When hypervolume is used as part of the selection orarchiving process in a multiobjective evolutionary algorithm, it isnecessary to determine which solutions contribute the least hypervolumeto a front. Little focus has been placed on algorithms thatquickly determine these solutions and there are no fast algorithmsdesigned specifically for this purpose. We describe an algorithm,IHSO, that quickly determines a solution’s contribution. Furthermore,we describe and analyse heuristics that reorder objectives tominimize the work required for IHSO to calculate a solution’s contribution.Lastly, we describe and analyze search techniques thatreduce the amount of work required for solutions other than theleast contributing one. Combined, these techniques allow multiobjectiveevolutionary algorithms to calculate hypervolume inline inincreasingly complex and large fronts in many objectives.