自适应杂交退火粒子群优化算法

doi:10.12305/j.issn.1001-506X.2022.11.22

摘要/Abstract

摘要：

为解决粒子群优化(particle swarm optimization, PSO)算法易早熟、后期收敛慢、收敛精度低等问题, 提出一种自适应杂交退火PSO算法。采用Sigmoid函数控制惯性权重, 平衡粒子的全局搜索和局部搜索能力; 采用双曲正切函数控制加速系数, 平衡粒子的自我认知和社会认知能力, 提高算法精度; 引入模拟退火算子, 使粒子在搜索过程中以一定概率接受差解, 增加粒子跳出局部最优的能力; 在算法后期引入杂交变异算子, 增加种群多样性, 进一步提高算法精度。基于3种标准测试函数对所提算法的性能进行了验证, 并与现有典型PSO算法进行了对比。结果表明, 所提算法在收敛精度及收敛速度上均具有一定提升。最后, 将所提算法应用于阵列天线方向图综合设计, 取得了较现有算法更优的结果。

关键词: 自适应粒子群优化, 模拟退火, 杂交变异, 方向图综合

Abstract:

To avoid premature convergence and improve its speed and accuracy of the particle swarm optimization (PSO) algorithm, an adaptive hybrid annealing PSO algorithm is proposed. A Sigmoid function is used to control the inertia weight to balance its global and local optimization capability. A hyperbolic tangent function is applied to control the acceleration coefficients to balance the self and social cognition capability of the proposed algorithm to improve its accuracy. A simulated annealing operator is used to ensure the capability of the proposed algorithm to jump out from the local optimal solution. At the last stage of the algorithm, a hybrid variation operator is used to increase its population diversity, hence further improving its accuracy. The performance of the proposed algorithm is verified based on three standard test functions and compared with typical PSO algorithms. The results show that the proposed algorithm has a great improvement in accuracy and convergence speed. Finally, the proposed algorithm is applied to array pattern synthesis, showing a better performance than existing algorithms.

Key words: adaptive particle swarm optimization (PSO), simulated annealing, hybrid variation, array pattern synthesis

中图分类号:

TP301.6

路复宇, 童宁宁, 冯为可, 万鹏程. 自适应杂交退火粒子群优化算法[J]. 系统工程与电子技术, 2022, 44(11): 3470-3476.

Fuyu LU, Ningning TONG, Weike FENG, Pengcheng WAN. Adaptive hybrid annealing particle swarm optimization algorithm[J]. Systems Engineering and Electronics, 2022, 44(11): 3470-3476.

图/表 8

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函数名	表达式	x_max	v_max
Rosenbrock	$f_1=\sum\limits_{i=1}^{D-1}\left(100\left(x_i^2-x_{i+1}\right)^2+\left(x_i-1\right)^2\right)$	2.048	0.204 8
Levy	$\begin{aligned} f_2=& \sin ^2\left(\pi w_1\right)+\sum\limits_{i=1}^{D-1}\left(w_i-1\right)^2\left[1+10 \sin ^2\left(\pi w_i+1\right)\right]+\\ &\left(w_D-1\right)^2\left[1+\sin ^2\left(2 \pi w_D\right)\right]\left(w_i=1+\frac{x_i-1}{4}\right) \end{aligned}$	10	1
Schwefel	$f_3=418.9829 D-\sum\limits_{i=1}^D x_i \sin \left(\sqrt{\mid x_i}\right)$	500	50

函数	维度	Criterion	PSO	ASAPAO	AHAPSO
f₁	D=10	avg	2.347 7	5.06E-2	2.34E-22
	D=10	min	3.907 2E-11	2.109 7E-11	1.499 8E-31
	D=30	avg	11.414 6	2.055 3	0.064 3
	D=30	min	0.029 1	0.009 1	4.499 3E-31
f₂	D=10	avg	0.253 9	4.8E-3	7.15E-32
	D=10	min	1.32E-7	5.01E-8	0
	D=30	avg	33.85	14.84	0.047 3
	D=30	min	24.17	1.563 3	0
f₃	D=10	avg	1.25E03	1.07E03	1.03E02
	D=10	min	2.287 3E-4	1.42E-4	1.27E-4
	D=30	avg	6.72E03	4.36E03	1.95E03
	D=30	min	2.91E03	1.22E03	3.81E-4

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