基于全局最优和差分变异的头脑风暴优化算法

doi:10.12305/j.issn.1001-506X.2022.01.33

摘要/Abstract

摘要：

针对头脑风暴优化(brain storm optimization, BSO)算法的选择操作中仅部分个体更新追随全局最优和变异操作中步长不能自适应的问题, 采用追随全局最优策略以充分利用全局最优信息, 并用差分变异代替原来的高斯变异以自适应调节变异步长, 提出了基于全局最优和差分变异的BSO(global-best difference-mutation brain storm optimization, GDBSO)算法。通过6个标准测试函数极值寻优的Matlab仿真对比研究表明GDBSO具有优良性能, 较好地解决了原BSO搜索效率低的问题, 提高了算法的寻优精度和收敛速度。GDBSO结合自主式水下航行器(autonomous underwater vehicle, AUV)路径规划应用的仿真验证了算法的有效性和可行性。

关键词: 全局最优, 差分变异, 头脑风暴优化算法, 自主式水下航行器, 路径规划

Abstract:

To solve the problems that only some new individuals follow the global-best in the selection operation of the brain storm optimization (BSO) algorithm and mutation step without adaptation in the mutation operation, a global-best difference-mutation BSO (GDBSO) algorithm is proposed. The following global optimal strategy is applied to make full use of the global optimal information and the difference mutation is used to replace the original Gaussian mutation to adjust the mutation step adaptively. The comparison of extremum optimization of six standard test functions in Matlab simulation shows that GDBSO solves the existing problem of low search efficiency of the original BSO and greatly improves the searching precision and speed of the algorithm. The simulation of GDBSO with autonomous underwater vehicle (AUV) path planning application verifies its availability and practicability.

Key words: global-best, difference-mutation, brain storm optimization (BSO) algorithm, autonomous underwater vehicle, path planning

中图分类号:

TP301.6

马威强, 高永琪, 赵苗. 基于全局最优和差分变异的头脑风暴优化算法[J]. 系统工程与电子技术, 2022, 44(1): 270-278.

Weiqiang MA, Yongqi GAO, Miao ZHAO. Global-best difference-mutation brain storm optimization algorithm[J]. Systems Engineering and Electronics, 2022, 44(1): 270-278.

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类型	函数名称	表达式	搜索区域
多峰	Ackley	${f_1}(x) = 20 + {\rm{e}} - 20\exp \left( { - 0.2\sqrt {\frac{1}{D}\sum\limits_{i = 1}^D {x_i^2} } + \exp \left( {\frac{1}{D}\sum\limits_{i = 1}^D {\cos } 2\pi {x_i}} \right)} \right.$	[-32, 32]
	Alpine	${f_2}(x) = \sum\limits_{i = 1}^D {\left\| {{x_i}\sin \left( {{x_i}} \right) + 0.1{x_i}} \right\|} $	[-10, 10]
	Griewank	${f_3}(x) = \frac{1}{{4000}}\sum\limits_{i = 1}^D {x_i^2} - \prod\limits_{i = 1}^D {\cos } \left( {\frac{{{x_i}}}{{\sqrt i }}} \right) + 1$	[-600, 600]
	Rastrigin	${f_4}(x) = \sum\limits_{i = 1}^D {\left[ {{x_i} - 10\cos \left( {2\pi {x_i}} \right) + 10} \right]} $	[-5.12, 5.12]
单峰	Sphere	${f_5}(x) = \sum\limits_{i = 1}^D {x_i^2} $	[-100, 100]
单峰	Schwefel	${f_6}(x) = \sum\limits_{i = 1}^D {\left\| {\;{x_i}\;} \right\|} + \prod\limits_{i = 1}^D {\left\| {\;{x_i}\;} \right\|} $	[-30, 30]

标准测试函数		f₁	f₂	f₃	f₄	f₅	f₆
平均值	p_r=0	8.88E-16	2.11E-41	5.47E-03	0.00E+00	1.46E-88	2.22E-44
	p_r=0.001	8.88E-16	2.77E-43	6.11E-03	1.99E-02	4.47E-88	3.04E-44
	p_r=0.005	8.88E-16	4.19E-39	4.88E-03	1.99E-02	4.23E-88	4.00E-43
	p_r=0.01	8.88E-16	1.22E-41	6.66E-03	0.00E+00	2.39E-87	1.37E-43
	p_r=0.05	8.88E-16	1.35E-38	4.98E-03	0.00E+00	5.21E-83	8.43E-42
	p_r=0.1	8.88E-16	9.77E-38	5.92E-03	0.00E+00	2.33E-78	1.84E-39
标准差	p_r=0	0.00E+00	1.46E-40	4.63E-03	0.00E+00	4.38E-88	2.38E-44
	p_r=0.001	0.00E+00	1.41E-40	4.68E-03	1.41E-01	2.14E-87	3.39E-44
	p_r=0.005	0.00E+00	2.79E-38	3.05E-03	1.41E-01	1.19E-87	5.19E-43
	p_r=0.01	0.00E+00	7.83E-41	5.13E-03	0.00E+00	6.08E-87	2.28E-43
	p_r=0.05	0.00E+00	5.44E-38	3.74E-03	0.00E+00	1.45E-82	1.32E-42
	p_r=0.1	0.00E+00	3.13E-37	4.40E-03	0.00E+00	5.61E-78	2.01E-39

标准测试函数		f₁	f₂	f₃	f₄	f₅	f₆
平均值	p_r=0	1.21E-01	5.51E-16	8.56E-03	2.32E+01	5.69E-139	9.83E-77
	p_r=0.001	1.29E-01	3.53E-16	8.91E-03	2.33E+01	1.23E-139	1.77E-76
	p_r=0.005	6.85E-02	4.42E-16	5.62E-03	2.35E+01	1.50E-139	1.59E-74
	p_r=0.01	1.95E-01	3.44E-16	7.53E-03	2.26E+01	1.92E-139	8.56E-76
	p_r=0.05	1.21E-01	3.22E-16	8.36E-03	2.48E+01	2.03E-134	2.87E-73
	p_r=0.1	1.48E-01	3.50E-16	8.32E-03	2.24E+01	4.08E-128	3.24E-69
标准差	p_r=0	3.06E-01	6.04E-16	8.35E-03	7.49E+00	2.53E-138	2.32E-76
	p_r=0.001	3.57E-01	4.92E-16	7.72E-03	8.50E+00	6.36E-139	5.89E-76
	p_r=0.005	2.77E-01	4.54E-16	4.58E-03	6.87E+00	7.36E-139	5.57E-74
	p_r=0.01	4.55E-01	4.60E-16	7.96E-03	7.36E+00	8.63E-139	2.92E-75
	p_r=0.05	3.32E-01	3.49E-16	9.12E-03	8.15E+00	1.04E-133	5.20E-73
	p_r=0.1	3.74E-01	4.57E-16	7.08E-03	5.50E+00	1.41E-127	8.02E-69

标准测试函数	BSO		GBSO		GDBSO		MBSO
标准测试函数	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
f₁	2.27E-05	1.18E-05	4.66E-10	1.37E-09	8.88E-16	0.00E+00	8.88E-16	0.00E+00
f₂	2.67E-06	3.59E-06	1.70E-12	9.17E-12	4.19E-39	2.79E-38	3.23E-22	2.24E-21
f₃	1.49E-01	1.65E-01	4.34E-03	2.84E-03	4.88E-03	3.05E-03	5.42E-03	4.45E-03
f₄	9.95E-02	3.23E-01	1.99E-02	1.41E-01	1.99E-02	1.41E-01	0.00E+00	0.00E+00
f₅	1.34E-10	1.25E-10	2.12E-19	8.08E-19	4.23E-88	1.19E-87	1.78E-66	4.30E-66
f₆	1.90E-05	7.41E-06	1.59E-10	4.67E-10	4.00E-43	5.19E-43	9.67E-33	1.15E-32

标准测试函数	BSO		GBSO		GDBSO		MBSO
标准测试函数	平均值	标准差	平均值	标准差	平均值	标准差	平均值	标准差
f₁	1.73E+00	5.77E-01	1.61E-10	7.63E-11	1.28E+00	6.68E-01	9.09E-01	6.15E-01
f₂	5.35E+00	3.00E+00	8.54E-05	3.94E-04	1.87E-15	9.34E-16	2.05E-15	1.25E-15
f₃	6.58E-03	7.57E-03	3.80E-03	2.64E-03	7.87E-03	9.18E-03	3.50E-03	1.80E-03
f₄	8.06E+01	2.20E+01	2.67E+01	5.45E+00	4.66E+01	1.14E+01	1.05E+02	2.96E+01
f₅	2.23E-07	1.94E-07	9.59E-19	1.08E-18	8.64E-125	5.56E-124	1.06E-90	3.45E-90
f₆	6.68E+02	1.03E+02	8.39E-08	3.88E-07	6.29E-74	1.87E-72	5.72E-51	9.21E-51