A Study on Improved Cockroach Swarm Optmzaton Algorthm 1 epartment of Computer Scence and Engneerng, Huaan Vocatonal College of Informaton Technology,Huaan 223003, Chna College of Computer and Informaton, Hoha Unversty, Nanjng 210098, Chna E-mal: cl211282@163.com Yan-hong Song a, Meng-an Sh b epartment of Computer Scence and Engneerng, Huaan Vocatonal College of Informaton Technology Huaan 223003, Chna Yu-ja Zha epartment of Chemstry, uke Unversty urham, NC 27708, USA Yue-tang Ban School of Busness, Nanjng Normal Unversty Nanjng, 210023, Chna The orgnal cockroach swarm optmzaton (CSO) algorthm has long been crtczed for the problems of "early mature". Ths paper descrbed a new cockroach-nspred algorthm, whch s called CSO wth global and local neghborhoods (CSOGL). In CSOGL, two knds of neghborhood models are desgnedn order to ncrease the dversty of promsng soluton. Based on above two neghborhood models, two knds of novel chase-swarmng behavors are proposed and appled to CSOGL. The comparson results show that the CSOGL algorthm outperform theorgnal CSO algorthms. CENet2017 22-23 July 2017 Shangha, Chna 1 Ths work s supported by the Natonal Natural Scence Foundaton of Chna ( project 71301078 and 60971088 ), the Qng Lan Project, the Natural Scence Foundaton of Educaton Bureau of Jangsu Provnce ( Project 16KJB520049 ) and Innovaton Foundaton of Huaan College of Informaton Technology ( Project hxyc2015001 ). Copyrght owned by the author(s) under the terms of the Creatve Commons Attrbuton-NonCommercal-Noervatves 4.0 Internatonal Lcense (CC BY-NC-N 4.0). http://pos.sssa.t/
1.Introducton In the past two decades, many nature- nspred algorthms have been proposed and appled to solve optmzaton problems, e.g., Genetc Algorthm (GA) [1], fferental Evoluton (E) [52, Partcle Swarm Optmzaton (PSO) [2-3], ant Colony Optmzaton (ACO) [4], etc. One of the recent developments n bologcally- nspred algorthms s a seres of cockroach-nspred algorthms. Chen frst proposed a cockroach swarm optmzaton (CSO) [5]. The CSO algorthm smulated the general behavor of cockroach, e.g., chase-swarmng, dsperson and ruthless, etc. Furthermore, the modfed CSO (MCSO) s presented by ntroducng the nertal weght n chase-swarmng operaton of CSO [6]. By studyng the recent dscoveres n the behavor of cockroaches, Havens et al. proposed a new cockroach-nspred algorthm, called roach nfestaton optmzaton (RIO) [7]. In essence, RIO has the dfferent searchng strategy wth CSO. That s, RIO was not the mproved verson of CSO, but can be regarded as an mproved verson of PSO. Based on RIO, Havens proposed the hungry RIO (HRIO). It has proved that HRIO has better performance than that RIO and PSO[7]. We have proposed a seres of cockroach-nspred algorthms for the robot path plannng (RPP) and rod-lke robot path plannng (RLRPP) problems[8]. However, practcal experence shows that the exstng cockroach-nspred algorthms for numercal optmzaton problem generally bear the problem of of "early mature", whch leads to the loss of dversty n the populaton. Therefore, the strategy of neghborhood can be ntroduced n the orgnal CSO algorthm. In ths paper, we propose a new varant of CSO, whch s called CSO wth global and local neghborhoods (CSOGL). The CSOGL algorthm extends the orgnal CSO, and a novel neghborhood scheme s proposed and appled n CSOGL. The neghborhood scheme can generate a local optmal global optmum P, whch s sgnfcantly dfferent from the CSO. Furthermore, a new Chase-Swarmng behavor s desgned for CSOGL, whch can mplement the better tradeoff between the local and global search durng the computng process. The organzaton of ths paper s as follows: Secton 2 descrbes the orgnal verson of CSO; Secton 3 gves the swarm scheme and the chase-swarmng strategy of CSOGL;The expermental results are llustrated n secton 4;Secton 5 concludes ths paper. 2.Cockroach Swarm Optmzaton The orgnal verson of CSO smulates some basc bologcal behavors of the cockroach, whch nclude chase-swarmng, dspersng, ruthless behavor. The CSO model s descrbed as follows: (1) Chase-swarmng behavor: 2
X,G+1 = { X,G+step r 1 ( P,G X,G ), X,G P, G X,G +step r 2 ( P g,g X,G ), X,G =P,G (2.1) Where, X,G s the cockroach current poston at the G-th generaton, step s a constant value, and the random numbers r 1 and r 2 [0,1]. P s the best poston of X,G, whch can be computed by followng equaton: P = Opt { X X - X vsual} (2.2) j j j here, vsual s the percepton constant. P g,g s the global best poston at the G-th teraton. (2) sperson behavor P = Opt{ X } (2.3) g X = X + rand(1, ) (2.4) where, rand (1, ) s a -dmensonal random poston that can be set wthn a certan range. (3) Ruthless behavor X r g = P (2.5) where, r s a random nteger wthn [1, N], P g s the global best poston. 3. Cso wth Global and Local Neghborhoods 3.1 The Neghborhood Model of CSO By many expermental researches, we found that CSO featured the problems of "early mature". Furthermore, we found that the swarm strategy of CSO s unreasonable. (a) Fgure 1: Swarm Strategy of CSO In Equaton (2), the swarm strategy X -X j vsual does not guarantee that each cockroach (b) 3
s n a sub-populaton or a sub-populaton wth a certan sze at the ntal stage of CSO (See Fg.1(a)). However, after some teraton, all cockroaches are near around P g and there exsts only one sub-populaton that s the entre populaton (See Fg. 1 (b)). In Fg. 1(a), the cockroach X 1 has no neghborhood n the range that s controlled by Equaton 2 and X 1 hence does not belong to any sub-populaton. It Means that many cockroach ndvduals are n the sub-populaton that only ncludes tself, and other cockroach ndvduals may be n a sub-populaton wth a bg sze. Ths problem can serously deterorate the dversty of promsng soluton. 3.2 Neghborhood Structures and Search Strategy of CSOGL In CSOGL, two knds of neghborhood structures are used, whch are smlar to the dea of lterature [9]. One s called the local structure, where each X,G+1 s computed by the best poston P,G. On the other hand, the second one s the entre populaton at current generaton G. K s defned as the scale of the neghborhood. Thus, the neghborhood structure can be llustrated as Fg. (2), whch s a rng topology struct. In Fg. (2), N s the number of all cockroaches n CSOGL. We assume K=5, then cockroach X has fve neghborhoods X +0, X +1, X +2, X +3 and X +4. There exst some overlappng neghborhoods (See Fg.3 ). Fgure 2: Neghborhood Model Fgure 3: Overlappng Neghborhoods Accordng to above two neghborhood models, there are two knds of chase-swarmng behavors. The chase-swarmng behavor for local neghborhood s as Equaton (3.1): F, G = X, G + ( P, G - X, G ) + ( X r1 - X r 2) (3.1) Tere, L, G denotes the new locaton found by the -th cockroach. Smlarly, the chaseswarmng behavor for global neghborhood s as Equaton (3.2): F = X + ( P - X ) + ( X - X ) (3.2), G, G g, G, G r3 r 4 In Equaton (3.1) and Equaton (3.2), the ndces r 1,r 2,r 3,r 4 [1, N]. 4
Above two chase-swarmng operatons are chosen wth a random method. Thus, the whole chase-swarmng behavor of CSOGL can be descrbed as Equaton (3.3) F,G = {X,G+( P,G X,G )+( X r1 X r2 ), rand (0,1)<0.5 X,G +(P g,g X,G )+( X r3 X r4 ), otherwse (3.3) where, rand (0, 1) s a unformly dstrbuted random number. In essence, the chaseswarmng behavors of local and global neghborhood correspond to the local and global searchng on CSOGL. Notce that F, G, s the new locaton found by the -th cockroach, whch doesn t mean that F, G, must be as poston of -th cockroach n G+1 generaton. Any one of F, G, and X, G, s chosen to be X, G,+1 by the greedy selecton scheme(see Equaton (3.4)). X,G+1 = {F,G,f ( f ( F,G )< f ( X,G )), mnmzaton problems X,G,otherwse The complete pseudo-code of CSOGL s gven n Algorthm 1. Algorthm 1: CSOGL 1 INPUT: Ftness functon: f(x), X 2 Set parameters and generate an 3 Choose the p g from whole 4 Choose the p for each cockraoch; 5 FOR t = 1 to G max 6 FOR = 1 to N 7 chase-swarmng operatons (E.q(8)); 8 greedy selecton scheme(see E.q(9)) 9 IF f(x, ) < f(p ) THEN 1 P = X ; 1 EN IF 1 IF f(x ) < f(p g ) THEN 1 P g = X ; 1 EN IF 1 EN FOR 1 EN FOR 1 Check termnaton condton Table1: Benchmark Test Functons (3.4) Fn escrpton Search Range Optmum Value Rastrgn Rosenbrock Schwefel2.22 Grewangk f (x)=10 + ((x 2 ) 10 cos(2π x )) =1 1 f (x)= (100 (x +1 x 2 2 =1 ) +(1 x ) 2 ) f (x)= f (x)=1+ =1 ( =1 x 2 5.12 x 5.12 30 x 30 10 x 10 x + x 4000 ) (cos( x )) 600 x 600 2 3 6 7 5
We perform large number of smulaton experments, and compare the CSOGL wth orgnal CSO, MCSO, RIO and HRIO. All the benchmark functons are tested wth 30 dmensons, and each test s run 20 tmes wth maxmum teraton 1000. Cockroach populaton sze N = 50 s used n ths paper for all the algorthms. Other control parameters of orgnal CSO and CSO varants are set accordng to lterature [5-7]. The test results are demonstrated n Table 2. In Table 2, Mean denotes the mean functon value, ST s the standard devaton of the functon value durng the 20 runs, and Best means the best functon values. For most of test functons, MCSO demonstrates better performance than that of CSO, RIO and HRIO. Compared wth MCSO, CSOGL can gve smaller functon values by usng the same numbers of functon evaluatons. That s, the performance of CSOGL s sgnfcantly superor to the exstng cockroach-nspred algorthm. The standard devaton of the functon value shows that CSOGL s stable. Table 2: Test results of CSO, MCSO, RIO, HRIO, and CSOGL Functon CSO MCSO RIO HRIO CSOGL Mean 3.602E+03 9.199E-11 3.814E-05 3.215E-04 0.000E+00 Rastrgn ST 5.573E+03 3.946E-10 3.444E-05 3.000E-04 0.000E+00 Best 3.134E-04 0.000E+00 2.710E-07 2.145E-07 0.000E+00 Mean 9.507E+11 2.900E+01 2.528E+06 3.357E+06 3.400E+01 Rosenbrock ST 2.271E+12 0.000E+00 4.053E+06 7.115E+06 0.000E+00 Best 4.407E+01 2.900E+01 1.677E+04 3.756E+04 2.700E+01 Mean 2.901E+54 6.359E-06 2.313E+02 2.440E+02 4.030E-17 Schwefel2.22 ST 1.297E+55 1.194E-05 1.319E+02 1.234E+02 2.314E-15 Best 3.685E+01 5.941E-08 6.740E+01 1.735E+01 4.251E-23 Mean 2.615E+01 3.315E-11 7.951E-01 7.775E-01 0.000E+00 Grewangk ST 3.663E+01 1.467E-10 3.758E-01 2.545E-01 0.000E+00 Best 6.391E-05 0.000E+00 2.932E-01 3.203E-01 0.00E+000 5. Smmary and Concluson In ths paper, we present the CSOGL algorthm for global numercal optmzaton wth contnuous varables. CSOGL s an mproved verson of CSO. However, CSOGL hasa novel swarm strategy and all-new chase-swarmng scheme, whch are sgnfcantly dfferent from exstng cockroach -nspred algorthms. We have compared the performance of CSOGL wth those of CSO, MCSO, RIO, and HRIO over a sute of 11 numercal optmzaton problems and concluded that CSOGL s more effectve n obtanng better qualty solutons. In most cases, CSOGL s more stable wth the relatvely smaller standard devaton. 6
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