For regular Pareto Fronts (PFs), such as those that are smooth, continuous, and uniformly distributed, using fixed weight vectors is sufficient for multi-objective optimization approaches using decomposition. However, when encountering irregular PFs-including degenerate, disconnected, inverted, etc. Fixed weight vectors can often cause a non-uniform distribution of the sets or even poor optimization results. To address this issue, this study proposes an adaptive many-objective evolutionary algorithm with a simplified hypervolume indicator. It synthesizes indicator assessment techniques with decomposition-based methods to facilitate self-adaptive and dynamic adjustment of the weight vectors in many-objective optimization methods. Specifically, based on the MOEA/D framework, it uses a simplified hypervolume indicator to accurately assess solution distribution. Simultaneously, applying the R2 indicator (as an approximation of hypervolume) dynamically regulates the update frequency of the weight vectors. Experimental results demonstrate that the proposed algorithm is efficient and effective when compared with six state-of-the-art algorithms.
Han et al. (Fri,) studied this question.