一种改进的引力搜索算法及其波束赋形

doi:10.19665/j.issn1001-2400.2020.02.012

摘要/Abstract

摘要：

针对引力搜索算法初始值的随机性对算法性能以及收敛速度带来的不利影响,提出了一种改进算法——伪反向学习引力搜索算法。首先将伪反向学习机制用于算法中,并且把算法的迭代次数分为多个学习周期,根据过往学习周期中反向学习的成功率来调整反向概率, 设计了一种可调反向概率,用以优化反向机制在算法演化过程中的作用时机,提高了算法的收敛速度;其次为改善反向学习操作频繁对种群多样性带来的削弱,定义了“精英粒子”,用其替换掉种群中适应度值较差的个体,提高了算法的优化精度。与已有文献中的算法相比,改进算法对单峰及多峰测试函数的平均最优值优化精度可提高10 ¹⁶;对不同类型波束的赋形结果中,改进算法对方向图旁瓣的优化精度可提高1.26dB至5.99dB; 在收敛速度最快的前提下,很大程度避免了其他几种优化算法易陷入局部最优的问题,整体性能最佳。

关键词: 引力搜索算法, 波束赋形, 反向机制, 可调反向概率, 精英粒子

Abstract:

In view of the adverse effect of the random initial value on the performance and convergence speed of the gravitation search algorithm, a quasi-oppositional gravity search algorithm (QOGSA) is proposed. The quasi-oppositional based learning OBL is embedded into the GSA algorithm, the number of iteration is divided into multiple learning cycle, the oppositional probability is adjusted according to the success rate of the past learning cycle, and an adjustable oppositional probability is designed to optimize the timing of the mechanism in the evolution, which improves the speed of the algorithm to search for the optimal solution greatly. On this basis, in order to improve the population diversity, elite particles are retained to the next generation population. They replace the particles with a poor fitness value and acquire a higher optimization accuracy. Compared with the existing algorithms in the literature, the optimization accuracy of the QOGSA for the average optimal value of the single-peak and multi-peak test functions can be improved by 1016. For the shaping results of different types of beam, the optimization accuracy of the improved algorithm for the sidelobe can be improved from 1.26dB to 5.99dB. On the premise of the fastest convergence speed, the QOGSA can greatly avoid the problem that other optimization algorithms tend to fall into local optimization, with the overall performance being the best.

Key words: gravitational search algorithm, shaped beam synthesis, opposition-based learning, adjustable oppositional probability, elite particles

中图分类号:

TN821+.91

孙翠珍,丁君,郭陈江. 一种改进的引力搜索算法及其波束赋形[J]. 西安电子科技大学学报, 2020, 47(2): 83-90.

SUN Cuizhen,DING Jun,GUO Chenjiang. Improved gravitational search algorithm for shaped beam forming[J]. Journal of Xidian University, 2020, 47(2): 83-90.

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参考文献 13

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函数	优化结果	理论值	IGSA	QOGSA
F₁	平均最优值	0	4.03×10^-5	6.23×10^-10
F₁	最优值中位数	0	4.07×10^-5	7.16×10^-10
F₂	平均最优值	0	0.16×10³	7.69×10^-13
F₂	最优值中位数	0	0.15×10³	3.46×10^-13
F₃	平均最优值	0	0.29	0.00916
F₃	最优值中位数	0	0.04	0.00978
F₄	平均最优值	0	0.03	4.06×10^-16
F₄	最优值中位数	0	3.7×10^-13	2.18×10^-16
F₅	平均最优值	1	3.70	0.9896
F₅	最优值中位数	1	2.07	0.9997

参数	期望值	粒子群算法	引力搜索算法	飞蛾扑火算法	IGSA	QOGSA
峰值旁瓣电平值/dB	<-25.00	-21.03	-22.38	-22.57	-24.31	-25.57
主瓣抖动/dB	1.0000	0.8351	0.7647	0.7682	0.7584	0.7315
零功率主瓣角度范围	85°~130°	84.2°~132.4°	83.8°~131.8°	84.2°~132.4°	84.2°~132.4°	83.8°~131°
零功率主瓣展宽/(°)	0.0	3.2	3.0	3.2	3.2	3.2

参数	期望值	粒子群算法	引力搜索算法	飞蛾扑火算法	IGSA	QOGSA
零功率主瓣展宽/(°)	0.5	0.6	0.6	0.6	0.6	0.6
峰值旁瓣电平值1/dB	<-30	-28.13	-29.67	-29.93	-31.35	-34.07
峰值旁瓣电平值2/dB	<-40	-37.65	-39.42	-39.87	-42.16	-43.64