An efficient many objective optimization algorithm with few parameters

Qingquan ZHANG, Jialin LIU, Xin YAO

Research output: Journal PublicationsJournal Article (refereed)peer-review

1 Citation (Scopus)


During the past two decades, numerous many-objective optimization evolutionary algorithms (MaOEAs) have been proposed to tackle the challenges traditional multi-objective evolutionary algorithms face, that is to deal with abundant non-dominated solutions and low selection pressure. Specifically, a series of sophisticated selection strategies have been adopted, some of which need additional pre-defined parameters or a significant amount of extra computation time, which retards their applications in real life. In this paper, we propose an efficient indicator-based MaOEA with few parameters, SDE+-MOEA, that uses an adaptive combination of commonly used selection methods to improve search efficiency based on SDE+. SDE+ addresses situations where SDE cannot distinguish individuals with the same SDE values. The adaptive selection method dynamically selects between one-time and iterative selection methods at different stages of evolution to improve the search efficiency. Furthermore, apart from the four parameters for generating offspring, our proposed SDE+-MOEA does not introduce additional parameters. We conduct experimental studies to compare SDE+-MOEA with 11 state-of-the-art algorithms, including 2REA, ISDE, θ-DEA, LMPFE, CVEA3, SRA, MOEA/DD, IBEA, Two_Arch2, NSGA-III, and SPEA2SDE using four representative performance indicators (HV, SP, PD and GD) on MaF benchmark with 5, 8, 10, and 15 objectives. Experimental studies demonstrate that, compared to the algorithms, SDE+-MOEA achieves better HV and competitive convergence and uniformity performance, while requiring few parameters. It means that SDE+-MOEA can find a solution set with better convergence and uniformity to help decision-makers understand the solved problems. Furthermore, SDE+-MOEA loses little spreadability since a better convergence often leads to a worse spread. © 2023 Elsevier B.V.
Original languageEnglish
Article number101405
JournalSwarm and Evolutionary Computation
Early online date10 Oct 2023
Publication statusPublished - Dec 2023
Externally publishedYes

Bibliographical note

This work was supported by the National Key R&D Program of China (Grant No. 2023YFE0106300 ), the National Natural Science Foundation of China (Grant No. 62250710682 ), the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021A1515011830 ), the Guangdong Provincial Key Laboratory (Grant No. 2020B121201001 ), the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (Grant No. 2017ZT07X386 ), the Shenzhen Fundamental Research Programs (Grant No. 20220815181327001 ), and the Research Institute of Trustworthy Autonomous Systems (RITAS).


  • Indicator-based selection
  • Many-objective evolutionary algorithm
  • Many-objective optimization
  • Multi-criteria decision-making
  • Multi-objective optimization


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