一种基于切比雪夫距离的隐式偏好多目标进化算法

doi:10.11896/jsjkx.210500095

计算机科学 ›› 2022, Vol. 49 ›› Issue (6): 297-304.doi: 10.11896/jsjkx.210500095

一种基于切比雪夫距离的隐式偏好多目标进化算法

孙刚¹, 伍江江¹, 陈浩¹, 李军¹, 徐仕远²

1 国防科技大学电子科学学院长沙 410073
2 北方工业大学信息学院北京 100144

收稿日期:2021-05-13 修回日期:2021-09-04 出版日期:2022-06-15 发布日期:2022-06-08
通讯作者: 陈浩(hchen@nudt.edu.cn)
作者简介:(sungang19@nudt.edu.cn)
基金资助:
国家自然科学基金(61806211,U19A2058);湖南省自然科学基金(2020JJ4103)

Hidden Preference-based Multi-objective Evolutionary Algorithm Based on Chebyshev Distance

SUN Gang¹, WU Jiang-jiang¹, CHEN Hao¹, LI Jun¹, XU Shi-yuan²

1 College of Electronic Science and Technology,National University of Defense Technology,Changsha 410073,China
2 School of Information Science and Technology,North China University of Technology,Beijing 100144,China

Received:2021-05-13 Revised:2021-09-04 Online:2022-06-15 Published:2022-06-08
About author:SUN Gang,born in 1988,postgraduate.His main research interests include multi-objective evolutionary algorithms and satellite range scheduling problems.
CHEN Hao,born in 1982,Ph.D,professor.His main research interests include data mining,machine learning and evolutionary computation.
Supported by:
National Natural Science Foundation of China(61806211,U19A2058) and Natural Science Foundation of Hunan Province(2020JJ4103).

摘要/Abstract

摘要： 偏好多目标进化算法作为多目标优化方法的重要分支,被广泛应用于科学研究和工程实践,具有重要的研究意义。为了求得多目标优化问题中的极点解及在各优化目标上性能最折衷的膝点解,提出了用切比雪夫距离来定义膝点的方法并给出了几何解释,基于此构建了一种求解极点解和膝点解的多目标进化算法HP-NSGA-II。该算法通过区域动态更新策略使得目标区域随迭代过程动态更新,最终收敛于目标区域;通过区域间平衡性保持策略确保各区域间个体数量的平衡性,使得个体较为均匀地分布在各区域内部。基于广泛采用的测试函数开展了充分的实验验证,结果表明,HP-NSGA-II算法在二维测试问题及三维测试问题上具有较好的收敛性、区域间平衡性以及区域可控性,可以准确求得测试问题的极点解及膝点解。

关键词: 多目标优化, 极点解, 进化算法, 偏好, 切比雪夫距离, 膝点解

Abstract: As an important branch of multi-objective optimization,preference-based multi-objective evolutionary algorithms have been widely used in scientific researches and engineering practices,which have important research significance.In order to obtain the extreme solutions and the knee solution with the most compromised performance over each optimization objective in multi-objective optimization problems,a definition of knee solution based on Chebyshev distance and its geometric interpretation is presented.Based on the definition,a multi-objective evolutionary algorithm HP-NSGA-II aiming to search for the extreme solutions and the knee solution is proposed.The regional dynamic updating strategy of the proposed algorithm updates the target regions dynamically in each iteration,and finally converges to the target regions.The strategy of maintaining the balance between regions ensures the balance of the number of individuals in each region,so that the individuals could be distributed evenly in each region.Based on widely used test functions,sufficient experimental verification is carried out,and the experimental results indicate that HP-NSGA-II algorithm can achieve better performance in terms of convergence,regional balance and regional controllability in two-dimensional and three-dimensional test problems,and can accurately obtain the extreme solutions and knee solution.

Key words: Chebyshev distance, Evolutionary algorithm, Extreme solution, Knee solution, Multi-objective optimization, Preference

中图分类号:

TP301.6

孙刚, 伍江江, 陈浩, 李军, 徐仕远. 一种基于切比雪夫距离的隐式偏好多目标进化算法[J]. 计算机科学, 2022, 49(6): 297-304. https://doi.org/10.11896/jsjkx.210500095

SUN Gang, WU Jiang-jiang, CHEN Hao, LI Jun, XU Shi-yuan. Hidden Preference-based Multi-objective Evolutionary Algorithm Based on Chebyshev Distance[J]. Computer Science, 2022, 49(6): 297-304. https://doi.org/10.11896/jsjkx.210500095

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一种基于切比雪夫距离的隐式偏好多目标进化算法

Hidden Preference-based Multi-objective Evolutionary Algorithm Based on Chebyshev Distance

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