o, { 1 2 d } whee, o d epeses value of daa a dmeso d. C Z se of K paos wh daa objecs assged o C = C,..., C. each pao { } Cluse cees o whch daa objecs ae assged,,..., Z = Z 1 Z 2 Z. { } Each cluse cee s epeseed as: Z = z, z... z, { 1 2 d } whee z d epeses value of cluse a dmeso d. Gve O he se of daa objecs, he goal of paoal cluseg s o deeme a pao { C,..., C } wh he followg cosas. ¹ f, = {1,..., K} C C Ç C º f, whee ¹ j, = {1,..., K} ad j = {1,..., K} K U = 1 C j = O 1 Z = å O O, whee = {1,..., K}, ÎC s he umbe of elemes belogg o cluse C. I geeal, he daa objecs ae assged o cluses based o dsace measues le Mahaa dsace, Eucldea dsace ad Mows dsace [3]. I ou sudy, he objecs ae assged o cluse usg he Eucldea dsace measue. Dffee sascal cea o fess measues have bee poposed he leaue o measue goodess of a pao. I hs pape, we have cosdeed he fess measues cosdeed by Sada ad K [4] fo compag paos geeaed by dffee cluseg algohms. The vaous fess measues cosdeed hs pape ae as follows: K K Mmzao of TRace Wh cea (TRW): Ths ceo s based o pooled wh goups scae max W. The pooled wh scae max W s defed as W = å K W = 1, whee W s he vaace max of he daa objec allocaed o cluse C, whee = {1,..., K}. ( )( ) ' W = å O l - O O l - O (1) l = 1 O l umbe of objecs cluse C. h dcae he l daa objec cluse C ad s he æ O ö l O = å (Veco of he ceod fo he cluse C l = 1ç ). è ø Maxmzao of Vaace Rao Cea (VRC): Ths ceo s based o pooled wh goups scae max W ad bewee goup scae maxes B. The bewee scae max B s defed as K ( )( ) ' B = å O - O O - O, (2) = 1 N O whee O = å. = 1 N The oal scae max T of N daa objecs s defed as T = B + W. ( ace( B) ) ( K -1) ( ace( W )) ( N - K ) æ ö ç VRC = è ø (3) æ ö ç è ø Mmzao of Mao s Cea (MC): Ths ceo s based o pooled wh goups scae max W ad oal scae max T. ( ( W )) de ( T ) ( ) de 2 MC = K (4) 3. Ioduco o PSO PSO s a populao based, coopeave seach heusc oduced by Keedy ad Ebeha [2] o fd opmal o ea soluos o a ucosaed opmzao poblem. The deas ha udele PSO ae sped by he socal behavo of bd flocg ad fsh schoolg. PSO s a eave mehod ha s based o he seach behavo of he swam a muldmesoal space. A pacle called Cue, a me sep has a poso veco x ad a velocy veco v. The fess fuco f deeme he qualy of a pacle s poso,.e., a pacle s poso epeses a soluo o he poblem beg solved. Each
IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 205 u pacle has a veco p called Bes ha epeses s ow bes poso ad has a assocaed fess value. The bes poso, he swam has vsed s soed a veco u g called G-Bes. Fo each pacle x he velocy veco s updaed accodg o (5). The pacle moves o he ew poso accodg o (6). Fo each pacle x he objecve fuco f s evaluaed. The bes poso of he pacle u u ad global bes poso g ae updaed. p ( ) ( ) v + = v + c p - x + c g - x + 1 + 1 x = x + v 1 1 1 2 2 Two cosas c1 ad c 2 ae called cogve ad socal acceleao coeffces, ad 1 2 ae wo ufomly dsbued adom vecos. The algohm eaes by updag he veloces ad posos of he pacles ul he soppg cea s me. 3.1 PSO Vaas Seveal vaaos of hs basc PSO scheme have bee poposed he leaue fo solvg couous opmzao poblems. Sh ad Ebeha [5,6] oduced he dea of a me vayg ea wegh PSO model. Ths was doe o adjus he swam s behavo fom al exploao of ee seach space o exploao of pomsg egos. Ebeha ad Sh [7] poposed aohe ea wegh vaao appoach whch ea wegh s adomly seleced accodg o a ufom dsbuo he age [0.5, 1]. Clec ad Keedy [8] oduced he cosco faco PSO o cool he covegece popees of he pacles. The cosco faco s mulpled by he ee equao 5 sead of ea wegh ω ode o cool he oveall velocy of he swam. I he Fully Ifomed Pacle Swam Opmze poposed by Medes e al. [9], a pacle uses fomao fom all s opologcal eghbos ahe ha he bes oe o cobue o s velocy adjusme. Raaweea e al. [10] poposed a Self-ogazg Heachcal Pacle Swam Opmze wh me vayg acceleao coeffces whee oly he socal ad cogve pa of he pacle ae cosdeed o esmae he ew velocy of each pacle. The pacles ae ealzed whe hee s sagao he seach space. Jaso ad Mddedof [11] poposed a Adapve Heachcal Pacle Swam Opmze wh dyamc adapao of populao opology. The opology cosdeed s a ee le sucue whee each ode of he ee epeses a pacle. Pacles move up o dow he heachy of he ee depedg o s soluo qualy. Recely, Chaejee ad Say [12] have poposed a ew o-lea vaao of ea wegh PSO model. (5) (6) 3.2 PSO algohm Cluseg PSO based cluseg algohm was fs poposed by Mewe e al. [13]. Xao e al. [14] poposed a hybd appoach o cluse he gee daa. Self Ogazg Maps (SOM) as he weghs of he odes he fs sage ad weghs wee opmzed usg PSO appoach. Che ad Ye [15] employed a PSO epeseao whch each pacle coespods o he ceods of he cluses. Twodmesoal ad hee-dmesoal daa wee used fo evaluao. Oma e al. [16] poposed a dyamc cluseg sysem based bay PSO ad K-meas algohm. The algohm auomacally defes he umbe of cluses ad employs a valdy dex o evaluae he cluses. Cohe e al., [17] poposed a Pacle Swam Cluseg (PSC) algohm whee each pacle epeses a ceod he pu daa space. The whole populao s eeded o pese he fal cluseg soluo. Sada ad K [4] compaed he pefomace of Dffeeal Evoluo (DE), Radom Seach (RS), PSO ad GA fo paoal cluseg poblems. The empcal esuls show ha PSO ad DE pefom bee compaed o GA ad K- meas algohms. Recely, Swagaham e al. [18] poposed a auomac cluseg echque usg a mpoved dffeeal evoluo algohm. I hs wo, we have cosdeed he daa ses used by Sada ad K [4] o evaluae he pefomace of he followg PSO vaas. a) Tme vayg ea wegh PSO model (SE-PSO) poposed by Sh ad Ebeha [5,6]. b) Sochasc ea wegh PSO model (ES-PSO) poposed by Ebeha ad Sh [7]. c) Cosco ype PSO model (CK-PSO) poposed by Clec ad Keedy [8]. d) Self-ogazg Heachcal Pacle Swam Opmze (R-PSO) wh me vayg acceleao coeffces poposed by Raaweea e al [10]. e) No lea ea wegh PSO model (CS-PSO) poposed by Chaejee ad Say [12]. 4. Geeal Sucue of PSO algohm fo daa cluseg Noaos used: T S D K N eao coue. maxmum umbe of eaos. swam sze. maxmum umbes of dmesos each daa objec. maxmum umbe of cluses. umbe of daa objecs o be cluseed. The daa objecs o be cluseed ae epeseed as a se:
206 IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 {,,..., 1 2 } N O = O O O. Each daa objec s epeseed as: O = o, o... o, { 1 2 d } whee o d epeses value of daa dmeso d. x poso of Cue Pacle (Cue) a eao. ( ) f x value of objecve fuco fo pacle (Cue) a eao. p Bes poso of pacle ll eao. f ( p ) value of objecve fuco fo p. g G-Bes poso of he swam. f ( g ) value of objecve fuco fo g. 4.1 Geeal Sucue Sep1: Geeae 2S+ 1 al soluos adomly accodg o he swam sze S. Sep2: Fo each of he 2S+ 1 al soluos, evaluae fo s fess measue. Sep3: Ialze Cue ( x ), Bes ( p ) ad he G-Bes ( g ) posos fom he 2S+ 1 al soluos, whee } = {1,..., S. Sep4: Sep5: Whle (emao codo o me) Fo each pacle = {1,..., S} Updae he poso ad velocy vecos of he cue pacle x usg PSO heuscs (SE-PSO, ES-PSO, CK-PSO, R-PSO, CS-PSO) Evaluae he pacle based o fess measue (TRW, VRC, MC). Updae Bes ( p ) ad he G-Bes ( g ) posos. Reu G-Bes ( g ) pacle. 5. Expemeal seup Fve dffee vaas of PSO algohms ae cosdeed hs sudy fo compaave evaluao coespodece o he hee cea s such as TRW, VRC ad MC. To evaluae he pefomace of he PSO vaas we have cosdeed bechma daa ses epoed by Sada ad K [4]. By cosdeg maxmum umbe of fucoal evaluaos as 100000, Sada ad K epoed he bes esuls by ug basc veso of PSO oduced by Keedy ad Ebeha [2], wh a populao sze of 50. Sada ad K epoed he bes esuls by ug GA wh a populao sze of 100. Fo DE, Sada ad K epoed bes esuls by cosdeg cossove faco as 0.9, scalg faco as 0.3 ad he populao sze of 50. The fou eal wold daases cosdeed hs sudy ae lsed he Table 1. Fo a fa compaso, all he PSO algohms cosdeed hs pape wee epeaed 50 mes wh he maxmum umbe of fucoal evaluaos as 100000 fo evaluag he pefomace measues. Table 1. Real Wold daa ses Daa Se Numbe Numbe Numbe of daa of Feaues of cluses Fshe Is daa 150 4 3 Vowel daa 871 3 6 Wscos Beas Cace daa 683 9 2 Rpley s glass daa 214 9 6 Pefomace of he PSO vaas ae measued based o he followg ceo: 1. Mea bes fess value of TRW, VRC ad MC measue. 2. Mea pece elave cease objecve value of TRW, VRC ad MC measue. 3. Peceage of umbe of us (.e., success %) ha each bes ow objecve fuco value ove 50 smulaos. 4. Ru Legh Dsbuo (RLD) as poposed by Hoos ad Suzle [19]. 6. Pefomace aalyss of PSO vaas 6.1 Mea bes fess value All he PSO vaas wee coded C++ ad ae allowed o u fo a maxmum of 100000 fucoal evaluaos. Expemes wee epeaed fo 50 mes ad mea bes fess value fo each algohm has bee calculaed wh espec o he objecve fucos cosdeed hs pape. The mea bes fess values fo he PSO vaas wee epoed he Table 2. The esuls wee compaed wh he Basc PSO algohm (B-PSO), Geec Algohm (GA) ad Dffeeal Evoluo (DE) Algohms. Fo a fa compaso we have esed he PSO vaas usg he same expemeal seup cosdeed by Sada ad K. The esuls dcae PSO vaas cosdeed hs sudy ae pefomg bee ha he basc PSO, GA ad DE algohms. I s evde fom he Table 2 ha PSO vaas mpove he bes ow VRC ad MC measue fo all he bechma poblems. The PSO vaas yeld soluos of same qualy fo he cace daase fo he TRW measue.
IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 207 Impoved qualy fo Vowel daase fo he TRW measue s also epoed he Table 2. 6.2 Mea pece elave cease objecve value The mea peceage elave cease objecve fuco values fo he bechma poblems ae gve Table 3, ad ae calculaed as follows: Le he heusc soluos yelded by he C-K PSO, S-E PSO, R-PSO, C-S PSO ad E-S PSO fo a gve poblem be deoed by F 1, F 2, F 3, F 4 ad F 5 especvely. These soluos ae elavely evaluaed as gve below. Mea peceage elave cease objecve fuco value of he soluo yelded by he appoach fo a mmzao poblem s ( F - m ( F, = 1,2,3, 4 ad 5) ) m ( F, = 1,2,3,4 ad 5) = 100 Smlaly, mea peceage elave cease objecve fuco value of he soluo yelded by he appoach fo he maxmzao poblem s ( max ( F, = 1,2,3,4 ad 5) - F ) max ( F, = 1,2,3, 4 ad 5) = 100 The esuls dcae R-PSO cosdeed hs sudy pefoms bee fo he Is daa ses. Fo he Cace daa se CS-PSO pefom bee fo TRW, VRC ad MC ceo. Fo he Vowel daase SE-PSO pefoms bee ha he ohe vaas. 6.3 Success Peceage: Table 4 epos he Peceage of umbe of us (.e., success %) ha each bes ow objecve fuco value ove 50 smulaos. The bes ow value epoed by Sada ad K [4] s used fo evaluao. The esuls show Table 4 dcae ha he PSO vaas cosdeed hs sudy pefom well fo he MC ad VRC measue. All he vaas ae able o each almos 100% success fo he VRC ad MC measue fo all he daa ses. Fo he TRW measue, cace ad vowel daases pefom bee compaed o s ad glass daase. 6.4 Ru Legh Dsbuo (RLD) To sudy he behavo of sochasc algohms wh espec o soluo qualy ad umbe of fucoal evaluaos, (7) (8) u legh dsbuo plos ae used. I hs pape we have adoped he mehodology poposed by Hoos ad Suzle [19] o plo he RLD. RLD s wee ploed fo all he daa ses wh espec o he objecve ude cosdeao. RLD plo shows he covegece of he PSO algohm wh espec o he umbe of fucoal evaluaos ad also dcaes he pobably of eachg a pe-specfed objecve fuco value ove specfed umbe of fucoal evaluaos. The pobably value (success ae) s he ao bewee he umbe of us fdg a soluo of cea qualy ad he oal umbe of us. I hs pape we have cosdeed he bes ow objecve fuco values epoed by Sada ad K [4] as pe-specfed values fo plog RLD s fo he pefomace measues cosdeed hs pape. RLD plos fo he bechma daases ae show he Fgue 1 o Fgue 12. Ru Legh Dsbuo fo each of he PSO vaas o s daa se fo TRW mecs ae show Fgue 1. The dsbuo shows ha S-E PSO s he fases fs hg algohm fo he bes ow value ad C-S PSO has a slow ceasg cuve o each bes ow value. All he PSO vaas ae able o fd a soluo of equed qualy, bu o vaa s capable of fdg soluo of equed qualy wh a pobably of 1.0. C-S PSO ad C-K PSO each soluo of equed qualy wh a pobably of 0.60. Fgue 2 shows he u legh dsbuo of cace daa se fo TRW measue. The dsbuo shows ha S-E PSO s he fases fs hg algohm fo he bes ow value ad C-S PSO has slow ceasg cuve o each bes ow value. All he PSO vaas ae able o each he bes-ow value wh a pobably of 1.0. Ru Legh Dsbuo of glass daa se fo TRW measue s show Fgue 3. The dsbuo shows ha S-E PSO has he fases fs hg me fo he bes-ow value ad C-S PSO has slow ceasg cuve o each besow value. All he PSO vaas ae able o each he bes-ow value ad C-S PSO fds he bes-ow value wh a pobably of 0.32. Fgue 4 shows he u legh dsbuo of vowel daa se fo TRW measue. The dsbuo shows ha S-E PSO s he fases fs hg algohm fo he bes ow value, ad C-S PSO has slow ceasg cuve o each bes ow value. All he PSO vaas ae able o each a soluo of equed qualy ad E-S PSO each a soluo of equed qualy wh a pobably of 0.94. Ru Legh Dsbuo of s daa se fo VRC measue s show Fgue 5.
208 IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 Table 2. Compaso of mea bes fess of PSO Vaas wh GA, DE ad Basc PSO algohm Daase Is Cace Glass Vowel Mea bes fess Cea GA DE B-PSO C-K PSO S-E PSO R-PSO C-S PSO E-S PSO MC 0.1984 0.1984 0.198 0.0642 0.0643 0.0630 0.0671 0.0635 TRW 7885.14 7885.14 7885.14 7885.31 7885.38 7885.48 7885.31 7885.34 VRC 561.63 561.63 561.63 628.56 628.60 628.72 628.59 628.53 MC 0.3565 0.3546 0.3527 0.1674 0.1666 0.1720 0.1660 0.1664 TRW 19323 19323 19324 19323 19323 19323 19323 19323 VRC 1026.26 1026.26 1026.26 1621.17 1621.19 1620.87 1621.19 1621.18 MC 0.02661 0.01984 0.03176 0.0058 0.0056 0.0056 0.0085 0.0058 TRW 341.09 336.06 339.04 348.48 345.19 351.11 348.23 346.87 VRC 121.94 124.62 122.74 145.58 146.75 145.07 147.88 148.63 MC 0.3199 0.2906 0.3032 0.1613 0.1612 0.1765 0.1730 0.1626 TRW 30943106 30690785 30734068 30689689 30689234 30692132 30688873 30688417 VRC 1450.45 1465.55 1463.33 1602.42 1603.12 1598.24 1599.17 1601.76 Noes: MC Mao s Cea (Mmzao Objecve) TRW TRace Wh Cea (Mmzao Objecve) VRC Vaace Rao Cea (Maxmzao Objecve) GA Geec Algohms esuls epoed Sada ad K, (2006) DE Dffeeal Evoluo esuls epoed Sada ad K, (2006) B-PSO Basc PSO esuls epoed Sada ad K, (2006) S-E PSO Tme vayg ea wegh PSO model poposed by Sh ad Ebeha (1998 ad 1999) E-S PSO Sochasc ea wegh PSO model poposed by Ebeha ad Sh (2001) C-K PSO Cosco ype PSO model poposed by Clec ad Keedy (2002) R-PSO Self-ogazg Heachcal Pacle Swam Opmze wh me vayg acceleao coeffces poposed by Raaweea e. al (2004) C-S PSO No lea ea wegh PSO model poposed by Chaejee ad Say (2006) Table 3. Mea pece elave cease objecve fuco value of heuscs Daase Cea C-K PSO S-E PSO R-PSO C-S PSO E-S PSO MC 1.8253 1.9748 0.0000 6.4227 0.7714 Is TRW 0.0250 0.0188 0.0000 0.0208 0.0303 VRC 0.0000 0.0009 0.0021 0.0000 0.0004 MC 0.8449 0.3364 3.6218 0.0000 0.2485 Cace TRW 0.0013 0.0001 0.0198 0.0000 0.0002 VRC 0.0000 0.0000 0.0000 0.0000 0.0000 MC 2.8924 0.2485 0.0000 52.3322 4.2574 Glass TRW 2.0514 1.2668 2.3955 0.5021 0.0000 VRC 0.9528 0.0000 1.7133 0.8789 0.4868 MC 0.0761 0.0000 9.4818 7.3552 0.8896 Vowel TRW 0.0442 0.0000 0.3044 0.2467 0.0848 VRC 0.0041 0.0027 0.0121 0.0015 0.0000
IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 209 The dsbuo shows ha R-PSO ad S-E PSO ae he fases fs hg algohms fo he bes-ow value ad C-S PSO has a slow ceasg cuve o each bes-ow value. All he PSO vaas ae able o fd a soluo of equed qualy wh a pobably of 1.0. Table 4 epos he Peceage of umbe of us (.e., success %) ha each bes ow objecve fuco Daase Cea Is Cace Glass Vowel Bes Kow C-K PSO S-E PSO R-PSO C-S PSO E-S PSO Value MC 0.198 100 100 100 100 100 TRW 7885.14 60 44 20 60 52 VRC 561.63 100 100 100 100 100 MC 0.3527 100 100 100 100 100 TRW 19323 100 100 100 100 100 VRC 1026.26 100 100 100 100 100 MC 0.01984 100 100 100 100 100 TRW 336.06 14 22 8 32 20 VRC 124.62 98 100 100 100 100 MC 0.2906 100 100 100 100 100 TRW 30690785 90 90 58 88 94 VRC 1465.55 96 92 98 98 98 The u legh dsbuo of cace daa fo VRC ceo s show Fgue 6. All he vaas each he bes-ow value wh 100 fuco evaluaos. Fgue 7 shows he u legh dsbuo of glass daase fo VRC ceo. The dsbuo show ha S-E PSO s he fases fs hg algohm fo he bes ow value ad C-S PSO has slow ceasg cuve o each opmal value fo he daase. All he PSO vaas ae able o fd a soluo of equed qualy wh a pobably of almos 1. Fgue 8 shows he u legh dsbuo of vowel daase fo VRC ceo. The dsbuo shows ha S-E PSO has he fases fs hg algohm fo he bes ow value ad C-S PSO has slow ceasg cuve o each bes ow value. All he PSO vaas ae able o fd a soluo of equed qualy wh a pobably of 0.90. The u legh dsbuo of s daa fo MC ceo s show Fgue 9. All vaas fd he bes-ow value wh 100 fuco evaluaos. All he PSO vaas ae able o fd a soluo of equed qualy wh a pobably of 1. The u legh dsbuo of cace daa fo MC ceo s show Fgue 10. All vaas fds he bes ow value wh 2000 fuco evaluaos. Fgue 11 shows he u legh dsbuo of glass daase fo MC ceo. The dsbuos show ha E-S PSO s he fases fs hg algohm fo he bes ow value ad C-K PSO has slow ceasg cuve o each opmal value. All he PSO vaas ae able o fd a soluo of equed qualy wh a pobably of 1. Fgue 12 shows he u legh dsbuo of vowel daase fo MC ceo. The dsbuos show ha S-E PSO s he fases fs hg algohm fo he bes ow value ad C-S PSO has slow ceasg cuve o each he bes ow value. All he PSO vaas ae able o fd a soluo of equed qualy wh a pobably of 1. Ieesg obsevaos ca be made fom he RLDs fo TRW measue. All PSO vaas each he bes-ow value as epoed by Sada ad K [4]. Fo all he bechma daa ses S-E PSO has he fases hg me ad C-S PSO has he slowes hg me o each he besow value. I s also obseved ha he covegece of he R-PSO s poo fo mos of he bechma daa ses. Aohe eesg obsevao fom he RLDs s ha C-S PSO has he maxmum pobably of fdg bes-ow value fo mos of he daases. Fo TRW measue all PSO vaas show sog sagao behavo. By cosdeg VRC measue, S-E PSO has he fases hg me ad C-S PSO has he slowes hg me fo he epoed bes-ow value. I s also foud ha E-S PSO ad CS-PSO has he maxmum pobably of fdg bes-ow value fo all he daases. The covegece of he PSO vaas fo he VRC measue s fase compag wh he TRW measue fo mos of he bechma poblems. Fo he MC measue, he covegeces of he PSO vaas ae slowe compaed o he VRC measue. All vaas each he epoed bes-ow value wh a pobably of 1. 7. Cocluso Few aemps have bee made o solve daa cluseg poblem usg PSO algohms. I hs pape he pefomace evaluao of well-ow PSO vaas fo daa cluseg usg eal wold daa ses has bee suded. The pefomaces of he PSO vaas wee compaed wh he basc PSO algohm, GA ad DE algohm. The compaave evaluao shows, he PSO vaas pefom bee fo mos of he bechma daases fo he VRC, TRW ad MC ceo ad also mpoves he bes-ow soluo avalable he leaue fo he VRC ad MC measues. Ru Legh Dsbuo aalyss has bee caed ou o sudy he sagao behavo ad covegece speed of he PSO vaas. Ru Legh Dsbuo (RLD) plo of he PSO vaas dcae he covegece s fase he case of SE-PSO whe a emao ceo s fxed o lesse umbe of fucoal evaluaos. As he umbe of fucoal evaluao ceases, esuls of compaso eveals ha o PSO vaa domaes all he ohes o all bechma daases.
210 IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 Fgue 1. RLD of IRIS daa se fo TRW measue Fgue 5. RLD of IRIS daa se fo VRC measue Fgue 2. RLD of CANCER daa se fo TRW measue Fgue 6. RLD of CANCER daa se fo VRC measue Fgue 3. RLD of GLASS daa se fo TRW Fgue 7. RLD of GLASS daa se fo VRC Fgue 4. RLD of VOWEL daa se fo TRW measue Fgue 8. RLD of VOWEL daa se fo VRC measue
IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 211 Fgue 9. RLD of IRIS daa se fo MC measue Fgue 10. RLD of CANCER daa se fo MC measue Fgue 11. RLD of GLASS daa se fo MC measue Acowledgemes The auhos ae haful o he hee evewes fo he suggesos ad commes o mpove he eale veso of he pape. Refeeces [1] Ru Xu ad Doald Wusch II, Suvey of Cluseg Algohms, IEEE Tasacos o Neual Newo, Vol. 16, No 3, May 2005. [2] Keedy, J., Ebeha, R. C., Pacle Swam Opmzao, Poceedgs of he 1995 IEEE Ieaoal Cofeece o Neual Newos, IEEE Pess Pscaaway, NJ, Vol. 4, pp. 1942 1948, 1995. [3] Ja, A.K., Muy, M.N., ad P.J. Fly, Daa Cluseg: A Revew, ACM compug Suvey, vol. 31, o 3, 1999. [4] Sada Pael, K, T., Dffeeal evoluo ad pacle swam opmzao paoal cluseg, compuaoal sascs & daa aalyss 50(5), 1220-1247, 2006. [5] Sh, Y., Ebeha, R., A modfed pacle swam opmze, I Poceedg of he 1998 IEEE Wold Cogess o Compuaoal Iellgece, Page 69-73, Pscaaway, NJ, IEEE Pess, 1998. [6] Sh, Y., Ebeha, R., Empcal sudy of pacle swam opmzao. I Poceedg of he 1999 IEEE Wold Cogess o Evoluoay Compug, Page 1945-1950. Pscaaway, NJ, IEEE Pess, 1999. [7] Ebeha, R., Sh, Y., Tacg ad opmzg dyamc sysems wh pacle swams. I Poceedg of 2001 IEEE Wold Cogess o Evoluoay Compug, Page 94-100. Pscaaway, NJ, IEEE Pess, 2001. [8] Clec, M., Keedy, J., The pacle swam-exploso, sably, ad covegece a muldmesoal complex space. IEEE Tasacos o Evoluoay Compuao 6, 58-73. 2002. [9] Medes, R., Keedy, J., Neves, J., The fully fomed pacle swam: smple, maybe bee, IEEE Tasaco o Evoluoay Compug, 8(3): 204-210, 2004. [10] Raaweea, A., Halgamuge, S.K., Waso, H.C., Self ogazao heachcal pacle swam opmze wh me vayg acceleao coeffces, IEEE Tasaco o Evoluoay Compug, 8(3): 240-255, 2004. [11] Jaso, S., Mddedof, M., A heachcal pacle swam opmze ad s adapve vaas, IEEE Tasaco o Sysem, Ma ad Cybeecs, pa B, 35(6), 1272-1282, 2005. [12] Chaejee, A., Say, P., No Lea ea wegh vaao fo dyamc adapao pacle swam opmzao, Compues ad Opeaos Reseach, 33, 859-871, 2006. [13] Va De Mewe, D.W., Egelbech, A.P., Daa cluseg usg pacle swam opmzao, Poceedgs of IEEE
212 IJCSNS Ieaoal Joual of Compue Scece ad Newo Secuy, VOL.8 No.1, Jauay 2008 Cogess o Evoluoay Compug 2003, Cabea, Ausala, 215-220, 2003. [14] Xao X, Dow ER, Ebeha RC, Mled ZB ad Oppel RJ, Gee Cluseg Usg Self-Ogazg Maps ad Pacle Swam Opmzao, Poc of he 17h Ieaoal Symposum o Paallel ad Dsbued Pocessg (PDPS '03),IEEE Compue Socey, Washgo DC, 2003. [15] Che, C.Y., Ye, F., Pacle swam opmzao algohm ad s applcaos o cluseg aalyss, Poceedgs of IEEE Ieaoal cofeece o Newog, Sesg ad Cool, 789-794, 2004. [16] Oma, M.G.H., Salma, A., Egelbech, A.P., Dyamc cluseg usg Pacle Swam Opmzao wh applcao mage segmeao, Pae Aalyss ad Applcao, Vol. 8, No. 4, 332 344, 2005. [17] Cohe, S.C.M., ad De Caso, L.N., Daa Cluseg wh Pacle swams, IEEE Cogess o Evoluoay Compuaos, Vacouve, Caada, 2006. [18] Swagaam Das, Ajh Abaham ad Am Koa, Auomac Cluseg Usg a Impoved Dffeeal Evoluo Algohm, IEEE Tasacos o Sysems Ma ad Cybeecs PART A, IEEE Pess, USA, 2008. [19] Hoos, H. H., Suzle, T., Sochasc Local seach: Foudao ad Applcaos, Moga Kaufma, Sa Facsco, CA, USA, 2004. R.Kah eceved he M.E. Compue Scece ad Egeeg fom Madua Kamaaj Uvesy, Madua 1998. She also obaed he B.E. (Elecocs ad Commucao Egg.) fom Bhaaha Uvesy, Combaoe 1996. She s cuely wog as Asssa Pofesso he Depame of Compue Scece ad Egeeg, Ama School of Egeeg, Combaoe. D.S.Aumugam eceved he Ph.D degee Compue Scece ad Egeeg fom Aa Uvesy, Chea 1990. He also obaed hs B.E. (Eleccal ad Elecocs Egg) ad M. Sc.(Egg) (Appled Elecocs ) degees fom PSG College of Techology, Combaoe, Uvesy of Madas 1971 ad 1973 especvely. He was wog he Decoae of Techcal Educao, Goveme of Taml Nadu fom 1974 a vaous posos fom Assocae Lecue, Lecue, Asssa Pofesso, Pofesso, Pcpal ad Addoal Deco of Techcal Educao. He has guded 4 PhD scholas ad gudg 10 PhD scholas. He has publshed 70 echcal papes eaoal ad aoal jouals ad cofeeces. Hs aea of ees s cludg cluseg, ewo secuy, bomecs ad eual ewos. He s pesely wog as a Chef Execuve, Baa Educaoal Tus, Combaoe. K.Rameshuma eceved he Ph.D degee Poduco Egeeg 2007. He also obaed hs B.E. (Mechacal Egeeg) ad M.E. (Poduco Egeeg) fom Bhaaha Uvesy, Combaoe 1990 ad 1991 especvely. He s pesely wog as a Pofesso he Depame of Mechacal Egeeg, Ama School of Egeeg, Combaoe.