关键词: 粒子群算法，交叉操作，收敛模型，自适应，单峰和多峰函数优化，约束优化

Abstract: Particle swarm optimization (PSO) has obvious shortcoming such as local convergence, whose performance of solving constrained optimization problems needs to be improved especially in aspect of convergence speed and optimum value. In this paper, penalty mechanism based self-adaptive crossover PSO was put forward to solve the above two problems by three levels. Aiming at the local convergence problem, crossover operation was brought into PSO. Population diversity model was used to maintain population diversity to achieve global optimum solution. Penalty mechanism based self-adaptive crossover PSO was put forward which improves H strategy and simplifies P strategy. The brought algorithm has better performance without obvious algorithm complexity increasing. According to velocity variety of particles during evolution, particle moving law and the impact of parameters were analyzed. A general calculating formula was put forward to control parameters for optimizing which extends application areas for PSO.

Key words: Particle swarm optimization, Crossover, Convergence model, Self-adaptive, Unimodal and multi-modal function optimizations, Constrained optimization