基于可达状态集扩张的粒子群算法收敛性改进

Convergence improvement of particle swarm optimization based on the expanding attaining-state set

针对粒子群算法(PSO)改进设计缺乏数学模型和理论依据支持的问题,研究建立了PSO的吸收态马尔可夫过程模型,并提出了可达状态集作为收敛性分析的关键指标.与以往的收敛性分析不同,研究从可达状态集扩张的角度提出了PSO收敛性对比的理论,并基于此提出了PSO全局收敛性改进的方法.最后,以改进综合学习粒子群算法CLPSO(comprehensive learning particle swarm optimization)为例验证了提出模型与理论的有效性.

Particle swarm optimization .（PSO） is lack of theoretical foundation support for design and improvement. This paper builds up an absorbing Markov process model of PSO, and proposed the attaining-state set as the key factor of convergence analysis. Differently from the prior research, the proposed theoretical results focus on the convergence comparison among the considered PSOs. Later, a convergence improvement method is put forward by the theorem of expanding attaining-state set. Finally, comprehensive learning PSO （CLPSO） is taken as case study and improved to be CLPSO by the proposed theorem. The numerical result proves the presented model and theorem to be valid.