Adaptive grouping difference variation wolf pack algorithm

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1 ( ) Journal of East China Normal University (Natural Science) No. 3 May 2017 : (2017) , (, ) :,,.,,,,.,,. : ; ; ; : TP301.6 : A DOI: /j.issn Adaptive grouping difference variation wolf pack algorithm ZHANG Qiang, WANG Mei (School of Computer and Information Technology, Northeast Petroleum University, Daqing Heilongjiang , China) Abstract: Due to the shortcomings that wolf pack algorithm is not high solving precision and easy to fall into the local convergence region, adaptive grouping difference variation wolf pack algorithm is proposed based on the excellent characteristics of cloud model transformation between qualitative and quantitative. Individual wolves are initialized by good-point set. Individual hunting behavior is accomplished through the cloud model theory and the self energy of the wolf is considered in the siege behavior. Finally, the differential evolution algorithm and the chaos theory are used to complete the individual variation to explore the global optimal location. The simulation results show that the proposed algorithm has fine capability of finding global optimum, especially for multi peak function. Key words: wolf pack algorithm; good-point set; differential variation; chaos 0,. Liu [1],, ; [2] : :,,,,. dqpi zq@163.com.

2 3, : 79 3,,, ; [3] ; [4] ; [5],., 3 :,,,, ;,, ;,,., (Adaptive Grouping Difference Variation Wolf Pack Algorithm, AGDV-WPA),,,,,,. 1, 3. (1) :,, h, x id = x id + rand( ) x stepa, (1), rand( ) [ 1, 1], x stepa, x id i d. (2) :,,, x id = x id + rand( ) x stepb (x gd x id ), (2), rand( ) [ 1, 1], x stepb, x id i d, x gd d. (3) :,,, ,,. [6] s, n n. [7-8],,.

3 80 ( ) 2017 G s s, r G s, p n (k) = {({r (n) 1 k}, {r (n) 2 k},, {r s (n) k}), 1 k n}, φ(n) φ(n) = C(r, ε)n 1+ε,, C(r, ε) r ε(ε > 0), p n (k), r., r = {2 cos(2πk/p), 1 k s}, p (p s)/2 s. 2.2,, ,.. (1) m, n. (2), m m, m + 1. (3).,,,. (4) m. Em(x) t = (e t 1(x), e t 2(x),, e t m(x)) t, α t i (x) = et i (x)/ m e t i (x), 1 i m, αt i (x) αt k (x), k (1,, i 1, i + 1,, m),,,, m 1 = m 1. α t i (x), m 2 = m (m 1) sin( π 2 t T ),,, m, 1. m = min{m 1, m 2 },, ( ). 2.4,,., h,,. (1) h,,., [9-11]., C(Ex, En, He), h,,. : (Ex) ; σ 2 (En) ; (He) h ;,, He = En λ, λ = λ max (λ max λ min ) t T,, λ max λ min λ, t, T. 2.4 ( ),,,, :,

4 3, : 81 [12-13]. n d jk = (x js x ks ) 2, s=1 F jk = f(x j) f(x k ) d jk, F jk = F kj. (3) x i F jk x nx., x g x nx, x i = x i + rand( ) step (x g x i ) + w (x nx x i ), (4), rand( ) [ 1, 1], step, w. (4), w,,,, w ;, w. w, [a, b] w. ( w = a + (b a) 1 f ( x i π sin f best 2 t )), T 2.5,.,,,,,.., [14-15],. [16]. :, ;,,. [17],,. k Chebyshev, [18] Chebyshev, (5). x w = x w + F ((x r1 x r2 ) + (x r3 x r4 )), (5.1) x w = cos(k arccosx w ), k = 2, (5.2), r1, r2, r3, r4, F.,, F i,

5 82 ( ) 2017 ;,, F i,. F i F i = F l + (F u F l ) f r1 f w f r2 f w f r3 f w f r4 f w. (6),. : f avg. : f avg f avg. : f avg Num. :, Num max, Num/2 Num Num max (5.1), 0 < Num < Num/2 (5.2). 3. ; :, t = 1, T, limit :. : 2.2, limit : 2.3. : 2.4 (3) (4). : 2.5 (5.1) (5.2) (6).. : t = t + 1,, 4 8, (Particle Swarm Optimization, PSO) (Genetic Algorithm, GA) [1] (Wolf Colony Algorithm, WCA) [2] (Wolf Pack Algorithm, WPA),. 100, 5 000, 20 ; PSO [19] ; GA P c = 0.95, P m = 0.05; 5,,,,,. 8. f 1 = sin2 x 2 1 +x , 100 x [ (x 2 i 100., 1 +x2 2 )]2, 0. f 2 = n [x 2 i 10 cos(2πx i) + 10], x i 5.12, n = 10., 0. f 3 = n x i + n x i, x i 10, n =

6 3, : f 4 = x x cos(3πx 1 + 4πx 2 ) + 0.3, 100 x i 100. f 5 = n Xi 2, 100 x i 100, n = 10., 0. f 6 = 20 + exp(1) 20 exp ( n n x 2 i ) exp ( 1 n n ) cos(2πx i ), x i , n = n f 7 = x 2 i n cos( xi i ) + 1, 600 x i 600, n = 10.,, 0. f 8 = n (x 2 i 10 cos(2πx i)), 5.12 x i 5.12, n = 10., 0. 1 f 1 Tab. 1 f 1 run simulation results comparison f 1 /s PSO E E E-01 GA 2.932E E+03 WCA 4.208E E E E-19 WPA 6.481E E E E-21 AGDV-WPA 9.135E E E E-25 2 f 2 Tab. 2 f 2 run simulation results comparison f 2 /s PSO E-01 GA E+02 WCA 3.863E E E E-11 WPA 2.536E E E E-19 AGDV-WPA 8.927E E E E-25 3 f 3 Tab. 3 f 3 run simulation results comparison f 3 /s PSO 3.603E E+04 GA 5.038E E+05 WCA 4.706E E E E-19 WPA 1.758E E E E-21 AGDV-WPA 1.351E E E E-25

7 84 ( ) f 4 Tab. 4 f 4 run simulation results comparison f 4 /s PSO 2.138E E E E-13 GA 2.459E E E E-11 WCA 4.198E E E E-17 WPA 2.636E E E E-21 AGDV-WPA 8.737E E E E-25 Tab. 5 5 f 5 f 5 run simulation results comparison f 5 /s PSO 9.667E E E-05 GA E+01 WCA 6.428E E E E-15 WPA 2.281E E E E-19 AGDV-WPA 2.547E E E E-25 Tab. 6 6 f 6 f 6 run simulation results comparison f 6 /s PSO 8.416E GA E+02 WCA 2.651E E E E-13 WPA 6.078E E E E-19 AGDV-WPA 4.746E E E E-25 Tab. 7 7 f 7 f 7 run simulation results comparison f 7 /s PSO E-02 GA E+02 WCA 2.713E E E E-15 WPA 4.812E E E E-19 AGDV-WPA 6.462E E E E-25

8 3, : 85 8 f 8 Tab. 8 f 8 run simulation results comparison f 8 /s PSO E+02 GA E+03 WCA 4.536E E E E-15 WPA 3.842E E E E-19 AGDV-WPA 9.132E E E E-25, (AGDV-WPA), :, PSO GA, WCA WPA, AGDV-WPA, AGDV-WPA,,,,,,,,,., WCA WPA AGDV-WPA, AGDV-WPA, WPA, AGDV-WPA, WCA WPA,,,, AGDV-WPA. 5,,,.,,,. :. [ ] [ 1 ] LIU C A, YAN X H, LIU C Y. The wolf colony algorithm and its application [J]. Chinese Journal of Electronics, 2011, 20(2): [ 2 ],,. [J]., 2013, 35(11): [ 3 ],. [J]., 2013, 30(9): [ 4 ],,. [J]., 2015, 35(6): [ 5 ],,. 0 1 [J]., 2014, 36(8): [ 6 ],. [M]. :, [ 7 ],,. [J]., 2015, 28(1): [ 8 ],. [J]., 2015, 30(4):

9 86 ( ) 2017 [ 9 ],, Niyongabo Julius. [J]., 2011, 24(1): [10],,. [J]., 2013, 30(4): [11],,,. [J]., 2015, 49(3): [12]. : [M]. :, [13],. [M]. :, [14],,. [J]., 2015, 52(12): [15],,. [J]., 2015, 42(6): [16],,,. [J]. ( ), 2014, 35(3): [17],,,. [J]., 2012, 33(1): [18],. [J]., 2011, 47(5): [19] POLI R, KENNEDY J, BLACKWELL T. Particle swarm optimization [J]. Swarm Intelligence, 2007(1): ( ) ( 77 ) [22] FOR W, LEMAN K, ENG H L, et al. A multi-camera collaboration framework for real-time vehicle detection and license plate recognition on highways[c]//proceedings of 2008 IEEE Intelligent Vehicles Symposium. IEEE, 2008: [23] ANAGNOSTOPOULOS C N E, ANAGNOSTOPOULOS I E, LOUMOS V, et al. A license plate-recognition algorithm for intelligent transportation system applications[j]. IEEE Transactions on Intelligent Transportation Systems, 2006, 7(3): [24]. [D]. :, [25] FELZENSZWALB P, MCALLESTER D, RAMANAN D. A discriminatively trained, multiscale, deformable part model[c]//proceedings of 2008 IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 2008: 1-8. [26],,. [J]., 2006, 11(8): [27],,,. [J]., 2009, 14(2): [28],. HSV [J]., 2013, 34(4): [29],,. Contourlet [J]., 2009, 38(l): [30] MILYAEV S, BARINOVA O, NOVIKOVA T, et al. Fast and accurate scene text understanding with image binarization and off-the-shelf OCR[J]. International Journal on Document Analysis and Recognition, 2015, 18(2): [31],. [J]., 2010, 31(3): (: )

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