Tent混沌和变邻域局部搜索优化的GSA

doi:10.19665/j.issn1001-2400.2019.05.017

Abstract

Abstract:

An improved gravitational search algorithm (GSA) optimized by Tent chaos and Variable neighborhood Local search (TVL-GSA) is proposed to overcome the problem of easily falling into local optimum and defect of improving accuracy. First, tent chaos is improved to initialize the population and enhance the global search ability of the algorithm by using its ergodic uniformity and randomness; second, the particle speed and gravity coefficient formulas are improved to accelerate the convergence speed; third, a variable neighborhood local search strategy based on Levy flight is designed to guide the population to escape from local optimum and improve search accuracy. Simulation results show that the new algorithm can effectively inhibit the local optimum and has a better optimization accuracy and stability than other test algorithms. The new algorithm is used to optimize the radial basis function neural network (RBFNN). The identification results of the nonlinear system show that the improved RBFNN has a better model approximation ability and generalization level than the standard RBFNN and back propagation neural networks (BPNN).

Key words: gravitational search algorithm, chaotic, local search, neural network, system identification

CLC Number:

TP18

LOU Ao,YAO Minli,JIA Weimin,YUAN Ding. Tent chaos and variable neighborhood local search optimized GSA[J].Journal of Xidian University, 2019, 46(5): 120-127.

Figures/Tables 16

函数名	函数表达式	理论最优	维数	区间
$F 1$	$f (x) = ∑ i = 1 n x i 2$	0	30	[-100,100]
$F 2$	$f (x) = ∑ i = 1 n - 1 [100 (x i + 1 - x i 2) 2 + (x i - 1) 2]$	0	30	[-30,30]
$F 3$	$f (x) = ∑ i = 1 n x i + ∏ i = 1 n x i$	0	30	[-10,10]
$F 4$	$f (x) = 0.1 {si n 2 (3 π x 1) + ∑ i = 1 n (x i - 1) 2 [1 + si n 2 (3 π x i + 1)] + (x n - 1) 2 [1 + si n 2 (2 π x n)]} + ∑ i = 1 n u (x i, 5,100,4)$	0	30	[-50,50]
$F 5$	$f (x) = - 20 exp (- 0.2 1 n ∑ i = 1 n x i 2 1 / 2 - exp (1 n ∑ i = 1 n cos (2 π x i)) + 20 + e$	0	30	[-32,32]
$F 6$	$f (x) = 14000 ∑ i = 1 n x i 2 - ∏ i = 1 n cos (x i i) + 1$	0	30	[-600,600]
$F 7$	$f (x) = 1500 + ∑ j = 1 25 1 j + ∑ i = 1 2 (x i - a ij) 6 - 1$	1	2	[-65.536, 65.536]
$F 8$	$f (x) = ∑ i = 1 11 a i - x 1 (b i 2 + b i x 2) b i 2 + b i x 3 + x 4 2$	0.000 3	4	[-5,5]
$F 9$	$f (x) = [1 + (x 1 + x 2 + 1) 2 (19 - 14 x i + 3 x 12 - 14 x 2 + 6 x 1 x 2 + 3 x 22)] × [30 + (2 x 1 - 3 x 2) 2 × (18 - 32 x 1 + 12 x 12 + 48 x 2 - 36 x 1 x 2 + 27 x 22)]$	3	2	[-2,2]

类型	函数	项目	GSA	I-GSA/PSO	GGSA	GPS	TVL-GSA
高维单峰	$F 1$	最优值	9.014×10^-14	4.411×10^-16	9.588×10^-17	4.560×10^-17	2.501×10^-111
		平均值	1.463×10^-13	6.694×10^-16	2.043×10^-16	8.274×10^-17	2.943×10^-103
		标准差	3.989×10^-14	1.943×10^-16	9.080×10^-17	2.848×10^-17	1.403×10^-102
	$F 2$	最优值	2.709×10	2.524×10	2.662×10	2.682×10	2.837×10^-4
		平均值	7.329×10	4.430×10	7.615×10	5.113×10	1.690×10
		标准差	1.061×10²	5.634×10	1.262×10	3.767×10	1.448×10
	$F 3$	最优值	1.595×10^-6	1.065×10^-7	8.785×10^-8	2.787×10^-8	1.847×10^-55
		平均值	2.234×10^-6	1.262×10^-7	1.427×10^-7	4.517×10^-8	2.531×10^-52
		标准差	9.353×10^-7	1.289×10^-8	6.676×10^-8	1.165×10^-8	5.214×10^-52
高维多峰	$F 4$	最优值	1.271×10^-6	5.393×10^-17	2.027×10^-17	1.992×10^-17	2.913×10^-32
		平均值	6.355×10^-6	1.100×10^-3	6.532×10^-17	1.823×10^-16	1.719×10^-31
		标准差	4.032×10^-6	3.500×10^-3	3.692×10^-17	2.240×10^-16	2.890×10^-31
	$F 5$	最优值	1.404×10	1.996×10	1.388×10	4.032×10^-9	8.882×10^-16
		平均值	1.936×10	1.998×10	1.850×10	6.481×10^-9	8.882×10^-16
		标准差	1.869	0.226×10^-1	2.127	1.411×10^-9	0.000
	$F 6$	最优值	2.332×10^-14	0.000	0.000	0.000	0.000
		平均值	1.720×10^-13	0.123×10^-1	4.811×10^-16	0.370×10^-2	0.000
		标准差	1.493×10^-13	0.112×10^-1	2.289×10^-16	0.740×10^-2	0.000
低维多峰	$F 7$	最优值	1.062	9.980×10^-1	9.980×10^-1	9.980×10^-1	9.980×10^-1
		平均值	2.299	1.296	2.089	1.891	9.980×10^-1
		标准差	1.889	0.480	1.091	0.869	0.000
	$F 8$	最优值	0.180×10^-2	4.861×10^-4	4.243×10^-4	6.801×10^-4	3.434×10^-4
		平均值	0.340×10^-2	0.100×10^-2	0.110×10^-2	0.110×10^-2	0.100×10^-2
		标准差	0.130×10^-2	2.445×10^-4	3.107×10^-4	2.382×10^-4	1.791×10^-4
	$F 9$	最优值	3.000	3.000	3.000	3.000	3.000
		平均值	3.000	3.000	3.000	3.000	3.000
		标准差	0.000	0.000	0.000	0.000	0.000

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类型	最小值	最大值	平均值	标准差
标准BPNN	1.158 9	1.448 3	1.289 9	0.085 7
标准RBFNN	0.100 4	0.169 5	0.122 0	0.023 4
优化后RBFNN	0.087 2	0.139 4	0.102 5	0.015 2

类型	最小值	最大值	平均值	标准差
标准BPNN	1.266 0	6.189 1	2.683 3	1.540 9
标准RBFNN	0.021 8	0.144 6	0.047 5	0.034 2
优化后RBFNN	0.009 8	0.084 1	0.031 6	0.022 9

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Tent chaos and variable neighborhood local search optimized GSA

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References 14

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