关键词: 微粒群优化算法, 梯度法, 优化效率, 鲁棒性

Abstract: By introducing the gradient method into the particle swarm optimization algorithm（PSO），a new hybrid particle swarm optimization algorithm named GPSO is proposed.In GPSO，the gradient method is applied to each particle to search further for a better position after each evolution of PSO，and then the particle swarm replaced by the better takes part in the evolution of the next generation.The presented hybrid method incorporates the advantages of the excellent global searching of the PSO and the local speedy convergence of the gradient method.Several numerical examples are used to demonstrate the high optimization efficiency and the robustness of the given method for either low-dimensional multimodal functions or high-dimensional multimodal or pathological functions.

Key words: Particle Swarm Optimization（PSO）, gradient method, optimization efficiency, robustness