基于收敛速度和多样性的多目标粒子群种群规模优化设计

Design of Population Size for Multi-objective Particle Swarm Optimization Algorithm Based on the Convergence Speed and Diversity

针对多目标粒子群优化算法种群规模难以确定的问题,文中提出了一种基于收敛速度和多样性的多目标粒子群优化(Convergence speed and Diversity-based Multi-Objective Particle Swarm Optimization,CD-MOPSO)算法.首先,利用优化过程的收敛速度和多样性指标构造种群规模适应度函数,完成了种群规模与优化性能关系的描述;其次,基于适应度函数设计了一种种群规模自适应调整方法,实现了种群规模的动态调整;最后,将提出的CD-MOPSO在基准优化问题ZDT上测试并应用于城市管网优化,实验结果显示CD-MOPSO能够根据求解问题自动调整种群规模,与NSGA-II、MOPSO。

To determine the population size of multi-objective particle swarm optimization algorithm(MOPSO),an improved MOPSO,based on the convergence speed and diversity,named CD-MOPSO,is proposed.Firstly,the fitness function of population size,which is developed by the convergence speed and diversity during the evolutionary process,is used to describe the relationship between the population size and the performance of MOPSO.Secondly,according to the fitness function,an adaptive adjustment method is designed to update the population size of MOPSO dynamically.Finally,the proposed CD-MOPSO is tested on the ZDT benchmark optimization problems and applied to a real optimization problem of urban pipe networks.The experimental results show that the proposed CD-MOPSO can adjust the population size automatically according to the problem,compared with the performance of NSGA,MOPSO,SPEA2 and EMDS-MOPSO,CD-MOPSO has faster convergence speed with better optimization results.