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

Abstract

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

CLC Number:

TP301.6

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

Figures/Tables 16

Fig.1

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Fig.2

Fig.3

Fig.4

Fig.5

Table 8

Fig.6

Table 9

Table 10

References 27

1	申海. 集群智能及其应用[M]. 北京: 科学出版社, 2019: 41- 43.
	SHEN H . Swarm intelligence and its application[M]. Beijing: Science Press, 2019: 41- 43.
2	SHI Y H. Brain storm optimization algorithm[C]//Proc. of the 2nd International Conference on Swarm Intelligence, 2011: 303-309.
3	SUN C H , DUAN H B , SHI Y H . Optimal satellite formation reconfiguration based on closed-loop brain storm optimization[J]. IEEE Computational Intelligence Magazine, 2013, 8 (4): 39- 51. doi: 10.1109/MCI.2013.2279560
4	DUAN H B , LI S T , SHI Y H . Predator-prey brain storm optimization for DC brushless motor[J]. IEEE Trans.on Magnetics, 2013, 49 (10): 5336- 5340. doi: 10.1109/TMAG.2013.2262296
5	CHEN J F, CHENG S, CHEN Y, et al. Enhanced brain storm optimization algorithm for wireless sensor networks deployment[C]// Proc. of the 6th International Conference on Swarm Intelligence, 2015: 373-381.
6	陈山, 宋樱, 房胜男. 基于头脑风暴优化算法的Wiener模型参数辨识[J]. 控制与决策, 2017, 32 (12): 2291- 2295.
	CHEN S , SONG Y , FANG S N . Parameter identification of Wiener systems using brain storm optimization algorithm[J]. Control and Decision, 2017, 32 (12): 2291- 2295.
7	梁志刚, 顾军华. 改进头脑风暴优化算法与Powell算法结合的医学图像配准[J]. 计算机应用, 2018, 38 (9): 2683- 2688.
	LIANG Z G , GU J H . Medical image registration by integrating modified brain storm optimization algorithm and Powell algorithm[J]. Journal of Computer Applications, 2018, 38 (9): 2683- 2688.
8	李怡敏, 王宝珠, 刘翠响. DBBSO算法在低空航线规划中的应用[J]. 现代电子技术, 2019, 42 (22): 108- 112.
	LI Y M , WANG B Z , LIU C X . Application of DBBSO algorithm in low-altitude air route planning[J]. Modern Electronics Technique, 2019, 42 (22): 108- 112.
9	CAO Z J, WANG L. An active learning brain storm optimization algorithm with a dynamically changing cluster cycle for global optimization[EB-OL]. [2021-01-13]. https://doi.org/10-1007/s10586-019-02918-0.
10	SHI Y H. Brain storm optimization algorithm in objective space[C]// Proc. of the IEEE Congress on Evolutionary Computation, 2015: 1227-1234.
11	CHENG S , QIN Q D , CHEN J F , et al. Brain storm optimization algorithm: a review[J]. Artificial Intelligence Review, 2016, 46 (4): 445- 458. doi: 10.1007/s10462-016-9471-0
12	LIU J N, PENG H, WU Z J, et al. Multi-strategy brain storm optimization algorithm with dynamic parameters adjustment[EB-OL]. [2021-01-13]. https://doi.org/10.1007/s10489-019-016007-0.
13	YANG Y T , SHI Y H , XIA S R . Advanced discussion mechanism-based brain storm optimization algorithm[J]. Soft Computing, 2015, 19 (10): 2997- 3007. doi: 10.1007/s00500-014-1463-x
14	DAI C , LEI X J . A multi-objective brain storm optimization algorithm based on decomposition[J]. Complexity, 2019, 2019, 5301284.
15	GUO Y N , YANG H C , CHEN M R , et al. Grid-based dynamic robust multi-objective brain storm optimization algorithm[J]. Soft Computing, 2020, 24 (10): 7395- 7475. doi: 10.1007/s00500-019-04365-w
16	PENG H , DENG C S , WU Z J . SPBSO: self-adaptive brain storm optimization algorithm with pbest guided step-size[J]. Journal of Intelligent and Fuzzy Systems, 2019, 36 (6): 5423- 5434. doi: 10.3233/JIFS-181310
17	ZHAN Z H, ZHANG J, SHI Y H, et al. A modified brain storm optimization[C]//Proc. of the IEEE Congress on Evolutionary Computation, 2012: 1969-1976.
18	ZHU H Y, SHI Y H. Brain storm optimization algorithms with k-medians clustering algorithms[C]//Proc. of the IEEE 7th International Conference on Advanced Computational Intelligence, 2015: 107-110.
19	EL-ABD M . Global-best brain storm optimization algorithm[J]. Swarm and Evolutionary Computation, 2017, 37, 27- 44. doi: 10.1016/j.swevo.2017.05.001
20	ZHU G P , KWONG S . Gbest-guided artificial bee colony algorithm for numerical function optimization[J]. Applied Mathematics and Computation, 2010, 217, 3166- 3173. doi: 10.1016/j.amc.2010.08.049
21	EL-ABD M . An improved global-best harmony search algorithm[J]. Applied Mathematics and Computation, 2013, 222, 94- 106. doi: 10.1016/j.amc.2013.07.020
22	XIANG W L , AN M Q , LI Y Z , et al. An improved global-best harmony search algorithm for faster optimization[J]. Expert Systems with Applications, 2014, 41 (13): 5788- 5803. doi: 10.1016/j.eswa.2014.03.016
23	DI L, ZHENG Z, XIA M, et al. Robot path planning based on an improved multi-objective PSO method[C]//Proc. of the 1st International Conference on Computer Engineering, Information Science & Application Technology, 2016: 496-501.
24	冯炜, 张静远, 王众, 等. 海洋环境下基于量子行为粒子群优化的时间最短路径规划方法[J]. 海军工程大学学报, 2017, 29 (6): 72- 77.
	FENG W , ZHANG J Y , WANG Z , et al. A time-optimal path planning method based on quantum-behaved particle swarm optimization in ocean environment[J]. Journal of Naval University of Engineering, 2017, 29 (6): 72- 77.
25	张岳星, 王轶群, 李硕, 等. 基于海图和改进粒子群优化算法的AUV全局路径规划[J]. 机器人, 2020, 42 (1): 120- 128.
	ZHANG Y X , WANG Y Q , LI S , et al. Global path planning for AUV based on charts and the improved particle swarm optimization algorithm[J]. Robot, 2020, 42 (1): 120- 128.
26	赵苗, 高永琪, 吴笛霄, 等. 复杂海战场环境下AUV全局路径规划方法研究[J]. 国防科技大学学报, 2021, 43 (1): 41- 48.
	ZHAO M , GAO Y Q , WU D X , et al. Research on AUV global path planning method in complex sea battle field environment[J]. Journal of National University of Defense Technology, 2021, 43 (1): 41- 48.
27	BASAK A, PAL S, DAS S, et al. Circular antenna array synthesis with a differential invasive weed optimization algorithm[C]// Proc. of the IEEE 10th International Conference on Hybrid Intelligent Systems, 2010: 153-158.

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

Global-best difference-mutation brain storm optimization algorithm

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 16

References 27

Related Articles 15

Recommended Articles

Metrics

Comments

算法	航行时间/s	侦查时间/s	杀伤时间/s	路径长度/m
BSO	62.373	0	0	628.071
GBSO	60.054	0	0	642.059
GDBSO	60.051	0	0	649.071
MBSO	60.488	0	0	647.989
振荡型IWO	63.050	0	0	645.469

算法	最优值	最差值	平均值	标准差
BSO	62.373	83.2123	71.509	5.401
GBSO	60.054	307.160	67.426	34.784
GDBSO	60.051	176.494	69.517	16.192
MBSO	60.488	199.142	70.974	19.119
振荡型IWO	63.050	81.994	69.781	3.982

[1]	Haobo FENG, Qiao HU, Zhenyi ZHAO. AUV swarm path planning based on elite family genetic algorithm [J]. Systems Engineering and Electronics, 2022, 44(7): 2251-2262.
[2]	Yongqi GAO, Weiqiang MA, Linsen ZHANG, Peng WANG, Miao ZHAO. Distributed multi-AUVs cooperative search method [J]. Systems Engineering and Electronics, 2022, 44(5): 1670-1676.
[3]	Dou CHEN, Xiuyun MENG. UAV offline path planning based on self-adaptive coyote optimization algorithm [J]. Systems Engineering and Electronics, 2022, 44(2): 603-611.
[4]	Yang YIN, Quanshun YANG, Zheng WANG, Yang LIU. USV cluster coverage search method with communication distance constraint [J]. Systems Engineering and Electronics, 2022, 44(12): 3821-3828.
[5]	Qingqing YANG, Yingying GAO, Yu GUO, Boyuan XIA, Kewei YANG. Target search path planning for naval battle field based on deep reinforcement learning [J]. Systems Engineering and Electronics, 2022, 44(11): 3486-3495.
[6]	Tong HAN, Andi TANG, Huan ZHOU, Dengwu XU, Lei XIE. Multiple UAV cooperative path planning based on LASSA method [J]. Systems Engineering and Electronics, 2022, 44(1): 233-241.
[7]	Lei LAI, Kun ZOU, Dewei WU, Baozhong LI. Multi-UAV cooperative path planning based on improved MOFA evolution of interactive strategy [J]. Systems Engineering and Electronics, 2021, 43(8): 2282-2289.
[8]	Zhiqiang JIAO, Jieyong ZHANG, Peiyang YAO, Xun WANG, Yichao HE. Distributed evolution method of C4ISR service deployment based on hierarchical structure [J]. Systems Engineering and Electronics, 2021, 43(6): 1572-1585.
[9]	Shiwei FAN, Ya ZHANG, Qiang HAO, Pan JIANG, Fei YU. Cooperative positioning and error estimation algorithm based on factor graph [J]. Systems Engineering and Electronics, 2021, 43(2): 499-507.
[10]	Wenming WANG, Jialu DU. Agent path planning based on regular hexagon grid JPS algorithm [J]. Systems Engineering and Electronics, 2021, 43(12): 3635-3642.
[11]	Yanan LI, Haibin HUANG, Liangming CHEN, Yufei ZHUANG, Xiaoli WANG. Energy-optimal three-dimensional path planning for AUV under changing ocean current environment [J]. Systems Engineering and Electronics, 2021, 43(12): 3667-3674.
[12]	Wengang LI, Liujiang WANG, Dexiang FANG, Yuwei LI, Jun Huang. Path planning algorithm combining A^* with DWA [J]. Systems Engineering and Electronics, 2021, 43(12): 3694-3702.
[13]	Yao HAN, Shaohua LI. UAV path planning based on improved artificial potential field [J]. Systems Engineering and Electronics, 2021, 43(11): 3305-3311.
[14]	Daidai CHEN, Wanyou LI. Local path planning algorithm for USV with towed cable [J]. Systems Engineering and Electronics, 2020, 42(9): 1988-1994.
[15]	Quanxian ZHANG, Bin ZENG, Houpu LI. Underway replenishment path planning method for distributed naval warfare under the influence of sea conditions [J]. Systems Engineering and Electronics, 2020, 42(10): 2312-2319.

标准测试函数	BSO		GBSO		GDBSO		MBSO
标准测试函数	平均迭代次数	成功率/%	平均迭代次数	成功率/%	平均迭代次数	成功率/%	平均迭代次数	成功率/%
f₁	-	-	290	92	73	100	89	100
f₂	-	-	285	100	95	100	128	100
f₃	20	4	233	96	125	94	122	88
f₄	108	98	95	98	53	100	55	100
f₅	278	100	275	100	41	100	50	100
f₆	-	-	290	98	80	100	96	100

标准测试函数	BSO		GBSO		GDBSO		MBSO
标准测试函数	平均迭代次数	成功率/%	平均迭代次数	成功率/%	平均迭代次数	成功率/%	平均迭代次数	成功率/%
f₁	1 935	60	2 879	96	520	96	648	98
f₂	-	-	2 868	76	525	100	671	100
f₃	960	72	2 576	90	183	90	106	96
f₄	-	-	-	-	-	-	-	-
f₅	1 733	100	2 798	100	330	100	408	100
f₆	-	-	2 896	2	598	100	765	100