微粒群算法中粒子运动稳定性分析  

Stability analysis of the particle dynamics in a particle swarm optimization

作　　者：胡成玉[1,2] 吴湘宁[1] 颜雪松[1] 

机构地区：[1]中国地质大学计算机学院,湖北武汉430074 [2]华中科技大学控制科学与工程系,湖北武汉430074

出　　处：《智能系统学报》2011年第5期445-449,共5页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金资助项目(60873107);中央高校基本科研业务费专项资金资助项目(CUGL090236)

摘　　要：在研究微粒群算法是否收敛时,粒子运动稳定是微粒群算法收敛的前提条件,在分析粒子运动稳定性时,大多数文献假定微粒群只有单个粒子,最优粒子位置和局部最优粒子位置固定不动,并且忽略粒子运动的随机性,这些假定忽视了粒子算法中粒子运动的本质.首先从评估函数出发,考虑到粒子间的交换性,给出了吸引位置存在的证明,然后利用随机过程理论对粒子的运动进行分析,证明了最优粒子的位置序列是不断靠近吸引位置,最后考虑粒子运动的随机性,利用时变差分系统理论,构造李亚普诺夫能量函数,得到了微粒群中任意粒子运动稳定的条件.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.

关 键 词：微粒群算法 粒子运动 稳定性分析 评估函数 随机过程 时变差分系统 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]