One-to-one ensemble mechanism for decomposition-based multi-Objective optimization

Multi-objective evolutionary algorithms based on decomposition (MOEA/Ds) have been generally recognized as competitive techniques for solving multi-objective optimization problems (MOPs) with complicated Paretooptimal sets. To date, ensemble methods have been developed for adaptively selecting evolution operators to enhance the performance of MOEA/Ds. However, most established ensemble methods ignore the variance of the characteristics of complicated MOPs throughout both the decision and objective spaces, and subproblems inevitably have distinct characteristics. Keeping these observations in mind, we propose a one-to-one ensemble mechanism, namely OTOEM, for adaptively associating each subproblem of an MOEA/D with a suitable evolution operator, which differs substantially from the established ensemble methods, in which all the subproblems of the MOEA/D are associated with the same evolution operator during each generation. Another novel feature of the OTOEM is that both the local and global credits of an evolutionary operator are considered in measuring its suitability for subproblems. Moreover, an adaptive rule is designed to stimulate evolution operators with higher overall credits to generate more new solutions and guarantee the continuity of the covariance matrix adaptation evolution strategy. The performance of the proposed OTOEM is evaluated by comparing it with eleven baseline MOEAs on 26 complicated MOPs, and empirical results demonstrate its powerful performance in terms of two widely used metrics, namely, the inverted generational distance and hypervolume.