HV-Net: Hypervolume Approximation based on DeepSets

TL;DR

HV-Net introduces a deep learning approach using DeepSets to accurately and efficiently approximate hypervolume in multi-objective optimization, outperforming traditional methods in error and runtime.

Contribution

The paper presents HV-Net, a novel neural network model leveraging DeepSets for hypervolume approximation, demonstrating improved accuracy and speed over existing methods.

Findings

HV-Net achieves lower approximation error than traditional methods.

HV-Net reduces runtime significantly compared to point-based and line-based methods.

Deep learning effectively models hypervolume approximation in multi-objective optimization.

Abstract

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.