Improved quick hypervolume algorithm

In this paper, we present an improved version of recently proposed Quick Hypervolume algorithm for calculating exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used as a quality indicator in multiobjective evolutionary algorithms and other multiobjective metaheuristics and the efficiency of calculating this indicator is of crucial importance especially in the case of large sets or many dimensional objective spaces. We use a similar divide and conquer scheme as in the original Quick Hypervolume algorithm, we modify, however, the way the problem is split into smaller sub-problems. Through both theoretical analysis and computational study we show that our approach improves computational complexity of the algorithm and practical running times.