Maximising hypervolume for selection in multi-objective evolutionary algorithms

When hypervolume is used as part of the selection or archiving process in a multi-objective evolutionary algorithm, the basic requirement is to choose a subset of the solutions in a non-dominated front such that the hypervolume of the subset is maximised. We describe and evaluate two algorithms to approximate this process: a greedy algorithm that assesses and eliminates solutions individually, and a local search algorithm that assesses entire subsets. We present empirical data which suggests that a hybrid approach is needed to get the best trade-off between good results and computational cost.