Offline and Online Objective Reduction via Gaussian Mixture Model Clustering

The objective reduction has been regarded as a basic issue in many-objective optimization. Existing objective reduction methods identify one set of essential objectives using an approximate nondominated front. However, if the Pareto front (PF) of a many-objective optimization problem (MaOP) is irregular, one single set of essential objectives may not be efficient for objective reduction. This article proposes to produce several different sets of essential objectives in objective reduction. More specifically, we use the Gaussian mixture model clustering to classify the obtained nondominated front into different subsets and perform objective reduction on each subset. Both an offline objective reduction method and an online objective reduction method are developed. The experimental results indicate that our proposed methods work well for MaOPs with degenerate or nondegenerate PFs.