A new adaptive decomposition-based evolutionary algorithm for multi- and many-objective optimization

In decomposition-based multi-objective evolutionary algorithms (MOEAs), a set of uniformly distributed reference vectors (RVs) is usually adopted to decompose a multi-objective optimization problem (MOP) into several single-objective sub-problems, and the RVs are fixed during evolution. When it comes to multi-objective optimization problems (MOPs) with complex Pareto fronts (PFs), the effectiveness of the multi-objective evolutionary algorithm (MOEA) may degrade. To solve this problem, this article proposes an adaptive decomposition-based evolutionary algorithm (ADEA) for both multi- and many-objective optimization. In ADEA, the candidate solutions themselves are used as RVs, so that the RVs can be automatically adjusted to the shape of the Pareto front (PF). Also, the RVs are successively generated one by one, and once a reference vector (RV) is generated, the corresponding sub-objective space is dynamically decomposed into two sub-spaces. Moreover, a variable metric is proposed and merged with the proposed adaptive decomposition approach to assist the selection operation in evolutionary many-objective optimization (EMO). The effectiveness of ADEA is compared with several state-of-the-art MOEAs on a variety of benchmark MOPs with up to 15 objectives. The empirical results demonstrate that ADEA has competitive performance on most of the MOPs used in this study.