关键词: 粒子群算法, 收敛性, 进化算法, 数学模型

Abstract:

Particle swarm optimization (PSO) is an intelligence algorithm simulated the social behavior of bird swarm or fish group. It is difficult for original formula of PSO to show mathematical essence and principle. Using the simplified modal of PSO, the current theoretical analysis of PSO has  constructed a mathematic modal that give a clear essence of PSO from mathematic view. Which has  illustrated that the PSO is an iteration evolutionary system. Using the mathematic modal of PSO, this paper develops a new evolutionary algorithm that velocity and location updating equation of PSO are replaced by the mathematic equations. And the some parameters of new algorithm are discussed and selected properly. With selection of appropriate parameters, the performance of new evolutionary algorithm is not inferior to standard PSO by simulation on benchmark functions. The new evolutionary algorithm is easy to understand and has mathematical meaning. Its parameters are fewer and easier to be analyzed than standard PSO.
 

Key words: particle swarm optimization, convergence, evolutionary algorithm, mathematic modal