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2 染色体の多様性調整可能な遺伝的アルゴリズムと 多種の最適化問題への応用 2017 年 3 月 前川 廣太郎
3 染色体の多様性調整可能な遺伝的アルゴリズムと 多種の最適化問題への応用 前川廣太郎 システム情報工学研究科 筑波大学 2017 年 3 月
4 WS MPGA
5 2.1 GA PDGA MPGA MPGA WS GA SGA MPGA WS GA Rastrign Rosenbrock Griewank Griewank Rosenbrock SGA Rosenbrock MPGA Rosenbrock WSGA p = Rosenbrock WSGA p = Rosenbrock WSGA p = GA A F
6 WS GA
7 2.1 GA,MPGA WSGA σ GA
8 1 2 1 [1, 2, 3, 4, 5] 2 1 [6, 7, 8, 9] [10, 11, 12, 13, 14] 6
9 [15, 16] [17, 18] [19, 20] 1 ([21, 22, 23, 24, 25, 26] GA GA (Massively Parallel model of Genetic Algorithm[27, 28] MPGA ) MPGA MPGA 7
10 Watts and Strogatz [29, 30] WS SGA MPGA WS GA 3 SGA MPGA GA 1 WS GA SGA MPGA WS GA 2 WS GA MPGA WS WS 8
11 GA 3 SGA MPGA WS GA 3 WS GA A 2 GA GA WS GA 9
12 2 2.1, [15, 16, 17, 18, 31, 32, 33, 34, 19, 20] Genetic Algorithm, GA GA 1 10
13 (Parallel Distributed Genetic Algorithm[35, 36] PDGA ) (Massively Parallel model of Genetic Algorithm[27, 28] MPGA ) PDGA GA GA GA MPGA PDGA MPGA GA PDGA MPGA MPGA 11
14 WS WS MPGA WS GA WS 2.1 GA,MPGA WSGA SGA MPGA WSGA 2.2 PDGA 2.3 MPGA WS GA
15 2.2 PDGA [35] PDGA GA 1 GA 1 MPGA [27] MPGA (Cellular GA) Asynchronous Massively Paralled Genetic Algorithm AMPGA AMPGA 1 0 MPGA Perego [37] MPGA MPGA GA 13
16 [38] Parameter-free Genetic Algorithm PfGA ) PfGA GA GA MPGA WS GA 14
17 2.3 WS MPGA.2.1 GA GA GA [39, 40] 15
![[41, 42, 43] GA PDGA](/docs-images/105/166699407/images/18-0.jpg "2.2 PDGA 2.2 PDGA 16")
18 [41, 42, 43] GA PDGA 2.2 PDGA 2.2 PDGA 16
19 PDGA GA MPGA PDGA MPGA (1) S I S i (i = 1, 2,..., I,S i S j, i I, S i ) (2) S i 2.3 ) (3) S i (4) (5) (3)(4) 17
20 2.3 MPGA MPGA MPGA 18
21 2 MPGA, MPGA MPGA WS 19
22 2.3.2 Watts and Strogatz GA MPGA WS [29] MPGA 2.2 V E G V E) V = {S 1, S 2,..., S I } (2.1) E S i MPGA WS 2.1 V E E S i 2.4 E p 0 < p < 1 0 MPGA 1 20
23 MPGA WS GA 2.4 WS WS Step1 2 Step2 Step3 MPGA MPGA WS GA WS GA 21
24 SGA MPGA GA 0 MPGA p = 0 SGA SGA WS 2.5 SGA MPGA WS GA 22
25 2.4 WS GA 3 SGA MPGA Rastrign Rosenbrock Griewank Rastrigin Griewank min(f (x) ) = F (0, 0,..., 0) = 0 Rosenbrock min(f (x) ) = F (1, 1,..., 1) = Rastrign function Rosenbrock function Griewank function Interdependence of variables none have have Shape multimodal unimodal multimodal Rastrign n ( F Rastrigin (x) = 10n + x 2 i 10 cos(2πx i ) ) (2.2) i=1 ( 5.12 x i < 5.12) 23
26 2.6 Rastrign Rastrign Rosenbrock n 1 ( F Rosenbrock (x) = 100(xi+1 x 2 i ) 2 + (1 x i ) 2) (2.3) i=1 ( x i < 2.048) Rastrign 24
27 2.7 Rosenbrock 2.7 Rosenbrock Griewank F Griewank (x) = 1 + n x 2 n i 4000 ( cos ( x i ) ) (2.4) i i=1 i=1 ( 512 x i < 512) Rosenbrock GA MPGA WS GA
28 2.8 Griewank 2.9 Griewank
29 2.3 SGA MPGA WSGA Number of experiments 50 Number of chromosomes 256 Number of Generation 3000 Dimensions of X 20 Crossover ratio 70% Mutation ratio 1% Number of group Short cut ratio %,1%,10%
30 2.4 SGA MPGA WSGA p = WSGA p = 0.01 WSGA p = 0.1 Rastrign function Rosenbrock function Griewank function SGA MPGA WSGA p = WSGA p = 0.01 WSGA p = 0.1 Rastrign function Rosenbrock function Griewank function Rastrign WS GAp = 0.1 Rosenbrock Griewank p = 0.01 WS GA WS GA 2 Rastrign Griewank Rosenbrock WS GAp = 0.1 SGA MPGA SGA MPGA SGA MPGA 28
31 2.10 Rosenbrock SGA 2.11 Rosenbrock MPGA 2.12 Rosenbrock WSGA p = Rosenbrock WSGA p = 0.01 Rosenbrock MPGA SGA ,2.11,2.12,2.13,2.14 SGA MPGA WS 29
32 2.14 Rosenbrock WSGA p = Rosenbrock D=2 Rosenbrock D=3 Conventional method Proposed method GA Zhu [44] Rosenbrock 2.6 D
33 2.5 GA WS MPGA WS GA MPGA MPGA 3 Rastrign WS GAp = 0.1 Rosenbrock Griewank WS GAp = 0.01 SGA WS MPGA WS GA 31
34 GA WS GA WS GA GA GA GA WS GA SGA MPGA 32
35 3.1 WS GA WS GA A 2 GA 3.1 GA WS GA
36
37 GA GA 2 SGA MPGA WS GA SGA SGA MPGA WS GA 2.3 GA [ ] M M N N N N) n C n C n = (G n 1, G n 2,, G n M ) (3.1) G n m = (S n m, D n m, R n m) (3.2) S n m {1, 2,, S max } (3.3) D n m {1, 2,, D max } (3.4) 35
38 R n m {1, 2,, R max } (3.5) S max = 6 D max = 2 R max = 8 G n m n m S n m Dn m R n m 3 n C n 3 M [ ] C n F (C n ) N (3.6) C n
39 3.1 Agent1 Agent2 Agent3 Agent4 1st period class1 class2 class3 class3 2nd period class4 class5 class3 3rd period class6 class6 class7 4th period class6 class6 class8 class8 5th period class9 class8 class8 6th period class10 class
40 3.2.2 GA N C n X 1 X 32Y Y 3 4 [ ] (6) F (C i ) min(f (C i )) 38
41 3.2 GA [ ] 2 C i = (G i 1, G i 2,, G i M) (3.7) C j = (G j 1, Gj 2,, Gj M ) (3.8)
42 m m C i = (G i 1, G i 2,, G i m, G i m+1, G i m+2,, G i M) (3.9) C j = (G j 1, Gj 2,, Gj m, G j m+1, Gj m+2,, Gj M ) (3.10) (3.9), (3.10) m m + 2 C i = (G i 1, G i 2,, G j m, G j m+1, Gj m+2,, Gi M ) (3.11) C j = (G j 1, Gj 2,, Gi m, G i m+1, G i m+2,, G j M ) (3.12) [ ] n G i n = (1, 1, 0) (1, 1, 6) 40
43
44 (1) (2) (3) (1) (2) (3),. GA 42
45 3.5 Step1 Step2 Step3 GA
46 [45, 46] GA [ ]
47 : X Y 4 X 4 Y 2 X 2/3 Y 1/3 2 : 45
48 3 : 46
49 3.4 [47, 48] 2 47
50 Frequency Frequency Frequency σ σ σ Distance Distance Distance σ σ σ 48
51 3.4.1 N V (= 1, 2, 3,..., N) E V V {(i, j) i V, j V } V, E G G = (V, E), (3.13) (i, j) = (j, i) i, j l i,j l i,j j = 2,..., n j L j P L : L 1 = 0 (3.14) j = 2,..., n T L : L j = l 1j (3.15) PL = {1}, TL = {2, 3,..., n} (3.16) 49
52 TL L k k L k = L k TL k PL TL = L j TL j L j = min L j, L k + l kj k N N 2 x 1 ± a x i x N ± a, y 1 ± b y i y N ± b, (3.17) (a, b ) E make(i) = {j l ij < F } F (i, j) V (3.17) σ 50
53
54
55 [49] A GA
56 σ 3.6 σ σ σ σ σ = 0.6 σ σ = 0.9 σ = 0.6 σ = 0.7 σ = 0.6 σ 54
57 3.14 GA WS GA GA 3.2 WS GA SGA MPGA 55
58 3.7 GA SGA MPGA WSGA minimum GA GA GA MPGA WS GA 3.7 WSGA WSGA GA 56
59 3.18,
60 3.6 2 WS GA SGA MPGA WS GA 20 5 σ = GA WSGA 90 58
61 3.10 A F
62
63
64 3.17 WS GA
65
66 4 2 WS GA MPGA WS WS GA 3 SGA MPGA WS GA WS GA SGA 3 WS GA A 2 GA GA WS GA WSGA 10 64
67 20 5 σ = 0.6 GA WS GA WS WS 65
68 WS GA 1 66
69 67
70 1) Kotaro Maekawa, Kazuhito Sawase, Hajime Nobuhara Multiresolution Dijkstra method based on multi-agent simulation and its application to genetic algorithm for class-room optimization Journal of Advanced Computational Intelligence and Intelligent Informatics Vol.18 No.2 pp ) K. Maekawa, D. Harima, M. Haris, K. Sawase, H. Nobuhara, Multi-resolution Dijkstra s algorithm for multi-agent simulation and its application to disaster management, The 3rd International Workshop on Soft Computing and Disaster Control (SocDic 2013), Bali, Indonesia, Nov. 9-10, ) K. Maekawa, an H. Nobuhara, WS model based Massively Parallel Genetic Algorithm and its Various Applications, The 31st International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2016), pp , Okinawa, Japan, Jul ,
71 4),, :,,57(3), , ( 5) GA ) GA ) Vol.28 pp ) : GA 69
72 and ) ) ),,,,, Bitcoin, 3 Web, WORKS, ),,,,, tweets, 3 Web, WORKS,
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- - GRIPS 1 traceroute IP Autonomous System Level http://opte.org/ GRIPS 2 Network Science http://opte.org http://research.lumeta.com/ches/map http://www.caida.org/home http://www.imdb.com http://citeseer.ist.psu.edu
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(a) 1 (b) 3. Gilbert Pernicka[2] Treibitz Schechner[3] Narasimhan [4] Kim [5] Nayar [6] [7][8][9] 2. X X X [10] [11] L L t L s L = L t + L s
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IPSJ SIG Technical Report 1,a) 1,b) 1,c) 1,d) 2,e) 2,f) 2,g) 1. [1] [2] 2 [3] Osaka Prefecture University 1 1, Gakuencho, Naka, Sakai,
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Vol.54 No (July 2013) [9] [10] [11] [12], [13] 1 Fig. 1 Flowchart of the proposed system. c 2013 Information
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