Improved quick hypervolume algorithm

In this paper, we present a significant improvement of the Quick Hypervolume algorithm, one of the state-of-the-art algorithms for calculating the exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used as the quality indicator in the 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, but in our algorithm we split the problem into smaller sub-problems in a different way. Through both theoretical analysis and a computational study we show that our approach improves the computational complexity of the algorithm and practical running times.