3 2017 5 ( ) Journal of East China Normal University (Natural Science) No. 3 May 2017 : 1000-5641(2017)03-0078-09, (, 163318) :,,.,,,,.,,. : ; ; ; : TP301.6 : A DOI: 10.3969/j.issn.1000-5641.2017.03.008 Adaptive grouping difference variation wolf pack algorithm ZHANG Qiang, WANG Mei (School of Computer and Information Technology, Northeast Petroleum University, Daqing Heilongjiang 163318, 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] : 2016-05-13 :,,,,. E-mail: dqpi zq@163.com.
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) :,,,. 2 2.1,,. [6] s, n n. [7-8],,.
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,, 5 12..,.. (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 ( ),,,, :,
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,
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] 0.729 8 1.496 18 1.496 18; GA P c = 0.95, P m = 0.05; 5,,,,,. 8. f 1 = 0.5 + sin2 x 2 1 +x2 2 0.5, 100 x [1+0.001(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 = 10. 0.
3, : 83 0. f 4 = x 2 1 + 2x 2 2 0.3 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 ( 1 1 5 n n x 2 i ) exp ( 1 n n ) cos(2πx i ), 32.768 x i 32.768, n = 10. 0. n f 7 = 1 4000 x 2 i n cos( xi i ) + 1, 600 x i 600, n = 10.,, 0. f 8 = 100 + 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 1.4106E-12 0.0097 9.72E-04 22.957 3.53E-01 GA 2.932E-10 0.642 0.261 25.687 1.62E+03 WCA 4.208E-12 9.607E-9 3.425E-10 7.263 8.13E-19 WPA 6.481E-12 9.071E-10 3.795E-11 5.361 6.39E-21 AGDV-WPA 9.135E-14 8.752E-13 3.287E-13 3.596 5.43E-25 2 f 2 Tab. 2 f 2 run simulation results comparison f 2 /s PSO 33.907 148.942 104.779 23.618 3.28E-01 GA 40.918 369.462 267.396 26.397 1.03E+02 WCA 3.863E-6 9.865E-6 5.739E-6 8.159 8.13E-11 WPA 2.536E-10 8.0412E-9 5.675E-10 6.014 6.39E-19 AGDV-WPA 8.927E-14 7.138E-12 3.294E-13 4.312 5.43E-25 3 f 3 Tab. 3 f 3 run simulation results comparison f 3 /s PSO 3.603E-4 0.632 0.273 33.268 3.62E+04 GA 5.038E-2 7.62 4.826 36.623 5.43E+05 WCA 4.706E-10 9.916E-9 8.034E-10 9.026 8.53E-19 WPA 1.758E-11 9.067E-10 5.495E-11 7.629 5.02E-21 AGDV-WPA 1.351E-14 9.783E-12 5.981E-13 5.257 3.99E-25
84 ( ) 2017 4 f 4 Tab. 4 f 4 run simulation results comparison f 4 /s PSO 2.138E-10 9.402E-8 5.504E-9 33.405 2.63E-13 GA 2.459E-8 7.713E-7 6.748E-8 36.526 6.25E-11 WCA 4.198E-10 9.075E-9 4.439E-9 7.958 8.53E-17 WPA 2.636E-12 8.512E-10 5.617E-11 5.837 5.02E-21 AGDV-WPA 8.737E-14 7.085E-13 3.464E-13 4.619 3.99E-25 Tab. 5 5 f 5 f 5 run simulation results comparison f 5 /s PSO 9.667E-5 0.019 9.81E-04 132.875 1.25E-05 GA 0.288 0.716 0.392 148.28 5.38E+01 WCA 6.428E-9 3.367E-6 7.362E-8 10.263 5.34E-15 WPA 2.281E-11 8.283E-9 6.632E-10 8.183 4.27E-19 AGDV-WPA 2.547E-14 6.541E-12 5.841E-13 6.578 3.26E-25 Tab. 6 6 f 6 f 6 run simulation results comparison f 6 /s PSO 8.416E-5 3.583 1.586 144.748 4.96 GA 2.783 11.687 7.539 162.846 1.07E+02 WCA 2.651E-7 8.916E-7 6.674E-7 10.121 7.13E-13 WPA 6.078E-11 9.075E-9 8.342E-10 8.163 6.01E-19 AGDV-WPA 4.746E-14 8.374E-12 6.719E-13 6.725 5.04E-25 Tab. 7 7 f 7 f 7 run simulation results comparison f 7 /s PSO 0.072 0.529 0.264 147.376 8.62E-02 GA 1.287 13.643 1.951 168.21 6.38E+02 WCA 2.713E-9 9.826E-7 8.629E-8 10.516 4.37E-15 WPA 4.812E-11 8.732E-9 7.276E-10 8.572 4.28E-19 AGDV-WPA 6.462E-14 7.751E-12 6.347E-13 6.039 4.61E-25
3, : 85 8 f 8 Tab. 8 f 8 run simulation results comparison f 8 /s PSO 5.952 40.732 17.725 139.393 4.31E+02 GA 9.924 78.752 30.639 162.634 6.35E+03 WCA 4.536E-10 9.526E-7 8.347E-8 11.253 5.62E-15 WPA 3.842E-11 9.232E-9 7.641E-10 9.235 4.69E-19 AGDV-WPA 9.132E-14 8.239E-12 6.351E-13 6.179 3.95E-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): 212-216. [ 2 ],,. [J]., 2013, 35(11): 2430-2438. [ 3 ],. [J]., 2013, 30(9): 2629-2632. [ 4 ],,. [J]., 2015, 35(6): 1633-1636. [ 5 ],,. 0 1 [J]., 2014, 36(8): 1660-1667. [ 6 ],. [M]. :, 1978. [ 7 ],,. [J]., 2015, 28(1): 80-89. [ 8 ],. [J]., 2015, 30(4): 715-720.
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