# Improved Quick Hypervolume Algorithm

arXiv: https://arxiv.org/abs/1612.03402 · HTML: https://mlsanity.com/paper/1612.03402/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2016.

## Built on by (most cited first, 2 of 2)

- [What if we Increase the Number of Objectives? Theoretical and Empirical Implications for Many-objective Optimization](https://mlsanity.com/paper/2106.03275/) (2021)
- [Multi-Value Alignment in Normative Multi-Agent System: Evolutionary Optimisation Approach](https://mlsanity.com/paper/2305.07366/) (2023)

## Abstract (arXiv)

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.