MaOEA/A2R：一种基于A2R支配关系的高维多目标进化算法

谢承旺; 付世炜

doi:10.12263/DZXB.20230723

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MaOEA/A2R：一种基于A2R支配关系的高维多目标进化算法

学术论文 | 更新时间：2025-12-08

- MaOEA/A2R：一种基于A2R支配关系的高维多目标进化算法
- MaOEA/A2R: A Many-Objective Evolutionary Algorithm Based on A2R Dominance Relation
- 电子学报 2024年52卷第8期页码：2758-2772
- 作者机构：
  
  1.华南师范大学数据科学与工程学院，广东汕尾 516600
  2.南宁师范大学计算机与信息工程学院，广西南宁 530100
- 作者简介：
  
  [ "谢承旺男，1974年9月出生于湖北省武汉市.华南师范大学数据科学与工程学院院长、教授.主要研究方向为智能计算的理论与应用.E-mail: chengwangxie@163.com" ]
  [ "付世炜男，1998年12月出生于山东省滨州市.南宁师范大学计算机与信息工程学院硕士研究生.主要研究方向为智能计算与多目标优化.E-mail: shiwei_fu1998@163.com" ]
- 基金信息：
  
  国家自然科学基金(61763010);广西自然科学基金(2021GXNSFAA075011)
- DOI：10.12263/DZXB.20230723
  中图分类号： TP181;
- 收稿：2023-07-29，
  
  修回：2023-11-22，
  
  纸质出版：2024-08-25
- 稿件说明：
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谢承旺, 付世炜. MaOEA/A2R：一种基于A2R支配关系的高维多目标进化算法[J]. 电子学报, 2024, 52(08): 2758-2772.

XIE Cheng-wang, FU Shi-wei. MaOEA/A2R: A Many-Objective Evolutionary Algorithm Based on A2R Dominance Relation[J]. Acta Electronica Sinica, 2024, 52(08): 2758-2772.
谢承旺, 付世炜. MaOEA/A2R：一种基于A2R支配关系的高维多目标进化算法[J]. 电子学报, 2024, 52(08): 2758-2772. DOI：10.12263/DZXB.20230723

XIE Cheng-wang, FU Shi-wei. MaOEA/A2R: A Many-Objective Evolutionary Algorithm Based on A2R Dominance Relation[J]. Acta Electronica Sinica, 2024, 52(08): 2758-2772. DOI：10.12263/DZXB.20230723

摘要

传统的Pareto支配关系在高维目标空间存在固有缺陷，而一些改进的支配方法在平衡高维目标解群的收敛性与多样性上尚有提升空间.基于此，提出一种参考向量关联区域（小生境）自动缩减的支配关系A2R（dominance relation based on the Automatically reduced region Associated with the Reference vector）.该支配方法在进化全过程中逐代缩减

小生境规模，从而实现收敛性与多样性自动平衡，而且不引入额外参数.另外，提出利用基于

-范式（

，

为目标数）的拥挤距离度量高维目标解群的多样性.将上述两种策略嵌入到经典的NSGA-II（Nondominated Sorting Genetic Algorithm II）框架，设计一种基于A2R支配关系的高维多目标进化算法MaOEA/A2R（Many-Objective Evolutionary Algorithm base on A2R）.该算法与其他5种代表性的高维多目标进化算法一同在5-、10-、15-和20-目标的DTLZ（benchmark MOP proposed by Deb， Thiele， Lau⁃manns， and Zitzler）和WFG（benchmark MOP pro⁃posed by Walking Fish Group）基准测试问题上进行IGD（Inverted Generational Distance）和HV（HyperVolume）性能测试.结果表明，MaOEA/A2R算法总体上具有较好的收敛性和多样性.由此表明，MaOEA/A2R是一种颇具前景的高维多目标进化算法.

Abstract

There exist some inherent defects in the traditional Pareto dominance relation in many-objective optimization space

while some modified dominance relations have much room for improvement in balancing the convergence and diversity of many-objective evolutionary population. Based on this

a new dominance relation (dominance relation based on the Automatically reduced region Associated with the Reference vector

A2R) automatically shrinks the region (niche) associated with the reference vector. Specially

it reduces the size of the niche from generation to generation along the whole evolutionary process in order to achieve a balance of convergence and diversity adaptively. Furthermore

the A2R does not introduce any additional parameter. In addition

the crowding distance measure based on

-normal form (

equals 1/

and

denotes the number of objectives) is used to improve the diversity of the solution set in many-objective space. Finally

the above two strategies are embedded into the framework of NSGA-II (Nondominated Sorting Genetic Algorithm II)

and then a many-objective evolutionary algorithm based on A2R (MaOEA/A2R) is designed. The MaOEA/A2R is compared with other five representative many-objective evolutionary algorithms (MaOEAs) on the DTLZ and WFG benchmark functions

with 5-

10-

15-

and 20-objective in terms of IGD (Inverted Generational Distance) and HV (HyperVolume) indicators. The empirical results overally show that MaOEA/A2R can obtain better convergence and diversity. Therefore

the proposed MaOEA/A2R is a promising many-objective evolutionary algorithm.

关键词

Keywords

references

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