电子、通信与自动控制

基于改善解集分布性的多目标优化

展开
  • 华东理工大学 能源化工过程智能制造教育部重点实验室,上海 200237
王学武(1972-),男,博士,副教授,主要从事智能优化算法、焊接机器人智能化技术、焊接自动化、系统建模、控制与优化研究。

收稿日期: 2022-10-18

  网络出版日期: 2023-03-07

基金资助

国家自然科学基金资助项目(62076095)

Multi-Objective Optimization Based on Improved Distribution of Solutions

Expand
  • Key Laboratory of Smart Manufacturing in Energy Chemical Process of the Ministry of Education,East China University of Science and Technology,Shanghai 200237,China
王学武(1972-),男,博士,副教授,主要从事智能优化算法、焊接机器人智能化技术、焊接自动化、系统建模、控制与优化研究。

Received date: 2022-10-18

  Online published: 2023-03-07

Supported by

the National Natural Science Foundation of China(62076095)

摘要

针对低维度多目标优化问题,目前的众多多目标优化算法已能保证足够接近问题的最优前沿,并兼顾解集的收敛性和多样性。然而,大多数算法往往忽略了解的分布性。在具有不规则帕累托前沿的多目标优化问题上,解的分布越均匀,越能充分覆盖问题的最优前沿超平面,提供给决策者的选择区间也越趋于合理。文中针对解的分布性的改善问题,以SPEA2算法为主框架,在改进个体适应度计算的基础上,提出一种新的多目标优化算法CM-SPEA2。该算法首先通过不等权重层次聚类法将种群划分为若干簇;然后改进原有杂乱度计算方法,衡量个体在所属簇内的杂乱度,寻找杂乱度最低的个体作为参考点;最后,基于其他个体与参考点的Manhattan距离计算表征分布性的算子并改进适应度函数,设置适应度阈值筛选参考点附近的非支配个体,从而间接调整环境选择策略,使保留的个体分布更加均匀,进而提升收敛性和多样性。对比实验结果表明,与一些类似的多目标优化算法相比,CM-SPEA2算法在IMOP、ZDT和VNT类型的测试问题上具有一定的优势。

本文引用格式

王学武, 方俊宇, 高进, 等 . 基于改善解集分布性的多目标优化[J]. 华南理工大学学报(自然科学版), 2023 , 51(8) : 137 -148 . DOI: 10.12141/j.issn.1000-565X.220668

Abstract

For low-dimensional multi-objective optimization problems, the existing multi-objective optimization algorithms have been able to ensure the proximity to the optimal front of the problem, and balance the convergence and the diversity of solution sets. However, the uniformity of the solution is ignored in most algorithms. In the multi-objective optimization problem with irregular Pareto front, the more uniform the distribution of solution is, the more the solution can reflect the true distribution of the optimal front of the problem, and the more reasonable the choices provided to decision makers. To improve the uniform distribution of solutions, a new multi-objective optimization algorithm CM-SPEA2 is proposed based on SPEA2 algorithm and the improved individual fitness calculation. In this algorithm, firstly, the initial population is divided into different clusters by means of hierarchical clustering. Next, the original calculation method of messy degree is improved to measure the messy degree of individuals in their clusters, and the individuals with the lowest messy degree are selected as reference points. Then, based on the Manhattan distance between other individuals and the reference point, the operator representing distribution is calculated and the fitness function is improved. Finally, the fitness threshold is set to screen non-dominated individuals near the reference point, so as to indirectly adjust the environmental selection strategy, make the distribution of retained individuals more uniform, thus improving the convergence and diversity. As compared with some similar multi-objective optimization algorithms, the proposed CM-SPEA2 algorithm has certain advantages in solving IMOP, ZDT and VNT test problems.

参考文献

1 ZHANG Q, LI H .MOEA/D:a multiobjective evolutionary algorithm based on decomposition[J].IEEE Transactions on Evolutionary Computation200711(6):712-731.
2 ZHANG C, GAO L, LI X,et al .Resetting weight vectors in MOEA/D for multiobjective optimization problems with discontinuous Pareto front[J].IEEE Transactions on Cybernetics202252(9):9770-9783.
3 QI Y, LI X, YU J,et al .User-preference based decomposition in MOEA/D without using an ideal point[J].Swarm and Evolutionary Computation201944:597-611.
4 DEB K, JAIN H .An evolutionary many-objective optimization algorithm using reference-point based non-dominated sorting approach,part I:solving problems with box constraints[J].IEEE Transactions on Evolutionary Computation201418(4):577-601.
5 DENG W, ZHANG X, ZHOU Y,et al .An enhanced fast non-dominated solution sorting genetic algorithm for multi-objective problems[J].Information Sciences2022585:441-453.
6 TIAN Y, CHENG R, ZHANG X,et al .An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility[J].IEEE Transactions on Evolutionary Computation201822(4):609-622.
7 TIAN Y, CHENG R, ZHANG X,et al .A strengthened dominance relation considering convergence and diversity for evolutionary many-objective optimization[J].IEEE Transactions on Evolutionary Computation201923(2):331-345.
8 PANICHELLA A .An adaptive evolutionary algorithm based on non-Euclidean geometry for many-objective optimization[C]∥Proceedings of the Genetic and Evolutionary Computation Conference.New York:Association for Computing Machinery,2019:595-603.
9 SONODA T, NATAKA M .MOEA/D-S3:MOEA/D using SVM-based surrogates adjusted to subproblems for many objective optimization[C]∥Proceedings of the 2020 IEEE Congress on Evolutionary Computation (CEC).Glasgow:IEEE,2020:1-8.
10 ZITLER M, LAUMANNS M, THIELE L .SPEA2:improving the strength Pareto evolutionary algorithm[M].Berlin:Springer-Verlag,2002:95-100.
11 翁理国,王安,夏旻,等 .基于局部搜索的改进SPEA2算法[J].计算机应用研究201431(9):2617-2619,2639.
  WENG Li-guo, WANG An, XIA Min,et al. Improved SPEA 2 based on local search[J].Application Research of Computers,2014,31(9):2617-2619,2639.
12 王学武,闵永,顾幸生 .基于密度聚类的多目标粒子群优化算法[J].华东理工大学学报(自然科学版)201945(3):449-457.
  WANG Xuewu, MIN Yong, GU Xingsheng .Multi-objective particle swarm optimization algorithm based on density clustering[J].Journal of East China University of Science and Technology201945(3):449-457.
13 HUA Y, JIN Y, HAO K .A clustering-based adaptive evolutionary algorithm for multiobjective optimization with irregular Pareto fronts[J].IEEE Transactions on Cybernetics2019(7):2758-2770.
14 李密青,郑金华,李珂 .一种非均匀分布问题分布性维护方法[J].电子学报201139(4):946-952.
  LI Mi-qing, ZHENG Jin-hua, LI Ke .A diversity maintenance method for non-uniform distribution problem[J].Acta Electronica Sinica201139(4):946-952.
15 郑金华,邹娟 .多目标进化优化[M].北京:科学出版社,2018:70-72.
16 TIAN Y, CHENG R, ZHANG X,et al .PlatEMO:a MATLAB platform for evolutionary multi-objective optimization[J].IEEE Computational Intelligence Magazine201712(4):73-87.
17 WANG H, JIAO L, YAO X .Two_arch2:An improved two-archive algorithm for many-objective optimization[J].IEEE Transactions on Evolutionary Computation201519(4):524-541.
18 COELLO C, CORTES N .Solving multiobjective optimization problems using an artificial immune system[J].Genetic Programming and Evolvable Machines20056(2):163-190.
19 SCHOTT J .Fault tolerant design using single and multicriteria genetic algorithm optimization[D].Cambridge:Massachusetts Institute of Technology,1995:199-200.
20 郭一楠,汤万宝,陈国玉,等 .动态多目标进化优化研究进展[J].信息与控制202150(2):162-173.
  GUO Yinan, TANG Wanbao, CHEN Guoyu,et al .Research progress on dynamic multi-objective evolutionary optimization[J].Information and Control202150(2):162-173.
文章导航

/