Balancing Convergence and Diversity in Decomposition-Based Many-Objective Optimizers


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

352 Citations (Scopus)


The decomposition-based multiobjective evolutionary algorithms (MOEAs) generally make use of aggregation functions to decompose a multiobjective optimization problem into multiple single-objective optimization problems. However, due to the nature of contour lines for the adopted aggregation functions, they usually fail to preserve the diversity in high-dimensional objective space even by using diverse weight vectors. To address this problem, we propose to maintain the desired diversity of solutions in their evolutionary process explicitly by exploiting the perpendicular distance from the solution to the weight vector in the objective space, which achieves better balance between convergence and diversity in many-objective optimization. The idea is implemented to enhance two well-performing decomposition-based algorithms, i.e., MOEA, based on decomposition and ensemble fitness ranking. The two enhanced algorithms are compared to several state-of-the-art algorithms and a series of comparative experiments are conducted on a number of test problems from two well-known test suites. The experimental results show that the two proposed algorithms are generally more effective than their predecessors in balancing convergence and diversity, and they are also very competitive against other existing algorithms for solving many-objective optimization problems. © 1997-2012 IEEE.
Original languageEnglish
Article number7120115
Pages (from-to)180-198
Number of pages19
JournalIEEE Transactions on Evolutionary Computation
Issue number2
Early online date9 Jun 2015
Publication statusPublished - Apr 2016
Externally publishedYes

Bibliographical note

This work was supported in part by the National Basic Research Program of China (973 Program) under Grant 2012CB316301; in part by the National Natural Science Foundation of China under Grant 61175110, Grant 61329302, and Grant 61305079; in part by the National S&T Major Projects of China under Grant 2011ZX02101-004; in part by the National Banking Information Technology Risk Management Projects of China; and in part by the China Scholarship Council. The work of X. Yao was supported in part by the Engineering and Physical Sciences Research Council under Grant EP/J017515/1 and in part by the Royal Society Wolfson Research Merit Award.


  • convergence
  • decomposition
  • diversity
  • Many-objective optimization
  • multiobjective optimization


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