Objective Reduction Using Objective Sampling and Affinity Propagation for Many-Objective Optimization Problems

Real-world optimization tasks often have more than three objectives, hence are Many-objective Optimization Problems (MaOPs). MaOPs are challenging because of the difficulties in obtaining the true Pareto front of high dimensionality. The number of objectives can be reduced. However, existing objective reduction methods are computationally expensive as they need to identify non-dominant solutions by running multi-objective evolutionary algorithms (MOEAs). In this paper, we propose an efficient yet effective objective reduction method, named Objective Reduction using Sampling and Affinity Propagation (ORSAP). First, a sampling method is used to collect points that can represent objectives by calculating objectives' improvements. Second, affinity propagation is adopted to cluster the objectives, so redundant objectives may group together. Then, only the centroid objectives are kept as non-redundant objectives. The experiments on a range of benchmark MaOP instances show that ORSAP can successfully retain non-redundant objectives and remove redundant ones with low computational cost. It is highly competitive compared to the state-of-the-art objective reduction methods. In addition, ORSAP can significantly improve optimization performance when integrating with MOEAs.