A Subspace-Based Non-Dominated Subset Selection Method

Environmental selection is an important process in multi-objective evolutionary algorithms (MOEAs). As the evolution progresses, the number of non-dominated solutions increases. This paper is focused on selecting a subset from excess non-dominated solutions for evolutionary or the final output. However, traditional selection methods in classical MOEAs encounter difficulties when dealing with candidate solutions that possess irregular topologies. Although the distance-based subset selection methods are not sensitive to the topologies of the candidate points, they have significant room for reducing computational complexity. In order to address the above issues, a subspace selection method is proposed in this paper. It partitions the objective space into multiple subspaces that have comparable volumes and shapes. The maximal minimum distance of each solution is considered to ensure that the sparsest solution is always chosen first. To save computational costs, only the solutions in the neighboring subspaces are taken into account. The experimental results demonstrate that the proposed subspace selection method outperforms classical selection methods in solving problems with various shapes of the Pareto front.