An Improved Particle Swarm Optimization Algorithm based on Membrane Structure

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1 IJCSI Internatonal Journal of Computer Scence Issues Vol. 10 Issue 1 No January 013 ISSN (Prnt): ISSN (Onlne): An Improved Partcle Swarm Optmzaton Algorthm based on Membrane Structure Yanhua Zhong 1 Shuzh Ne 1 epart. Of Electroncs and Informaton TechnologyJangmen Polytechnc Jangmen Chna epart. Of Electroncs and Informaton TechnologyJangmen Polytechnc Jangmen Chna Abstract Presented a new hybrd partcle swarm algorthm based on P systems through analyzng the workng prncple and mproved strategy of the elementary partcle swarm algorthm. Used the partcles algorthm combned wth the membrane to form a communty partcles use wheel-type structure to communcate the current partcle wthn the communty. The partcles as Representatve compete for the optmal partcle of the hgher level. Utlzed the Obectve Functons to test the desgned algorthm performance compared wth other partcle swarm optmzaton algorthms the experment results shown that the desgned algorthm has better performance n seekng Optmzaton soluton qualty robustness and convergence speed. Keywords: P system; Partcle swarm; Hybrd ntellgent algorthm 1.Introducton Partcle swarm optmzaton (PSO) s a class of a stochastc optmzaton algorthm based on swarm ntellgence. In PSO algorthm each ndvdual look as a partcle n a d- dmensonal search space fly at a certan speed n the search space dynamcally adust the speed accordng to themselves and companon flyng experence. Each of the partcles has an obectve functon to determne the adaptaton value partcles search the optmal soluton followed the current optmal partcle n the soluton spaces fnd the optmal soluton by teraton. In each teraton partcle by trackng ndvdual extreme values and global extreme values to update myself n the process of lookng for the two extremes the partcle updates own speed and locaton accordng to the correspondng locaton [1]. PSO has easy to understand and mplement the global search ablty and other characterstcs much broader feld of scence and engneerng concern has become the fastest growng ntellgent optmzaton algorthms. As PSO's performance depends on the algorthm parameters to overcome these shortcomngs natonal researchers have proposed varous measures for mprovement. These mprovements am s to mprove the partcle dversty and enhance the global exploraton ablty of partcle or to mprove local development capacty and enhance the convergence speed and accuracy [-4]. There are usually two knd of combnaton way: Frst used other adaptve optmzaton shrnkage factor nerta weght and acceleraton constants; second combned wth PSO and other evolutonary algorthm operators or other technology. Juang C F. combned the ant algorthm and the PSO for solvng dscrete optmzaton problems; Robnson et al [4] and Juang the combnaton of GA and PSO are used to optmze the antenna desgn and recurrent neural network desgn [4-5]; ocuments [6] dvded the populaton nto more sub-populaton and then the dfferent sub-populatons usng PSO or GA or ndependent evoluton of hll-clmbng; Naka et al [7] have studed that the selecton operaton of GAs ntroduced nto the PSO accordng to select a certan rate of reproducton to copy better ndvduals; Angelne [8] ntroduced tournament selected nto the PSO algorthm accordng to the current locaton of ndvdual ftness to each ndvdual and compared to several other ndvduals and then compare the results to the whole group based on sortng the half of the partcle n the current group replace the worst half of the poston and speed of the poston and speed whle preservng the memory of ndvduals of each ndvdual the poston; El-b et al [9] proposed crossover operaton on the partcle poston and speed; Hgash et al [10] ntroduced Gaussan mutaton to PSO; Mranda [11] used the varaton selecton and breedng a varety of operatng at the same tme update the formula n the neghborhood of the locatons and nerta weght and acceleraton constants; Zhang et al [1-14] usng dfferental evoluton operator to select the speed of update formula n the poston of partcles; And Kannan et al [15] usng dfferental evoluton to optmze the PSO nerta weght and acceleraton constants. ocument [16] proposed a dscrete quantum ndvdual PSO; ocument [17] proposed the quantum PSO that update partcle poston based on behavor of quantum. In ths paper combne membrane computng deas wth standard PSO form a membrane communty soluton space Copyrght (c) 013 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

2 IJCSI Internatonal Journal of Computer Scence Issues Vol. 10 Issue 1 No January 013 ISSN (Prnt): ISSN (Onlne): the partcle n the communty wll be quck convergence soluton space effects. The partcles as Representatve compete the optmal partcle of the hgher level. Ths can effectvely prevent the fall nto local mnmum premature convergence or stagnaton..hybrd Algorthm esgn.1p System Studed NA computng for many years nspred by bologcal cells Gheorghe Păun proposed the membrane computng n 000 [3] through dealng wth compounds from layered structure of lvng cells to abstract the computng model. The model s called membrane systems or P system A P system of n dmensonal can be expressed as the followng formula: ( V T C w... w ( R1 1)...( )) 1 m R m m In formulary (1) V s alphabet ts elements are called obects; T V s output alphabet; C V T s catalyst ts elements don't change n the evolutonary process don't create new characters too however perform some evoluton rules requred ts; s a membrane structure that contan m membranes each membrane and ts enclosed area show wth a label set of H H {1 m} then m s ' s dmensonal; w V (1 m (1) ) show multple sets that contan obects n the regon of membrane structure m V s the collecton of arbtrary character strng composed of V s character; Evoluton rules s a bnary set of ( uv ) Usually wrtten as u v u s the strng of * V v v' or v v' v ' s the character strng of collecton { a a a a V1 m} s the specal characters here out n don t belong to V When a rule contans membrane s dssolved whle the mplementaton of the rules regard the length of u as the rules of u v'radus R (1 m) s the fnte set of evoluton rules each R s assocated wth the regon of n the membrane structure of s the second order n R whch s the preferental relatons Whch s the preferental relaton that mplementaton the rules of n. In short P system conssts of three parts: herarchcal structure of membrane; the multple set of obects; evoluton rules..partcle Swarm Optmzaton Partcle swarm optmzaton (PSO) s ntalzed to a group of random partcles (random solutons) and then terate to fnd the optmal soluton. In each teraton the partcles by trackng the two extreme to update ther own the frst one s the partcle tself to fnd the optmal soluton ths soluton s called ndvdual extreme; the other one s the whole populaton to fnd the optmal current soluton ths extreme s a global extreme. In addton you can also use part of the partcles rather than the entre populaton as a neghbor; the extreme n all neghbors s the local mnmum. Suppose a -dmensonal target n the search space there are N partcles to form a communty n whch the - th partcle s represented as a -dmensonal vector X ( x 1 x x ) 1 N () The frst partcles flyng" velocty s also a - dmensonal vector expressed as V ( v 1 v v ) 1 3 (3) Each partcle also mantans a memory of ts prevous poston represented as p p p p ) 1 N ( 1 (4) The optmal poston can be search n whole group whch can be represented as g p p p ) ( g1 g g (5) When found these two optmal values the partcles update ther speed and poston accordng to the followng formula (6) and (7). v w v c r p x c r p x d d c ) ( 1 1 d d gd d x d x d v c Where 1 are learnng factor also known as the acceleraton constant r 1 r are random numbers n Range [01]. Equaton (6) on the rght conssts of three parts the frst part of the "nerta (nerta)" or "momentum (momentum)" part reflects the movement of partcles "habt (habt)" the partcle has the speed to mantan ther prevous trend; the second part of "cogntve (cognton)" part reflects the hstorcal experence of the partcles on ther own memory (memory) or memory (remembrance) the partcle has the locaton close to ther hstorcal trends; thrd part of "socal (socal) "part reflects the partcle collaboraton and knowledge sharng between groups of hstorcal experence the partcle wth the group or neghborhood close to the hstorcal locaton trend. Accordng to experence Usually take [ ] c1 c v d v v max max s velocty of partcle r 1 r d (6) (7) Copyrght (c) 013 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

3 IJCSI Internatonal Journal of Computer Scence Issues Vol. 10 Issue 1 No January 013 ISSN (Prnt): ISSN (Onlne): vmax s random numbers n Range [01] s a constant set by the user to lmt the speed of the partcle..3hybrd Algorthm Partcle swarm optmzaton based on Membrane computng s assgned to dfferent groups of partcles n the membrane a membrane s equvalent to the communty the membrane partcles are selected the of ts specfc partcles and use the dfference between hm and the neghbor vector nstead of the standard PSO velocty update formula "part of ndvdual conscousness." Topology of populatons of membrane between each partcle usng wheel-type structure can further mprove the performance of the algorthm to avod premature convergence phenomenon. In ths structure each partcle wth the center partcle exchange nformaton n the membrane the partcle n the communty as representatves of the partcle n the hgher level competton the topology shown n Fgure 1. Wth a knockout way to fnd ths optmal soluton to mprove the speed of dssemnaton of nformaton to avod loss of nformaton to better mprove the effcency of the algorthm. Center Partcle Partcle Step 5: For each partcle compare ts ftness value F [] and ndvdual extremum Then replace p ( ) wth F [] ; Step 6:the partcle p ( ) f F [ ] p ( ) t t p n the membranes compare ts ftness value F [] and Global extremum g place g wth F [] ;; t f F [] p t t t Then re Step 7: Accordng to formula (6) (7) update the partcle velocty v and poston x. Step 8: If the end condtons are met to elect the partcle the algorthm ends otherwse return to Step 4. 3.Algorthm test and analyss To verfy the performance of the algorthm we proposed n ths paper based on partcle swarm optmzaton membrane structure (mpso) wth standard PSO algorthm (spso) [1] dfferental evoluton partcle swarm optmzaton [113] GA partcle swarm optmzaton [6] for comparson. In the experment we selected fve standard optmzaton functons to test these algorthms each functon uses 10- dmensonal search space. 3.1Test functons Fg. 1 Partcle swarm based on P systems membrane envronment Partcle swarm optmzaton based on P system process s as follows: Step 1: the establshment of the structure contans m membranes each membrane and the surroundng areas use label set H {1 m}. Step : The partcles were randomly assgned to the m -membranes. Step 3: ntalze the partcle swarm ncludng populaton sze N the number of representatves of membranes each partcle poston x and veloctyv. Step 4: to assess the ftness value F [] of each partcle; t 1) F1 e Jone's functon The smplest test functon s e Jong's functon 1. It s also known as sphere model. It s contnuos convex and unmdal. Functon defnton: f1( x) x ; x [ ] 1 Global mnmum: ) F Axs parallel hyper-ellpsod The axs parallel hyper-ellpsod s smlar to e Jong's functon 1. It s also known as the weghted sphere model. Agan t s contnuos convex and unmodal. Functon defnton: f ( x) x ; x [ ] 1 (9) Global mnmum: 3) F3 Sum of dfferent Powers The sum of dfferent powers s a commonly used unmodal test functon. Functon defnton: (8) Copyrght (c) 013 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

4 IJCSI Internatonal Journal of Computer Scence Issues Vol. 10 Issue 1 No January 013 ISSN (Prnt): ISSN (Onlne): ( 1) f 3( x) x ; x [ 11] 1 (10) Global mnmum: 4) F4 Rastrgn's functon Rastrgn s functon s based on functon 1 wth the addton of cosne modulaton to produce many local mn-ma. Thus the test functon s hghly multmodal. However the locaton of the mnma s regularly dstrbuted. Functon defnton: f 4 ( x) 10 x 10 cos( x ); x [ ] 1 (11) Global mnmum: 5) F5 Schwefel's functon Schwefel's functon s deceptve n that the global mnmum s geometrcally dstant over the parameter space from the next local mnma. Therefore the search algorthms are potentally prone to convergence n the wrong drecton. Functon defnton: f5( x) x sn x ; x [ ] ` (1) Global mnmum: f ( ) ; We use the standard ntalzaton range but the partcular functon to facltate the dsplay of ts performance ts ntalzaton to narrow the scope of [-1 1]. For all of the functon we use the 10-dmensonal search space Table I shows the fve test functon the ntalzaton and the search space. Table 1: Functon ntalzaton settngs test functon Search Intalzaton range doman F1 e Jone's functon 1 [ ] [ -1 1 ] F Sum of dfferent Powers [ -1 1 ] [ -1 1 ] F3 Rastrgn's functon 6 [ ] [ ] F4Axs parallel yper-ellpsod [ ] [ ] F5 Schwefel's functon 7 [ ] [ ] 3.Performance analyss As the optmzaton result s random for scentfc comparson algorthms we take the average of the results whch ndependently test each test functon 50 tmes. For each run the end result of 1000 teratons to compare the accuracy of algorthm convergence. Can be found by observng MPSO has better optmzaton ablty for varous functons especally for multmodal functon of search capablty s much hgher than other comparson algorthms. Table 4. shows Statstcs for average optmal results of the algorthm whch the fve Obectve functons are run 50 tmes ndependently. m x S PSO EPSO GAPSO MPSO F F e e e e- 007 F e e e e- 036 F F In the table F s testng functon N s the search space N s runnng tmes Gmax teratve tmes s Algorthm parameters analyss Some of the parameter settngs for MPSO such as populaton sze may have an mportant effect on the performance of the algorthm so experment to verfy the relatonshp between algorthm parameters and performance. The functon F5 was be selected as the evaluaton functon to test the algorthm convergence precson under dfferent parameter settngs. Assumng populaton 30 partcle number 30 n one membrane Exchange partcle 0 at a tme swtchng tme 40 generatons the followng s assumng other condtons reman unchanged followng the case of change n one parameter expermental results are as follows: Number of partcles wthn populatons populaton szes was taken and 50. Populaton sze (number of membranes) were taken twenty thrty forty populatons. Exchange partcle tme exchange tme were taken 30 generatons 40generatons 50 generatons. The number of partcles each exchange the number of exchange partcles were taken Convergence precson Each populaton 30 partcles Each populaton 40 partcles Each populaton 50 partcles Iteraton tmes Fg. Number of partcles wthn populatons Table : Convergence value of average F N Gma Average Copyrght (c) 013 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

5 IJCSI Internatonal Journal of Computer Scence Issues Vol. 10 Issue 1 No January 013 ISSN (Prnt): ISSN (Onlne): Convergence precson populatons 40 populatons 0 populatons As seen n Fgure 4 the results of dfferent exchange tmng whch were to take tmng ( ) generaton. When teraton take to the 30 that the results s However The algorthm cannot converge to the global mnmum when the exchange tmng was set 50. The number of partcles each exchange are shown n Fgure 5 When the partcles were set n (15 0 5) the optmzaton effect s had lttle fluctuaton but each tme exchange 15 partcles s better. Convergence precson Iteraton tmes Fg. 3 Populaton sze Iteraton thrty tmes Iteraton forty tmes Iteraton ffty tmes Iteraton tmes Convergence precson Fg. 4 Exchange partcle tme 15 partcles exchange every tme 5 partcles exchange every tme 35 partcles exchange every tme Iteraton tmes Fg. 5 The number of partcles each exchange By several key parameters for mpso to be set dfferent values expermental results as follows: As show n the Fgure that the number of partcles wthn populatons has lttle effect on convergence accuracy. In each set 40 partcles wthn a populaton have the convergence results. Fgure 3 shows the number of membrane was set n the experment the number of membrane were set to ( ) the populatons that was set 40 has obvous advantages. 4.Concluson In ths paper proposed a new hybrd partcle swarm algorthm based on P system whch s through the analyss of elementary partcle swarm algorthm the workng prncple and mprovement a strategy. And the algorthm s excellent n fndng extreme for multmodal functon. But there s stll much scope for mprovement n ths algorthm populaton exchange between the partcles are too smple stupd and tend to a sngle. Future mprovements can be used wth the gudance of the dynamc evoluton of membranes exchange accordng to the algorthm to optmze condtons for specfc partcle exchange operaton. Hybrd evolutonary algorthm s one trend n the feld of evolutonary algorthms so that the advantages of dfferent algorthms can be ntegrated and "better faster cheaper to get the soluton of the problem t s a valuable research drecton. References [1] Kennedy J Eberhart R. Partcle swarm optmzaton. n: Proceedngs of the 4th IEEE Internatonal Conference on Neural Networks Pscataway: IEEE Servce Center 1995 pp [] Zhang G. XLu C. XGheorghe M.Pâté F. Solvng satsfablty problems wth membrane algorthms. Proceedngs of the Fourth Internatonal Conference on Bo- Inspred Computng: Theores and Appleatons.009:9-36. [3] Fen Zhou et al.a Partcle Swarm Optmzaton Based on P systems. 010 Sxth Internatonal Conference on Natural Computaton (ICNC 010).pp [4] Gh. Pˇ aun. Computng wth membranes. Journal of Computer and System Scences.000 1(61): [5] Juang C F. A Hybrd of Genetc Algorthm and Partcle Swarm Optmzaton for Recurrent Network esgn. IEEE Transactons on Systems Man and Cybernetcs (Part B- Cybernetcs) (): [6] Krnk T and Løvberg M The Lfecycle Model: Combnng Partcle Swarm Optmzaton Genetc Algorthms and Hll Clmbers. In Proc. of PPSN 00 pp [7] S. Naka T. Gen T.Yura and Y. Fukuyama. A hybrd partcle swarm optmzaton for dstrbuton state estmaton. IEEE Trans. Power Syst pp Feb [8] Angelne P.J.Usng Selecton to Improve Partcle Swarm Optmzaton. In Proc of the IEEE Congress on Evolutonary Computaton. Anchorage USA [9] El-b H. Youssef M. El-Metwally and Z. Osman. Load flow soluton usng hybrd partcle swarm optmzaton. In Copyrght (c) 013 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.

6 IJCSI Internatonal Journal of Computer Scence Issues Vol. 10 Issue 1 No January 013 ISSN (Prnt): ISSN (Onlne): Proc. Int. Conf.Elect. Electron. Comput. Eng. Sep. 004 pp [10] Hgash N Iba H. Partcle Swarm Optmzaton wth Gaussan Mutaton. n Proc. of the 003 Congress on Evolutonary Computaton [11] V. Mranda and N. Fonseca. EPSO: evolutonary partcle swarm optmzaton a new algorthm wth applcatons n power systems. n IEEE/PES Transmsson and strbuton Conf. Exhbton Asa Pacfc Oct. 00 vol. pp [1] W. Zhang and X. Xe. EPSO: Hybrd partcle swarm wth dfferental evoluton operator. n Proc. IEEE Int. Conf. Syst. Man Cybern. Oct. 003 vol. 4 pp [13] H. Talb and M. Batouche Hybrd partcle swarm wth dfferental evoluton for multmodal mage regstraton. n Proc. IEEE Int. Conf. Ind. Technol. ec. 004 vol. 3 pp [14] P. Moore and G. Venayagamoorthy. Evolvng combnatonal logc crcuts usng partcle swarm dfferental evoluton and hybrd EPSO. Int. J. Neural Syst. vol. 16 no. pp [15] S. Kannan S. Slochanal and N. Padhy. Applcaton of partcle swarm optmzaton technque and ts varants to generaton expanson problem. ELSERVIER Electrc Power Syst. Res. vol. 70 no. 3 pp Aug [16] [S. Yang M. Wang and L. Jao. A quantum partcle swarm optmzaton. n roc. IEEE Congr. Evol. Comput. Jun. 004 vol. 1 pp [17] J. Sun Partcle Swarm Optmzaton wth Partcles Havng Quantum Behavor. n Proc. 004 Congress on Evolutonary Computaton pp Copyrght (c) 013 Internatonal Journal of Computer Scence Issues. All Rghts Reserved.