Improved Quick Hypervolume Algorithm
This is an incremental improvement for researchers and practitioners using multiobjective evolutionary algorithms who need faster hypervolume calculations.
The paper tackles the problem of efficiently calculating exact hypervolume for multiobjective optimization by improving the Quick Hypervolume algorithm, resulting in better computational complexity and practical running times.
In this paper, we present a significant improvement of Quick Hypervolume algorithm, one of the state-of-the-art algorithms 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, but in our algorithm we split the problem into smaller sub-problems in a different way. Through both theoretical analysis and computational study we show that our approach improves computational complexity of the algorithm and practical running times.