[1]HU Chengyu,WU Xiangning,YAN Xuesong.Stability analysis of the particle dynamics in a particle swarm optimization[J].CAAI Transactions on Intelligent Systems,2011,6(5):445-449.
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Stability analysis of the particle dynamics in a particle swarm optimization

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 6 Number of periods: 2011 5 Page number: 445-449 Column: 学术论文—人工智能基础 Public date: 2011-10-30
Title:
Stability analysis of the particle dynamics in a particle swarm optimization
Author(s):
HU Chengyu1; 2;  WU Xiangning1;  YAN Xuesong1
1.School of Computer Science, China University of Geosciences, Wuhan 430074, China;
2.Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Keywords:
particle swarm optimization;  particle dynamics;  stability analysis;  evaluation function;  stochastic process;  timevarying differential system
CLC:
TP301.6
DOI:
-
Abstract:
When investigating the convergence of a particle swarm optimization, the stability of the particle dynamics must be guaranteed first. When analyzing stability of particle dynamics, most studies assume that the particle swarm has only one particle and that the positions of the optimum particle and the locally optimum particle are fixed and invariable. Furthermore, the randomicity of particle movement is omitted. These assumptions ignore the essence of particle movement in a particle swarm optimization. Starting from the evaluation function, this paper proved the existence of the attraction position, taking into consideration the exchangeability among multiple particles. It also analyzed the movement of particles using the stochastic process theory, proving that the position sequence of the optimum particle is continuously approaching the attraction position. Finally, considering the randomicity of particle movement and using the timevarying model, the Lyapunov energy function was constructed and the condition for stability of any particle’s movement in the particle swarm was given.
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