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• A many objective evolutionary algorithm based on decomposition and moth search is proposed. • Random and adaptive weights is used to break the limitation of uniform distribution weights. • Mutual evaluation value is used to evaluate the optimal individual in the neighborhood. • Improving scale factor α in MSA is to improve the performance of the proposed algorithm. Decomposition-based multi-objective evolutionary algorithm (MOEA/D) has good performance in solving multi-objective problems (MOPs) but poor performance in solving many-objective optimization problems (MaOPs). The weight vectors in MOEA/D are relatively fixed, which results in poor performance when dealing with complex MaOPs. In this paper, random and adaptive weights are introduced into MOEA/D to break the limitation of fixed weight vectors. And the moth search algorithm (MSA) is used as an operator to improve global search ability. The updating strategies in MSA are more consistent with the neighborhood learning strategy adopted in MOEA/D. In addition, to enable MSA to find the optimal solution in the neighborhood on the MaOPs to update other individuals. This paper introduces mutual evaluation value for evaluating the optimal individual in the neighborhood, and the proposed algorithm is abbreviated as MOEA/DMS. In comparative experiments on the MaF test suite, hypervolume (HV) and inverted generational distance (IGD) are used to measure MOEA/DMS and other many-objective evolutionary algorithms (MaOEAs). The results show that MOEA/DMS has an excellent performance in dealing with MaOPs. Besides, MOEA/DMS is compared with other state-of-the-art MaOEAs on two combinatorial MaOPs. The results show that MOEA/DMS also has significant advantages in dealing with combinatorial MaOPs. [ABSTRACT FROM AUTHOR]

Abstract Maintaining population diversity is critical for multi-objective evolutionary algorithms (MOEAs) to solve many-objective optimization problems (MaOPs). Reference vector guided MOEAs have exhibited superiority in handling this issue, where a set of well distributed reference points on a unit hyperplane are generated to construct the reference vectors. Nevertheless, the pre-defined reference vectors could not well handle MaOPs with irregular (e.g., convex, concave, degenerate, and discontinuous) Pareto fronts (PFs). In this paper, we propose two new reference vector adaptation strategies, namely Scaling of Reference Vectors (SRV) and Transformation of Solutions Location (TSL), to handle irregular PFs. Particularly, to solve an MaOP with a convex/concave PF, SRV introduces a specific center vector and adjusts the other reference vectors around it by using a scaling function. TSL transforms the location of well-diversified solutions into a set of new reference vectors to handle degenerate/discontinuous PFs. The two strategies are incorporated into three representative MOEAs based on reference vectors and tested on benchmark MaOPs. The comparison studies with other state-of-the-art algorithms demonstrate the efficiency of the new strategies. [ABSTRACT FROM AUTHOR]