Updating exclusive hypervolume contributions cheaply

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 a technique that improves the performance of hypervolume contribution based front selection schemes. This technique improves performance by allowing the update of hypervolume contributions after the addition or removal of a point, where these contributions would previously require full recalculation. Empirical evidence shows that this technique reduces runtime by up 72-99% when compared to the cost of full contribution recalculation on DTLZ and random fronts.