Particle Swarm Optimization Guided Genetic Algorithm: A Novel Hybrid Optimization Algorithm

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1 ISSN (Prnt) : ISSN (Onlne) : V. Jagan Mohan et al. / Internatonal Journal o Engneerng and Technology (IJET) Partcle Swarm Optmzaton Guded Genetc Algorthm: A Novel Hybrd Optmzaton Algorthm V. Jagan Mohan #1, T. Arul Dass Albert # Department o Electrcal & Electroncs Engneerng, Karpagam Academy o Hgher Educaton, Combatore, Inda 1 jaganmohansla@yahoo.co.n drtaruldossalbert@gmal.com Abstract In real world applcatons, optmzaton s an nevtable stage n any engneerng desgn. In recent days the optmzaton theory s also used nto other scences whch requre precson n ts nal result. Ths topc sounds lke a promsng doman or research almost n all areas o scence and technology. Perhaps several soluton methods are proposed or solvng problems that requre optmzaton algorthms, n that also the algorthms nspred by natural selecton are domnant among them. Ths paper proposes a hybrd algorthm that ntegrates two well establshed methods, one the genetc algorthm (GA) and the other the partcle swarm optmzaton (PSO) algorthm. Here the GA wll be the man optmzer and the PSO wll be used to gude the GA to locate optmal solutons quckly and eectvely. Several benchmark test problems are solved and the applcablty o the proposed hybrd algorthm s well establshed. Keyword- Genetc Algorthm, Partcle Swarm Optmzaton, Sot Computng, Benchmark Problems I. INTRODUCTION In recent days, real world optmzaton problems any engneerng desgn s a real challenge. Smlarly, the optmzaton theory s also under pnng nto other scences whch requres the applcaton o cost based desgn. Ths topc emerges as a promsng topc or research almost n almost dverse elds o scence and technology. As sad earler, several soluton methods are developed or solvng optmzaton problems, among them the algorthms nspred by natural selecton are domnant [1]. In ths ntroducton secton, a bre revew o lterature wll be revewed bascally wth an ntenton only on hybrd algorthms that ntegrates two well establshed methods, one the genetc algorthm (GA) and the other the partcle swarm optmzaton (PSO) algorthm. In [1], a new evolutonary learnng algorthm s based on a hybrd o genetc algorthm (GA) and partcle swarm optmzaton (PSO) called HGAPSO s proposed. Here ndvduals n a new generaton are created, not only by crossover and mutaton operaton as n GA, but also by PSO. In another research s [], a hybrd method combnng genetc algorthms (GA) and partcle swarm optmzaton (PSO), or the global optmzaton o multmodal unctons s developed. [] proposes a soluton mprovement phase can be asssted by knowledge stored wthn the parent solutons, eectvely allowng parents to teach ther osprng how to mprove ther tness. In ths paper, the evoluton o each ndvdual o the total populaton, whch conssts o the parents and the osprng, s realzed wth the use o a Partcle Swarm Optmzer. Subsequently, a supply chan management wth b-level lnear programmng to supply chan dstrbuton problem was solved usng hybrd o genetc algorthm (GA) and partcle swarm optmzaton (PSO) [4]. In another work, [5], a hybrd Partcle Swarm Optmzaton (PSO) and Genetc Algorthm (GA) method s used or gene selecton, and Support Vector Machne (SVM) s adopted as the classer. In [6], a novel PSO-GA-based hybrd algorthm wth dyng probablty or the ndvduals and the war/dsease process or the populaton. [7] ntroduces, Hybrd Partcle Swarm Optmzaton and Genetc Algorthm (HPSOGA) s proposed to solve the mult-uav ormaton reconguraton problem, whch s modeled as a parameter optmzaton problem. In [8] an evolutonary-based clusterng algorthm based on a hybrd o genetc algorthm (GA) and partcle swarm optmzaton algorthm (PSOA) or order clusterng n order to reduce surace mount technology (SMT) setup tme. Also n [9], novel combned genetc algorthm (GA)/partcle swarm optmzaton (PSO) s presented or optmal locaton and szng o DG on dstrbuton systems. Subsequently n [1], Adaptve Genetc Algorthm (AGA) and Partcle Swarm Optmzaton (PSO) are mplemented to get optmal schedules and storage assgnments or Fleble Manuacturng Systems. Based on the above revew o lterature conned only to the hybrdzaton o genetc algorthm (GA) and the partcle swarm optmzaton (PSO) algorthm, the unctonal ntegraton proposed n ths research s unque o ts knd. It s demonstrated that the etensve search behavour o GA and the ehaustve search capablty o PSO are superor n searchng better optmal ponts. In the ollowng secton we wll dscuss n detal the proposed unctonal uson o GA and PSO. DOI: /jet/17/v9/17981 Vol 9 No Apr-May 17 68

2 ISSN (Prnt) : ISSN (Onlne) : V. Jagan Mohan et al. / Internatonal Journal o Engneerng and Technology (IJET) II. PROPOSED HYBRID ALGORITHM Ths secton wll descrbe how two powerul optmzaton algorthms nspred by natural selecton are ntegrated together to eectvely solve comple optmzaton problems. Two powerul algorthms wdely appled n several lterature to solve comple engneerng optmzaton problems: one s GA and the other s PSO. Snce both the algorthms are sucently dscussed n detal n several publshed lteratures, ths paper wll gve an overvew o these methods and wll descrbe the proposed hybrd GA-PSO method subsequently. t. A. Genetc Algorthm: An Overvew GA s a randomzed search method nspred based on bologcal evolutonary rue o survval o the ttest [11]. GA starts ts search rom the set o populaton strngs that are assumed as potental solutons, randomzed wthn the search range. Inspred by natural evoluton, the algorthm wll evolve new potental solutons called as osprngs rom prevous parents. Perhaps GA s lmted or eploraton eatures, causng slow or poor convergence and poor robustness. Thus problems lke premature convergence and trappng local optma are prone when dealng comple optmzaton problems. t. B. Partcle swarm optmzaton: An Overvew PSO s one o the latest evolutonary technques developed by Eberhart and Kennedy [1,1]. PSO s nspred based on socal nteracton o brd lockng or sh schoolng. The partcles also called as potental solutons, move throughout the multdmensonal soluton space and the postons o each partcles were adjusted accordng to ts own best poston, and best among all ts group. PSO does all under the survval o the ttest algorthm as the entre group wll be used rom begnnng to end. Slow or poor convergence and poor robustness are agan a demert or PSO. C. Proposed archtecture o the hybrd GA-PSO: The man dea behnd ths proposal s, ater the tness evaluatons are made or each parent n the present populaton, selecton wll be done usng roulette wheel and two parents are selected based on ther tness rankng and crossover wll be perormed. In ths crossover, two parents wll share ther chromosomes to produce two o-sprngs, whch wll be the new parent n the net generaton. Unlke ths regular crossover, whch wll lead to possble dramatc change n search drecton due to crossover echange, among ths two parents the best ndvdual wll be used as gbest and the other one wll be retaned as pbest. Thus only one parent wll be dsturbed and produced by ths operaton derved rom PSO. Ths wll help the hybrd algorthm to search the space ehaustvely. Addtonally ths PSO operaton wll not be done or the entre crossover phase, nstead a random o 5% n the begnnng stage and gradually reduced to 5% o the total populaton n the entre run o the algorthm. k1 k k1 v (1) v k 1 v k k c1rand( pb) crand( k gb) () Fg. 1. (a) Crossover operaton n GA (b) Velocty and poston update n PSO As an eample, let us assume two parents are selected or crossover as shown n Fg 1. The tness value or parent A, B and osprng s 1458, 8889, 885 respectvely. Now nstead o ths, we use a velocty equaton to update the poston o parent B usng the dea derved rom PSO and the equaton s gven or reerence. Here the gbest s 1458, pbest s Wth regular parameter settng the new poston or parent B wll be estmated as 745 usng the velocty and poston update equaton n (1 & ). Thus the possblty o arrvng at better results wll be large when gong or ths hybrdzaton approach. Thus the proposed sht o producton o new populaton n GA wll be guded by PSO wth a 5% probablty s establshed. A detaled lowchart o the proposed hybrd GA-PSO algorthm s shown n gure. DOI: /jet/17/v9/17981 Vol 9 No Apr-May 17 69

3 ISSN (Prnt) : ISSN (Onlne) : V. Jagan Mohan et al. / Internatonal Journal o Engneerng and Technology (IJET) Intalze populaton Evaluate the tness Select the parents usng roulette wheel Random parents selecton Perorm crossover Update the poston eqn (1 & ) Mutaton phase New parents Reduce random parent % Ma. Iteraton reached Stop Fg.. Flowchart o the proposed hybrd GA-PSO The percentage o random parents selected wll be reduced durng the course o run rom 5% to 5% usng the ollowng equaton (): rndprnt ((.5.5) / ma ter ) ter () In the net secton the proposed algorthm wll smulated or a sample o 1 benchmark problems wdely used or smulaton studes. III. NUMERICAL ILLUSTRATIONS In order to valdate the perormance o the proposed hybrd GA-PSO algorthm and demonstrate ts superorty over the other algorthms n ndng the better solutons, 1 standard bench mark problems are solved. These benchmark problems are wdely used n several lteratures [14,15]. All the smulatons are carred out wth ollowng smulaton parameters as summarzed n Table 1. TABLE I. Smulaton parameters Method Populaton Ma. Iteraton Probablty / Inerta GA and.1 PSO to.4 The proposed hybrd algorthm also uses the same parameters approprately at the stage when the technques are used. The objectve unctons, constrants and ther predetermned solutons are lsted n Table or easy reerence. The purpose o ths paper s now well valdated rom the smulaton results. Smulaton results are shown n Table.The eperment compares the Hybrd GA-PSO to other algorthms such as PSO and GA. The results or mamum teratons are reported n Table takng nto consderaton the ollowng perormance ndees: the Best optmum so ar, the mean o the Best soluton and the Standard Devaton o optmum soluton obtaned so ar. The best result rom the proposed method s summarzed or each benchmark uncton. Observng ths table, the proposed GA-PSO searches better results than GA and PSO or all tred unctons. In partcular, the eperment records the sgncant derence n demonstraton whch delberately llustrates the better trade-o between eploraton and eplotaton n the search space. DOI: /jet/17/v9/17981 Vol 9 No Apr-May 17 6

4 ISSN (Prnt) : ISSN (Onlne) : V. Jagan Mohan et al. / Internatonal Journal o Engneerng and Technology (IJET) subject to 5 5 TABLE II. Benchmark unctons Wayburn Seader 1 Functon,. 1,, 1.597,.86 X Wayburn Seader Functon subject to 5 5..,1,.45,1 Wayburn Seader Functon X subject to X, X ,6.187 X Subject to X Subject to D 1 Subject to D 5 1 Wole Functon X, X 1. 5 X,,, X Zettl Functon..99, Sphere Functon.,,, Stepnt Functon. X, X. 791 Subject to ,,, 144 n Styblnsk-Tang Functon. Subject to ,.954, Subject to 5 5 Trecann Functon.,,, 78., Zrll or Alu-Pentn s Functon X Subject to , X, X. 5 DOI: /jet/17/v9/17981 Vol 9 No Apr-May 17 61

5 ISSN (Prnt) : ISSN (Onlne) : V. Jagan Mohan et al. / Internatonal Journal o Engneerng and Technology (IJET) Fgure presents the convergence curves or all the methods PSO, GA and the proposed algorthm consderng as benchmark unctons (a) F16, (b) F16, (c) F164, (d) F168, (e) F144, () F145, (g) F174, and 9h) F175, rom the epermental set. Among them, the rate o convergence o GA-PSO s the astest, whch eplores the soluton space swtly and determnes the best soluton n less o 5 teratons n an average compared to the other two algorthms GA-PSO PSO GA OBJECTIVE FUNCTION (a) (b) (c). ITERATION 1.8 GA-PSO PSO.6 GA (d) OBJECTIVE FUNCTION. 1 (e) () (g) (h) 4 INTERATION 1 Fg. Convergence plot o the three methods to solve the benchmark problems DOI: /jet/17/v9/17981 Vol 9 No Apr-May 17 6

6 ISSN (Prnt) : ISSN (Onlne) : V. Jagan Mohan et al. / Internatonal Journal o Engneerng and Technology (IJET) TABLE III. Smulaton results o the three methods to solve the benchmark problems Case Method Best Mean Standard Devaton F 16 PSO..4.1 GA...18 Hybrd GA-PSO...7 F 16 PSO.6.8. GA Hybrd GA-PSO...7 F 164 PSO GA Hybrd GA-PSO F 168 PSO...4 GA Hybrd GA-PSO...7 F 174 PSO GA Hybrd GA-PSO F 17 PSO.5.6. GA Hybrd GA-PSO...7 F 141 PSO..6.1 GA Hybrd GA-PSO...6 F 144 PSO GA Hybrd GA-PSO F 145 PSO.4.7. GA Hybrd GA-PSO...5 F 175 PSO GA Hybrd GA-PSO IV. CONCLUSION Ths research proposes a hybrd algorthm that ntegrates two well establshed methods, one the genetc algorthm (GA) and the other the partcle swarm optmzaton (PSO) algorthm. Here the GA wll be the man optmzer and the PSO wll be used to gude the GA to locate optmal solutons quckly and eectvely. The eploraton capablty o the PSO s utlzed by the GA or both eploraton and ehaustve search. Thus comple search spaces are well searched and qualty solutons are swtly determned. Several benchmark test problems are solved and the applcablty o the proposed hybrd algorthm s well establshed. Based on the smulaton results, the proposed algorthm can be appled or solvng real tme optmzaton problems DOI: /jet/17/v9/17981 Vol 9 No Apr-May 17 6

7 ISSN (Prnt) : ISSN (Onlne) : V. Jagan Mohan et al. / Internatonal Journal o Engneerng and Technology (IJET) REFERENCES [1] Juang, C. F.. A hybrd o genetc algorthm and partcle swarm optmzaton or recurrent network desgn. IEEE Transactons on Systems, Man, and Cybernetcs, Part B (Cybernetcs), 4(), , 4 [] Kao, Y. T., & Zahara, E. A hybrd genetc algorthm and partcle swarm optmzaton or multmodal unctons. Appled Sot Computng, 8(), , 8 [] Marnaks, Y., & Marnak, M.. A hybrd genetc Partcle Swarm Optmzaton Algorthm or the vehcle routng problem. Epert Systems wth Applcatons, 7(), , 1. [4] Kuo, R. J., & Han, Y. S.. A hybrd o genetc algorthm and partcle swarm optmzaton or solvng b-level lnear programmng problem A case study on supply chan model. Appled Mathematcal Modellng, 5(8), , 11. [5] L, S., Wu, X., & Tan, M. Gene selecton usng hybrd partcle swarm optmzaton and genetc algorthm. Sot Computng, 1(11), , 8 [6] Sh, X. H., Lang, Y. C., Lee, H. P., Lu, C., & Wang, L. M. An mproved GA and a novel PSO-GA-based hybrd algorthm. Inormaton Processng Letters, 9(5), 55-61, 5. [7] Duan, H., Luo, Q., Sh, Y., & Ma, G. Hybrd partcle swarm optmzaton and genetc algorthm or mult-uav ormaton reconguraton. IEEE Computatonal Intellgence Magazne, 8(), 16-7, 1. [8] Kuo, R. J., & Ln, L. M.. Applcaton o a hybrd o genetc algorthm and partcle swarm optmzaton algorthm or order clusterng. Decson Support Systems, 49(4), , 1. [9] Morad, M. H., & Abedn, M. A combnaton o genetc algorthm and partcle swarm optmzaton or optmal DG locaton and szng n dstrbuton systems. Internatonal Journal o Electrcal Power & Energy Systems, 4(1), 66-74, 1. [1] Asokan, P., Jerald, J., Arunachalam, S., & Page, T. Applcaton o adaptve genetc algorthm and partcle swarm optmsaton n schedulng o jobs and AS/RS n FMS. Internatonal Journal o Manuacturng Research, (4), 9-45, 8. [11] Holland, J. H., Genetc algorthms. Scentc Amercan, 67(1), 66-7, 199. [1] Sh, Y., & Eberhart, R. A moded partcle swarm optmzer. In Evolutonary Computaton Proceedngs, IEEE World Congress on Computatonal Intellgence., The 1998 IEEE Internatonal Conerence on (pp. 69-7). IEEE, [1] Eberhart, R. C., & Sh, Y., Comparson between genetc algorthms and partcle swarm optmzaton. In Internatonal Conerence on Evolutonary Programmng (pp ), [14] Jaml, M., & Yang, X. S., A lterature survey o benchmark unctons or global optmsaton problems. Internatonal Journal o Mathematcal Modellng and Numercal Optmsaton, 4(), , 1. [15] Grosan, C., & Abraham, A., Hybrd evolutonary algorthms: methodologes, archtectures, and revews. In Hybrd evolutonary algorthms (pp. 1-17), 7. AUTHOR PROFILE V. Jagan Mohan, s a research scholar n the Department o Electrcal & Electroncs Engneerng, Karpagam Academy o Hgher Educaton, Combatore, he s dong hs research n the eld o sot computng applcaton n power system optmzaton problems. T. Arul Dass Albert, s a proessor and research supervsor n the Department o Electrcal & Electroncs Engneerng, Karpagam Academy o Hgher Educaton, Combatore, he s dong hs research n the eld o sot computng applcaton n power system optmzaton problems. DOI: /jet/17/v9/17981 Vol 9 No Apr-May 17 64