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

Abstract

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

CLC Number:

TP18

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.

Figures/Tables 18

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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

Adaptive Golden Eagle Algorithm Based on Symmetric Mapping Search Strategy and its Application

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函数	度量标准	PSO	GWO	WOA	EO	GEO	MERGEO
F₁	AVG	2.54×10^-2	1.27×10^-1	2.54×10^-2	2.54×10^-2	1.84×10^-14	0.00×10⁰
F₁	STD	1.39×10^-1	2.89×10^-1	1.39×10^-1	1.39×10^-1	5.96×10^-14	0.00×10⁰
F₂	AVG	1.75×10^-45	5.50×10^-103	1.10×10^-193	1.41×10^-107	3.35×10^-47	1.28×10^-147
F₂	STD	9.37×10^-45	2.39×10^-102	0.00×10⁰	7.05×10^-107	8.41×10^-47	7.02×10^-147
F₃	AVG	2.18×10^-4	1.13×10^-27	1.58×10^-72	4.34×10^-27	1.51×10^-3	1.24×10^-135
F₃	STD	2.87×10^-4	1.27×10^-27	5.96×10^-72	6.51×10^-27	1.51×10^-3	6.77×10^-135
F₄	AVG	1.42×10⁰	5.69×10^-1	5.51×10^-2	5.80×10^-3	4.76×10^-6	7.98×10^-13
F₄	STD	5.42×10⁰	3.76×10^-1	3.57×10^-2	3.13×10^-2	4.18×10^-6	9.22×10^-13
F₅	AVG	-8.10×10²	-9.10×10²	-9.50×10²	-9.51×10²	-9.57×10²	-9.60×10²
F₅	STD	1.06×10²	5.97×10¹	2.09×10¹	2.25×10¹	1.19×10¹	5.78×10^-13
F₆	AVG	2.37×10^-31	8.04×10^-6	2.35×10^-5	7.89×10^-32	0.00×10⁰	0.00×10⁰
F₆	STD	3.68×10^-31	9.55×10^-6	5.23×10^-5	2.41×10^-31	0.00×10⁰	0.00×10⁰
F₇	AVG	2.76×10^-2	5.14×10^-2	3.03×10^-2	3.33×10^-6	6.35×10^-1	2.56×10^-10
F₇	STD	5.40×10^-2	2.69×10^-2	3.00×10^-2	7.18×10^-7	5.29×10^-1	3.22×10^-10
F₈	AVG	4.87×10^-3	6.65×10^-1	5.87×10^-1	1.97×10^-2	1.17×10^-2	3.97×10^-3
F₈	STD	1.06×10^-2	2.73×10^-1	3.07×10^-1	3.84×10^-2	1.23×10^-2	6.58×10^-3
F₉	AVG	1.07×10²	2.76×10⁰	0.00×10⁰	3.97×10⁰	1.94×10¹	0.00×10⁰
F₉	STD	3.17×10¹	3.20×10⁰	0.00×10⁰	3.18×10⁰	6.98×10⁰	0.00×10⁰
F₁₀	AVG	4.27×10^-1	1.80×10^-1	1.17×10^-1	1.97×10^-1	7.06×10^-1	5.02×10^-51
F₁₀	STD	7.85×10^-2	4.07×10^-2	6.99×10^-2	3.20×10^-2	1.06×10^-1	2.56×10^-50

参数	设定值
种群数目	30
迭代次数	100
区域面积S	50 m×50 m
节点个数	40
感知半径R_s	5 m
通信半径R_c	10 m

算法	T_s(x₁)	T_h(x₂)	R(x₃)	L(x₄)	最优成本
MERGEO	0.790 1	0.390 5	40.935 7	191.702 50	5 908.291 8
GEO	0.901 5	0.446 7	46.654 0	127.862 60	6 157.045 1
WOA	0.812 5	0.437 5	42.089 3	176.639 00	6 059.741 0
GWO	0.812 5	0.437 5	42.089 2	176.758 70	6 051.563 9
GSA	1.125 0	0.625 0	55.988 7	84.454 20	8 538.835 9
PSO	0.812 5	0.4375	42.089 2	176.746 50	6 061.077 7
HHO	0.851 2	0.422 4	44.088 7	153.545 60	6 032.674 6
RSA	0.840 1	0.419 0	43.381 2	161.555 60	6 034.759 1
RFO	0.814 2	0.445 2	42.202 3	176.621 45	6 113.319 5

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