A Two-State Dynamic Decomposition-Based Evolutionary Algorithm for Handling Many-Objective Optimization Problems

Lining Xing, Jun Li (), Zhaoquan Cai and Feng Hou
Additional contact information
Lining Xing: School of Mathematics and Big Data, Foshan University, Foshan 528225, China
Jun Li: School of Management, Hunan Institute of Engineering, Xiangtan 411104, China
Zhaoquan Cai: Shanwei Institute of Technology, Shanwei 516600, China
Feng Hou: School of Mathematical and Computational Sciences, Massey University, Albany 4442, New Zealand

Mathematics, 2023, vol. 11, issue 3, 1-21

Abstract: Decomposition-based many-objective evolutionary algorithms (D-MaOEAs) are brilliant at keeping population diversity for predefined reference vectors or points. However, studies indicate that the performance of an D-MaOEA strongly depends on the similarity between the shape of the reference vectors (points) and that of the PF (a set of Pareto-optimal solutions symbolizing balance among objectives of many-objective optimization problems) of the many-objective problem (MaOP). Generally, MaOPs with expected PFs are not realistic. Consequently, the inevitable weak similarity results in many inactive subspaces, creating huge difficulties for maintaining diversity. To address these issues, we propose a two-state method to judge the decomposition status according to the number of inactive reference vectors. Then, two novel reference vector adjustment strategies, set as parts of the environmental selection approach, are tailored for the two states to delete inactive reference vectors and add new active reference vectors, respectively, in order to ensure that the reference vectors are as close as possible to the PF of the optimization problem. Based on the above strategies and an efficient convergence performance indicator, an active reference vector-based two-state dynamic decomposition-base MaOEA, referred to as ART-DMaOEA, is developed in this paper. Extensive experiments were conducted on ART-DMaOEA and five state-of-the-art MaOEAs on MaF1-MaF9 and WFG1-WFG9, and the comparative results show that ART-DMaOEA has the most competitive overall performance.

Keywords: decomposition-based MaOEA; active reference vector; two-state method; ART-DMaOEA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/3/493/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/3/493/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:3:p:493-:d:1038046

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().