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

doi:10.3969/j.issn.0372-2112.2018.09.031

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摘要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、SPEA2和EMDS-MOPSO相比具有更快的收敛速度和更好的优化结果.

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	韩红桂
	武淑君

关键词 ：多目标粒子群优化算法, 种群规模, 自适应调整方法, 动态调整, 适应度函数, 收敛速度, 多样性, 基准测试函数, 城市管网优化

Abstract：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.

Key words： multi-objective particle swarm optimization algorithm (MOPSO) population size adaptive adjustment method dynamic adjustment fitness function convergence speed diversity benchmark test functions urban pipe networks optimization

收稿日期: 2017-09-19 出版日期: 2017-11-28

TP18

基金资助:国家自然科学基金（No.61622301）；北京市自然科学基金（No.4172005）；科技部水专项（No.2017ZX07104）

作者简介: 韩红桂 男,1983年08月生于江苏泰州.现为北京工业大学教授、博士生导师.主要研究方向为城市污水处理过程智能优化控制.E-mail:rechardhan@bjut.edu.cn;武淑君 女,1995年01月生于河南邓州.现为北京工业大学信息学部硕士研究生.主要研究方向为污水处理过程智能优化.E-mail:wushujun@emails.bjut.edu.cn

引用本文:

韩红桂, 武淑君. 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[J]. 电子学报, 2018, 46(9): 2263-2269. HAN Hong-gui, WU Shu-jun. Design of Population Size for Multi-objective Particle Swarm Optimization Algorithm Based on the Convergence Speed and Diversity. Acta Electronica Sinica, 2018, 46(9): 2263-2269.

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http://www.ejournal.org.cn/CN/10.3969/j.issn.0372-2112.2018.09.031 或 http://www.ejournal.org.cn/CN/Y2018/V46/I9/2263

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