Stability analysis of particle swarm optimization using swarm activity
群活性与粒子群优化的稳定性分析

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.