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 the efficiency of calculating this indicator is of crucial importance especially in the case of large set or many dimensional 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 running time of its implementation.