Improving the multiobjective evolutionary algorithm based on decomposition with new penalty schemes

Shengxiang Yang*, Shouyong Jiang, Yong Jiang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


It has been increasingly reported that the multiobjective optimization evolutionary algorithm based on decomposition (MOEA/D) is promising for handling multiobjective optimization problems (MOPs). MOEA/D employs scalarizing functions to convert an MOP into a number of single-objective subproblems. Among them, penalty boundary intersection (PBI) is one of the most popular decomposition approaches and has been widely adopted for dealing with MOPs. However, the original PBI uses a constant penalty value for all subproblems and has difficulties in achieving a good distribution and coverage of the Pareto front for some problems. In this paper, we investigate the influence of the penalty factor on PBI, and suggest two new penalty schemes, i.e., adaptive penalty scheme and subproblem-based penalty scheme (SPS), to enhance the spread of Pareto-optimal solutions. The new penalty schemes are examined on several complex MOPs, showing that PBI with the use of them is able to provide a better approximation of the Pareto front than the original one. The SPS is further integrated into two recently developed MOEA/D variants to help balance the population diversity and convergence. Experimental results show that it can significantly enhance the algorithm’s performance.

Original languageEnglish
Pages (from-to)4677-4691
Number of pages15
JournalSoft Computing
Issue number16
Early online date18 Feb 2016
Publication statusPublished - 1 Aug 2017

Bibliographical note

Funding Information:
This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of U.K. under Grant EP/K001310/1 and the National Natural Science Foundation of China under Grant 61273031.

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.


  • Adaptive penalty scheme
  • Decomposition
  • Multiobjective evolutionary algorithm
  • Penalty boundary intersection
  • Subproblem-based penalty scheme


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