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

Research output: Contribution to journalArticlepeer-review


  • Yuan Yuan
  • Hua Xu
  • Bo Wang
  • Bo Zhang
  • Xin Yao

Colleges, School and Institutes


The decomposition-based multiobjective evolutionary algorithms 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 in preserving 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., multiobjective evolutionary algorithms 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.


Original languageEnglish
Number of pages19
JournalIEEE Transactions on Evolutionary Computation
Publication statusE-pub ahead of print - 9 Jun 2015