Adaptive artificial fish swarm algorithm utilizing gene exchange

doi:10.11772/j.issn.1001-9081.2021040775

Journal of Computer Applications ›› 2022, Vol. 42 ›› Issue (3): 701-707.DOI: 10.11772/j.issn.1001-9081.2021040775

Special Issue: 人工智能； 2021年中国计算机学会人工智能会议(CCFAI 2021)

• 2021 CCF Conference on Artificial Intelligence (CCFAI 2021) • Previous Articles Next Articles

Adaptive artificial fish swarm algorithm utilizing gene exchange

Zongzheng LI, Kaiqing ZHOU(), Yun OU, Lei DING

College of Information Science and Engineering，Jishou University，Jishou Hunan 416000，China

Received:2021-05-13 Revised:2021-08-05 Accepted:2021-08-10 Online:2021-11-09 Published:2022-03-10
Contact: Kaiqing ZHOU
About author:LI Zongzheng， born in 1997， M. S. candidate. His research interests include machine learning， soft computing.
OU Yun， born in 1979， M. S.， lecturer， His research interests include soft computing， fuzzy Petri net.
DING Lei， born in 1972， Ph. D.， professor. His research interests include neural network， graphics and image processing.
Supported by:
National Natural Science Foundation of China(62066016);Natural Science Foundation of Hunan Province(2020JJ5458);Science and Technology Research Program of Hunan Education Department(19A414)

基于基因交换的自适应人工鱼群算法

李宗正, 周恺卿(), 欧云, 丁雷

吉首大学信息科学与工程学院，湖南吉首 416000

通讯作者: 周恺卿
作者简介:李宗正（1997—），男，湖南益阳人，硕士研究生，主要研究方向：机器学习、软计算
欧云（1979—），男，湖南衡阳人，讲师，硕士，主要研究方向：软计算、模糊Petri网
丁雷（1972—），男，湖南岳阳人，教授，博士，CCF会员，主要研究方向：神经网络、图形图像处理。
基金资助:
国家自然科学基金资助项目(62066016);湖南省自然科学基金资助项目(2020JJ5458);湖南省教育厅科学研究项目(19A414)

Abstract

Abstract:

Focusing on the unbalance issue between local optimization and global optimization and the inability to jump out of the local optimum of Artificial Fish Swarm Algorithm （AFSA）， an Adaptive AFSA utilizing Gene Exchange （AAFSA-GE） was proposed. Firstly， an adaptive mechanism of view and step was utilized to enhance the search speed and accuracy. Then， chaotic behavior and gene exchange behavior were employed to improve the ability of jumping out of the local optimum and the search efficiency. Ten classic test functions were selected to prove the feasibility and robustness of the proposed algorithm by comparing it with the other three modified AFSAs， which are Normative Fish Swarm Algorithm （NFSA）， FSA optimized by PSO algorithm with Extended Memory （PSOEM-FSA）， and Comprehensive Improvement of Artificial Fish Swarm Algorithm （CIAFSA）. Experimental results show that AAFSA-GE achieves better results in local and global search ability than those of PSOEM-FSA and CIAFSA，and better search efficiency and better global search ability than those of NSFA.

Key words: Artificial Fish Swarm Algorithm (AFSA), adaptive view and step, gene exchange, chaotic behavior, function optimization

摘要：

针对人工鱼群算法（AFSA）不能完美地平衡局部寻优与全局寻优，且缺乏跳出局部最优能力等问题，提出了一种基于基因交换的自适应人工鱼群算法（AAFSA-GE）。首先利用自适应的视野和步长提高搜索的速度及精度，然后利用混乱行为和基因交换行为增强跳出局部最优的能力并提高搜索效率。为了证明算法的有效性，在实验中使用了10种经典的测试函数将所提算法与规范鱼群算法（NFSA）、基于扩展记忆粒子群优化算法的人工鱼群算法（PSOEM-FSA）、综合改进人工鱼群算法（CIAFSA）等改进鱼群算法进行了比较。实验结果表明，AAFSA-GE较PSOEM-FSA、CIAFSA具有更优秀局部寻优能力和全局寻优能力，较NFSA具有更高的搜索效率以及更好的全局寻优能力。

关键词: 人工鱼群算法, 自适应视野和步长, 基因交换, 混乱行为, 函数优化

CLC Number:

TP391

Zongzheng LI, Kaiqing ZHOU, Yun OU, Lei DING. Adaptive artificial fish swarm algorithm utilizing gene exchange[J]. Journal of Computer Applications, 2022, 42(3): 701-707.

李宗正, 周恺卿, 欧云, 丁雷. 基于基因交换的自适应人工鱼群算法[J]. 《计算机应用》唯一官方网站, 2022, 42(3): 701-707.

Figures/Tables 4

Fig. 1 Flowchart of AAFSA-GE

Tab.1 Test functions

函数名	表达式	取值范围
Sphere	$f (x) = ∑ i = 1 N x i 2$	（-100，100）
Ackley	$f (x) = - 20 e x p - 0.2 1 D ∑ i = 1 N x i 2 - e x p 1 D ∑ i = 1 N c o s 2 π x i) + 20 + e$	（-32，32）
Quadric	$f (x) = ∑ i = 1 N ∑ j = 1 N x j 2$	（-100，100）
Rastrigin	$f (x) = ∑ i = 1 N (x i 2 - 10 c o s (2 π x i) + 10)$	（-5.12，5.12）
Griewank	$f (x) = ∑ i = 1 N x i 2 4 000 - ∏ i = 1 N c o s x i / i + 1$	（-600，600）
Rosenbrock	$f (x) = ∑ i = 1 N - 1 100 (x i + 1 - x i 2) 2 + (1 - x i) 2$	（-2.048，2.048）
Levy	$f (x) = ∑ i = 1 N - 1 (x i - 1) 2 (1 + s i n 2 (3 π x i + 1)) + s i n 2 (3 π x i + 1) + x N - 1 1 + s i n 2 (3 π x N)$	（-10，10）
Sumpower	$f (x) = ∑ i = 1 N x i i + 1$	（-1，1）
Elliptic	$f (x) = ∑ i = 1 N (106) i - 1 D - 1 x i 2$	（-100，100）
Alipine	$f (x) = ∑ i = 1 N x i s i n (x i) + 0.1 x i$	（-10，10）

Tab.1 Test functions

函数名	表达式	取值范围
Sphere	$f (x) = ∑ i = 1 N x i 2$	（-100，100）
Ackley	$f (x) = - 20 e x p - 0.2 1 D ∑ i = 1 N x i 2 - e x p 1 D ∑ i = 1 N c o s 2 π x i) + 20 + e$	（-32，32）
Quadric	$f (x) = ∑ i = 1 N ∑ j = 1 N x j 2$	（-100，100）
Rastrigin	$f (x) = ∑ i = 1 N (x i 2 - 10 c o s (2 π x i) + 10)$	（-5.12，5.12）
Griewank	$f (x) = ∑ i = 1 N x i 2 4 000 - ∏ i = 1 N c o s x i / i + 1$	（-600，600）
Rosenbrock	$f (x) = ∑ i = 1 N - 1 100 (x i + 1 - x i 2) 2 + (1 - x i) 2$	（-2.048，2.048）
Levy	$f (x) = ∑ i = 1 N - 1 (x i - 1) 2 (1 + s i n 2 (3 π x i + 1)) + s i n 2 (3 π x i + 1) + x N - 1 1 + s i n 2 (3 π x N)$	（-10，10）
Sumpower	$f (x) = ∑ i = 1 N x i i + 1$	（-1，1）
Elliptic	$f (x) = ∑ i = 1 N (106) i - 1 D - 1 x i 2$	（-100，100）
Alipine	$f (x) = ∑ i = 1 N x i s i n (x i) + 0.1 x i$	（-10，10）

Tab.2 Initial parameters of AAFSA-GE

参数	值	参数	值
β	0.05	try_number	5
ω	1.1	拥挤度因子δ	0.75
ξ	100	种群数目N	50
Ψ	0.6或1	M1	n/2
visual	$U - L$	M2	5n
step	0.5visual

Tab.2 Initial parameters of AAFSA-GE

参数	值	参数	值
β	0.05	try_number	5
ω	1.1	拥挤度因子δ	0.75
ξ	100	种群数目N	50
Ψ	0.6或1	M1	n/2
visual	$U - L$	M2	5n
step	0.5visual

Tab. 3 Experimental results comparison of several methods

函数名	对比指标	AAFSA-GE	NFSA	PSOEM-FSA	CIAFSA
Alipine	Best	1.52E-64	4.11E-34	4.79E-07	1.94E-06
	Mean	1.93E-59	3.56E-26	6.87E-06	8.98E-06
	SD	3.55E-59	9.75E-08	5.39E-06	1.18E-05
Sumpower	Best	1.33E-41	1.00E-197	1.43E-15	4.57E-13
	Mean	1.25E-38	7.10E-179	9.70E-10	1.72E-09
	SD	2.44E-38	0	1.69E-09	3.47E-09
Elliptic	Best	0	2.95E-48	1.03E-02	2.18E+01
	Mean	7.00E-56	1.09E-46	5.73E+00	8.40E+03
	SD	1.01E-55	1.58E-46	1.04E+01	3.51E+03
Levy	Best	0	1.50E-32	4.79E-07	1.94E-06
	Mean	0	1.50E-32	6.87E-06	8.98E-06
	SD	0	0	5.39E-06	1.18E-05
Rosenbrock	Best	8.10E-16	0	1.99E-14	2.54E-14
	Mean	2.36E-12	1.94E-30	6.55E-10	1.45E-05
	SD	3.91E-12	6.14E-30	1.87E-10	3.81E-05
Ackley	Best	4.44E-16	8.88E-16	1.68E-07	1.79E-06
	Mean	4.44E-16	3.73E-15	1.02E-04	3.56E-04
	SD	0	1.50E-15	1.11E-04	3.95E-04
Sphere	Best	2.93E-155	1.14E-55	3.08E-13	1.00E-12
	Mean	1.81E-147	1.14E-52	6.19E-08	6.51E-03
	SD	3.54E-147	1.64E-52	1.11E-07	2.59E-03
Griewank	Best	0	9.86E-03	2.94E-08	7.47E-06
	Mean	0	3.49E-02	1.07E-01	1.52E-02
	SD	0	1.68E-02	1.84E-01	3.47E-01
Rastrigin	Best	0	0	3.09E-10	4.56E-09
	Mean	0	0	8.34E-06	2.06E-06
	SD	0	0	2.40E-05	4.55E-06
Quadric	Best	1.35E-69	2.10E-14	1.16E-08	9.04E-05
	Mean	5.08E-63	4.75E-09	1.16E-04	9.34E+00
	SD	1.02E-62	9.13E-09	2.63E-05	2.11E+01

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Adaptive artificial fish swarm algorithm utilizing gene exchange

基于基因交换的自适应人工鱼群算法

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