Abstract: The Standard Particle Swarm Optimizer（SPSO） may lead to premature convergence when optimizing complex optimization problems.A Hybrid Three Sub-Swarm Particle Swarm Optimizer（HTSPSO） is presented to improve the performance of PSO.The swarm is divided into three sub-swarms and the sub-swarms work cooperatively to preserve the diversity of the swarm in the late stage of iterations.Experiments are conducted on four benchmark problems.The results demonstrate significant improvement in performance over the traditional PSOs.Furthermore，the PSO method is applied to solve a class of min-max-min problems and the numerical examples are proposed.

Key words: Particle Swarm Optimizer（PSO）, three sub-swarm, min-max-min problem

摘要： 针对标准粒子群算法求解复杂优化问题时容易出现过早收敛的问题，提出了混合三群协同粒子群算法（HTSPSO），将粒子群分为3个协同优化的子群，保持迭代后期粒子群的多样性。在4个经典测试函数上的仿真实验表明，新算法较传统PSO算法收敛更快，精度更高。将粒子群算法应用于求解一类min-max-min问题，并给出了数值算例。

关键词: 粒子群优化算法, 三子群协同, min-max-min问题