群活性与粒子群优化的稳定性分析

Stability analysis of particle swarm optimization using swarm activity

在探讨粒子轨迹的随机过程的基础上,用根轨迹特征值的谱半径来描述粒子群优化的PSO动态系统的稳定性区域;提出并结合实例用群活性刻画了PSO稳定区域中不同参数区间上群行为的动态特征,利用不动点技术通过数值实验描绘出PSO群活性谱及性能图,解释了先前一些文献上提出的典型参数集之所以能够取得满意性能的理由,利用PSO稳定三角中线提出保证PSO收敛性能的参数设置指导策略.

In the analysis of particle swarm optimization（PSO）, particle trajectories are considered stochastic processes, and the stability region of the PSO dynamic system is illustrated by the eigenvalues and the spectrum radius. Through practical applications, we propose a new term, swarm activity, to characterize the dynamic behaviors of the swarm with different parameters in the stability region. By applying the fixed-point technique, we depict the swarm activity spectralbased performance maps of the PSO from numerical experiments. These maps account for the typical parameter sets put forth in existing literature for realizing desirable performances, and reconfirm the strategies of using the median of PSO stability triangle in adjusting parameters to ensure the convergence of the PSO.