Soft Computing

, Volume 22, Issue 12, pp 3997–4012 | Cite as

Adjust weight vectors in MOEA/D for bi-objective optimization problems with discontinuous Pareto fronts

  • Chunjiang Zhang
  • Kay Chen Tan
  • Loo Hay Lee
  • Liang GaoEmail author
Methodologies and Application


Multi-objective evolutionary algorithm based on decomposition (MOEA/D) is a recently proposed algorithm which is a research focus in the field of multi-objective evolutionary optimization. It decomposes a multi-objective problem into subproblems by mathematic programming methods and applies evolutionary algorithms to optimize the subproblems simultaneously. MOEA/D is good at finding Pareto solutions which are evenly distributed. However, it can be improved for problems with discontinuous Pareto fronts (PF). Many solutions will assemble in breakpoints in this situation. A method for adjusting weight vectors for bi-objective optimization problems with discontinuous PF is proposed. Firstly, this method detects the weight vectors which need to be adjusted using a property of MOEA/D. Secondly, the reserved vectors are divided into several subsets. Thirdly, after calculating the ideal number of vectors in each subset, vectors are adjusted evenly. Lastly, the corresponding solutions are updated by a linear interpolation. Numerical experiment shows the proposed method obtains good diversity and convergence on approached PF.


MOEA/D Adjust weight vector Multi-objective evolutionary algorithm (MOEA) Discontinuous Pareto fronts 



This research work is supported by the National Key Technology Support Program under Grant No. 2015BAF01B04, and the National Natural Science Foundation of China (NSFC) under Grant Nos. 51421062 and 61232008, and China Scholarship Council (CSC).

Compliance with ethical standards

Conflict of interest

All author declares that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Chunjiang Zhang
    • 1
    • 2
  • Kay Chen Tan
    • 3
  • Loo Hay Lee
    • 4
  • Liang Gao
    • 1
    Email author
  1. 1.The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhanPeople’s Republic of China
  2. 2.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.Department of Computer ScienceCity University of Hong KongKowloon TongHong Kong
  4. 4.Department of Industrial and Systems EngineeringNational University of SingaporeSingaporeSingapore

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