In most cases (including this work), the hypervolume indicator is used as an analysis tool to asses the quality and diversity of a Pareto set after an optimization campaign has transpired. However, it can also be used as an ASF to which aims to find solutions which maximize the dominated hypervolume. In this case, the solutions in D are considered one at a time, which simplifies the calculation of H to the volume of the hyperrectangle with corners at y and r,