基于群体划分的冠状病毒群体免疫优化算法

doi:10.16183/j.cnki.jsjtu.2022.470

摘要/Abstract

摘要：

针对冠状病毒群体免疫优化(CHIO)算法收敛速度慢、求解精度低的问题,提出一种基于群体划分的冠状病毒群体免疫优化(SD-CHIO)算法.基于适应度均匀原则将初始群体划分为两部分,即全局寻优个体与局部寻优个体.对于全局寻优个体,在其位置更新中加入差分变异与漫反射变异策略,分别用来增强全局寻优个体之间的交流与群体多样性,从而提高算法的全局搜索能力.对于局部寻优个体,在其位置更新中引入一种自适应快速收敛策略:基于增量法进行精英预测,并加入一种自适应收敛系数使局部寻优个体能快速收敛至精英解,以提升算法的局部搜索能力.数值实验表明:SD-CHIO能够有效提高原算法的收敛速度与精度,并表现出明显优于其他元启发式算法的全局与局部搜索能力以及一定的工程价值.

关键词: 冠状病毒群体免疫优化算法, 群体划分, 自适应快速收敛, 差分变异, 漫反射变异

Abstract:

Aimed at the drawbacks of coronavirus herd immunity optimizer (CHIO), i.e., slow convergence speed and low optimization accuracy, a CHIO based on swarm division (SD-CHIO) is proposed. Based on the principle of uniform fitness, the initial swarm is divided into two parts, i.e., exploration individuals and exploitation individuals. For exploration individuals, differential mutation and diffuse reflection mutation are adopted in position update in order to enhance the communication among exploration individuals and swarm diversity respectively, so as to improve the exploration capability of the algorithm. For exploitation individuals, an adaptive fast convergence strategy is proposed in position update: elite prediction is conducted based on the incremental method, and an adaptive convergence coefficient is employed to ensure that exploitation individuals can quickly converge to the elite solution, which improves the exploitation capability of the algorithm. The numerical experiments demonstrate that SD-CHIO significantly improves the convergence speed and accuracy of the conventional algorithm, exhibiting better exploration and exploitation capabilities than other meta-heuristic algorithms do as well as certain value in engineering.

Key words: coronavirus herd immunity optimizer (CHIO), swarm division, adaptive fast convergence, differential mutation, diffuse reflection mutation

中图分类号:

TP301

李博群, 孙志锋. 基于群体划分的冠状病毒群体免疫优化算法[J]. 上海交通大学学报, 2024, 58(4): 555-564.

LI Boqun, SUN Zhifeng. A Coronavirus Herd Immunity Optimizer Based on Swarm Division[J]. Journal of Shanghai Jiao Tong University, 2024, 58(4): 555-564.

图/表 9

图1

图2

表1

基准测试函数

函数名称	函数表达式	搜索范围
Sphere	F₁(x)= $∑ j = 1 D x j 2$	[-100, 100]
Schwefel P2.21	F₂(x)= $m a x j = 1,2, …, D x j$	[-100, 100]
Schwefel P2.22	F₃(x)= $∑ j = 1 D x j$ + $∏ j = 1 D x j$	[-10, 10]
Noise	F₄(x)= $∑ j = 1 D$ j $x j 4$ +random[0, 1)	[-100, 100]
Rastrigin	F₅(x)= $∑ j = 1 D x j 2 - 10 c o s (2 π x j) + 10$	[-5.12, 5.12]
Griewank	F₆(x)= $14000 ∑ j = 1 D x j 2$ - $∏ j = 1 D$ cos $x j j$ +1	[-600, 600]
Salomon	F₇(x)=-cos(2π $∑ j = 1 D x j 2$ )+0.1 $∑ j = 1 D x j 2$ +1	[-100, 100]
Ackley	F₈(x)=-20exp(-0.2 $1 D ∑ j = 1 D x j 2$ )-exp[ $1 D ∑ j = 1 D$ cos(2πx_j)]+20+e	[-32, 32]
Shifted Griewank	F₉(x)= $14000 ∑ j = 1 D$ (x_j-o_j)²- $∏ j = 1 D$ cos $x j - o j j$ +1	[-600, 600]
Shifted Ackley	F₁₀(x)=-20exp(-0.2 $1 D ∑ j = 1 D (x j - o j) 2$ )-exp[ $1 D ∑ j = 1 D$ cos 2π(x_j-o_j)]+20+e	[-32, 32]
Shifted+Rotated Rastrigin	F₁₁(x)= $∑ j = 1 D z j 2 - 10 c o s (2 π z j) + 10$ , z=M[0.051 2(x-o)]	[-100, 100]
Shifted+Rotated Levy	F₁₂(x)=sin²(πw₁)+ $∑ j = 1 D - 1$ (w_j-1)² $1 + 10 s i n 2 (π w j - 1)$ +(w_D-1)² $1 + s i n 2 (2 π w D)$ , w_j=1+ $z j - 1 4$ , z=M[0.051 2(x-o)]	[-100, 100]

表1

图3

表2

不同元启发式算法的函数测试结果

函数	算法	μ/A	s/A	函数	算法	μ/A	s/A	函数	算法	μ/A	s/A
F₁	PSO	7.90×10^-3	1.15×10^-2	F₅	PSO	5.93×10¹	1.73×10¹	F₉	PSO	2.84×10^-2	2.04×10^-2
	DE	5.93×10^-4	3.42×10^-4		DE	1.54×10²	9.87×10⁰		DE	3.37×10^-2	6.18×10^-2
	ABC	2.43×10¹	1.52×10¹		ABC	2.38×10²	1.25×10¹		ABC	1.20×10⁰	9.48×10^-2
	WOA	1.48×10^-74	6.76×10^-74		WOA	3.79×10^-15	2.08×10^-14		WOA	1.12×10¹	3.58×10⁰
	SSA	2.45×10^-7	7.25×10^-7		SSA	5.16×10¹	1.68×10¹		SSA	1.71×10^-2	1.49×10^-2
	CHIO	1.21×10⁴	3.08×10³		CHIO	1.71×10²	1.75×10¹		CHIO	1.48×10²	3.48×10¹
	ICHIO	5.69×10^-43	1.62×10^-43		ICHIO	2.07×10²	7.68×10¹		ICHIO	1.28×10²	2.35×10¹
	SD-CHIO	0	0		SD-CHIO	0	0		SD-CHIO	3.76×10^-8	2.53×10^-8
F₂	PSO	7.58×10⁰	1.79×10⁰	F₆	PSO	2.49×10^-2	1.78×10^-2	F₁₀	PSO	2.19×10⁰	3.63×10⁰
	DE	9.34×10⁰	1.81×10⁰		DE	3.44×10^-2	6.30×10^-2		DE	5.98×10^-3	1.46×10^-3
	ABC	6.48×10¹	4.07×10⁰		ABC	1.22×10⁰	9.54×10^-2		ABC	4.15×10⁰	3.25×10^-1
	WOA	4.97×10¹	2.52×10¹		WOA	8.37×10^-3	4.59×10^-2		WOA	1.56×10¹	1.27×10⁰
	SSA	1.25×10¹	3.51×10⁰		SSA	1.64×10^-2	1.12×10^-2		SSA	2.71×10⁰	8.22×10^-1
	CHIO	7.37×10¹	3.41×10⁰		CHIO	1.13×10²	3.12×10¹		CHIO	1.73×10¹	7.18×10^-1
	ICHIO	4.25×10^-22	9.60×10^-23		ICHIO	0	0		ICHIO	1.63×10¹	3.05×10^-1
	SD-CHIO	9.51×10^-163	0		SD-CHIO	0	0		SD-CHIO	1.88×10^-5	5.49×10^-6
F₃	PSO	1.39×10⁰	3.45×10⁰	F₇	PSO	9.68×10^-1	1.99×10^-1	F₁₁	PSO	1.62×10¹	2.78×10⁰
	DE	4.89×10^-3	1.53×10^-3		DE	8.74×10^-1	1.03×10^-1		DE	3.72×10¹	2.25×10⁰
	ABC	2.96×10^-1	7.37×10^-2		ABC	3.17×10⁰	4.13×10^-1		ABC	3.66×10¹	5.15×10⁰
	WOA	3.84×10^-51	1.51×10^-50		WOA	1.43×10^-1	6.26×10^-2		WOA	3.14×10¹	2.17×10¹
	SSA	2.08×10⁰	1.49×10⁰		SSA	1.90×10⁰	4.60×10^-1		SSA	1.62×10¹	7.29×10⁰
	CHIO	8.19×10⁴	4.46×10⁵		CHIO	1.84×10¹	1.30×10⁰		CHIO	7.26×10¹	9.96×10⁰
	ICHIO	2.87×10^-22	4.10×10^-23		ICHIO	4.46×10^-1	5.71×10^-2		ICHIO	4.93×10¹	8.15×10⁰
	SD-CHIO	4.26×10^-164	0		SD-CHIO	0	0		SD-CHIO	1.02×10¹	2.81×10⁰
F₄	PSO	4.73×10^-2	1.34×10^-2	F₈	PSO	5.26×10^-1	7.42×10^-1	F₁₂	PSO	2.99×10^-3	1.63×10^-2
	DE	1.60×10^-1	3.11×10^-2		DE	7.47×10^-3	2.10×10^-3		DE	1.39×10^-12	7.12×10^-12
	ABC	3.09×10^-1	8.71×10^-2		ABC	4.17×10⁰	3.96×10^-1		ABC	3.07×10^-5	5.28×10^-5
	WOA	3.14×10^-3	2.68×10^-3		WOA	4.09×10^-15	3.00×10^-15		WOA	1.81×10⁰	1.60×10⁰
	SSA	2.38×10^-1	9.11×10^-2		SSA	2.53×10⁰	8.36×10^-1		SSA	3.77×10^-1	4.89×10^-1
	CHIO	1.36×10²	1.33×10²		CHIO	1.67×10¹	8.05×10^-1		CHIO	2.77×10⁰	6.26×10^-1
	ICHIO	1.65×10^-3	6.31×10^-4		ICHIO	1.13×10^-14	2.94×10^-15		ICHIO	1.36×10⁰	3.81×10^-1
	SD-CHIO	1.51×10^-4	8.50×10^-5		SD-CHIO	8.88×10^-16	0		SD-CHIO	4.90×10^-13	7.87×10^-13

表2

图4

图5

图6

表3

参考文献 19

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算法	μ/A	s/A	F_{pv, min}/A	E_iden/%	I_ph/A	I_sd/μA	A_c	R_s/Ω	R_sh/Ω
PSO	4.27×10^-3	9.19×10^-3	1.55×10^-3	28.77	0.7604	0.5933	1.5455	0.0338	79.7655
DE	1.56×10^-3	1.11×10^-4	1.42×10^-3	23.33	0.7605	0.5466	1.5367	0.0341	73.7699
ABC	2.09×10^-3	2.65×10^-4	1.60×10^-3	27.32	0.7599	0.5812	1.5435	0.0337	77.7783
WOA	3.72×10^-2	2.91×10^-2	1.36×10^-3	9.10	0.7596	0.2638	1.4613	0.0373	66.2019
SSA	3.10×10^-3	3.34×10^-3	1.26×10^-3	19.23	0.7600	0.4574	1.5174	0.0351	79.7338
CHIO	6.21×10^-2	4.14×10^-2	4.63×10^-3	31.37	0.7646	0.5986	1.5466	0.0348	87.1315
ICHIO	7.42×10^-2	5.45×10^-2	9.82×10^-3	32.61	0.7574	0.0267	1.2671	0.0473	67.8832
SD-CHIO	1.27×10^-3	1.09×10^-4	1.03×10^-3	4.33	0.7607	0.3591	1.4924	0.0360	58.3065