Investigation of Modified Bee Colony Algorithm with Particle and Chaos Theory

Transcription

1 Internatonal Journal of Control and Automaton, pp Investgaton of Modfed Bee Colony Algorthm wth Partcle and Chaos Theory Guo Cheng Shangluo College, Zhangye, Gansu, Chna Abstract Foragng behavor of anmal wdely concerns researchers. Some swarm ntellgence algorthms, such as ant colony optmzaton algorthm, partcle swarm optmzaton algorthm, artfcal fsh swarm algorthm, and so on, have been developed. Artfcal bee colony algorthm (ABC), whch s based on self-organzaton model, has been proposed. Its applcaton s manly used n the feld of numercal optmzaton. Researchers verfy the outstandng performance n functon optmzaton doman accordng to the comparson wth other algorthms wth varous mprovements. Artfcal bee colony algorthm tself has better performance n solvng hgh dmenson functon. It needs not large populaton sze and can guarantee the global convergence. In the paper, from the vew of mprovng the convergence rate of the algorthm, search operators have been studed and a faster algorthm has been proposed. At the same tme, the search regon has been optmzed. Accordng to the example verfcaton, the new algorthm s effectve and the algorthm can be used n the optmzaton feld. Keywords: modfed algorthm, artfcal bee colony, partcle, chaos 1. Introducton In recent years, research on the foragng behavor of anmal s wdely concerned by researchers. Some swarm ntellgence algorthms, such as ant colony optmzaton algorthm, partcle swarm optmzaton algorthm, artfcal fsh swarm algorthm, et al., have been developed. In 005, artfcal bee colony algorthm (Artfcal Bee Colony, ABC) [1-3], whch s based on self-organzaton model [4-5], has been proposed. Its applcaton s manly used n the feld of numercal optmzaton [6-13]. Thus, domestc and foregn researchers verfy the outstandng performance n functon optmzaton doman accordng to the comparson to other algorthms wth a varety mprovement of the algorthm. Present research on ABC algorthm s stll n the explorng stage [14-16]. As wth other ntellgent algorthms, many mprovements have been proposed for the algorthm. For the ntalzaton, orthogonal expermental desgn [17-19] and chaotc search [0-1] ntalzaton has been ntroduced to make the ntal populaton dstrbuton better; For the nectar source selecton by the followng bee, strateges, such as Boltzmann mechansm [], champonshp [3], orderng strategy [4], splttng strategy [5], ant-roulette strategy, pheromone senstvty strategy [6], et al., has been developed; For mprovng the search operators, there are sharng factor wth dynamc change method, speed updatng formula derved from partcle swarm algorthm (PSO), quantum coordnate model, and addton of other search modes: crawlng process n monkey algorthm, dfferental evoluton, and so on; In the aspect of swarm varety, partcle swarm algorthms are often used to establsh the dual populaton model, and some nteractons are often desgned. ue to the overall good performance of artfcal bee colony algorthm for ndvdual updatng and dffcult n fallng nto local optmum, t often ntroduced as an searchng operator nto other algorthms, such as the ant colony ISSN: IJCA Copyrght c 015 SERSC

2 Internatonal Journal of Control and Automaton algorthm, partcle swarm, frefly algorthm, and so on, to mprove the convergence speed and soluton accuracy. Keep balance between global exploraton and local explotaton s the key to keep the better performance of swarm ntellgence algorthm. In the standard artfcal bee colony algorthm (ABC algorthm), randomly selected neghbor strategy s adopted n the searchng nectar source poston for hred bee and follow bee. Ths would lead to weak local development ablty although good global exploratory ablty. Partcle swarm optmzaton s used to make the hre bee get the global optmum gudance n explorng new source locaton. Ths can mprove the performance of the algorthm and decrease the amount of calculaton. Artfcal bee colony algorthm tself has better results n solvng hgh dmenson functon. It needs not large populaton sze and can guarantee the global convergence. However, solvng speed s qute slow, and the number of the generatons would be larger when the dmensons are hgher. In ths paper, from the vew of mprovng the convergence rate of the algorthm, search operators have been studed and a faster algorthm has been proposed. At the same tme, the search regon has been optmzed. The man contrbuton s the proposton of the new algorthm to ncrease the convergence speed. The remander of the paper s shown as the followng: Standard ABC algorthm s lsted n secton. Modfed ABC algorthm s shown n secton 3. Adaptve search space ntroducton s shown n secton 4. The verfcaton s shown n secton 5 and the concluson s descrbed n secton 6.. Standard ABC Algorthm In standard ABC algorthm, the bee swarm s composed of leadng bee, follow bee and scout bee. The number of food sources s the same as leadng bees and scout bees. The basc processes are as follows: Step1: Intalze the leadng bees random, and one leadng bee s set for a food source, and calculates the concentraton of the food accordng to the objectve functon. Then, optmal locaton and the optmal ftness would be recorded. Step: Each lead bee wll be preceded as follows: randomly choose to a neghbor of leadng bee, and randomly select one dmenson. Locaton s updated accordng to the formula (1). where k { 1,,..., Num}, but k 1}, and Num s the number of leadng bees; J {1,,..., dm}, and m s the dmenson space; Rand s a random number and Rand [0 1, ] ; If ftness of the new poston s better, the new locaton would be updated as the current locaton. Or else, the non-renewable countng number would plus 1. newx x * rand 1) * ( x x ) (1) j j ( j kj Step3: Probablty of every lead beng selected would be calculated accordng to formula. Ft s the ftness of leadng bee. ftness P () SN / j 1 ftness Step4: Each follow bee would be proceedng as follows: a leadng bee would select n accordance wth the roulette wheel strategy and the poston would be updated accordng to equaton (1). If the new poston s better, the selected bee would be updated n the current poston, otherwse, the number Bas would plus 1. A leadng bee can be selected by many follow bees repeatedly, whch means that leadng bee wth greater ftness degree would be selected wth bgger probablty. Step5: The locaton and concentraton of optmal food sources of ths generaton would be recorded. j 31 Copyrght c 015 SERSC

3 Internatonal Journal of Control and Automaton Step6: Leadng bee wth the maxmum number Bas would be selected, and the leadng bee would be as a scout bee f the number s bgger than Lmt. Then, poston, ftness and Bas would be ntalzed. The parameter Lmt plays a role of reborn of lead bee wth the long-term wth no updatng. Step7: If the generaton number s smaller than the maxmum number, t should be go to step to the next generaton, otherwse, output the results. The flow chart of ABC s shown n Fgure 1. Fgure 1. Flow Chart of ABC In the bee colony foragng behavor, populaton s dvded nto three categores of hre bee, follow bee, and scout bee, respectvely. They have the prmary exploraton, redevelopment and avod stagnaton effect. From the algorthm structure, bee colony algorthm and other ntellgent optmzaton algorthm are qute dfferent, and there s more room for mprovement. For example, n genetc algorthm and partcle swarm algorthm, the group has no dvson of labor. That s to say that n each generaton all ndvduals are selected accordng to the probablty for a certan operaton. The probablty may change wth the teraton. The bees are dvded nto two man groups (hre bee and follow bee) and form a two stage operatons. Approprate adjustments are used to mantan the populaton dversty wth scout bees. The hre bee and the follow bee would update the locaton accordng to the formula 1. Nectar source selected by follow bee s accordng to the probablty calculated by Equaton, and then roulette wheel s adopted to choose. The nectar source wth hgher ftness s chosen wth bgger probablty, whch has been developed for a second tme. The search s stll n accordance wth equaton 1. Bee colony algorthm wth sngle Copyrght c 015 SERSC 313

4 Internatonal Journal of Control and Automaton dmenson search and greedy choce may lead to strong global exploraton ablty and weak local explotaton ablty. Then t should be mproved. 3. Modfed ABC Algorthm In the partcle swarm optmzaton (PSO), the partcle updates the poston accordng to the followng equaton: Where, v j( t 1) vj( t) c1r1 ( t)( pj( T) xj( t)) cr ( t)( pgj( t) xj( t)) (3) xj ( t 1) xj( t) vj( t 1) (4) ( x1, x T x,..., x ) s the poston of partcle ; V,..., vd,..., x ) ( v 1, v p,..., p ) ( p1, p T s the velocty; T s the ndvdual extreme value; T g ( pg1, pg,..., pg s the global extreme value; p ) t s the current generaton number; r 1,r s the random number belong to [ 0 1, ] ; s the nerta weght, and c 1,c are the acceleraton coeffcent. PSO algorthm makes good use of the pror knowledge, and t has hgher performance n local searchng. In the standard ABC algorthm, leadng bee and follow bee would take strategy of randomly selected neghbor n updatng poston. So, f ntroduce the global optmal soluton and set one bulletn board to show the global optmal locaton wth only vsble to the leadng bee. The leadng be would update the poston accordng to the formula (5), and other varables wll update the poston accordng to equaton (1). newxj ( 1 rand) * xj rand * GBest1 j (5) Where, GBest s the optmal global poston. For the standard ABC, exstng study adds the cross reacton wth optmum global poston based on the equaton (1), and studes the coeffcent of the global components. Makng full use of the PSO algorthm, ndvdual extremum and asynchronous learnng factor have been defned n the algorthm, and drop the parameter. Ths method s more dffcult to resolve and decreases the soluton effcency. So, n the paper, we proposed another method: selectng the current food source nstead of selectng a random neghbor. 4. Adaptve Search Space Introducton 4.1 ynamc Adjustments of the Search Space Set the spatal soluton s N, and each soluton s a vector wth dmenson. Intal state, we wll generate the soluton accordng to equaton (6): vj xj(xj - xkj ) (6) And the soluton s: X (x, x,...x ) Then, d X (x 1, x,...xd ) (7) X (x, x,...x ) n n1 n nd 314 Copyrght c 015 SERSC

5 Internatonal Journal of Control and Automaton Y (y, y,..., y,...x 1 d ) (max( x 11, x 1,..., x n1 ), max( x 1, x,..., x..., max( x13, x3,..., xn ),..., max( x1d, xd,..., xnd )) (8) Where, component y means the dstrbuton of populatons n the dmenson of. The bgger y means greater dstrbuton of populaton n dmenson coordnates of. When the search reach a certan number of teratons, maxmum possble change nterval of Y would be used to generate the populaton, and then calculate the ftness value. The ftness values would be evaluated and then contnue to search after the evaluaton. After the teraton, the nterval of generatng the ntal populaton would be gradually shrunk, and the teratve process wll be speed up to mprove the effcency of the whole algorthm. In accordance wth the method descrbed before, the search space s contractble, then two problems would be appeared: a) optmal soluton may be excluded from the reducton of the search space, and the optmal soluton of such problems cannot be searched; b) the moton range of the ndvdual poston s greatly reduced, and the local optmal breakng ablty of the algorthm s decreased. If most of the ndvduals are n moton near the local extremum of the same algorthm, the solvng process would be prone to temporary stagnaton. Then, breakng the lmtaton of the local extremum may need for a long perod of tme, and may stll not be able to break through ths lmtaton and fallng nto local optmum. Therefore, we should solve the problems accordng so some method. In the paper, we wll manly uses two methods n the solvng process: a) the populaton wll be dvded nto two parts, one part s used for the dynamc adjustment of the search area to accelerate the convergence speed, whle another part s stll n the orgnal space. The soluton at the space edge wll not be gnored, smulaton results show the feasblty of the method; b) when the search space s adjusted, next compresson would not be processed mmedately. But n each tme after compresson, teraton would be processed for several tmes to make the group to have a process of adaptaton to a new envronment. Then, the next tme compresson would be gven. 4. Chaotc Search Chaos s a knd of nonlnear phenomena and t s wdely exst n nature. It seems confusng but wth exquste structure, and has the characterstcs of randomness, ergodcty and regularty. It can traversal all the state wth no repeatablty n a certan range accordng to ther own laws. The general chaos refers to the state of moton whch s obtaned by the determnstc randomness equatons. Varables wth chaotc state are called chaotc varables. For example, the logstc map s a typcal chaotc system wth the followng equaton: zn 1 zn (1 zn ); n 01,,,... (9) Where, s the control parameters, and the equaton (5) can be regarded as a dynamc system. When s determned by the ntal value, any value of z [0 1, ] can be 0 n ), calculated for a fxed perod of tme sequences z 0, z1, z,..., when 4, the system s n complete chaos. ue to the ergodcty of chaos, the optmzaton algorthm wth chaos s easy to jump out of local optmal soluton. As a good search mechansm, many studes, whch combned the chaos and swarm ntellgence algorthms, have been publshed. For example, chaotc genetc algorthm can be obtaned wth the chaos operator used n the genetc algorthm (GA) and chaotc partcle swarm optmzaton algorthm can be obtaned wth the combnaton of chaotc theory and partcle swarm optmzaton (PSO). Both the methods have better search performance. Copyrght c 015 SERSC 315

6 Internatonal Journal of Control and Automaton In the ABC algorthm, f a soluton s stll not mproved through lmt cycles, t means that the soluton s n the local optmum, and then a new soluton wll randomly generate to replace t. In the paper, we wll make use of the chaotc search to assgn the soluton to jump out of the local optmum. The man dea s the use of the ergodcty of chaos to generate chaotc sequence based on current search stagnaton soluton. The optmal poston n chaotc sequences generated would be used to replace the orgnal poston. Stagnaton solutons by ths treatment wll make the search evolve contnuously to mprove the convergence speed and accuracy. Ths paper assumes that search stagnaton soluton s: X x, x,..., x ), x [ a, b ] (10) k ( k1 k kd k And t wll be processed wth chaos operator. Accordng to equaton (9). The man steps are descrbed as the followng: (1) Mappng X k to Logstc equaton doman [0, 1]: x a 0 k k Z b a ; k 1,,..., n; 1,,..., d (11) () Logstc equaton was used to generate chaotc varable teraton sequence: m 1,,..., C ) Z m k ( max Where, C max s the maxmum number of teratons n chaos search. (3) The chaotc sequence m 1,,..., C ) mappng Z m k wll be processed by nverse ( max m k a ( b a zk to the orgnal soluton space. That s to say that we x ) ' ' ' ' acqure the X k ( x k1, x k,..., x kd ). The ftness value f ' f( X k ') calculated would be compared wth the soluton of the orgnal, and the best soluton would be retaned. (4) If maxmum teratve algebrac has been reached, the optmzaton process would be fnshed, or else, return to the step (). Then, selecton strateges should be determned. In the algorthm, tournament method would be used n the selecton strategy for bee to search food source. Because the tournament selecton only adapt relatve value as the selecton standard and has no requrement to postve and negatve ftness, the algorthm can avod premature convergence and stagnaton phenomenon to a certan extent. The flow chart of the algorthm s shown n the followng: (1) Intalze the swarm soluton x ( 1,..., n) ; () Calculate the ftness value of each solutonx ; (3) etermnaton of whether to adjust the search space. If meet the adjustng demands, the leadng bee would generate the new soluton space wth equaton v y rand(01, ) y, or else t should generate the new soluton wth v j x r x x ). Ftness values of the new soluton should be calculated. j j( j kj (4) If the ftness value of v s better than or else, obtan the x. x, v would be used to replace the x, P ft / ft (5) Probablty P for x should be calculated wth equaton 1 and the tournament method. Where, s the ftness value of soluton and s the number of soluton. (6) The follow bee would select food source (soluton) accordng to P, and generate new soluton v, then calculate the ftness value. (7) If the ftness value s better than, wll be replaced by or keep constant. SN 316 Copyrght c 015 SERSC

7 Internatonal Journal of Control and Automaton (8) etermne whether to gve up one soluton. If t exsts, a new soluton would be generated by chaos search to replace t. (9) Record the current optmal soluton. (10) If t meets the termnaton condton, the optmal soluton would be output, or else go to step (3). 5. Verfcaton T In order to test the new algorthm, 9 standard test functons, all of whch are wdely used n the feld of functon optmzaton, have been tested. efnton and test functon space are gven and ther theoretcal optmal values are 0. All the results calculated by the new algorthm are compared wth ABC algorthm and the mproved ABCP algorthm. Specfc algorthm parameters are set wth the follows: All of numbers of leadng bees follow bees and food sources are 50; test functons are wth dmensons number of 50; the lmt s 10; each functon wll terate 1000 tmes. In order to test the algorthm performance, for each test functon, the algorthms wll run 50 tmes. Parameters of optmal soluton, the worst soluton, average value, varance, mean runnng tme s selected to examne the algorthm performance. (1) Contnuous type functon wth sngle mode Functon 1( x [ 1 f 100, 100] Table 1. Comparson of the Algorthms Algorthm Mean value Optmal value Worst value Varance Operaton tme (equvalent value) ABC ABCP algorthm Functon ( x j [ 1 1 f 100, 100] Table. Comparson of the Algorthms Algorthm Mean value Optmal value Worst value Varance Operaton tme (equvalent value) ABC ABCP algorthm Copyrght c 015 SERSC 317

8 Internatonal Journal of Control and Automaton Functon f 3( x x j [ 100, 100] 1 j 1 Table 3. Comparson of the Algorthms Algorthm Mean value Optmal value Worst value Varance Operaton tme (equvalent value) ABC ABCP algorthm Functon f 100, 100] 4( max x [ Table 4. Comparson of the Algorthms Algorthm Mean value Optmal value Worst value Varance Operaton tme (equvalent value) ABC ABCP algorthm () Non-contnuous type functon wth sngle mode Ths functon s manly used to test the search precson and executon performance. The functon s: 5( x [ 100, 100 f ] Table 5. Comparson of the Algorthms Algorthm Mean value Optmal value Worst value Varance Operaton tme (equvalent value) ABC ABCP algorthm f (3) The nose functon 4 6( x rand[0 1,)[ x 0.5] [ 1 18, 18] 318 Copyrght c 015 SERSC

9 Internatonal Journal of Control and Automaton Table 6. Comparson of the Algorthms Algorthm Mean value Optmal value Worst value Varance Operaton tme (equvalent value) ABC ABCP algorthm (4) Mult modal functon Ths type of functon has more than one local extreme value, and ther global extreme values are often dffcult to search. These functons can be used to test global search performance and premature avod convergence of the algorthm. Functon 7( x 10 cos(x ) 10] [ 1 f 5.1 5,.1] Table 7. Comparson of the Algorthms Algorthm Mean value Optmal value Worst value Varance Operaton tme (equvalent value) ABC ABCP algorthm Functon sn( 1 8( 0.5 [ ( x ) 1 x 0.5) f 5.1 5,.1] Table 8. Comparson of the Algorthms Algorthm Mean value Optmal value Worst value Varance Operaton tme (equvalent value) ABC ABCP algorthm Functon x f 9( x cos 1 [ 600, 600] Copyrght c 015 SERSC 319

10 Internatonal Journal of Control and Automaton Table 9. Comparson of the Algorthms Algorthm Mean value Optmal value Worst value Varance Operaton tme (equvalent value) ABC ABCP algorthm Fgure. Comparson for Functon 1 Fgure. Comparson for Functon 3 From the Table 1-7 and Fgure and Fgure 3, we can see the new algorthm has a better performance. It has hgh accuracy of the optmal soluton and less operaton tmes. 6. Concluson Swarm ntellgence algorthms, such as ant colony optmzaton algorthm, partcle swarm optmzaton algorthm, artfcal fsh swarm algorthm, have been developed. Artfcal bee colony algorthm (ABC), whch s based on self-organzaton model, has been proposed. It has better performance n solvng hgh dmenson functon and need not large populaton sze to get better convergence performance. In the paper, from the vew of mprovng the convergence rate of the algorthm, search operators have been studed and a faster algorthm has been proposed. At the same tme, the search regon has been optmzed. In the verfcaton, the accuracy of the optmal 30 Copyrght c 015 SERSC

11 Internatonal Journal of Control and Automaton soluton found by the new algorthm s obvously mproved and wth less teraton tmes. At the same tme, the operaton tme s shorter. The new algorthm mproved the search ablty and reduces the search tme. It can be used n the optmzaton of functon. Acknowledgment Ths paper supported by the project of the Scentfc research project n shaanx provnce department of educaton(no.013jk0597)" Image sparse representaton method and applcaton research ",and s supported by Scentfc research foundaton of Shangluo Unversty(No.1SKY010)" Feature extracton method based on the maxmum margn crteron ". References [1]. T.. Seeley, The wsdom of the hve the socal physology of honey bee colones, Cambrdge, Massachusetts: Harvard Unversty Press, (1995). []. X. Zhengguang, X. Jun and W. Yanfe, Representatve artfcal bee colony algorthms, A survey LISS 01 - Proceedngs of nd Internatonal Conference on Logstcs, Informatcs and Servce Scence, (013), pp [3]. R. Amr, A. A. Youssf and S. Eldn, Introducng Adaptve Artfcal Bee Colony algorthm and usng t n solvng travelng salesman problem, Proceedngs of 013 Scence and Informaton Conference, SAI, (013), pp [4]. S. Sumedha, C. Abhshek and C. Manoj, Self-organzaton archtecture and model for wreless sensor networks, Proceedngs Internatonal Conference on Electronc Systems, Sgnal Processng, and Computng Technologes, ICESC, (014), pp [5]. I. Takesh, Self-organzaton model for the energy cluster formaton wth dstrbuted energy network, IEEE Symposum on Computatonal Intellgence Applcatons n Smart Grd, CIASG, (013), pp [6]. W. Yuyong, Y. Janqao and Y. Yongdou, Parameter optmzaton of support vector machne based on artfcal bee colony algorthm, Journal of Computatonal Informaton Systems, vol. 10, no. 1, (014), pp [7]. H. Shayegh and A. Ghasem, A modfed artfcal bee colony based on chaos theory for solvng nonconvex emsson/economc dspatch, Energy Converson and Management, vol. 79, (014), pp [8]. Y. Zhen, Z. Ya, Z. W. Lan and Z. L, Extensve partcle swarm artfcal bee colony algorthm for functon optmzaton, Appled Mechancs and Materals, vol , (014), pp [9]. L. Jun-Qng, P. Quan-Ke and T. M. Fath, A dscrete artfcal bee colony algorthm for the multobjectve flexble job-shop schedulng problem wth mantenance actvtes, Appled Mathematcal Modellng, vol. 38, no. 3, (014), pp [10]. W. Zhaowe, L. Xaoxang and Z. Jaje, Performance evaluaton n color-based mage retreval usng artfcal bee colony algorthm, Journal of Informaton and Computatonal Scence, vol. 11, no. 4, (014), pp [11]. G. We-Feng, L. San-Yang and H. Lng-Lng, Enhancng artfcal bee colony algorthm usng more nformaton-based search equatons, Informaton Scences, vol. 70, (014), pp [1]. L. Jan-Sha, W. Yao-We, L. Xu-Ln, T. Hong-Tao and. Qao-Yng, Applcaton of hybrd artfcal bee colony algorthm n mxed assembly lnes sequencng, Computer Integrated Manufacturng Systems, CIMS, vol. 0, no. 1, (014), pp [13]. Z. Janzhong, L. Xang, O. Shuo, Z. Ru and Z. Yongchuan, Mult-objectve artfcal bee colony algorthm for short-term schedulng of hydrothermal system, Internatonal Journal of Electrcal Power and Energy Systems, vol. 55, (014), pp [14]. A. M. Shaful, U. K. M. Was and I. M. Monrul, Self-adaptaton of mutaton step sze n artfcal bee colony algorthm for contnuous functon optmzaton, Proceedngs of th Internatonal Conference on Computer and Informaton Technology, ICCIT, (010), pp [15]. Z. Yanyu, Z. Peng, W. Yang, Z. Baohu and K. Fangjun, Lnear weghted gbest-guded artfcal bee colony algorthm, Proceedngs 01 5th Internatonal Symposum on Computatonal Intellgence and esgn, ISCI, vol., (01), pp [16]. T. Mlan, B. Nebojsa and S. Nadezda, Adjusted artfcal bee colony (ABC) algorthm for engneerng problems, WSEAS Transactons on Computers, vol. 11, no. 4, (01), pp [17]. S. Qang, Effects of apparatus parameters on MFL sgnals usng orthogonal expermental desgn, Appled Mechancs and Materals, vol , (011), pp [18]. J. Ljun, S. Yunfeng, L. Hongfe, S. Xaol, Z. We and Z. Apng, Applcaton of orthogonal expermental desgn n synthess of mesoporous boactve glass, Mcroporous and Mesoporous Materals, vol. 184, (014), pp Copyrght c 015 SERSC 31

12 Internatonal Journal of Control and Automaton [19]. W. Guangmng, M. Xandong, H. Tanjang and Z. abng, Expermental and analytcal study on factors nfluencng bommetc undulatng fn propulson performance based on orthogonal expermental desgn, Advanced Robotcs, vol. 7, no. 8, (013), pp [0]. L. Ln, H. Janmng and S. Boan, A new hybrd method of genetc algorthm, Tabu and Chaotc search for CVRPTW, Proceedngs 010 IEEE Internatonal Conference on Intellgent Computng and Intellgent Systems, ICIS, vol., (010), pp [1]. Z. Png, W. Png, Y. Hong-Yang and F. Chun, Bogeography-based optmzaton algorthm by usng chaotc search, Journal of the Unversty of Electronc Scence and Technology of Chna, vol. 41, no. 1, (01), pp []. Y. Kentaro, Y. Takayuk, Y. Masato, M. Toshro, I. Kazuhro and N. Shnj, A level set-based topology optmzaton usng the lattce-boltzmann method, Nhon Kka Gakka Ronbunshu, C Hen/Transactons of the Japan Socety of Mechancal Engneers, Part C, vol. 79, no. 80, (013), pp [3]. K. A. Hussenzadeh and K. Behrooz, A new algorthm for constraned optmzaton nspred by the sport league champonshps, 010 IEEE World Congress on Computatonal Intellgence, WCCI IEEE Congress on Evolutonary Computaton, CEC, (010). [4]. Q. Lan and S. Lngja, Research on two-stage supply chan orderng strategy optmzaton based on system dynamcs, LISS 01 - Proceedngs of nd Internatonal Conference on Logstcs, Informatcs and Servce Scence, (013), pp [5]. L. G. Mng, S. We, Q. X. ong, Z. Y. Hao and Z. Q. Je, The optmal parttonng strategy for onlne verfcaton based on GN splttng algorthm, Appled Mechancs and Materals, vol , (013), pp [6]. F. Stefka, A. Krassmr and M. Pencho, Intutonstc fuzzy estmaton of the ant colony optmzaton startng ponts, Lecture Notes n Computer Scence, 7116 LNCS, (01), pp. -9. Authors Guo Cheng, , He born n Zhangye, Gansu. He s a Master of Scence. Now, he s a lecturer n Shangluo Unversty, and hs research drectons are r computatonal ntellgence and pattern recognton. 3 Copyrght c 015 SERSC