Improved Quick Hypervolume Algorithm

TL;DR

This paper introduces an improved version of the Quick Hypervolume algorithm that enhances computational efficiency for calculating hypervolume in multiobjective optimization, especially for large and high-dimensional datasets.

Contribution

The paper proposes a novel splitting strategy within the divide and conquer framework, reducing complexity and improving practical performance over the original algorithm.

Findings

Reduced computational complexity

Faster practical running times

Effective for large and high-dimensional datasets

Abstract

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.