Generating data sets with known hypervolume & estimating the dominated hypervolume of random datasets

This paper presents two methods for generating data sets with known dominated hypervolumes. The first method, based on creating a block pyramid of dimension 2 or greater generates highly structured data with limited flexibility in number of Pareto points and results in a Pareto front with all points residing on a hyperplane. The second method generates Pareto sets with an arbitrary number of points and some control over the shape of the front (convex or concave). Both methods provide an exact dominated hypervolume, and so can be used to provide test data for testing algorithms that calculate hypervolume approximations. Additionally, the paper presents a method to estimate the expected hypervolume of a set of Pareto points that are distributed on the face of a simplex, and demonstrates the sensitivity of the ratio of the hypervolume to the dimensionality of the problem.