Incrementally maximising hypervolume for selection in multi-objective evolutionary algorithms

Several multi-objective evolutionary algorithms compare the hypervolumes of different sets of points during their operation, usually for selection or archiving purposes. The basic requirement is to choose a subset of a front such that the hypervolume of that subset is maximised. We describe and evaluate three new algorithms based on incremental calculations of hypervolume using the new incremental hypervolume by slicing objectives (IHSO) algorithm: two greedy algorithms that respectively add or remove one point at a time from a front, and a local search that assesses entire subsets. Empirical evidence shows that using IHSO, the greedy algorithms are generally able to out-perform the local search and perform substantially better than previously published algorithms.