# HV-Net: Hypervolume Approximation based on DeepSets

arXiv: https://arxiv.org/abs/2203.02185 · HTML: https://mlsanity.com/paper/2203.02185/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2022.

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

- [Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement](https://mlsanity.com/paper/2310.15195/) (2023)
- [Multi-objective optimization via equivariant deep hypervolume approximation](https://mlsanity.com/paper/2210.02177/) (2022)

## Abstract (arXiv)

In this letter, we propose HV-Net, a new method for hypervolume approximation in evolutionary multi-objective optimization. The basic idea of HV-Net is to use DeepSets, a deep neural network with permutation invariant property, to approximate the hypervolume of a non-dominated solution set. The input of HV-Net is a non-dominated solution set in the objective space, and the output is an approximated hypervolume value of this solution set. The performance of HV-Net is evaluated through computational experiments by comparing it with two commonly-used hypervolume approximation methods (i.e., point-based method and line-based method). Our experimental results show that HV-Net outperforms the other two methods in terms of both the approximation error and the runtime, which shows the potential of using deep learning technique for hypervolume approximation.