The Study of Teaching-learning-based Optimization Algorithm

Transcription

1 Advanced Scence and Technology Letters Vol. (AST 06), pp The Study of Teachng-learnng-based Optmzaton Algorthm u Sun, Yan fu, Lele Kong, Haolang Q,, Helongang Insttute of Technology, Harbn, Chna Northeast Agrcultural, Harbn, Chna 900@qq.com, @qq.com, Konglele979@hotmal.com, Haolangq6@6.com Abstract. Ths paper presents an adaptve drecton strategy(ads)to mprove the searchng ablty for the TLBO algorthm. The mproved algorthm s tested through searchng the optmal ponts for a few typcal testng functons. The testng result shows that the mproved TLBO algorthm could obtan better optmal solutons n shorter tme. Compared to the normal TLBO algorthm, the stablty and effectveness of the mproved algorthm are ncreased greatly. Keywords: Heurstc algorthm; Teachng-learnng-based optmzaton algorthm; Adaptve drecton strategy; Nonlnear optmzaton Introducton Many real lfe problems could be modeled as nonlnear mathematcal models or global optmzaton models as equaton (): max f ( x, x,, x ) n subect to () mn The heurstc algorthms nclude genetc algorthm (GA), partcle swarm optmzaton (PSO), colony algorthm (ACA), artfcal bee colony (ABC) algorthm and frework exploson optmzaton (FEO) algorthm has been used wdely to solve these problems [-5]. In 0 R.V.Rao proposed the TLBO algorthm based on the populaton heurstc algorthm. Ths algorthm has less parameters to be dentfed and performs well n solvng the optmzaton problem for the real contnuous functons [6-8]. Basc TLBO TLBO s nclude two phases: the frst phase s the teacher phase, n whch the students gan knowledge from the teachers; the second phase s the learner phase n whch the students gan knowledge through communcaton wth other students [9 ]. ISSN: 87- ASTL Copyrght 06 SERSC

2 Advanced Scence and Technology Letters Vol. (AST 06). Teacher Phase Frst, dentfy the learnng ablty of each student, or D fference - Mean as shown n equaton (), Dfference - Mean r ( Best, TF M ) () n whch r s a random number between (0,). The r dentfes the learnng degree. TF s the teachng affectng factor, t denotes the how much does the teachng nfluencng the average value of the group. The value of TF s ether or. The equaton to dentfy the TF s shown as equaton (), T F round[ rand(0,)( )] () Dfference _ Mean Upon the, the updatng rule for the teacher phase s shown as equaton (), new, old, Dfference _ Mean () old where, s the th orgnal ndvdual n the populaton, new, s the new correspondng updated ndvdual. If, old has a better ftness value than,, new then, old wll replace,.. Leaner Phase For each ndvdual the ftness value. If, randomly choose another ndvdual s better than ( )and compare, then update the value followng equaton (5), r( ) (5) new, Otherwse, update the value followng equaton (6) r( ) (6) new, Smlar to the teacher phase, f new, s better than, then replace by new,. Repeat the procedure for the entre group to update the populaton once more. ADS Frst fnd the nfluence factor of the communcaton, as shown n Eqn (7) f ( ) (7) f ( ) f ( ) 06 Copyrght 06 SERSC

3 Advanced Scence and Technology Letters Vol. (AST 06) where f ( ) s the ftness value of the ndvdual. current generaton. by Eqn (8) and (9). s the teacher of the s the th ndvdual of the populaton. The teacher s updated ( ) (8) (), () ( ) (9) (),,, If the obtaned ndvdual has a better ftness value than, replace by the obtaned ndvdual. () () The relatonshp between,,, and s shown n Fgure. () (),,, Fg.. The locaton of the updated teacher Suppose the varables mentoned above locate near one of the optmal value, and the ftness value functon of the updated teacher s shown n Fgure, then t s lkely () to obtan a better teacher from and., (), Fg.. The relatonshp between the updated teacher and the orgnal teacher Calculate the nfluencng factor, as shown n Eqn (0) f ( ) (0) f ( ) f ( ) where, f ( ) s the ftness value of. The updatng of an ndvdual s dvded nto two cases, f and () s a better soluton than, the updatng rule s shown n Eqn () ) () () new, ( () ( ) () () new, new, Copyrght 06 SERSC 07

4 Advanced Scence and Technology Letters Vol. (AST 06) Otherwse, follow Eqn () and () ( ) () () new, () ( ) () () new, new, If the obtaned soluton s better than, then replace wth the new value. The evoluton process of the mproved TLBO s llustrated as below. Frst, create an optmzaton model, and ntate the correspondng parameters. Then randomly generate the ntal populaton followed by updatng the populaton. Repeat the updatng process untl populaton satsfes the endng condton. The evoluton process of the mproved TLBO s shown n Fgure. Begn Create the optmzaton model Defne parameters Generate ntal populaton Calculate ndvdual s ftness Confrm the teacher N Execute teacher phase ADS for teacher phase Execute learner phase adopted ADS If meet the stop condton Y End Fg.. The flowchart of the ADS-TLBO algorthm 08 Copyrght 06 SERSC

5 Advanced Scence and Technology Letters Vol. (AST 06). Testng and analyss In ths part, the performance of the TLBO s tested by 5 dfferent benchmark testng functon. Functon : 5 mn f cos x 0.5( x.5) ( x 0.800) -0 x, x 0 (5) Ths s a functon wth multple optmal values, 760 local optmal values and one * global optmal value. The optmal soluton s x (.5, 0.800), wth obectve functon value f ( x * ) The searchng process s easly trapped n the local optmal soluton Functon : a max f x b x (6) a, b 0.05, 5. x, x 5. The global optmal soluton for ths functon s x * (0,0),wth maxmum value f ( x * ) 600 Functon : mn f ( x) 500 x, x 500 x sn x (7) The optmal soluton s x * (0.9687,0.9687),wth mnmum value f ( x * ) Functon : mn f ( x) 5 S T x x x x 8x x x x 8x x x ; g 0; g 0; g (,,,9,) x x x 7 x x x x 0 0 x 5 x x x 5 7 x 0 0; 0 0; 0 0; ( x) 8x ( x) x 9 ( x) x 0 x x x 5 8 0; x x 0 9 0; x 0; 00 ( 0,,) (8) Copyrght 06 SERSC 09

6 Advanced Scence and Technology Letters Vol. (AST 06) The feasble regon conssts of only 0.000% of the searchng regon. In the optmal soluton pont, there are 6 nequalty functon lmts the searchng. The optmal soluton s x * (,,,,,,,,,,,,, ),wth obectve functon value f ( x * ) 5 Functon 5: 00 x 5 x 5 x 5 max f ( x) 00 S. T. x p x q x r (9) 0 x 0,, p, q, r,,, 9 The feasble searchng regon conssts of 9 ndependent spheres. The condton for pont (x, x, x) to be feasble soluton s satsfyng any of the constrans correspondng to p, q, r. The optmal soluton s x (5,5,5 ) wth f ( x * ).The populaton sze s chosen to be 50, the maxmum evoluton tme s set to be 00. The testng result of the algorthm s shown n Table. Table. The testng result of the testng functon Functon Method Best Mean Worst Ave tmes/s Ave Gen /tmes f f f f f5 B-TLBO ADS-TLBO B-TLBO ADS-TLBO B-TLBO ADS-TLBO B-TLBO ADS-TLBO B-TLBO ADS-TLBO From Table, ADS-TLBO algorthm has hgher effcency n solvng the constraned and unconstraned optmzaton problem and s more stable. 5 Concluson Ths paper presents an mproved TLBO algorthm for solvng nonlnear optmzaton problem. The ntroducng of self-learnng process of the teacher greatly mproves the searchng effcency. The proposed mproved methods ncrease the searchng and 0 Copyrght 06 SERSC

7 Advanced Scence and Technology Letters Vol. (AST 06) updatng ablty of the algorthm. The testng result wth the benchmark testng functon, t can be seen that the mproved algorthm has satsfactory result for fndng the optmal value of dfferent types of functon. It shows that the mproved ADS-TLBO s feasble and effectve. References. Deep, K., Thakur, M.: A new mutaton operator for real coded genetc algorthms, Appled Mathematcs and Computaton 9 (007) 0. Goldberg, D.: Genetc algorthms n search, optmzaton, and machne learnng, Addson-Wesley, New York (989). Back, T.: Evolutonary algorthms n theory and practce, Oxford Unversty Press (996). Kennedy, V., Eberhart, R.: Partcle swarm optmzaton. In: Proceedngs of the IEEE Internatonal Conference on Neural Networks p Clerc, M.: Partcle swarm optmzaton, ISTE Publshng Company (006) 6. Karaboga, D.: An dea based on honey bee swarm for numercal optmzaton. Techncal report-tr06. ErcyesUnversty, Engneerng Faculty, Computer Engneerng Department Basturk, B., Karaboga, D.: An artfcal bee colony (ABC) algorthm for numerc functon optmzaton. In: IEEE Swarm Intellgence Symposum Karaboga, D., Basturk, B.: On the performance of artfcal bee colony (ABC) algorthm, Appled Soft Computng, 8 (008), pp Dorgo, M., Stutzle, T.: Ant colony optmzaton, MIT Press (00) Copyrght 06 SERSC