Two new reference vector adaptation strategies for many-objective evolutionary algorithms

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. (C) 2019 Elsevier Inc. All rights reserved.