Affiliations: School of Computer Science and Technology, Xidian University, Xi’an, Shaanxi, China
Correspondence:
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Corresponding author: Yuping Wang, School of Computer Science and Technology, Xidian University, Xi’an, Shaanxi 710071, China. E-mail: [email protected].
Abstract: Many-objective optimization problems (MaOPs) have great challenges for traditional Pareto-based multi-objective evolutionary algorithms (MOEAs). One of the main reasons is that Pareto dominance cannot effectively rank/evaluate the solutions, resulting in almost random selection of the new population and no quality guarantee of the solutions in the new population. To overcome this shortcoming, in this paper, a new fitness evaluation mechanism is proposed for MaOPs. It uses a tailor-made integration of convergence and diversity measures, and can well balance convergence and diversity in solution evaluation. Specifically, to cooperate it with the subsequent selection mechanism, a new global convergence strength-based convergence measure is designed to avoid the interference from solution’s local information. To overcome the shortcoming that the existing angle-based diversity measure cannot distinguish the contributions to diversity of two solutions which have the same angle with reference direction, a new angle-distance based diversity measure is designed, which can accurately evaluate the contribution of each solution to diversity. Furthermore, to well balance the convergence and diversity, the proposed convergence measure and diversity measure have the same order of magnitude. As a result, the proposed convergence-diversity balanced fitness evaluation mechanism can accurately evaluate each solution’s quality and then properly increase the selection pressure. The proposed method is compared with five state-of-the-art many-objective evolutionary algorithms by experiments on 120 test instances of 24 benchmark problems with up to 20 objectives and a real world problem. The results indicate the competitiveness and effectiveness of our proposed algorithm in keeping a good balance between convergence and diversity.
