Soft Computing

, Volume 23, Issue 4, pp 1219–1237 | Cite as

MOEA3D: a MOEA based on dominance and decomposition with probability distribution model

  • Ziyu HuEmail author
  • Jingming Yang
  • Huihui Cui
  • Lixin Wei
  • Rui Fan
Methodologies and Application


In multi-objective evolutionary optimization, maintaining a good balance between convergence and diversity is particularly crucial to decision makers, especially when tackling problems with complicated Pareto sets. According to the analysis of dominance-based and decomposition-based selection mechanisms in multi-objective evolutionary algorithms, a multi-objective evolutionary algorithm based on the combination of local non-dominated rank and global decomposition is presented. The Gauss distribution model and differential evolution based on history information are employed as evolutionary operators. Various comparative experiments are conducted on 19 unconstraint test MOPs, and our empirical results validate the effectiveness and competitiveness of our proposed algorithm in solving MOPs of different types.


Multi-objective optimization Evolutionary algorithm Exploration and exploitation Differential evolution Soft computing 



This work was supported by the National Natural Science Foundation of China (No. 61074099), Natural Science Foundation of Hebei(No. F2016203249), Innovation Project for Postgraduate of Hebei Province (No. CXZZBS2017049) and the Cultivation Program Project for Leading Talent of innovation team in Colleges and universities of Hebei Province (No. LJRC013). The authors would like to thank the editor and anonymous reviewers for their helpful comments and suggestions to improve the quality of this paper.

Compliance with ethical standards

Conflict of interest

The authors declared that we have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Supplementary material

500_2017_2840_MOESM1_ESM.pdf (13.8 mb)
Supplementary material 1 (pdf 14115 KB)


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Ziyu Hu
    • 1
    Email author
  • Jingming Yang
    • 1
  • Huihui Cui
    • 1
  • Lixin Wei
    • 1
  • Rui Fan
    • 1
  1. 1.Institute of Electrical EngineeringYanshan UniversityQinhuangdaoPeople’s Republic of China

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