On Comparison between Evolutionary Programming Network based Learning and Novel Evolution Strategy Algorithm-based Learning

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1 Proceedings of he ICEECE December -4 (003), Dhaka, Bangladesh On Comparison beween Evoluionary Programming Nework based Learning and vel Evoluion Sraegy Algorihm-based Learning M. A. Khayer Azad, Md. Shafiqul Islam and M. M. A. Hashem 1 Deparmen of Compuer Science and Engineering Khulna Universiy of Engineering and Technology Khulna 903, Bangladesh ABSTRACT This paper presens wo differen evoluionary sysems - Evoluionary Programming Nework (EPNe) [1] and vel Evoluions Sraegy (NES) Algorihm []. EPNe does boh raining and archiecure evoluion simulaneously, whereas NES does a fixed nework and only rains he nework. Five muaion operaors proposed in EPNe o reflec he emphasis on evolving ANN s behaviors. Close behavioral links beween parens and heir offspring are mainained by various muaions, such as parial raining and node spliing. On he oher hand, NES uses wo new geneic operaors - subpopulaion-based max-mean arihmeical crossover and ime-varian muaion. The above-menioned wo algorihms have been esed on a number of benchmark problems, such as he medical diagnosis problems (breas cancer, diabees, and hear disease). The resuls and he comparison beween hem are also presen in his paper. 1. INTRODUCTION w-a-days, neural nework is used in. many applicaions such as roboics, missile proecion, and rocke even in cooker. A number of algorihms are developed o rain he nework and evolve he archiecure. Mos applicaions use feed forward ANNS and he back-propagaion (BP) raining algorihm. The problem of designing a near opimal ANN archiecure for an applicaion remains unsolved. There have been many aemps in designing ANN archiecures auomaically, such as various consrucive (sars wih minimal and adds) and pruning algorihms [3, 4] (opposie of consrucive). This paper describes a new evoluionary sysem, i.e., EPNe, for evolving feed forward ANNS. I combines. The archiecural evoluion wih he weigh learning. I also describcs a vel Evoluion Suaegy (NES) Algorihm [4, 5, 6,1] ha eliminaes he problems which are encounered in conemporary ESs. NES uses a unique recombinaion operaor which has a collecive ineracion of individuals wihin a paricular subpopulaion of he populaion. This algorihm also uses a ime-varian Gaussian muaion scheme based on observed naural phenomena. This paper also describes he comparison beween EPNe and NES using he hree medical diagnosis problems. In his paper i is shown ha NES is comparaively beer han EPNe.. EVOLVING ARTIFICIAL NEURAL NETWORK ARCHITECTURES There are wo maor approaches o evolving ANN archiecures. One is he evoluion of pure archiecures (i.e. archiecures wihou weighs). Connecion weighs will be rained afer a near opimal archiecure has been found. The oher is he simulaneous evoluion of boh archiecures and weighs. I is clear ha he evoluion of pure archiecures has difficulies in evaluaing finess accuraely. As a resul, he evoluion would be inefficien. de1 de (a) (a) 10 de (b) 10 de (b) Fig.1: (a) An ANN and (b) Is genoypic represenaion, assuming ha each weigh is represened by 4 binary bis, Zero weigh implies no connecion. Fig.: (a) An ANN which is equivalen o ha given in figure 1(a) and (b) Is genoypic represenaion. 1 Corresponding auhor hashem@cse.kue.ac.bd

2 Proceedings of he ICEECE, December -4, Dhaka, Bangladesh This problem no only makes he evoluion inefficien, bu also makes crossover operaors more difficul o produce highly fi offspring. I is unclear wha building blocks acually are in his siuaion. For example, ANNS shown in Fig. 1(a) and Fig (a) are equivalen, bu hey have differen genoypic represenaions as shown by Fig. 1(b) and Fig. (b) using a direc encoding scheme. 3. EVOLUTIONARY PROGRAMMING NETWORK Evoluionary Programming (EP s) emphasis on he behavioral link beween parens and heir offspring also mached well wih he emphasis on evolving ANN behaviors, no us circuiry. In is curren implemenaion, EPNe is used o evolve feed forward ANNs wih sigmoid funcions. However, his is no an inheren consrain. In fac, EPNe has minimal consrain on he ype of ANNs which may be evolved. The maor seps of EPNe can be described by Fig. 3, which are explained below [7, 8, 9]: 1. Generae an iniial populaion of M neworks a random. The number of hidden nodes and he iniial connecion densiy for each nework are uniformly generaed a random wihin cerain ranges. The random iniial weighs are uniformly disribued inside a small range.. Parially rain each nework in he populaion on he raining se for a cerain number of epochs using a modified BP (MBP) wih adapive learning raes. The number of epochs, K 0, is specified by he user. The error value E of each nework on he validaion se is checked afer parial raining. If E has no been significanly reduced, hen he assumpion is ha he nework is rapped in a local minimum and he nework is marked wih failure. Oherwise he nework is marked wih success. 3. Rank he neworks in he populaion according o heir error values, from he bes o he wors. 4. If he bes nework found is accepable or he maximum number of generaion has been reached, sop he evoluionary process and go o sep 10. Oherwise coninue. 5. Use he rank-based selecion o choose one paren nework from he populaion. If i mark is success, go o sep 6, or else go o sep Parially rain he paren nework for K 1 epochs using he MBP o obain an offspring nework and mark i in he same way as in sep, where K 1 is a user specified parameer. Replace he paren neworks wih he offspring in he curren populaion and go o sep Firs decide he number of hidden nodes N hidden o be deleed by generaing a uniformly disribued random number beween 1 and a user-specified maximum number. N hidden is normally very small in he experimens, no more han 3 in mos cases. Then delee N hidden hidden nodes from he paren nework uniformly a random. Parially rain he pruned nework by he MBP o obain an offspring nework. If he offspring nework is beer han he wors nework in he curren populaion, replace he wors by he offspring and go o sep 3. Oherwise discard his offspring and go o sep 8. Randomized iniializaion of ANNs Iniial parial raining Rank-based selecion Muaions Obain he new generaion Sop Furher raining Hybrid raining Successful Hidden node deleion Successful Connecion deleion Successful Connecion/ node addiion Fig. 3: Maor seps of EPNe 8. Calculae he approximae imporance of each connecion in he paren nework using he nonconvergen mehod. Decide he number of connecions o be deleed in he same way as ha described in sep 8. Randomly delee he connecions from he paren nework according o he calculaed imporance. Parially rain he pruned nework by he MBP o obain an offspring nework. If he offspring nework is beer han he wors nework in he curren

3 Proceedings of he ICEECE, December -4, Dhaka, Bangladesh populaion, replace he wors by he offspring and go o sep 3. Oherwise discard his offspring and go o sep Decide he number of connecions and nodes o be added in he same way as ha described in he sep 7. Calculae he approximae imporance of each virual connecion wih zero weigh. Randomly add he connecions o he paren nework o obain Offspring 1 according o heir imporance. Addiion of each node is implemened by spliing a randomly seleced hidden node in he paren nework. The new grown nework afer adding all nodes is offspring. Parially rain offspring 1 and offspring by he MBP o obain a survival offspring. Replace he wors nework in he curren populaion by he offspring and go o sep Afer he evoluionary process, rain he bes nework furher on he combined raining and validaion se unil i converges. The above evoluionary process appears o be raher complex, bu is essence is an EP algorihm wih five muaions: hybrid raining, node deleion, connecion deleion, connecion addiion and node addiion. 3.1 Encoding Scheme for Feedforward Arificial Neural Neworks The feed forward ANNs considered by EPNe are generalized mulilayer perceprons [10] (p.7-73). The archiecure of such neworks is shown in Fig. 4, where X and Y are inpus and oupus respecively. xi X i, 1 i m i 1 ne i wk x, m< i m + N + n 1 x f ne ), m m + n + N ( Yi = xi + m + N, 1 i n where f is he following sigmoid funcion: 1 f ( z) 1 z e m and n are he number of inpus and oupus respecively, N is he number of hidden nodes. The direc encoding scheme is used in EPNe o represen ANN archiecures and connecion weighs (including biases). EPNe evolves ANN archiecures and weighs simulaneously and needs informaion abou every connecion in an ANN. Two equal size marices and one vecor are used o specify an ANN in EPNe. The size of he wo marices is (m + N + n) (m + N + n), where m and n are he number of inpu and oupu nodes respecively, and N is he maximum number of hidden nodes allowable in he ANN. One marix is he conneciviy marix whose enries can only be 0 or 1. The oher is he corresponding weigh marix whose enries are real numbers. 3. Finess Evaluaion and Selecion Mechanism The finess of each individual in EPNe is solely deermined by he inverse of an error value defined by Eq. (1) [14] over a validaion se conaining T paerns: T n o max o min (1) E 100. ( di( ) yi( )) T. n 1i 1 where o max and o min are he maximum and minimum values of oupu coefficiens in he problem represenaion, n is he number of oupu nodes, and are desired and acual oupus of node i for paern. Eq.(1) was suggesed by Prechel [11] o make he error measure less dependen on he size of he validaion se and he number of oupu nodes. Hence a mean squared error percenage was adoped. o max and o min were he maximum and minimum values of oupus [11]. x: 1 X Inpu m X m m + 1 i - 1 i m+n+1 m +N +n Fig. 4: A fully-conneced feedforward arificial neural nework [10] (pp.73) Y 1 Oupu Y n

4 Proceedings of he ICEECE, December -4, Dhaka, Bangladesh 3.3 Archiecure Muaions In EPNe, only when he raining fails o reduce he error of an ANN will archiecural muaions akes place. For archiecural muaions, node or connecion deleions are always aemped before connecion or node addiions in order o encourage he evaluaion of small ANNs. Connecion or node addiions will be ried only afer node or connecion deleions fail o produce a good offspring. Using he order of muaions o encourage parsimony of evolved ANNs represens a dramaically differen approach from using a complexiy erm in he finess funcion. I avoids he ime-consuming rial-and-error process of selecing a suiable coefficien for he regulaion erm Hidden de Deleion Cerain hidden nodes are firs deleed uniformly a random from a paren ANN. The maximum number of hidden nodes ha can be deleed is se by a user specified parameer. Then he muaed ANN is parially rained by he MBP. This exra raining process can reduce he sudden behavioral change caused by he node deleion. If his rained ANN is beer han he wors ANN in he populaion, he wors ANN will be replaced by rained one and no furher muaion will ake place. Oherwise connecion deleion will be aemped Connecion Deleion Cerain connecions are seleced probabilisically for deleion according heir imporance. The maximum number of connecions ha can be deleed is se by a user-specified parameer. Similar o he case of node deleion, he ANN will be parially rained by he MBP afer cerain connecions have been deleed from i. If he rained ANN is beer han he wors ANN in he populaion, he wors ANN will be replace by he rained one and no furher muaion will ake place. Oherwise node/connecion addiion will be aemped Connecion and de Addiion Cerain connecions (wih zero weighs) are added o a paren nework iniialized wih small random weighs. The new ANN will be parially rained by he MBP and denoed as Offspring 1.The new ANN produced by node addiion is denoed as Offspring afer i is generaed, i will also be parially rained by he MBP. Then i has o compee wih Offspring 1 for survival. The survived one will replace he wors ANN in he populaion. 4. NOVEL EVOLUTION STRATEGY Two imporan variaion (geneic) operaors are based on some naural evidence of evoluion for he NES algorihm. 1. Subpopulaion-Based Max-mean Arihmeical Crossover (SB MAC).. Time-Varian Muaion (TVM). 4.1 Subpopulaion-Based Max-mean Arihmeical Crossover The paren populaion () consising of individuals is divided ino l subpopulaions in each generaion such ha each subpopulaion will have l, max individuals. The individuals is defined as an elie individual ha ( 1) maximized a cos funcion, f wihin he -h subpopulaion, and mean-individual (virual paren) is creaed from he -h subpopulaion excluding, max he. w he crossover operaion is defined o produce wo (, ) offspring 1 as (1 ) 1,max (1 ), max (3) where is seleced from URN[0,1] and is sampled a new for each obec variable of he individuals. The parameer l is called an exogenous parameer of he mehod. x Ψ Subpopulaion 1 Elie A x B C () Fig. 5: Subpopulaion Based Max-mean Arihmeical Crossover (SBMAC). 4. Time-Varian Muaion The TVM is defined for a child as ha of ESs do as i i ( ). Ni (0,1) i { 1,..., n} (4) N (.,.) where i indicaes ha he Gaussian random value wih zero-mean and uniy variance, and i is sample anew for each value of he index i. And () is he ime-varian muaion sep generaing funcion a he generaion, which is defined by (1 ) ( ) 1 T r x D E Elie Subpopulaion Opimal poin (5) where r is seleced from URN[0,1], T is he maximal generaion number, is a real-valued parameer deermining he degree of dependency on he F Ψ 1 x 1

5 Proceedings of he ICEECE, December -4, Dhaka, Bangladesh generaions. The parameer is also called an exogenous parameer of he mehod. 4.3 NES Algorihm The general pseudo-code ype srucure of he proposed novel evoluion sraegy (NES) algorihm which uilizes he above menioned wo variaion operaors is shown in Fig. 6. Algorihm_NES() { = 0; /* Iniialize he generaion couner*/ Iniialize_Populaion(); Evaluae_Populaion(); while (NOT erminaion condiion saisfied) do { Apply_SBMAC();/*Crossover operaion*/ Apply_TVM(); /*Muaion operaion*/ Evaluae_Populaion(); Alernae_Generaion(); + +; /* Increase he generaion couner*/ } } Fig. 6: A pseudo-code srucure of NES Iniial populaion The iniial populaion, (0) consising of individuals, is generaed by using a Uniform Random Number (URN) wihin desired domain of he obec variables. Afer evaluaing he individuals o heir finess funcion, his populaion is considered as parens for he nex generaion Crossover In he crossover he SBMAC is used o produce he offspring populaion. For each subpopulaion, l offspring are generaed. Thus, numbers of offspring are generaed for he l subpopulaions a he generaion Muaion In he muaion phase, he TVM operaor is used o muae all variables of an offspring. Thus he offspring populaion undergoes his muaion scheme. I is ough o be aken care ha iniially his ype of muaion migh violae he domain of he obec variables. In case of domain violaions for any offspring, ha offspring is lef wihou muaion Evaluaion Afer muaion operaion, each offspring is evaluaed is cos funcion (funcion) for a possible soluion in each generaion Alernaion of Generaion In he alernaion of generaion, ( )-ES is used. Tha is, among -1 parens which were evaluaed a he former generaion, and children which are evaluaed in he curren generaion, he -1 + individuals are ordered according o heir cos funcion values and he bes individuals will be seleced for he nex generaion. 5. EXPERIMENTAL STUDIES In order o evaluae EPNe s abiliy in evolving ANNs ha generalize well, EPNe was applied o four realworld problems in he medical domain (i.e., breas cancer, diabees, hear disease problem). All he daa ses were obained from he UCI machine learning benchmark reposiory (hp://ics.uci.edu in direcory/pub/machinelearning-daabase). The daa ses are also applied in vel Evoluionary Sraegy (NES) algorihm. 5.1 The Medical Diagnosis Problems The medical diagnosis problems menioned above have he following common characerisics [11]: The inpu aribues are similar o a human exper would use in order o solve he same problem. The oupus represen eiher he classificaion of a number of undersandable classes or he predicion of a se of undersandable quaniies. In pracice, all hese problems are solved by human expers. Examples are expensive o ge. This has he consequence ha he raining ses are no very large The Breas Cancer Daa Se The breas cancer daa se was originally obained from W. H. Wolberg a he Universiy of Wisconsin Hospials, Madison. The daa se conains 9 aribues and 699 examples of which 458 are benign examples and 41 are malignan examples The Diabees Daa Se This daa se was originally donaed by Vincen Sigillio from Johns Hopkins Universiy and was consruced by consrained selecion from a larger daabase held by he Naional Insiue of Diabees and Digesive and Kidney Diseases. All paiens represened in his daa se are females of a leas 1 years old and of Pima Indian heriage living near Phoenix, Arizona, USA. This is a wo class problem wih class value 1 inerpreed as esed posiive for diabees. There are a oal of 768 examples are used of which 500 examples of class 1 and 68 of class. There are 8 aribues for each example The Hear Disease Daa Se This daa se comes from he Cleveland Clinic Foundaion and was supplied by Rober Derano of he V. A. Medical Cener, Long Beach, CA. The purpose of he daa se is o predic he presence or absence of hear disease. This daabase conains 13 aribues, which have been exraced from a larger se of 75. There are 35 aribues for each example. 5. Experimenal seup All he daa ses used by EPNe were pariioned ino hree ses: a raining se, a validaion se, and a esing se. In he following experimens, each daa se was pariioned as follows: For he breas cancer daa se, he firs 349 examples were used for he raining se, he following 175

6 Proceedings of he ICEECE, December -4, Dhaka, Bangladesh examples for validaion se, and he following 175 examples for esing se. For he diabees daa se, he firs 384 examples were used for he raining se, he following 19 examples for validaion se, and he following 19 examples for esing se. For he hear disease daa se, he firs 134 examples were used for he raining se, he following 68 examples for validaion se, and he following 68 examples for esing se. The inpu aribues of he diabees daa se and hear disease daa se were rescaled o beween 0.0 and 1.0 by a linear funcion. The oupu aribues of all he problems were encoded using a 1-of-m oupu represenaion for m classes. 5.3 Conrol Parameers Conrol parameers in EPNe used in he experimens were: populaion size (0), iniial connecion densiy (1.0) (iniial connecion weighs beween -0.5 o +0.5), fixed bias (-1.5), learning rae (0.15), number of muaed hidden nodes (1), number of muaed connecions (1 o 3). Number of hidden nodes of each individual in he iniial populaion ranges: 1 o 3 (breas cancer); o 8 (diabees); 3 o 5 (hear disease). Number of epochs (K 0 ) for raining each individual in he iniial populaion was: 50 (breas cancer and diabees) and 60 (hear disease). The number of epochs for he parial raining during evoluion (i.e., K 1 ) was 0 for he hree problems. The number of epochs for raining he bes individual on he combined raining and esing daa se was 70 for all he problems. A run of EPNe was erminaed if he average error of he populaion had no decreased by more han a hreshold value ε (0.01 for he hree problems) afer consecuive G 0 (10) generaions or a maximum number of generaions (500) were reached. These parameers were chosen afer some limied preliminary experimens and no mean o be opimal. The conrol parameers for NES were se o be he same for all he hree problems: he populaion size (0), he iniial connecion densiy (1.0) (i.e., iniial connecion weighs were beween -0.5 o +0.5), iniial bias (-0.5 o +0.5), he exogenous parameer, γ (8.0), and he maximum number of generaion, T (500), size of subgroup l (4). The numbers of hidden nodes for each individual in he populaion were: 3 (breas cancer), 8 (diabees), and 5 (hear disease). Table 1: Archiecures of evolved Arificial Neural Neworks by EPNe (over 30 runs) Number Number of Number of Daa se of hidden connecions generaions nodes Breas cancer Diabees Hear disease Mean SD Min 1 60 Max Mean SD Min 1 60 Max Mean SD Min Max Table : Accuracies of rained and evolved ANN by EPNe and only rained by NES (raining) Daa se EPNe NES (error) (error) Mean SD Breas Min cancer Max Mean SD Diabees Min Max Mean SD Hear Min disease Max Table3: Validaion of EPNe and NES Daa Se EPNe NES Diabees 64.1% 64.6% Table 4: Tesing of EPNe and NES (Wrong classificaion in percenage) Daa Se EPNe NES Diabees 4% 5% 5.4 Experimenal Resuls All he resuls ha obained in he experimen are shown below using ables and figures; he error values are calculaed using Eq. (1). Fig. 7: Evoluion hisories of ANN by EPNe and NES for he Breas Cancer problem.

7 Proceedings of he ICEECE, December -4, Dhaka, Bangladesh REFERENCES Fig. 8: Evoluion hisories of ANN by EPNe and NES for he diabees problem. Fig. 9: Evoluion hisories of ANN by EPNe and NES for he Hear Disease problem. 6. CONCLUSIONS In order o reduce he noise in finess evaluaion, EPNe evolves ANN archiecures and weighs simulaneously. On he oher hand a novel evoluion sraegy (NES) learning algorihm rained he weighs of a fixed archiecure. The evoluion simulaed by EPNe is closer o he Lamarckian evoluion han o he Darwinian one learned weighs and archiecures in one generaion are inheried by he nex generaion. This is quie differen from mos geneic approaches where only archiecures no weighs are passed o he nex generaion. EPNe encourages parsimony of evolved ANNs by ordering is muaions, raher han using a complexiy (regularizaion) erm in he finess funcion. I avoids he edious rial-and-error process o deermine he coefficien for he complexiy erm. vel evoluion sraegy (NES) algorihm also esed on a number of benchmark problems, including he hree medical diagnosis problems. This algorihm uilized wo new geneics operaors subpopulaion-based max-mean arihmeical crossover and ime-varian muaion were absraced based on some naural meaphor and biological observaions, which are closely resembled o naural evolved sysems. This algorihm came ino view o be responded as simple as inexpensive. From he experimenal resuls we see ha NES gives a fas decay han ha of EPNe and NES algorihm ha only rains a fixed nework gives beer accuracy han ha of EPNe for he hree medical diagnosis problems, for he raining daa se and validaion daa se bu for he esing daa se NES gives comparaively less accuracy han ha of EPNe. [1] X. Yao and Y. Liu, A New Evoluionary Sysem for Evolving Arificial Neural Neworks, IEEE Trans. on Neural Neworks, pp [] K. Waanabe and M. M. A. Hashem, Evoluionary Compuaions: New Algorihms and Their Applicaions o Evoluionary Robos, Springer Verlag, 004. [3] S. E. Fahlman and C. Lebiere, The cascadecorrelaion learning archiecure, in Advances in Neural Informaion Processing Sysem (D. S. Tourezky, ed.), pp , Morgan Kaufmann, San Maeo, CA, [4] N. Burgress, A consrucive algorihm ha converges for real-valued inpu paerns, Inernaional Journal of Neural Sysems, vol. 5, no. 1, pp , [5] M. M. A. Hashem, K. Waanabe and K. Izumi (1997), Evoluion Sraegy: A New Time-Varian Muaion for Fine Local Tuning, Procs. of he 1997 SICE Inernaional Sessions, Tokushima, Japan, pp [6] M. M. A. Hashem, K. Waanabe and K. Izumi (1998), A New Evoluion Sraegy and Is Applicaion o Solving Opimal Conrol Problems, JSME Inernaional Journal, Series C, 41(3), pp [7] X. Yao and Y. Liu, Evolving arificial neural neworks for medical applicaions, in Proc. of 1995 Ausralia-Korea Join Workshop on Evoluionary Compuaion, pp. 1-16, KAIST, Taeon, Korea, Sepember, [8] X. Yao and Y. Liu, Evolving arificial neural neworks hrough evoluionary programming, in Evoluionary Programming V: Proc. of he Fifh Annual Conference on Evoluionary Programming, (L. Fogel, P. Angeline, and T. Bäck, eds.), p. To appear, MIT Press [9] X. Yao and Y. Liu, Towards designing arificial neural neworks by evoluion, in Proc. of In. Symp. on Arificial Life and Roboics (AROB), Beppu, Oia, Japan, pp , 18-0 February [10] P. J. Werbos, The Roos of Backpropagaion: From Ordered Derivaives o Neural Neworks and Poliical Forecasing. [11] L. Prechel, Probenl a se of neural nework benchmark problems and benchmarking rules, Tech. Rep. 1/94, Fakulä für Informaik, Universiä Karlsruhe, 7618 Karlsruhe, Germany, Sepember [1] M. M. A. Hashem, Global Opimizaion Through a New Class of Evoluionary Algorihm, PhD Disseraion, Saga Universiy, Japan, (1999).