基于对称映射搜索策略的自适应金鹰算法及应用

doi:10.16180/j.cnki.issn1007-7820.2024.08.002

摘要/Abstract

摘要：

金鹰优化算法(Golden Eagle Optimizer,GEO)是一种基于种群的元启发式算法,其模拟了金鹰的合作狩猎行为。针对GEO算法中存在的求解精度差和陷入局部最优等问题,文中提出了一种改进MERGEO(Mapped Elitist Reverse GEO)算法。在原算法基础上采用对称映射搜索策略、自适应精英策略和随机反向学习机制这3种方法平衡了算法的探索和开发阶段,获得了规避局部最优能力和较好的优化精度。在10个基准测试函数上对该算法进行独立策略有效性分析、可扩展性分析以及同其他算法的优化性能比较分析。实验结果表明,改进后的MERGEO算法具有较强的竞争力和良好的优化能力。将改进后的算法用于无线传感器网络的覆盖优化问题和压力容器设计问题研究,验证了其实际应用价值。

关键词: 金鹰优化算法, 元启发式算法, 对称映射搜索策略, 自适应精英策略, 随机反向学习, 可扩展性分析, 无线传感器网络的覆盖优化, 压力容器设计

Abstract:

The GEO(Golden Eagle Optimizer) is a population-based meta-heuristic algorithm that simulates the cooperative hunting behavior of golden eagles. In view of the problem of poor solution accuracy and local optima traps in the GEO algorithm, this study proposes an improved MERGEO (Mapped Elitist Reverse GEO) algorithm. Based on the original algorithm, symmetric mapping search strategy, adaptive elite strategy and random backward learning mechanism, are used to balance the exploration and development stages of the algorithm, and obtain the ability to avoid local optimal and better optimization accuracy. The independent strategy effectiveness analysis, scalability analysis and optimization performance comparison with other algorithms are carried out on 10 benchmark test functions. The experimental results show that the improved MERGEO algorithm has strong competitiveness and good optimization ability. The improved algorithm is applied to the coverage optimization problem of wireless sensor networks and pressure vessel design problem, which verifies the practical application value of improved algorithm.

Key words: golden eagle optimization algorithm, meta-heuristic algorithm, symmetric mapping search strategy, adaptive elite strategy, stochastic reverse learning, scalability analysis, coverage optimization of wireless sensor network, pressure vessel design

中图分类号:

TP18

周徐虎, 李世港, 罗仪, 张伟. 基于对称映射搜索策略的自适应金鹰算法及应用[J]. 电子科技, 2024, 37(8): 8-16.

ZHOU Xuhu, LI Shigang, LUO Yi, ZHANG Wei. Adaptive Golden Eagle Algorithm Based on Symmetric Mapping Search Strategy and its Application[J]. Electronic Science and Technology, 2024, 37(8): 8-16.

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函数	名称	维度	范围
F₁	Beale	2	[-4.50,4.50]^D
F₂	Matyas	2	[-10.00,10.00]^D
F₃	Sphere	30	[-100.00,100.00]^D
F₄	Step	30	[-5.12,5.12]^D

函数	名称	维度	范围	最优值
F₅	Egg holder	2	[-512.00,512.00]^D	-959.640 7
F₆	Himmelblau	2	[-5.00,5.00]^D	0
F₇	Penalized 1	30	[-50.00,50.00]^D	0
F₈	Penalized 2	30	[-50.00,50.00]^D	0
F₉	Rastrigin	30	[-5.12,5.12]^D	0
F₁₀	Salomon	30	[-100.00,100.00]^D	0

算法	参数
PSO	c₁=2,c₂=2,w=[0.9,0.2]
GWO	a=[2,0]
WOA	a₁=[2,0],a₂=[-2,-1],b=1
EO	a₁=2,a₂=1,GP=0.5

函数	度量标准	GEO	MGEO	EGEO	RGEO	MERGEO
F₁	AVG	1.84×10^-14	6.00×10^-15	1.46×10^-32	0.00×10⁰	0.00×10⁰
F₁	STD	5.96×10^-14	3.28×10^-14	6.42×10^-32	0.00×10⁰	0.00×10⁰
F₂	AVG	3.35×10^-47	1.88×10^-50	1.19×10^-112	5.25×10^-71	1.28×10^-147
F₂	STD	8.41×10^-47	5.50×10^-50	3.69×10^-112	1.70×10^-70	7.02×10^-147
F₃	AVG	1.51×10^-3	1.52×10^-27	2.23×10^-7	2.87×10^-7	1.24×10^-135
F₃	STD	1.25×10^-3	6.89×10^-27	1.71×10^-7	2.05×10^-7	6.77×10^-135
F₄	AVG	4.76×10^-6	3.05×10^-6	1.52×10^-9	7.82×10^-10	7.98×10^-13
F₄	STD	4.18×10^-6	2.69×10^-6	1.87×10^-9	4.97×10^-10	9.22×10^-13
F₅	AVG	-9.57×10²	-9.59×10²	-9.57×10²	-9.60×10²	-9.60×10²
F₅	STD	1.19×10¹	2.17×10⁰	1.19×10¹	5.78×10^-13	5.78×10^-13
F₆	AVG	0.00×10⁰	0.00×10⁰	0.00×10⁰	0.00×10⁰	0.00×10⁰
F₆	STD	0.00×10⁰	0.00×10⁰	0.00×10⁰	0.00×10⁰	0.00×10⁰
F₇	AVG	6.35×10^-1	1.18×10^-4	4.49×10^-1	2.08×10^-2	2.56×10^-10
F₇	STD	5.29×10^-1	2.25×10^-4	4.95×10^-1	5.03×10^-2	3.22×10^-10
F₈	AVG	1.17×10^-2	6.54×10^-3	4.17×10^-2	4.40×10^-3	3.97×10^-3
F₈	STD	1.23×10^-2	6.82×10^-3	6.38×10^-2	5.48×10^-3	6.58×10^-3
F₉	AVG	1.94×10¹	3.55×10^-16	2.24×10¹	2.37×10¹	0.00×10⁰
F₉	STD	6.98×10⁰	1.95×10^-15	1.01×10⁰	8.49×10⁰	0.00×10⁰
F₁₀	AVG	7.06×10^-1	1.22×10^-1	1.24×10⁰	4.20×10^-1	5.02×10^-51
F₁₀	STD	1.06×10^-1	9.96×10^-2	2.31×10^-1	9.97×10^-2	2.56×10^-50

函数	度量标准	30		100		500		1 000
函数	度量标准	GEO	MERGEO	GEO	MERGEO	GEO	MERGEO	GEO	MERGEO
F₃	AVG	1.51×10^-3	1.24×10^-135	2.39×10²	1.35×10^-131	3.86×10⁴	2.77×10^-130	1.19×10⁵	1.38×10^-128
F₃	STD	1.25×10^-3	6.77×10^-135	6.95×10¹	7.42×10^-131	2.82×10³	1.52×10^-129	7.71×10³	7.03×10^-128
F₄	AVG	4.76×10^-6	7.98×10^-13	8.65×10^-1	5.57×10^-3	1.52×10²	2.71×10¹	4.75×10²	1.19×10²
F₄	STD	4.18×10^-6	9.22×10^-13	1.97×10^-1	1.91×10^-3	9.77×10⁰	1.45×10⁰	1.58×10¹	3.24×10⁰
F₇	AVG	6.35×10^-1	2.56×10^-10	5.99×10⁰	4.61×10^-4	4.07×10²	1.31×10^-1	9.77×10⁴	3.51×10^-1
F₇	STD	5.29×10^-1	3.22×10^-10	1.06×10⁰	2.07×10^-4	7.83×10²	1.59×10^-2	6.13×10⁴	2.25×10^-2
F₈	AVG	1.17×10^-2	3.97×10^-3	1.69×10²	1.62×10⁰	1.46×10⁶	4.86×10¹	1.51×10⁷	9.89×10¹
F₈	STD	1.23×10^-2	6.58×10^-3	2.89×10¹	1.97×10⁰	4.50×10⁵	9.31×10^-1	2.94×10⁶	6.61×10^-1
F₉	AVG	1.94×10¹	0.00×10⁰	1.26×10²	0.00×10⁰	2.55×10³	0.00×10⁰	6.62×10³	0.00×10⁰
F₉	STD	6.98×10⁰	0.00×10⁰	2.48×10¹	0.00×10⁰	7.30×10¹	0.00×10⁰	1.75×10²	0.00×10⁰
F₁₀	AVG	7.06×10^-1	5.02×10^-51	5.61×10⁰	3.77×10^-33	2.58×10¹	6.41×10^-19	4.04×10¹	1.09×10^-30
F₁₀	STD	1.06×10^-1	2.56×10^-50	5.23×10^-1	2.05×10^-32	7.80×10^-1	3.51×10^-18	1.29×10⁰	5.72×10^-30