粒子群优化算法模型分析

Model Analysis of Particle Swarm Optimizer

粒子群优化算法在优化问题中体现出良好的性能,但目前还没有对其运动特性,尤其是参数的选择与当粒子群体陷入局部极值点导致的早熟收敛情况的详细分析．分析了PSO算法中的三种粒子模型(Gbest,Pbest,Commom模型)的运动特性,给出了Gbest模型和Pbest 模型在没有新息获取时,单信息条件下的最大搜索空间．进一步证明了在减少了Lipschitz条件约束的条件下,Common模型渐进稳定的充分条件,将算法中惯量因子的取值范围扩大到 (-1,1),并从物理上进行了解释．

Particle swarm optimizer （PSO） exhibits good performance for optimization problems. However, there is little analysis about the kinetic characteristic, parameter selection and the situation where algorithem falls into stagnate to cause premature convergence. In the paper, the kinetic characteristic of three models of PSO （Gbest, Pbest, Common model） are analyzed. The largest covering space （LCS） of the Gbest model and the Pbest model are deduced without new information. Furthermore, under the condition that the Lipschitz constraint is reduced, the sufficient conditions for asymptotic stability of parameters are proved. And the inertia weight w value is enhanced to （-1, 1）.