# R2-based Hypervolume Contribution Approximation

arXiv: https://arxiv.org/abs/1805.06773 · HTML: https://mlsanity.com/paper/1805.06773/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2018.

## Built on by (most cited first, 3 of 3)

- [Benchmarking Subset Selection from Large Candidate Solution Sets in Evolutionary Multi-objective Optimization](https://mlsanity.com/paper/2201.06700/) (2022)
- [Learning to Approximate: Auto Direction Vector Set Generation for Hypervolume Contribution Approximation](https://mlsanity.com/paper/2201.06707/) (2022)
- [Preference-Shaped Expected Hypervolume and R2 Improvement: Exact Computation and Monotonicity](https://mlsanity.com/paper/2605.28746/) (2026)

## Abstract (arXiv)

In this letter, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Comparing with a traditional method which is based on the R2 indicator to approximate the hypervolume, the new method can directly approximate the hypervolume contribution and will utilize all the direction vectors only in the hypervolume contribution region. The new method, the traditional method and the Monte Carlo sampling method together with two exact methods are compared through comprehensive experiments. Our results show the advantages of the new method over the other methods. Comparing with the other two approximation methods, the new method achieves the best performance for comparing hypervolume contributions of different solutions and identifying the solution with the smallest hypervolume contribution. Comparing with the exact methods, the new method is computationally efficient in high-dimensional spaces where the exact methods are impractical to use.