Optimizing Back-Propagation using PSO_Hill and PSO_A*

Transcription

1 Inernaional Journal of Scienific and Research Publicaions, Volume 3, Issue 4, April Opimizing Back-Propagaion using PSO_Hill and PSO_A* Priyanka Sharma *, Asha Mishra ** * M.Tech Scholar of compuer science & Engineering, BSAITM, Faridabad ** Deparmen of compuer science & Engineering, BSAITM, Faridabad Absrac- Back propagaion algorihm (BPA) have he complexiy, local minima problem so we are using Paricle Swarm opimizaion (PSO) algorihms o reduce and opimize BPA. In his paper, wo varians of Paricle Swarm Opimizaion (PSO) PSO_Hill and PSO_A* is used as opimizaion algorihm. PSO_Hill and PSO_A* algorihms are analyzed and evaluaed on he basis of heir advanages, applied o feed forward neural nework(fnn) for back propagaion algorihm(bpa) which is a gredien desen echnique. where BPA is used for non_linear problems. These non_linear problems are improved by a PSO_Hill and PSO_A* algorihms. Index Terms- BPA, PSO_hill, PSO_A*, ANN O I. INTRODUCTION pimizaion is an acive area of research as many algorihms ha are inroduced earlier are complex and no opimize so beer opimizaion algorihms are needed. The objecive of opimizaion algorihm is o find a soluion o saisfying a se of consrains such ha objecive funcion is maximized or minimized. Paricle swarm opimizaion (PSO) is an alernaive populaion-based evoluionary compuaion echnique. I has been shown o be capable of opimizing hard mahemaical problems in coninuous or binary space. The paricle swarm opimizaion (PSO) algorihm is based on he evoluionary compuaion echnique [11-13]. PSO opimizes an objecive funcion by conducing populaion-based search. The populaion consiss of poenial soluions, called paricles, similar o birds in a flock. The paricles are randomly iniialized and hen freely fly across he muli-dimensional search space. While flying, every paricle updaes is velociy and posiion based on is own bes experience and ha of he enire populaion. The updaing policy will cause he paricle swarm o move oward a region wih a higher objec value. Evenually, all he paricles will gaher around he poin wih he highes objec value. PSO processes he search scheme using populaions of paricles where each paricle is equivalen o a candidae soluion of a problem [9]. The paricle moves according o an adjused velociy, which is based on ha paricle s experience and he experience of is companions. For he D-dimensional funcion f(.), he i h paricle for he j h ieraion can be represened as X j = X 1, X 2 X n W j= W 1, W 2 W n Assume ha he bes local posiion of he j h paricle a hen nh ieraion is represened as L_bes j =L_bes 1, L_bes 2. L_bes n The bes posiion amongs all he paricles, G_bes, from he firs ieraion o he j h ieraion, where bes is defined by some funcion of he swarm, is G_bes j =G_bes 1, G_bes2.G_bes n The original paricle swarm opimizaion algorihm can be expressed as follows: P j = X j *W j V j = f(p j ) means V j =1/(1+exp(-P j )) V j +1 = V j +r1* c1(l_bes j -X j )+r2*c2(g_bes j -X j ) X j +1 = X j + V i +1 r1and r 2 are random variables acs as learning signals such ha 0 r 1, r 2 1. where W j is he ineria weigh a he j h ieraion. The weighing facors, C 1 and C 2 are used as consans. In his paper, he opimizaion and analysis of back propagaion algorihm is done by paricle swarm opimizaion, and wo varian of paricle swarm opimizaion PSO_Hill and PSO_A*and heir algorihm, archiecure are proposed. This paper is organized as follows. In Secion II, we explained original swarm echniques ha are PSO and ACO. In Secion III, we explained original Back-propagaion nework wih algorihms. In secion IV, we explained Relaed work in PSO. In Secion V, we explained proposed work (PSO_Hill and PSO_A* varians wih diagram and algorihm). In secion VI, we explained Conclusion of paper. II. SWARM TECHNIQUES Swarm inelligence (SI) is he collecive behavior of decenralized, self-organized sysems, naural or arificial. The concep is employed in work on arificial inelligence. SI sysems are ypically made up of a populaion of simple agens ineracing locally wih one anoher and wih heir environmen. The inspiraion ofen comes from naure, especially biological sysems. The agens follow very simple rules, and alhough here

2 Inernaional Journal of Scienific and Research Publicaions, Volume 3, Issue 4, April is no cenralized conrol srucure dicaing how individual agens should behave, local, and o a cerain degree random, ineracions beween such agens lead o he emergence of "inelligen" global behavior, unknown o he individual agens. Naural examples of SI include an colonies, bird flocking, animal herding, bacerial growh, and fish schooling. Two well known approaches of swarm inelligence are: An Colony Opimizaion (ACO): An colony opimizaion (ACO) is a class of opimizaion algorihms modeled on he acions of an an colony [2], [13]. ACO mehods are useful in problems ha need o find pahs o goals. Arificial 'ans' simulaion agens locae opimal soluions by moving hrough a parameer space represening all possible soluions. Naural ans lay down pheromones direcing each oher o resources while exploring heir environmen. The simulaed 'ans' similarly record heir posiions and he qualiy of heir soluions, so ha in laer simulaion ieraions more ans locae beer soluions. Paricle Swarm Opimizaion (PSO): Paricle Swarm Opimizaion (PSO) is a swarm-based inelligence algorihm [6] influenced by he social behavior of animals such as a flock of birds finding a food source or a school of fish proecing hemselves from a predaor. A paricle in PSO is analogous o a bird or fish flying hrough a search (problem) space. The movemen of each paricle is co-coordinaed by a velociy which has boh magniude and direcion. Each paricle posiion a any insance of ime is influenced by is bes posiion and he posiion of he bes paricle in a problem space. The performance of a paricle is measured by a finess value, which is problem specific. Each paricle will have a finess value, which will be evaluaed by a finess funcion o be opimized in each generaion. Each paricle knows is bes posiion L_bes and he bes posiion so far among he enire group of paricles G_bes. The L_bes of a paricle is he bes resul (finess value) so far reached The paricle swarm opimizaion (PSO) algorihm is based on he evoluionary compuaion echnique. PSO opimizes an objecive funcion by conducing populaion-based search. The populaion consiss of poenial soluions, called paricles, similar o birds in a flock. The paricles are randomly iniialized and hen freely fly across he muli-dimensional search space. While flying, every paricle updaes is velociy and posiion based on is own bes experience and ha of he enire populaion. The updaing policy will cause he paricle swarm o move oward a region wih a higher objec value. Evenually, all he paricles will gaher around he poin wih he highes objec value. PSO aemps o simulae social behavior, which differs from he naural selecion schemes of geneic algorihms. PSO processes he search scheme using populaions of paricles, which corresponds o he use of individuals in geneic algorihms. Each paricle is equivalen o a candidae soluion of a problem. The paricle moves according o an adjused velociy, which is based on ha paricle s experience and he experience of is companions. A) Convenional Paricle Swarm Opimizaion The paricle swarm opimizaion algorihm was inroduced by Kennedy and Eberhar in 1995 [6], [13]. The algorihm consiss of a swarm of paricles flying hrough he search space. Each individual i in he swarm conains parameers for posiion x i and velociy v i, where x i R n, v i R n while n is he dimension of he search space. The posiion of each paricle represens a poenial soluion o he opimizaion problem. The dynamics of he swarm are governed by a se of rules ha modify he velociy of each paricle according o he experience of he paricle and by adding a velociy vecor o he curren posiion, he posiion of each paricle is modified. As he paricles move around he space, differen finess values are given o he paricles a differen locaions according o how he curren posiions of paricles saisfy he objecive. A each ieraion, each paricle keeps rack of is local bes posiion, L_bes and depending on he social nework srucure of he swarm, he global bes posiion, G_bes. B) Applicaion of PSO 1. Neural Nework Training 2. Telecommunicaions 3. Daa Mining 4. Design and Combinaorial opimizaion 5. Power sysems 6. Signal processing III. BACK-PROPAGATION ALGORITHM The back- propagaion algorihm is used in layered feedforward ANNs [14]. This means ha he arificial neurons are organized in layers, and send heir signals forward, and hen he errors are propagaed backwards. The nework receives inpus by neurons in he inpu layer, and he oupu of he nework is given by he neurons on an oupu layer. There may be one or more inermediae hidden layers. The backpropagaion algorihm uses supervised learning, which means ha we provide he algorihm wih examples of he inpus and oupus we wan he nework o compue, and hen he error (difference beween acual and expeced resuls) is calculaed. The idea of he back propagaion algorihm is o reduce his error, unil he ANN learns he raining daa. The raining begins wih random weighs, and he goal is o adjus hem so ha he error will be minimal. The basic back propagaion algorihm consiss of hree seps. 1) The inpu paern is presened o he inpu layer of he nework. These inpus are propagaed hrough he nework unil hey reach he oupu unis. This forward pass produces he acual or prediced oupu paern. 2) The acual nework oupus are subraced from he desired oupus and an error signal is produced. 3) This error signal is hen he basis for he back propagaion sep, whereby he errors are passed back hrough he neural nework by compuing he conribuion of each hidden processing uni and deriving he corresponding adjusmen needed o produce he correc oupu. The connecion weighs are hen adjused and he neural nework has jus learned from an experience. 4) Learning parameers are used o conrol he raining process of a back propagaion nework. 5) The learn rae is used o specify wheher he neural nework is going o make major adjusmens afer each

3 Inernaional Journal of Scienific and Research Publicaions, Volume 3, Issue 4, April learning rial or if i is only going o make minor adjusmens. 6) Momenum is used o conrol possible oscillaions in he weighs, which could be caused by alernaely signed error signals. IV. RELATED WORK Pillai, K. G. [1] explains a novel overlapping swarm inelligence algorihm is inroduced o rain he weighs of an arificial neural nework. Training a neural nework is a difficul ask ha requires an effecive search mehodology o compue he weighs along he edges of a nework. The back propagaion algorihm, a gradien based mehod, is frequenly used o rain mulilayer feed-forward neworks. On he oher hand, raining algorihms based on evoluionary compuaion have been used o rain mulilayer feed-forward neworks in an aemp o overcome he limiaions of gradien based algorihms wih mixed resuls. This paper inroduces an overlapping swarm inelligence echnique o rain mulilayer feedforward neworks. The resuls show ha OSI mehod performs eiher on par wih or beer han he oher mehods esed. M. Conforh and Y. Meng [2] propose a swarm inelligence based reinforcemen learning (SWIRL) mehod o rain arificial neural neworks (ANN). Basically, wo swarm inelligence based algorihms are combined ogeher o rain he ANN models. An Colony Opimizaion (ACO) is applied o selec ANN opology, while Paricle Swarm Opimizaion (PSO) is applied o adjus ANN connecion weighs. To evaluae he performance of he SWIRL model, i is applied o double pole problem and robo localizaion hrough reinforcemen learning. Exensive simulaion resuls successfully demonsrae ha SWIRL offers performance ha is compeiive wih modern neuro-evoluionary echniques, as well as is viabiliy for realworld problems. Marco Dorigo and Mauro Biraari [3] defines Swarm inelligence as he discipline ha deals wih naural and arificial sysems composed of many individuals ha coordinae using decenralized conrol and self-organizaion. In paricular, he discipline focuses on he collecive behaviors ha resul from he local ineracions of he individuals wih each oher and wih heir environmen. Examples of sysems sudied by swarm inelligence are colonies of ans and ermies, schools of fish, flocks of birds, herds of land animals. Some human arifacs also fall ino he domain of swarm inelligence, noably some mulirobo sysems, and also cerain compuer programs ha are wrien o ackle opimizaion and daa analysis problems. Y. Karpa and Tugrul Ozel [4] propose a concep of paricle swarm opimizaion, which is a recenly developed evoluionary algorihm, is used o opimize machining parameers in hard urning processes where muliple conflicing objecives are presen.the relaionships beween machining parameers and he performance measures of ineres are obained by using experimenal daa and swarm inelligen neural nework sysems (SINNS). The resuls showed ha paricle swarm opimizaion is an effecive mehod for solving muli-objecive opimizaion problems, and an inegraed sysem of neural neworks and swarm inelligence can be used in solving complex machining opimizaion problems. James kennedy and Russell Eberhar [5] propose a concep for he opimizaion of nonlinear funcions using paricle swarm mehodology is inroduced. The evoluion of several paradigms is oulined, and an implemenaion of one of he paradigms is discussed. Benchmark esing of he paradigm is described, and applicaions, including nonlinear funcion opimizaion and neural nework raining, are proposed. The relaionships beween paricle swarm opimizaion and boh arificial life and geneic algorihms are described. V. PROPOSED WORK 5.1) Analysis of Differen Algorihm: This is done on he basis of analysis of heir advanage o inroduce proposed varians for opimizaion. In his we analysis he limiaion of BPA and o opimize BPA we use PSO approach ) Disadvanages in BPA: a) Local Minima b) Low Speed c) Higher cos of compuaion d) Error Problem e) Gloal Maxima bu less as compared o Local f) Less accuracy 5.1.2) PSO Advanages: a) PSO can be applied o scienific research and Engineering. b) High compuaional speed c) Learning achieved from paricle own experienced d) Learning achieved from experience of cooperaion beween paricles 5.2) Proposed Varians for opimizaion: 1) PSO_hill 2) PSO_A* 5.2.1) PSO_hill Advange: a) High compuaional speed b) Srong abiliy in global search c) Higher Accuracy d) Learning achieved from paricle own experienced e) Learning achieved from experience of cooperaion beween paricles ) PSO_Hill variables Noaions: X: Iniial paricle posiion. W: Weigh for each paricle. n: Toal no. of ieraions. P curr = curren posiion of paricles P bes = paricle bes posiion

4 Inernaional Journal of Scienific and Research Publicaions, Volume 3, Issue 4, April ) PSO_Hill Diagram: Iniialize posiion X i, velociy and weigh w. Iniialize posiion X j, velociy and weigh w. P j=x j*w j P j= W j* X j Vj= 1/(1+exp(-v j)) V j = 1/(1+exp(-p j)) P j=goal j<n Goal=V j Selec bes among paricle, compue p_global YE S Curren is beer han Searched Sae P_global=p_goal Se p curr=p bes N O Compue finess funcion Opimized Opimized Sop Sop 5.2.4) PSO_Hill Algorihm: 1) Sar wih iniializing paricle posiion X, heir velociy V, Weigh W, p_loc 0, p_glob 0,n 0 2) If goal=v j hen erminae i; Oherwise 3) P j =X j *W j 4) Vj=1/(1+exp(-p j )) 5) If (j<n) 6) { 7) If(Evaluae a new posiion which is beer han curren posiion bu no goal) 8) { 9) Curr_posiion=beer_posiion; 10) Else 11) Keep curren posiion & coninue he search o find goal 12) } 13) Else 14) Reurn o sep 2 o coninue ill i reaches o goal 5.3.1) PSO_A* Advanages: I. Mos heurisic soluion II. Opimized in erms of finess funcion 5.3.2) PSO_A* Diagram: 5.2.3) PSO_A* Variables Noaions: Open_lis: A lis which have nodes ha are generaed bu no expanded. Closed_lis: A lis which have nodes ha are expanded and is childrens are available o search program ) PSO_A* Algorihm: 1. Sar wih iniial posiion of paricles and place hem on open node, p_loc 0,p_glob If (open_lis=empy) sop and reurn as failure 3. Selec p_loc paricles n from open lis ha has smalles finess funcion 4. { 5. if node n= goal node 6. reurn success 7. sop 8. } 9. Oherwise 10. Expand he successor paricles of node n and as node n is explored so keep i on closed lis 11. For each successor h 12. { 13. If h is no in open_lis or closed_lis 14. { 15. Aach a back poiner o n paricle o backrack i 16. {

5 Inernaional Journal of Scienific and Research Publicaions, Volume 3, Issue 4, April Compue finess of paricle f*(h) 18. Else 19. Compue lowes or p_glob (g*(h)) 20. } 21. Place on open lis 22. Reurn o Sep o ill he goal VI. CONCLUSION In his paper, wo varians of he paricle swarm opimizaion scheme is presened. Two PSO Varians PSO_Hill and PSO_A* are proposed wih heir algorihm, archiecure, advanages and disadvanages, which can be used o he opimize he BPA. In nex paper, a hird sraegy is proposed PSO_Hill_A* on he basis of srengh of wo varians PSO_Hill and PSO_A* algorihm. The paricle local bes and global bes posiions help he varians o move owards he soluion. REFERENCES [1] Pillai, K. G, Overlapping swarm inelligence wih arificial neural nework,swarm inelligence(sis),2011 IEEE Symopsium,15 april [2] Mahew Conforh and Yan Meng, Reinforcemen Learning for Neural Neworks using Swarm Inelligence, 2008 IEEE Swarm Inelligence Symposium, S. Louis MO USA, Sepember 21-23, 2008 [3] [3] Macro Dorigo and Mauro Biraari (2007), Scholarpedia, 2(9) Swarm inelligence, hp:// Marco Dorigo (2007) An colony opimizaion. Scholarpedia, 2(3):1461. [4] Yiği Karpa and Tuğrul Özel, Swarm-Inelligen Neural Nework Sysem (SINNS) Based Muli-Objecive Opimizaion Of Hard Turning,Transacions of NAMRI/SME Volume 34, [5] James Kennedy' and Russell Eberhar2, Paricle Swarm Opimizaion,, Washingon, DC 20212,kennedy_jim@bls.gov,hp:// orks/hw3/_reading6%201995%20paricle%20swarming.pdf, 1995 IEEE. [6].Kennedy and R.Eberhar, Paricle swarm opimizaion,proceedings of. IEEE Inernaional Conference on Neural Neworks, pp , 1995 [7] Boonserm Kaewkamnerdpong and Peer J. Benley, percepive Paricle Swarm Opimizaion:An Invesigaion [8] Jui-Fang Chang, Shu-Chuan Chu, John F. Roddick and Jeng-Shyang Pan, A Parallel Paricle Swarm Opimizaion Algorihm wih Communicaion Sraegies, Journal of Informaion Science and Engineering 21, (2005) [9] R. Eberhar and J. Kennedy, A new opimizer using paricle swarm heory in Proceedings of 6h Inernaional Symposium on Micro Machine and Human Science, 1995, pp [10] J. Kennedy and R. Eberhar, Paricle swarm opimizaion, in Proceedings of IEEE Inernaional Conference on Neural Neworks, 1995, pp [11] P. Tarasewich and P. R. McMullen, Swarm inelligence, Communicaions of he ACM, Vol. 45, 2002, pp [12] Niu Mahuriya and Dr. Ashish Bansal, Applicabiliy of back propagaion neural nework for recruimen daa mining, Inernaional Journal of Engineering Research & Technology (IJERT), ISSN: , Vol. 1 Issue 3, May [13] V.Selvi and Dr.R.Umarani, Comparaive Analysis of An Colony and Paricle Swarm Opimizaion Techniques, Inernaional Journal of Compuer Applicaions ( ), Volume 5 No.4, Augus 2010 [14] Carlos Gershenson, Arificial Neural Neworks for Beginners AUTHORS Firs Auhor Priyanka Sharma received B.TECH degree in Compuer Science and Engineering wih Hons. from Maharshi Dayanand Universiy in 2011 and is persuing M.Tech. in Compuer Engineering. Presenly, She is working as Lecurer in Compuer Engineering deparmen in RITM, Palwal. Her areas of ineress are Arificial Neural Nework, Sof Compuing, Paern Recogniion., priya.sharma090@gmail.com Second Auhor Asha Mishra received B.E. degree in Compuer Science & Engineering from NIT, Assam and M.Tech in Compuer Science from A.I.T.M, Palwal. Presenly, she is working as Senior Lecurer in Compuer Engineering deparmen in B.S.A. Insiue of Technology & Managemen, Faridabad. Her areas of ineress are DBMS, Analysis & Design of Algorihm and Nework Securiy., asha1.mishra@gmail.com