ANFIS Based Time Series Prediction Method of Bank Cash Flow Optimized by Adaptive Population Activity PSO Algorithm

Transcription

1 Informaon 25, 6, 3-33; do:.339/nfo633 Arcle OPEN ACCESS nformaon ISSN ANFIS Based Tme Seres Predcon Mehod of Bank Cash Flow Opmzed by Adapve Populaon Acvy PSO Algorhm Je-Sheng Wang * and Chen-Xu Nng School of Elecronc and Informaon Engneerng, Unversy of Scence and Technology Laonng, Anshan 444, Laonng, Chna; E-Mal: NCX775467@63.com * Auhor o whom correspondence should be addressed; E-Mal: wang_jesheng@26.com or wangjesheng@usl.edu.cn; Tel.: ; Fax: Academc Edor: Wlly Suslo Receved: 2 May 25 / Acceped: 9 June 25 / Publshed: 24 June 25 Absrac: In order o mprove he accuracy and real-me of all knds of nformaon n he cash busness, and solve he problem whch accuracy and sably s no hgh of he daa lnkage beween cash nvenory forecasng and cash managemen nformaon n he commercal bank, a hybrd learnng algorhm s proposed based on adapve populaon acvy parcle swarm opmzaon (APAPSO) algorhm combned wh he leas squares mehod (LMS) o opmze he adapve nework-based fuzzy nference sysem (ANFIS) model parameers. Through he nroducon of merc funcon of populaon dversy o ensure he dversy of populaon and adapve changes n nera wegh and learnng facors, he opmzaon ably of he parcle swarm opmzaon (PSO) algorhm s mproved, whch avods he premaure convergence problem of he PSO algorhm. The smulaon comparson expermens are carred ou wh BP-LMS algorhm and sandard PSO-LMS by adopng real commercal banks cash flow daa o verfy he effecveness of he proposed me seres predcon of bank cash flow based on mproved PSO-ANFIS opmzaon mehod. Smulaon resuls show ha he opmzaon speed s faser and he predcon accuracy s hgher. Keywords: me seres predcon; bank cash flow; adapve nework-based fuzzy nference sysem; parcle swarm opmzaon algorhm

2 Informaon 25, 6 3. Inroducon In recen years, me seres modelng and predcon are one of he mos acve research opcs n academc research and engneerng pracce [ 2]. Tme seres modelng s usually a chronologcal seres of observed daa (nformaon) accordng o he me sequence, whose values are sampled a nvarable me nervals. Researchers ofen predc fuure changes based on he hsorcal daa. For example, accordng o he suaon n he pas or he curren perod of he marke sales, changes of sock prces, populaon growh and he bank s deposs and whdrawals n he fuure are predced. Tme seres forecasng affecs he lfe of people everywhere, so has an mporan praccal sgnfcance and research prospecs n every feld of oday s socey, whch s also an mporan drecon n he compuer applcaon feld. The bank cash flow forecasng managemen nformaon sysem s desgned o creae a sysem managemen plaform for he predcon and analyss of commercal bank cash flow. I wll realze he cash flow daa sascs summary, he cash flow shor-erm and long-erm predcons, and he managemen nformaon relaed o commercal bank cash flow under hree levels: secondary branches (Cash Operaon Cener), branch (Busness Lbrary) and Nework. Is purpose s o provde effecve daa of all levels of organzaon o analyze and assess cash busness operaon condons. I wll also provde effecve sysem managemen means for he cash operaon managers and decson-makng people a all levels. Arfcal neural nework (ANN) s a very good approxmaon mehod, whch has characerscs of adapve and self-learnng [3 4]. However, ANN s easy o fall no local mnmum. Combned wh he fuzzy nference sysem, a new knd of nonlnear predcon mehod was proposed, namely: adapve neural fuzzy nference sysem (ANFIS) [5]. Ths mehod can use boh fuzzy rules and he srucure of he neural nework o realze adapve self-learnng, hus he predcon accuracy s hgher han he sngle arfcal neural nework. In order o furher mprove he predcon precson of he adapve ANFIS sysem, he PSO algorhm s also appled o opmze s srucure parameers. A new hybrd approach, combnng parcle swarm opmzaon and adapve-nework-based fuzzy nference sysem for shor-erm wnd power predcon n Porugal s proposed, forecasng accuracy s aanable usng he proposed approach [4 6]. The radal bass funcon neural nework (RBFNN) wh a nonlnear me-varyng evoluon parcle swarm opmzaon (NTVE-PSO) algorhm s developed, and Smulaon resuls llusrae ha he proposed NTVE-PSO-RBFNN has beer forecasng accuracy and compuaonal effcency for dfferen elecrcy demands [7 ]. An mproved PSO-based arfcal neural nework (ANN) s developed, he resuls show ha he proposed SAPSO-based ANN has a beer ably o escape from a local opmum and s more effecve han he convenonal PSO-based ANN [ 4]. A ranng algorhm s based on a hybrd of parcle swarm opmzaon (PSO) and evoluonary algorhm (EA) o predc he mssng values from a me seres of 5 daa pons, where expermenal resuls show ha PSO-EA algorhm s effecve [5]. Amng a he exsed problem n he predcon of commercal bank cash flow, a hybrd learnng algorhm s proposed based on an mproved PSO algorhm combned wh LMS o opmze he ANFIS confguraon parameers, whch s adoped o realze he predcon of cash flow me seres. The smulaon resuls show he effecveness of he proposed mehod. The paper s organzed as follows: n Secon 2, he echnque of he adapve nework-based fuzzy nference sysem (ANFIS) s nroduced.

3 Informaon 25, 6 32 The opmzaon of ANFIS parameers based on mproved PSO-LMS algorhm s presened n Secon 3. The smulaon expermens and resuls analyss are nroduced n deal n Secon 4. Fnally, he concluson llusraes he las par. 2. Adapve Nework-Based Fuzzy Inference Sysem (ANFIS) J.-S.R. Jang proposed an adapve nework-based fuzzy nference sysem (ANFIS) based on he T-S model n he early 99s [7]. I s a new ype of neural nework, whose man feaure s he organc blend of fuzzy logc and neural nework. Sugeno Fuzzy model, also known as TSK fuzzy model, was pu forward by Takag, Sugeno and Kang [4], whch s a sysemac mehod o produce fuzzy rules based on a gven npu-oupu daa se. Because he lneary of rules depends on he sysem npu varables, he Sugeno model s an deal mulvarable conroller, whch can be appled o nonlnear dynamc sysems wh varey operang condons. The ypcal srucure of ANFIS s shown n Fgure [7]. Assume ha he consdered fuzzy nference sysem has wo npus x and y, sngle oupu f. For he frs order Sugeno fuzzy model, he common rule se wh wo fuzzy f hen rules s descrbed as follows. Rule : f x s A and y s B, hen: f px qy r () Rule 2: f x s A2 and y s B2, hen: f2 px 2 qy 2 r2 (2) x y The frs layer The fourh layer The hrd layer The second layer xy A The ffh layer A2 B B2 W W2 N N W W2 xy W W2 f f2 f Fgure. Typcal ANFIS srucure dagram. I can be seen from he ANFIS srucure ha he sysem has wo adapaon layers (layer and layer 4). The frs layer has hree adjusable premse parameers relaed o npu membershp funcons. The fourh layer has hree adjusable conclusons parameers relaed o he frs-order polynomal. The roo mean square error (RMSE) under he curren premse parameers and concluson parameers s calculaed by: ˆ k ( k 2 ) / k RMSE f f (3)

4 Informaon 25, Opmzaon of ANFIS Parameers Based on Improved PSO-LMS Algorhm 3.. Improved PSO Algorhm In order o avod he algorhm s premaure fall no local opmum and mprove he populaon dversy and he convergence precson, he merc funcon of populaon dversy s defned based on he analyss of he convergence of he PSO algorhm. An adapve populaon acvy parcle swarm opmzaon (APAPSO) algorhm s proposed accordng o he relaonshp beween he populaon dversy and parcle velocy. In hs proposed mproved PSO algorhm, he nera wegh s adjused adapvely on he bass of he changes of he populaon dversy and regulaon funcon, so as o mprove he parcle swarm dversy and he ably of he algorhm jumpng ou of he local opmal soluons Merc Funcon of Populaon Dversy The populaon dversy reflecs he dsrbuon of parcles n he searchng space. The acve degree of parcles can be expressed by he curren velocy of parcles. The hgher he acve degree, he bgger he search scope of he populaon, herefore he dversy of he populaon can be refleced hrough he populaon acvy. The average acvy level of he populaon parcles can be quanfed as he mean square error of veloces. So can be very good o undersand and grasp he curren sae of he enre populaon by sudyng he changes n he sze of populaon velocy mean square error. The speed of he populaon parcle mean square error s defned as he populaon acvy, whch s descrbed as follows: N D 2 PA vj vavg ND j N vavg v N (4) where s he number of eraons; N and D are he number of parcles and he spaal dmenson respecvely; vj s j-h dmensonal velocy of he -h parcle; vavg represens he average velocy of he parcle swarm. The above defnon shows ha he group velocy varance PA() can reflec he exen of he aggregaon of all parcles n he soluon space, ha s o say he dversy of parcles n he populaon. The smaller he PA(), he smaller he dversy of parcles. Conversely, he dversy s bgger. Ierave search of parcles s a non-lnear opmzaon process. The curren eraon algebra of parcles can be undersood as a momen for he parcles n he search process. Because he nera wegh n he PSO algorhm s beween and, herefore, he merc funcon of he populaon dversy s desgned as follows: 2 (5) arcanpa F where he value of F() s he dversy of he populaon merc funcon a he me. Accordng o he Equaon (5), when he populaon acvy s smaller, he F() value s larger. Conversely, when he populaon acvy s larger, he F() value s smaller. When he velocy mean square error of he parcle swarm decreases gradually o zero, ndcaes ha he dversy of he populaon connues o decrease

5 Informaon 25, 6 34 and he parcles end o be conssen gradually, whch shows ha he sze of he populaon dversy measure funcon value can represen he dfference beween he parcles n he populaon Adapve Inera Wegh Adjusmen Mechansm The sudes have shown ha wh he runnng of PSO algorhm, he ndvdual parcles n he populaon wll end o be conssen evenually. Thus he value of he funcon F() wll be bgger and bgger. Therefore, canno only be reled o represen he populaon dversy. A presen mos of he leraure wdely adops lnear decreasng sraegy of nera wegh, ha s o say w wll declne n he consan speed wh he number of eraons. Because he sraegy wh wegh values s small n he laer algorhm, he global search ably s weak. So wll make he algorhm s easy o fall no local opmum and he consan speed decreasng wll also reduce he effcency of searchng. As he eraon proceeds, F() should be weakened. Therefore, he regulaory funcon φ() s nroduced, whch s shown n he Equaon (6): 2 2 exp 2 T 3 where s he number of curren eraon; T s he epoch of algorhm ermnaon. When T s 3, he char of φ() s shown n Fgure (6) Fgure 2. Curve of regulang funcon. I can be seen from Fgure 2 ha f he sze of F() φ() s as a measure of he degree of parcles endng o be conssen n he whole populaon, on he bass of F() φ(), he mporan parameer of he PSO algorhm, neral facor s adapve dynamc adjused accordng o he changes of opmal condons. Ths can no only help avodng he defecs of PSO algorhm easly fallng no local exreme, bu also speed up he convergence speed of he algorhm and mprove he convergence precson of he algorhm n a grea exen. So n he APAPSO algorhm, he sraegy of nera wegh

6 Informaon 25, 6 35 adapve dynamc adjusmen s used. I changes along wh he populaon dversy merc funcon and regulaon funcon. The nera wegh adjusmen mechansm s shown n Equaon (7): w w w w F mn max mn (7) where s he number of curren eraon; wmn and wmax are he mnmum and maxmum values of he nera wegh, respecvely Algorhm Procedure of APAPSO-LMS Algorhm Each learnng process of he hybrd learnng algorhm ncludes he learnng sage of he premse parameers and he concluson parameers. In he premse parameers learnng phase, an mproved PSO algorhm s adoped for each ndvdual o calculae he excaon nensy and he normalzed excaon nensy of all he rules. In he concluson parameer learnng phase, he LMS mehod s used o denfy hese lnear parameers. Afer obanng all parameers, he oupu error of each npu daa can be calculaed. The specfc algorhm procedure s descrbed as follows. Sep : Inalze he number of eraons n =. Randomly nalze he parcle swarm. The poson n n vecor of he -h parcle s X d and he velocy vecor s V d ( m, d D, m s he sze of parcle populaon, D s he dmenson of searchng space, ha s also he number of prerequse parameers); Sep 2: Make he poson vecor of each parcle n urn as he premse parameers of ANFIS, and hen calculae he ncenve nensy wj and he normalzed ncenve nensy ( j l, l s he number of rules). Calculae he coeffcen marx A by he npu daa se and he normalzed ncenve nensy w, and hen use he leas square mehod o denfy he concluson parameers ˆ. Fnally based on j Equaon (3) o calculae he roo mean square errors (RMSE) of he correspondng parcles produced by he ANFIS, whch s named as he parcle s fness value RMSE n ; Sep 3: Compare he curren fness value RMSE n of each parcle wh he bes fness value pbes self. If RMSE n < pbes, hen pbes = RMSE n n n, P = X ; Sep 4: Compare he fness value RMSE n of each parcle wh he bes fness value gbes of he parcle swarm. If RMSE n < gbes, hen gbes = RMSE n n n, P g = X ; Sep 5: The velocy and he poson vecors of each parcle are updaed. Based on he n V d Equaons (4) (7), he nera wegh w() of parcles s updaed. Sep 6: Check wheher he ermnaon condon of he PSO algorhm s me. If he prese accuracy or he maxmum number of eraons s reached, end he opmzng process and oupu he opmal soluon; oherwse go o Sep 2 and connue he nex eraon. n X d 4. Tme Seres Predcon of Bank Cash Flow Based on APAPSO-ANFIS In order o demonsrae he effecveness of he proposed APAPSO-ANFIS algorhm, and verfy s raonaly o predc he bank cash flow me seres, based on he colleced nformaon and he marke daa of a commercal bank, he APAPSO-ANFIS s used o realze he me seres forecasng of bank cash flow by adopng he MATLAB R22a smulaon plaform. In hs paper, he nvenory lm daa of each day from 2 o 22 of a commercal bank are seleced as he expermenal daa (a oal of 95 sample pons). The daa were carred ou he normalzaon

7 Informaon 25, 6 36 pre-reamen, where he frs 975 daa s seleced as he ranng daa se, and he remanng 2 daa s seleced as he esng daa se. As used heren, ANFIS conans 6 rules and each npu varable s assgned wo membershp funcons. The oal numbers of he adjused parameers are 4, ncludng 24 premse (non-lnear) parameers and 8 concluson (lnear) parameers. The number of parcles N s 3; he number of eraons s ; he learnng facors c = c2 = 2; he scope of he nera wegh w s [.5,.2]; he membershp funcon of ANFIS s he bell-shaped funcon. Four npu varables are gven [ x( 8), x( 2), x( 6), x( )]. Thus, he nal membershp funcon and her correspondng ermnaon membershp funcons afer he mproved PSO algorhm learnng are shown n Fgures 3 and 4, respecvely Fgure 3. Inal membershp funcon dagram of four npu varables. The fnal membershp funcon of x ( - 8) The fnal membershp funcon of x(-2) The fnal membershp funcon of x(-6) The fnal membershp funcon of x() Fgure 4. Fnal membershp funcons dagrams. Clearly seen from he comparson of he chars above, here are changes n he four membershp funcons afer learnng, whch proves ha he mproved algorhm s feasble and effecve. The predcon resuls and he error curves are obaned based on he mproved PSO algorhm, whch are shown n Fgures 5 and 6. I can be seen from Fgures 5 and 6 ha he predced resuls are very deal.

8 Informaon 25, 6 37 In order o show he advanage of APAPSO-LMS algorhm o opmze he parameers of ANFIS, hree dfferen algorhms (he BP-LMS algorhm, PSO-LMS algorhm wh nera wegh lnear decreasng sraegy and he APAPSO-LMS algorhm) are used o opmze ANFIS. The expermenal comparson resuls of RMSE evoluon curve s shown n Fgure 7. The smulaon predcon expermenal resuls are shown n Fgures 8 and 9. Respecvely, and he comparson resuls of predcon errors are shown n Fgure..8 x 7.6 Raw daa APAPSO-LMS Invenory lm (Yuan) me/days Fgure 5. Predcon resuls based on APAPSO-LMS algorhm. 2 x 6.5 The error value (Yuan) Fgure 6. Error curve based on APAPSO-LMS algorhm.

9 Informaon 25, 6 38 x -3 The curve of ranng RMSE Roo mean square error(rmse) ANFIS:PSO-LMS ANFIS:BP-LMS ANFIS:APAPSO-LMS Epochs Fgure 7. Comparson resuls of RMSE..5 x 7.4 Raw daa BP-LMS.3 Invenory lm (Yuan) me/days Fgure 8. Predcon resuls based on BP-LMS algorhm.

10 Informaon 25, x 7.4 Raw daa PSO-LMS.3 Invenory lm (Yuan) me/days Fgure 9. Predcon resuls based on PSO-LMS algorhm. 5 x PSO-LMS BP-LMS APAPSO-LMS The error value (Yuan) me/days Fgure. Comparson resuls of predcon errors. Seen from he Fgure 7 ha when he BP-LMS mehod s used o opmze ANFIS and he number of eraons runs o abou 55 generaon, he opmzaon error almos reaches a sable value. When usng PSO-LMS algorhm of nera wegh decreasng lnearly sraegy, alhough he opmzaon effec s

11 Informaon 25, 6 3 beer han BP-LMS algorhm and he convergence rae s ncreased, bu he resul s no very deal. Tha s o say ha when he number of eraons runs o abou 6 generaons, he opmzaon error no longer reduces, he algorhm s probably fallng no a local opmum. When he APAPSO-LMS algorhm s used o opmze ANFIS, he error decreases all he me unl generaons n he enre opmzaon process, and he rae of convergence and opmzaon resuls are much beer han he prevous wo algorhms. Because he nera wegh of parcles can be adjused adapvely, he global search capably and he local exploaon ably of he algorhm can be balanced well, whch can effecvely avod he premaure convergence and mprove he algorhm comprehensve opmzaon performance. By comparng he smulaon resuls (Fgures 8 ), can be seen more nuvely ha he proposed APAPSO-LMS predcon algorhm has much smaller error han he BP- LMS and PSO-LMS algorhm, and he predcon accuracy s hgher. So, can be concluded ha he APAPSO-LMS algorhm s effecve for he mprovemen of PSO algorhm and has a ceran praccal sgnfcance. In order o more clearly evaluae he predcve performance of he APAPSO-LMS algorhm, he resuls analyss s carred ou based on he followng fve performance ndexes. The predcon error s he devaon beween he predced resuls and he acual resuls, whch deermnes he predcon accuracy. y, y2,, yn are he acual observaons of predced objec and yˆ ˆ ˆ, y2,, yn are he predced values. () Absolue error of predced pons a ˆ y y,,2,, n (8) where a s he absolue error a he pon. Obvously, a s he mos drec measure ndex of he predcon error, bu s affeced by he measuremen un of he predced objecs. So s unsuable as he fnal measure ndcaor of predcon accuracy. (2) Relave error of predced pons a ˆ y y aˆ,,2,, n y y (9) where a s he relave error a he pon, whch s usually expressed as a percenage and o measure he accuracy of he predced values relave o he observed values a he predced pon. (3) Predcon accuracy of he predcon pons A ˆ y y y ˆ y y y () A y ˆ y y () where A s he predcon accuracy a he predcon pon. (4) Mean square error (MSE) Mean square error (MSE) s a knd of convenen mehod o measure he average error o evaluae he degree of daa change, whch s descrbed as follows. 2 n MSE (y y) (2) n

12 Informaon 25, 6 3 (5) Compuaonal loadng The mehod of compuaonal load s used n hs paper o add c drecon as a sared mer, and hen pu oc drecon a he end of program as a ermnae mer, and reurnng he oal me snce he c drecon s sared. The above menoned hree predcon algorhms are used o realze he me seres predcon of bank cash flow. The smulaon resuls summarzed based on he ranng daa and esng daa are shown n Table. I can be seen from Table ha ranng daa obaned accuracy s hgher han he esng daa, bu he program runnng me s much longer, because he fng degree of usng ranng daa s beer and esng daa need no spend more me o ran he parameers. Alhough PSO-LMS algorhm may fall no local opmum lead o he compuaonal me of he proposed APAPSO-LMS predcon algorhm s relavely longer, bu for he me seres predcon of bank cash flow has he hghes accuracy and he effecveness of he proposed mehod s verfed once agan. In concluson, by comparng he expermens resuls, can be seen ha he proposed predcon mehod s more suable for bank cash flow me seres forecasng and analyss. Table. Performance comparson resuls. Performance ndcaors Tranng daa Tesng daa BP-LMS PSO-LMS APAPSO-LMS BP-LMS PSO-LMS APAPSO-LMS MSE Absolue error Relave error of (%) Predcon accuracy (%) Compuaonal me (s) 6.35% 3.9%.2% 6.68% 3.76%.43% 93.65% 96.8% 98.8% 93.32% 96.24% 98.57% 8.96 s 5.37 s s 3.24 s 3.68 s 3.7 s 5. Conclusons A hybrd learnng algorhm based on adapve populaon acvy parcle swarm opmzaon (APAPSO) algorhm and he leas squares mehod (LMS) s proposed o opmze he parameers of ANFIS model, whch s used o realze he me seres forecasng of commercal bank cash flow. By he nroducon of measure funcon of speces dversy and adapve nera wegh adjusmen mechansms, he algorhm opmzaon capably and convergence accuracy are mproved and he convergence rae s acceleraed o a grea exen. The smulaon resuls verfy he proposed algorhm has beer applcably for bank cash flow me seres forecasng. Acknowledgmens Ths work s parally suppored by he Program for Chna Posdocoral Scence Foundaon (Gran No. 2495), he Program for Laonng Excellen Talens n Unversy (Gran No.LR248), and he Projec by Laonng Provncal Naural Scence Foundaon of Chna (Gran No ).

13 Informaon 25, 6 32 Auhor Conrbuons Je-Sheng Wang parcpaed n he concepon, desgn, nerpreaon, and commened on he manuscrp. A subsanal amoun of Chen-Xu Nng s conrbuon o he draf wrng, crcal revson daa collecon, and analyss and algorhm smulaon of hs paper was underaken. Boh auhors have read and approved he fnal manuscrp. Conflcs of Ineres The auhors declare no conflc of neres. References. Wang, J.-S. Parameers Opmzaon of ANFIS Based on Parcle Swarm Opmzaon. J. Perochem. Unv. 27, 2, Bar-Joseph, Z. Analyzng me seres gene expresson daa. Bonformacs 24, 2, Dong, Z. Sudy on he me-seres modelng of Chna s per capa GDP. Conemp. Manag. 26,, Sugeno, M.; Kang, G.T. Srucure denfcaon of fuzzy model. Fuzzy Ses Sys. 988, 28, Caalao, J.P.S.; Pousnho, H.M.I.; Mendes, V.M.F. Hybrd wavele-pso-anfis approach for shor-erm elecrcy prces forecasng. IEEE Trans. Power Sys. 2, 26, Pousnho, H.M.I.; Mendes, V.M.F.; Caalão, J.P.S. A hybrd PSO-ANFIS approach for shor-erm wnd power predcon n Porugal. Energy Convers. Manag. 2, 52, Meng, Y.-B.; Zou, J.-H.; Gan, X.-S.; Zhao, L. Research on WNN aerodynamc modelng from flgh daa based on mproved PSO algorhm. Neurocompung 22, 83, Zhao, L.; Yang, Y. PSO-based sngle mulplcave neuron model for me seres predcon. Exper Sys. Appl. 29, 36, Kuo, I.H.; Horng, S.J.; Kao, T.W.; Ln, T.L.; Lee, C.L.; Pan, Y. An mproved mehod for forecasng enrollmens based on fuzzy me seres and parcle swarm opmzaon. Exper Sys. Appl. 29, 36, Lee, C.M.; Ko, C.N. Tme seres predcon usng RBF neural neworks wh a nonlnear me-varyng evoluon PSO algorhm. Neurocompung 29, 73, Ca, X.; Zhang, N.; Venayagamoorhy, G.K.; Wunsch, D.C. Tme seres predcon wh recurren neural neworks raned by a hybrd PSO-EA algorhm. Neurocompung 27, 7, Chuang, L.Y.; Ln, Y.D.; Chang, H.W.; Yang, C.H. An mproved PSO algorhm for generang proecve SNP barcodes n breas cancer. PLoS One 22, 7, e Lu, S.; Xu, L.; L, D.; L, Q.; Jang, Y.; Ta, H.; Zeng, L. Predcon of dssolved oxygen conen n rver crab culure based on leas squares suppor vecor regresson opmzed by mproved parcle swarm opmzaon. Compu. Elecron. Agrc. 23, 95, Kavous-Fard, A.; Same, H.; Marzban, F. A new hybrd modfed frefly algorhm and suppor vecor regresson model for accurae shor erm load forecasng. Exper Sys. Appl. 24, 4, Wang, S.; Wu, L. An mproved PSO for bankrupcy predcon. Adv. Compu. Mah. Appl. 22,, 6.

14 Informaon 25, Shan, L.; Zhang, H.; Wang, J.; Xu, H.; Tang, J. Parameers opmzaon and mplemenaon of mxed kernels ɛ-svm based on mproved PSO algorhm. Jsuanj Yngyong Yanju 23, 3, (n Chnese) 7. Jang, J.S.R. ANFIS: Adapve-nework-based fuzzy nference sysem. IEEE Trans. Sys. Man Cybern. 993, 23, by he auhors; lcensee MDPI, Basel, Swzerland. Ths arcle s an open access arcle dsrbued under he erms and condons of he Creave Commons Arbuon lcense (hp://creavecommons.org/lcenses/by/4./).