Comparative Study between FPA, BA, MCS, ABC, and PSO Algorithms in Training and Optimizing of LS-SVM for Stock Market Prediction

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1 Comparatve Study between FPA, BA, MCS, ABC, and PSO Algorthms n ranng and Optmzng of LS-SVM for Stock Market Predcton Osman Hegazy 1*, Omar S. Solman 1 and Mustafa Abdul Salam 2 Faculty of Computers and Informaton, Caro Unversty, Egypt 1 Hgher echnologcal Insttute (H..I), enth of Ramadan cty, Egypt 2 Receved: 16-February-215; Revsed: 22-March-215; Accepted: 28-March ACCENS Abstract In ths Paper, fve recent natural nspred algorthms are proposed to optmze and tran Least Square- Support Vector Machne (LS-SVM). hese algorthms are namely, Flower Pollnaton Algorthm (FPA), Bat algorthm (BA), Modfed Cuckoo Search (MCS), Artfcal Bee Colony (ABC), and Partcle Swarm Optmzaton (PSO). hese algorthms are proposed to automatcally select best free parameters combnaton for LS- SVM. Sx fnancal techncal ndcators derved from stock hstorcal data are used as nputs to proposed models. Standard LS-SVM and ANN are used as benchmarks for comparson wth proposed models. Proposed models tested wth sx datasets representng dfferent sectors n S&P 5 stock market. Proposed models were used to predct daly, weekly, and monthly stock prces. Results presented n ths paper showed that the proposed models have quck convergence rate at early stages of the teratons. hey acheved better accuracy than compared methods n prce and trend predcton. hey also overcame over fttng and local mnma problems found n ANN and standard LS-SVM. Keywords Least Square- Support Vector Machne,Flower Pollnaton Algorthm, Bat algorthm, Modfed Cuckoo Search, Artfcal Bee Colony, Partcle Swarm Optmzaton, and stock market predcton. 1. Introducton Stock market predcton s the process of attemptng to specfy the future value of company stock based on ts hstorcal data. It has been at focus snce the good predcton can maxmze nvestor's gans. Predcton of stock market s not an easy task, because the nature of stock market data s varable, nonlnear, volatle, and close to random-walk. Also choosng a sutable tranng and predcton method s stll very crtcal problem [1]. echncal ndcators were from the frst methods used to predct stock market trend and prce [2].hey are mathematcal functons that use stock hstorcal data to determne the future prce. hey are classfed n two classes, oscllators or leadng ndcators, and laggng ndcators [2]. Leadng ndcators are desgned to lead prce movements. he laggng ndcators follow the prce acton and are referred to as trend-followng ndcators. Artfcal Neural Networks (ANNs) are consdered one of the most commonly machne learnng technques used n stock market predcton. In most cases ANNs suffer from over-fttng problem due to the large number of parameters to fx, and the lttle pror user knowledge about the relevance of the nputs n the analysed problem [3]. Support vector machnes (SVMs) have been developed as an alternatve that avod ANNs lmtatons. SVMs compute globally optmal solutons, unlke those obtaned wth ANNs, whch tend to fall nto local mnma [4]. Least squares support vector machne (LS-SVM) method whch s presented n [5], s a reformulaton of the tradtonal SVM algorthm. Although LS-SVM smplfes the SVM procedure, the regularzaton parameter and the kernel parameters play an mportant role n the regresson system. herefore, t s necessary to establsh a methodology for properly selectng the LS-SVM free parameters. *Author for correspondence 35

2 he perceved advantages of evolutonary strateges as optmzaton methods motvated the authors to consder such stochastc methods n the context of optmzng SVMs. A survey and overvew of evolutonary algorthms (EAs) s found n [6]. EAs or natural nspred algorthms used n ths work are Flower Pollnaton Algorthm (FPA), Bat algorthm (BA), Cuckoo Search (CS), Artfcal Bee Colony (ABC), and Partcle Swarm Optmzaton (PSO). Flower Pollnaton Algorthm (FPA) was proposed by Yang n 212[7]. It s nspred by the pollnaton process of flowers [7]. he man purpose of a flower s ultmately reproducton va pollnaton. Flower pollnaton s typcally assocated wth the transfer of pollen, and such transfer s often lnked wth pollnators such as nsects, brds, bats and other anmals [8]. In [9] FPA was appled successvely for dfferent economc load dspatch problems. In [1] FPA was appled n nonlnear algebrac systems wth multple solutons. In [11] bnary FPA was appled to feature selecton applcaton. In [12] FPA algorthm was used for multobjectve optmzaton. In [13] Study of FPA algorthm for contnuous optmzaton s presented. In [14] FPA algorthm wth dmenson mprovement s ntroduced. Bat algorthm (BA) was proposed by Yang n 21 [15]. It s consdered a new meta-heurstc algorthm for contnuous optmzaton. BA s based on the fascnatng capablty of mcrobats (echolocaton) to fnd ther prey and dscrmnate dfferent types of nsects even n complete darkness. BA has demonstrated to outperform some well-known nature-nspred optmzaton technques lke GA, and PSO algorthms [15].BA s appled n contnuous optmzaton n the context of engneerng desgn optmzaton.ba can deal wth hghly nonlnear problem effcently and can fnd the optmal solutons accurately [16].Case studes nclude pressure vessel desgn, car sde desgn, sprng and beam desgn, truss systems, tower and tall buldng desgn and others.. BA can handle multobjectve problems effectvely [17]. In [18], a detaled study of combned economc load and emsson dspatch problems usng bat algorthm s presented. hey concluded that bat algorthm s easy to mplement and much superor to ABC and GA algorthms n terms of accuracy and effcency. In [19] a comparson study of bat algorthm wth PSO, GA, and other algorthms n the context for e-learnng s presented. hey concluded 36 Internatonal Journal of Advanced Computer Research that bat algorthm has clearly some advantages over other algorthms. In [2] A New Bat Based Back- Propagaton (BA-BP) Algorthm s presented. hey suggested that the computatonal effcency of BPNN tranng process s hghly enhanced when combned wth BA algorthm. Cuckoo Search (CS) algorthm s proposed by Yang and Deb n 29 [21]. It s consdered a naturenspred meta-heurstc algorthm for contnuous optmzaton [21]. CS s based on the brood parastsm of some cuckoo speces. CS s enhanced by the Levy flghts [22], rather than by smple sotropc random walks. CS algorthm was appled to engneerng desgn applcatons; t has superor performance over other algorthms for a range of contnuous optmzaton problems such as sprng desgn and welded beam desgn problems [23, 24, and 25]. Zheng and Zhou [26] provded a varant of cuckoo search usng Gaussan process. Modfed Cuckoo Search (MCS) algorthm s proposed by Walton proposed n 211 [27]. MCS mproved standard CS algorthm especally n terms of convergence to global mnmum n real world applcatons. Artfcal Bee Colony (ABC) s proposed by D. Karaboga n 25 for real parameter optmzaton [28]. It s nspred by the ntellgent behavour of honey bees. Karaboga and Basturk have nvestgated the performance of the ABC algorthm on unconstraned numercal optmzaton problems whch s found n [29], [3], [31] and ts extended verson for the constraned optmzaton problems n [32]. Hybrd artfcal bee colony-based approach for optmzaton of mult-pass turnng operatons s used n [33]. A study on Partcle Swarm Optmzaton (PSO) and ABC algorthms for multlevel thresholdng s ntroduced n [34]. ABC optmzaton was used for mult-area economc dspatch n [35]. Partcle Swarm Optmzaton algorthm (PSO) s proposed by James Kennedy and Russell Eberhart n 1995 [36]. PSO s one of the most used EAs. It s motvated by socal behavour of organsms such as brd flockng and fsh schoolng [36]. he PSO algorthm, whle makng adjustment towards "local" and "global" best partcles, s smlar to the crossover operaton used by genetc algorthms [37]. In [38], [39] authors proved that SVM optmzed by PSO gave better accuracy than standard SVM model. Ju Y. et al. [4] concluded that hybrd CI approaches

3 AIA-BPNN and ASA-BPNN are better than sngle CI technque BPNN-SCG and recommended for stock prce. hs paper proposes fve hybrd models. hese are FPA-LS-SVM, BA-LS-SVM, MCS-LS-SVM, ABC- LS-SVM, and PSO-LS-SVM models. hese models are hybrdzng optmzaton algorthms (FPA, BA, MCS, ABC, and PSO) respectvely, fnancal techncal ndcators, and LS-SVM model. he performance of LS-SVM s based on the selecton of hyper parameters C (cost penalty), ϵ (nsenstve-loss functon) and γ (kernel parameter). Optmzaton algorthms were used to fnd the best parameter combnaton for LS-SVM. he rest of paper s organzed as follows: Secton 2 presents the Least square support vector machne (LS-SVM) model; Secton 3 presents the FPA algorthm; Secton 4 presents the BA algorthm; Secton 5 presents the MCS algorthm; Secton 6 presents the ABC algorthm; Secton 7 presents the PSO algorthm; Secton 8 s devoted for the proposed models and ts mplementaton n daly, weekly, and monthly stock prce predcton; In Secton 9 the results are dscussed. he man conclusons of the work are presented n Secton Least Square Support Vector Machne (LS-SVM) Least squares support vector machnes (LS-SVM) are least squares versons of support vector machnes (SVM), whch are a set of related supervsed learnng methods that analyse data and recognze patterns, and whch are used for classfcaton and regresson analyss. In ths verson one fnds the soluton by solvng a set of lnear equatons nstead of a convex quadratc programmng (QP) problem for classcal SVMs. LS-SVM classfers, were proposed by Suykens and Vandewalle [41]. Let X s nput data matrx and s output vector. Gven the tranng data set, where, the LS-SVM goal s to construct the functon, whch represents the dependence of the output on the nput. hs functon s formulated as f ( x) W ( x) b (1) Where W and (x) vectors, and b R : p n R R are n1 column. LS-SVM algorthm computes the functon (1) from a smlar mnmzaton problem 37 found n the SVM method [4]. However the man dfference s that LS-SVM nvolves equalty constrants nstead of nequaltes, and t s based on a least square cost functon. Furthermore, the LS-SVM method solves a lnear problem whle conventonal SVM solves a quadratc one. he optmzaton problem and the equalty constrants of LS-SVM are defned as follows: y w ( x ) b e (3) Where e s the n1error vector, 1 s a n1vector C R wth all entres 1, and s the tradeoff parameter between the soluton sze and tranng errors. From Eq. (2) a Lagranan s formed, and dfferentatng wth respect to Largrangan multplers), we obtan I Z 1 CI I Z 1 I W b e a y Where I represents the dentty matrx and Z [ ( x1), ( x2),..., ( )] w, b, e, a ( a s x n From rows one and three n Eq. (4) Ce a hen, by defnng the kernel matrx C 1 (4) w Z a and K ZZ, and the parameter, the condtons for optmalty lead to the followng overall soluton 1 mn j( w, e, b) w w w, e, b 1 b K I a y (5) Kernel functon K types are as follows: Lnear kernel K( x, x ) x x (6) Polynomal kernel of degree d: K ( x, x ) ) 1 1 C e (2) 2 2 d (1 x x / c (7) Radal bass functon RBF kernel : 2 K( x, x ) exp( x / ) (8) x 2

4 MLP kernel : K( x, x ) tanh( kx x ) (9) 3. Flower Pollnaton Algorthm (FPA) Flower Pollnaton Algorthm (FPA) s a novel algorthm nspred by the pollnaton process of flowers [7]. Pollnaton can be acheved by selfpollnaton or cross-pollnaton. Cross-pollnaton, or allogamy, means pollnaton can occur from pollen of a flower of dfferent plant, whle self-pollnaton s the fertlzaton of one flower, such as peach flowers, from pollen of the same flower or dfferent flowers of the same plant, whch often occurs when there s no relable pollnator avalable. Botc, cross-pollnaton may occur at long dstance, and the pollnators such as bees, bats, brds and fles can fly a long dstance, thus they can consdered as the global pollnaton. In addton, bees and brds may behave as Levy flght behavor [42], wth jump or fly dstance steps obey a Levy dstrbuton. Furthermore, flower constancy can be used an ncrement step usng the smlarty or dfference of two flowers. he characterstcs of pollnaton process, flower constancy and pollnator behavor, were dealzed n the followng rules [7]: 1. Botc and cross-pollnaton s consdered as global pollnaton process wth pollen carryng pollnators performng Levy flghts. 2. Abotc and self-pollnaton are consdered as local pollnaton. 3. Flower constancy can be consdered as the reproducton probablty s proportonal to the smlarty of two flowers nvolved. 4. Local pollnaton and global pollnaton s controlled by a swtch probablty. Due to the physcal proxmty and other factors such as wnd, local pollnaton can have a sgnfcant fracton p n the overall pollnaton actvtes. In the global pollnaton step, flower pollens are carred by pollnators such as nsects, and pollens can travel over a long dstance. hs ensures the pollnaton and reproducton of the fttest, and thus we represent the fttest as. he frst rule can be formulated as bee s updated usng the Eq. (1): ( ) (1) 38 Internatonal Journal of Advanced Computer Research Where s the soluton vector at teraton and s the current best soluton. he parameter s the strength of the pollnaton whch s a step sze. Snce nsects may move over a long dstance wth varous dstance steps, a Levy flght can be used to mmc ths characterstc effcently [17]. L > wll be drawn from a Levy dstrbuton as shown n Eq. (11) ( ) ( ) ( ) (11) Here ( ) s the standard gamma functon, and ths dstrbuton s vald for large steps s >. he local pollnaton (Rule 2) and flower constancy can be represented as n Eq. (12): ( ) (12) Where and are soluton vectors drawn randomly from the soluton set. he parameter s drawn from unform dstrbuton n the range from to Bat Algorthm (BA) Bat Algorthms (BA), whch s a new nature nspred algorthm for contnuous optmzaton s proposed by Yang n 21 [15]. Yang developed the bat algorthm wth the followng three dealzed rules: a. All bats use echolocaton to sense dstance, and they also know the dfference between food/prey and background barrers n some magcal way. b. Bats fly randomly wth velocty at poston wth a frequency, varyng wavelength and loudness to search for prey. hey can automatcally adjust the wavelength (or frequency) of ther emtted pulses and adjust the rate of pulse emsson, dependng on the proxmty of ther target. c. Although the loudness can vary n many ways, we assume that the loudness vares from a large (postve) to a mnmum constant value. Frst, the ntal poston, velocty and frequency are ntalzed for each bat. For each tme step, the movement of the vrtual bats s gven by updatng ther velocty and poston usng Eq. (13), Eq. (14) and Eq. (15) respectvely, as follows:

5 ( ) (13) ( ) (14) (15) Where denotes a randomly generated number wthn the nterval [, 1]. Recall that denotes the value of decson varable for bat at tme step.he result of n Eq. (13) s used to control the pace and range of the movement of the bats. he varable represents the current global best locaton (soluton) whch s located after comparng all the solutons among all the bats. In order to mprove the varablty of the possble solutons, Yang [15] has employed random walks. Prmarly, one soluton s selected among the current best solutons for local search and then the random walk s appled n order to generate a new soluton for each bat; (16) Where, stands for the average loudness of all the bats at tme, and s a random number. For each teraton of the algorthm, the loudness and the emsson pulse rate are updated, as follows: (17) ( ) (18) Where and are constants. At the frst step of the algorthm, the emsson rate, and the loudness, are often randomly chosen. Generally, and. 5. Modfed Cuckoo Search (MCS) he cuckoo search algorthm (CS) can easly fnd the optmum [16] but, as the search reles entrely on random walks, a fast convergence cannot be guaranteed. Modfed Cuckoo Search (MCS) made two modfcatons to the orgnal CS algorthm to ncrease the convergence rate. he frst modfcaton s made to the sze of the Lévy flght step sze α. In CS, α s constant and the value α = 1 s employed [21]. In the MCS, the value of α decreases as the number of generatons ncreases. hs s done for the same reasons that the nerta constant s reduced n the PSO,.e. to encourage more localzed searchng as the ndvduals, or the 39 Internatonal Journal of Advanced Computer Research eggs, get closer to the soluton. An ntal value of the Lévy flght step sze A = 1 s chosen and, at each generaton, a new Lévy flght step s calculated usng α=a/ G, where G s the generaton number. hs exploratory search s only performed on the fracton of nests to be abandoned. he second modfcaton s to add nformaton exchange between the eggs to speed up convergence to a mnmum. In the CS, there s no nformaton exchange between ndvduals and, essentally, the searches are performed ndependently. 6. Artfcal Bee Colony (ABC) Artfcal Bee Colony (ABC) algorthm was proposed by Karaboga n 25 for real parameter optmzaton [28]. It s nspred by the ntellgent behavor of honey bees. he colony of artfcal bees conssts of three groups of bees: employed, onlooker and scout bees. Half of the colony composed of employed bees and the rest consst of the onlooker bees. he number of food sources/nectar sources s equal wth the employed bees, whch means one nectar source s responsble for one employed bee. he am of the whole colony s to maxmze the nectar amount. he duty of employed bees s to search for food sources (solutons). Later, the nectars amount (solutons qualtes/ftness value) s calculated. hen, the nformaton obtaned s shared wth the onlooker bees whch are watng n the hve. he onlooker bees decde to explot a nectar source dependng on the nformaton shared by the employed bees. he onlooker bees also determne the source to be abandoned and allocate ts employed bee as scout bees. For the scout bees, ther task s to fnd the new valuable food sources. hey search the space near the hve randomly [43]. In ABC algorthm, suppose the soluton space of the problem s D-dmensonal, where D s the number of parameters to be optmzed. he ftness value of the randomly chosen ste s formulated as follows: ( ) (19) he sze of employed bees and onlooker bees are both SN, whch s equal to the number of food sources. here s only one employed bee for each food source whose frst poston s randomly generated. In each teraton of ABC algorthm, each

6 employed bee determnes a new neghbourng food source of ts currently assocated food source and computes the nectar amount of ths new food source by ( ) (2) Where;,,. If the new food source s better than that of prevous one, then ths employed bee moves to new food source, otherwse t contnues wth the old one. After all employed bees complete the search process; they share the nformaton about ther food sources wth onlooker bees. An onlooker bee evaluates the nectar nformaton taken from all employed bees and chooses a food source wth a probablty related to ts nectar amount by Equaton: (21) Where s the ftness value of the soluton whch s proportonal to the nectar amount of the food source n the poston and SN s the number of food sources whch s equal to the number of employed bees. Later, the onlooker bee searches a new soluton n the selected food source ste, the same way as exploted by employed bees. After all the employed bees explot a new soluton and the onlooker bees are allocated a food source, f a source s found that the ftness hasn t been mproved for a predetermned number of cycles (lmt parameter), t s abandoned, and the employed bee assocated wth that source becomes a scout bee. In that poston, scout generates randomly a new soluton by: ( ) (22) Where; s random number n range [, 1]., are the lower and upper borders n the jth dmenson of the problem space. 7. Partcle Swarm Optmzaton Algorthm (PSO) PSO s a heurstc search method whch s derved from the behavor of socal groups lke brd flocks or fsh swarms [36]. PSO moves from a set of ponts to 4 another set of ponts n a sngle teraton wth lkely mprovement usng a combnaton of determnstc and probablstc rules. he PSO has been popular because of ts ease of mplementaton, and the ablty to effectvely solve hghly nonlnear, mxed nteger optmzaton problems that are typcal of complex engneerng systems. Optmzaton s acheved by gvng each ndvdual n the search space a memory for ts prevous successes, nformaton about successes of a socal group and provdng a way to ncorporate ths knowledge nto the movement of the ndvdual [36]. herefore, each ndvdual (called partcle) s characterzed by ts poston x, ts velocty v, ts personal best poston p and ts neghborhood best poston p g. he elements of the velocty vector for partcle are updated as pb sb c q x x ) c ( x x ) (23) j j j 1,.., 1 ( j j 2 j j n pb Where, w s the nerta weght, x s the best varable vector encountered so far by partcle, sb and x s the swarm best vector,.e. the best varable vector found by any partcle n the swarm, so far c 1 and c2 are constants, and q and r are random numbers n the range (, 1). Once the veloctes have been updated, the varable vector of partcle s modfed accordng to x. (24) j x j j he cycle of evaluaton followed by updates of veloctes and postons (and possble update of pb x and x sb ) s then repeated untl a satsfactory soluton has been found. 8. he proposed models he proposed models are based on the study and gatherng of stock hstorcal data (Hgh, Low, Open, Close, and Volume) of S&P 5 stock market. he gathered data are sampled nto three categores (daly, weekly, and monthly). hen fnancal techncal ndcators are extracted and calculated from the collected hstorcal data. hese techncal are namely RSI, MFI, MACD, EMA, PMO, and SO. he selected ndcators are from all types of ndcators to make the system more robust and more accurate.

7 Indcators are used as nputs to proposed model. After extractng the ndcators features, fve models were constructed by optmzng and traned LS-SVM wth fve dfferent optmzaton algorthms (FPA, BA, MCS, ABC, and PSO). hese models are used n the predcton of daly, weekly, and monthly stock prces. Standard LS-SVM, and ANN are used as benchmarks for comparson wth proposed model. he proposed models are evaluated by four dfferent crterons. Evaluaton crterons are RMSE, MAE, SMAPE, and PMRE. he proposed models archtecture contans seven nputs vectors represent the hstorcal data and sx derved techncal ndcators from raw datasets, and one output represents next prce. he proposed models are summarzed n Fg. 1. Prce Momentum Oscllator (PMO) PMO s an oscllator based on a Rate of Change (ROC) calculaton that s exponentally smoothed twce. Because the PMO s normalzed, t can also be used as a relatve strength tool. Stocks can thus be ranked by ther PMO value as an expresson of relatve strength. C = today s close prce DAC = close prce ten days ago he followng was used to calculate PMO: (25) Relatve Strength Index (RSI) A techncal momentum ndcator that compares the magntude of recent gans to recent losses n an attempt to determne overbought and oversold condtons of an asset. he formula for computng the Relatve Strength Index s as follows. ( ) (26) Where RS = Avg. of x days up closes dvded by average of x days down closes. Money Flow Index (MFI) hs one measures the strength of money n and out of a securty. he formula for MFI s as follows. ( ) (27) Where, P s typcal prce, and V s money Vol. Money Rato (MR) s calculated as: ( ) (28) ( ( )) (29) Exponental Movng Average (EMA) hs ndcator returns the exponental movng average of a feld over a gven perod of tme. EMA formula s as follows. (3) Where s oday s close and Y s Yesterday s close. Stochastc Oscllator (SO) he stochastc oscllator defned as a measure of the dfference between the current closng prce of a securty and ts lowest low prce, relatve to ts hghest hgh prce for a gven perod of tme. he formula for ths computaton s as follows. ( ) ( ) (31) Fg.1: he proposed models steps he fnancal techncal ndcators, whch are calculated from the raw datasets, are calculated as follows: 41 Where, CP s Close prce, LP s Lowest prce, HP s Hghest Prce, and LP s Lowest Prce. MovngAverage Convergence/Dvergence (MACD) hs functon calculates dfference between a short and a long term movng average for a feld. he

8 formulas for calculatng MACD and ts sgnal as follows. (32) Where, E s EMA (CP) (33) 9. Results and Dscussons In ths secton FPA, MCS, BA, ABC, and PSO algorthms are compared n optmzng LS-SVM. he number of flowers, nests, bats, bees, and partcles are 5 and traned for 1epochs. hese models were traned and tested wth daly datasets for sx companes cover dfferent sectors n S&P 5 stock markets. hese companes are Adobe, Bank of Amerca (BAC), Exxon moble, General Electrc (GE), Peps, and Pfzer. Datasets perods are as follows whch avalable n [44]. Smulaton results are done usng matlab 212b. Daly datasets perod are from Feb. 211 to Feb Weekly datasets perod are from Feb. 24 to Feb Monthly datasets perod are from Feb. 2 to Feb hese datasets are dvded nto tranng part (7%) and testng part (3%). In table 1 the RMSE of daly stock market predcton s summarzed for all compared algorthms. From table one can notce that FPA algorthm acheved lowest sum of RMSE value wth lttle advance over BA, ABC, MCS, and PSO algorthms. In table 2 the RMSE of weekly stock market predcton for all compared models s presented. FPA algorthm also acheved lowest sum of RMSE. In table 3 the RMSE of monthly stock market predcton s outlned. BA algorthm acheved lowest sum of RMSE value wth lttle advance over FPA, ABC, MCS, and PSO algorthms. able 1: RMSE of daly results RMSE FPA BA ABC MCS PSO SVM ANN Adobe BAC Exxon GE Peps Pfzer Sum of RMSE able 2: RMSE of weekly results RMSE FPA BA ABC MCS PSO SVM ANN Adobe BAC Exxon GE Peps Pfzer Sum of RMSE able 3: RMSE of monthly results RMSE FPA BA ABC MCS PSO SVM ANN Adobe BAC Exxon GE Peps pfzer Sum of RMSE

9 1. Conclusons In ths paper fve bo nspred algorthms were proposed to tran and optmze LS-SVM model. From results we can notce that standard LS-SVM and ANN models cannot overcome the overfttng problem and have slow convergence speed. Also these algorthms stll suffer from fallng n local mnma problem. Usng natural nspred algorthms or global search technques help n overcomng the problems of tradtonal learnng algorthms. FPA, ABC, BA, PSO, MCS algorthms n most cases convergences to a global mnmum whle tradtonal LS-SVM and ANN models faled. Proposed hybrd FPA-LS-SVM method acheved lowest error values (RMSE) n daly, weekly, and weekly stock prce predcton. All proposed models (FPA-LS-SVM, BA- LS-SVM, ABC-LS-SVM, MCS-LS-SVM, and PSO- LS-SVM) could easly manpulate the fluctuaton of stock tme seres whle LS-SVM and ANN models faled to cope wth these fluctuatons. Convergence speed of proposed models to global mnmum s very fast compared to classcal methods. References [1] C. Olver, Blase Pascal Unversty: Neural network modelng for stock movement predcton, state of art. 27. [2] P.Fernández-Blanco1, D.Bodas-Sag1, F.Soltero1, J.I.Hdalgo1, echncal market ndcators optmzaton usng evolutonary algorthms, Proceedngs of the 28 GECCO conference companon on Genetc and evolutonary computaton, ACM New York, NY, USA,28, pp [3] X. Leng, and H. Mller, Input dmenson reducton for load forecastng based on support vector machnes, IEEE Internatonal Conference on Electrc Utlty Deregulaton, Restructurng and Power echnologes (DRP24), 24, pp [4] V. Cherkassky, and Y. Ma, Practcal Selecton of SVM Parameters and Nose Estmaton for SVM regresson, Neural Networks, 17(1), pp , 24. [5] J. Suykens, V. Gestel, and J. Brabanter, Least squares support vector machnes, World Scentfc, 22. [6] A. Carlos, B. Gary, and A. Davd, Evolutonary Algorthms for Solvng Mult-Objectve Problems, Sprnger, 27. [7] X.S. Yang, Flower pollnaton algorthm for global optmzaton: Unconventonal Computaton and Natural Computaton 212, 43 Internatonal Journal of Advanced Computer Research Lecture Notes n Computer Scence, Vol. 7445, pp (212). [8] B. J. Glover, Understandng Flowers and Flowerng: An Integrated Approach, Oxford Unversty Press, (27). [9] R. Prathba, M. Balasngh Moses, S. Sakthvel, Flower Pollnaton Algorthm Appled for Dfferent Economc Load Dspatch Problems, Internatonal Journal of Engneerng and echnology (IJE), Vol 6 No 2 Apr-May 214, pp [1] G.M. platt, Applcaton of Flower Pollnaton Algorthm n nonlnear algebrac systems wth multple solutons, Engneerng Optmzaton IV. [11] D Rodrgues, X.S. Yang, A.N. de Souza, J.P. Papa, Bnary Flower Pollnaton Algorthm and Its Applcaton to Feature Selecton, Sprnger, Recent Advances n Swarm Intellgence and Evolutonary Computaton Studes n Computatonal Intellgence Volume 585, 215, pp [12].S Yang, M. Karamanoglu,. He, Flower pollnaton algorthm: A novel approach for multobjectve optmzaton, Engneerng Optmzaton, Volume 46, Issue 9, 214. [13] S. Łukask, P. Kowalsk, Study of Flower Pollnaton Algorthm for Contnuous Optmzaton, Intellgent Systems'214, Advances n Intellgent Systems and Computng Volume 322, 215, pp [14] R. Wang and Y.Zhou, Flower Pollnaton Algorthm wth Dmenson by Dmenson Improvement, Mathematcal Problems n Engneerng, vol. 214, Artcle ID , 9 pages, 214. do:1.1155/214/ [15] X. S., Yang, A New Metaheurstc Bat-Inspred Algorthm, n: Nature Inspred Cooperatve Strateges for Optmzaton (NISCO 21) (Eds. Cruz, C.; Gonzalez, J. R.; Pelta, D. A.; errazas, G), Studes n Computatonal Intellgence Vol. 284, Sprnger Berln, pp , 21. [16] X. S., Yang and A. H. Gandom, Bat algorthm: a novel approach for global engneerng optmzaton, Engneerng Computatons, Vol. 29, No. 5, pp , 212. [17] X. S., Yang, Bat algorthm for mult-objectve optmsaton, Int. J. Bo-Inspred Computaton, Vol. 3, No. 5, pp , 211. [18] B., Ramesh, V. C. J., Mohan, V. C. V., Reddy, Applcaton of bat algorthm for combned economc load and emsson dspatch, Int. J. of Electrcal Engneerng and elecommuncatons, Vol. 2, No. 1, pp. 1 9,213. [19] K., Khan, A. Saha, A comparson of BA, GA, PSO, BP and LM for tranng feed forward neural networks n e-learnng context, Int. J. Intellgent Systems and Applcatons (IJISA), Vol. 4, No. 7, pp , 212.

10 [2] N.M. Naw, M. Z. Rehman, A. Khan, A New Bat Based Back-Propagaton (BA-BP) Algorthm, Sprnger, Advances n Intellgent Systems and Computng Vol. 24, pp , 214. [21] X. S., Yang, S.Deb, Cuckoo search va Lévy flghts. Proceedngs of World Congress on Nature & Bologcally Inspred Computng (NaBIC 29, Inda), IEEE Publcatons, USA 29; p [22] I.Pavlyukevch, Le vy flghts, non-local search and smulated annealng. J Comput Phys, 27, 226: [23] A.H. Gandom, X.S. Yang, A.H. Alav (213) Cuckoo search algorthm: a metaheurstc approach to solve structural optmzaton problems. Eng Comput 29(1): do:1.17/s y. [24] A.H. Gandom, X.S. Yang, S. alatahar, S. Deb (212) Coupled eagle strategy and dfferental evoluton for unconstraned and constraned global optmzaton. Comput Math Appl 63(1): [25] X.S. Yang, S. Deb (21) Engneerng optmzaton by cuckoo search. Int J Math Modell Num Opt 1(4): [26] H.Q. Zheng, Y Zhou (212) A novel cuckoo search optmzaton algorthm based on Gauss dstrbuton. J Comput Inf Syst 8: [27] S.Walton, O.Hassan, K.Morgan and M.R.Brown "Modfed cuckoo search: A new gradent free optmsaton algorthm" Chaos, Soltons & Fractals Vol 44 Issue 9, Sept 211 pp DOI:1.116/j.chaos [28] D. Karaboga, An Idea Based On Honey Bee Swarm for Numercal Optmzaton, echncal Report-R6, Ercyes Unversty, Engneerng Faculty, Computer Engneerng Department, 25. [29] B. Basturk, and D. Karaboga, An Artfcal Bee Colony (ABC) Algorthm for Numerc functon Optmzaton, IEEE Swarm Intellgence Symposum, Indanapols, Indana, USA, 26. [3] D. Karaboga, and B. Basturk, A Powerful And Effcent Algorthm For Numercal Functon Optmzaton: Artfcal Bee Colony (ABC) Algorthm, Journal of Global Optmzaton, 39(3), 27, [31] D. Karaboga, and B. Basturk, On he Performance Of Artfcal Bee Colony (ABC) Algorthm, Appled SoftComputng journal, 8(1), 28, [32] D. Karaboga, and B. Basturk, Artfcal Bee Colony (ABC) Optmzaton Algorthm for Solvng Constraned Optmzaton Problems, Advances n SoftComputng: Foundatons of Fuzzy Logc and Soft Computng, 4529, 27, [33] A.R. Yldz, Optmzaton of cuttng parameters n mult-pass turnng usng artfcal bee colonybased approach, Informaton Scences: an Internatonal Journal, 22, 213, [34] A. Gupta Stock market predcton usng Hdden Markov Models, IEEE Engneerng and Systems (SCES), 212 Students Conference on, pp.1-4, 212. [35] M. Basu, Artfcal bee colony optmzaton for mult-area economc dspatch, Internatonal Journal of Electrcal Power & Energy Systems, (49), 213, [36] D. N. Wlke. Analyss of the partcle swarm optmzaton algorthm, Master's Dssertaton, Unversty of Pretora, 25. [37] A.S. Khall An Investgaton nto Optmzaton Strateges of Genetc Algorthms and Swarm Intellgence. Artfcal Lfe (21). [38] Z. Guo, H. Wang, Q. Lu: Fnancal tme seres forecastng usng LPP and SVM optmzed by PSO Sprnger, Soft Computng Methodologes and Applcatons, December 212. [39] G. e: he Optmzaton of Share Prce Predcton Model Based on Support Vector Machne, Internatonal Conference on Control, Automaton and Systems Engneerng (CASE), pp.1-4., 3-31 July 211. [4] Y. Ju: Computatonal Intellgence Approaches for Stock Prce Forecastng, IEEE Internatonal Symposum on Computer, Consumer and Control (IS3C), pp , 212. [41] J. Suykens, J. Vandewalle, Least squares support vector machne classfers, Neural Processng Letters, Vol. 9 (3), 293-3, [42] I. Pavlyukevch, Levy flghts, non-local search and smulated annealng, J. Computatonal Physcs, 226, (27). [43] P. Mansour, B. Asady, and N. Gupta, A Novel Iteraton Method for solve Hard Problems (Nonlnear Equatons) wth Artfcal Bee Colony Algorthm, World Academy of Scence, Engneerng and echnology, 5(11), 211, [44] last accessed 11 Jan Osman Hegazy receved hs Ph.D. n Computer Engneerng n 1977 from Lecester Unversty, UK. Currently, he s Professor at the Department of Informaton Systems, Faculty of Computers and Informaton, Caro Unversty, Egypt. He has more than 1+ publcatons n the areas of Data Mnng, Data Engneerng, Cloud Computng, and Computatonal Intellgence n nternatonal journals and nternatonal conferences. He has supervsed over 5 44

11 M.Sc. s and over 3 Ph.D. n computer scence and nformaton systems. Emal: Osman.hegazy@gmal.com Omar Solman receved hs PhD n Operatons Research department, Faculty of Computers and Informaton, Caro Unversty, Egypt n 21. He has more than 5+ publcatons n the areas of Computatonal Intellgence and Optmzaton n nternatonal journals and nternatonal conferences. Mustafa Abdul Salam receved the B.S from faculty of Computers and Informaton, Zagazg Unversty, Egypt n 23, and obtaned M.Sc. s degree n nformaton system from faculty of Computers and Informaton, Menufya Unversty, Egypt n 29. He s Ph.D. student at faculty of Computers and Informaton, Caro Unversty. He s teachng assstant at nformaton system department, Hgher echnologcal Insttute. He has contrbuted more than 1+ techncal papers n the areas of Data Mnng, Computatonal Intellgence, and Natural- Inspred algorthms n nternatonal journals and nternatonal conferences. 45