工程科学学报.第43卷，第6期：745-753.2021年6月 Chinese Journal of Engineering,Vol.43,No.6:745-753,June 2021 https://doi.org/10.13374/j.issn2095-9389.2020.10.31.001;http://cje.ustb.edu.cn 多目标粒子群优化算法研究综述 冯茜2，李擎，3)区，全威》，裴轩墨) 1)北京科技大学自动化学院，北京1000832)华北理工大学机械工程学院，唐山0632103)北京科技大学工业过程知识自动化教育部重 点实验室，北京100083 ☒通信作者，E-mail:liging@ies.ustb.edu.cn 摘要针对多目标粒子群优化算法的研究进展进行综述.首先，回顾了多目标优化和粒子群算法等基本理论：其次，分析了 多目标优化所涉及的难点问题：再次，从最优粒子选择策略，多样性保持机制.收敛性提高手段，多样性与收敛性平衡方法，迭 代公式、参数、拓扑结构的改进方案5个方面综述了近年来的最新成果：最后，指出多目标粒子群算法有待进一步解决的问 题及未来的研究方向 关键词多目标优化：粒子群算法：收敛性：多样性：进化算法 分类号TP18 Overview of multiobjective particle swarm optimization algorithm FENG Qian2),LI Qing,QUAN Wei,PEI Xuan-mo 1)School of Automation and Electrical Engineering,University of Science and Technology Beijing,Beijing 100083,China 2)College of Mechanical Engineering,North China University of Science and Technology,Tangshan 063210,China 3)Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education,University of Science and Technology Beijing,Beijing 100083,China Corresponding author,E-mail:liqing@ies.ustb.edu.cn ABSTRACT In the real world,the development model of optimization problems tends to be diversified and large scale.Therefore, optimization technologies are facing severe challenges in terms of nonlinearity,multi-dimensionality,intelligence,and dynamic programming.Multiobjective optimization problems have multiple conflicting objective functions,so the unique optimal solution is impossible to obtain when optimizing,and multiple objective values must be considered to obtain a compromise optimal solution set. When traditional optimization methods treat complex multiobjective problems,such as those with nonlinearity and high dimensionality, good optimization results are difficult to ensure or even infeasible.The evolutionary algorithm is a method that simulates the natural evolution process and is optimized via group search technology.It has the characteristics of strong robustness and high search efficiency. Inspired by the foraging behavior of bird flocks in nature,the particle swarm optimization algorithm has a simple implementation,fast convergence,and unique updating mechanism.With its outstanding performance in the single-objective optimization process,particle swarm optimization has been successfully extended to multiobjective optimization,and many breakthrough research achievements have been made in combinatorial optimization and numerical optimization.Consequently,the multiobjective particle swarm algorithm has far- reaching research value in theoretical research and engineering practice.As a meta-heuristic optimization algorithm,particle swarm optimization is widely used to solve multiobjective optimization problems.This paper summarized the advanced strategies of the multiobjective particle swarm optimization algorithm.First,the basic theories of multiobjective optimization and particle swarm optimization were reviewed.Second,the difficult problems involving multiobjective optimization were analyzed.Third,the 收稿日期：2020-10-31 基金项目：国家自然科学基金资助项目(61673098)多目标粒子群优化算法研究综述 冯    茜1,2)，李    擎1,3) 苣，全    威1)，裴轩墨1) 1) 北京科技大学自动化学院，北京 100083    2) 华北理工大学机械工程学院，唐山 063210    3) 北京科技大学工业过程知识自动化教育部重 点实验室，北京 100083 苣通信作者，E-mail：liqing@ies.ustb.edu.cn 摘    要    针对多目标粒子群优化算法的研究进展进行综述. 首先，回顾了多目标优化和粒子群算法等基本理论；其次，分析了 多目标优化所涉及的难点问题；再次，从最优粒子选择策略，多样性保持机制，收敛性提高手段，多样性与收敛性平衡方法，迭 代公式、参数、拓扑结构的改进方案 5 个方面综述了近年来的最新成果；最后，指出多目标粒子群算法有待进一步解决的问 题及未来的研究方向. 关键词    多目标优化；粒子群算法；收敛性；多样性；进化算法 分类号    TP18 Overview of multiobjective particle swarm optimization algorithm FENG Qian1,2) ，LI Qing1,3) 苣 ，QUAN Wei1) ，PEI Xuan-mo1) 1) School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China 2) College of Mechanical Engineering, North China University of Science and Technology, Tangshan 063210, China 3) Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, University of Science and Technology Beijing, Beijing 100083, China 苣 Corresponding author, E-mail: liqing@ies.ustb.edu.cn ABSTRACT    In the real world, the development model of optimization problems tends to be diversified and large scale. Therefore, optimization  technologies  are  facing  severe  challenges  in  terms  of  nonlinearity,  multi-dimensionality,  intelligence,  and  dynamic programming.  Multiobjective  optimization  problems  have  multiple  conflicting  objective  functions,  so  the  unique  optimal  solution  is impossible to obtain when optimizing, and multiple objective values must be considered to obtain a compromise optimal solution set. When traditional optimization methods treat complex multiobjective problems, such as those with nonlinearity and high dimensionality, good optimization results are difficult to ensure or even infeasible. The evolutionary algorithm is a method that simulates the natural evolution process and is optimized via group search technology. It has the characteristics of strong robustness and high search efficiency. Inspired by the foraging behavior of bird flocks in nature, the particle swarm optimization algorithm has a simple implementation, fast convergence, and unique updating mechanism. With its outstanding performance in the single-objective optimization process, particle swarm optimization has been successfully extended to multiobjective optimization, and many breakthrough research achievements have been made in combinatorial optimization and numerical optimization. Consequently, the multiobjective particle swarm algorithm has far￾reaching  research  value  in  theoretical  research  and  engineering  practice.  As  a  meta-heuristic  optimization  algorithm,  particle  swarm optimization  is  widely  used  to  solve  multiobjective  optimization  problems.  This  paper  summarized  the  advanced  strategies  of  the multiobjective  particle  swarm  optimization  algorithm.  First,  the  basic  theories  of  multiobjective  optimization  and  particle  swarm optimization  were  reviewed.  Second,  the  difficult  problems  involving  multiobjective  optimization  were  analyzed.  Third,  the 收稿日期: 2020−10−31 基金项目: 国家自然科学基金资助项目（61673098） 工程科学学报，第 43 卷，第 6 期：745−753，2021 年 6 月 Chinese Journal of Engineering, Vol. 43, No. 6: 745−753, June 2021 https://doi.org/10.13374/j.issn2095-9389.2020.10.31.001; http://cje.ustb.edu.cn