Abstract: In order to improve the distribution of multi-objective PSO algorithm, crowding-density is introduced for the update of elite set. The basic idea is: the crowding-density of each individual in the group is calculated, and then a partial order set is set up according to the objective function value and crowding-density. Individuals are selected from the partial order set according to the principle of proportional selection, and the elite set is updated. The convergence and distribution of improved algorithm are studied by means of numerical experiments, and results show that the convergence of improved algorithm is roughly equal with the conventional multi-objective particle swarm optimization algorithm, but the distribution of improved algorithm has been significantly improved.

Key words: multi-objective optimization, Particle Swarm Optimization（PSO）, crowding-density, distribution

摘要： 为了改善粒子群多目标优化算法的分布性，引入了聚集密度以进行精英集的更新。其基本思想为：计算群体中每个个体的聚集密度，根据目标函数值和聚集密度定义一个偏序集，采用比例选择原则依次从偏序集中选择个体，更新精英集。通过数值实验用量化指标研究了新算法的收敛性和分布性，结果表明：新算法的收敛性与常规粒子群多目标优化算法相当，但分布性有了明显的提高。

关键词: 多目标优化, 粒子群优化算法, 聚集密度, 分布性