GHVC-Net: Hypervolume Contribution Approximation Based on Graph Neural Network

Guotong Wu, Yang Nan, Ke Shang, Hisao Ishibuchi

Abstract: This paper proposes a framework called GHVC-Net that uses the graph neural network (GNN) model to approximate each solution's hypervolume contribution (HVC). GHVC-Net is permutation invariant and can handle solution sets of arbitrary size, similar to the properties of GNN. Compared to HVC-Net (i.e., a machine learning model for HVC approximation), GHVC-Net achieves better accuracy with less training time. GHVC-Net is also compared with traditional approximation methods, such as line-based and point-based methods, to demonstrate its ability to identify the solution with the smallest (largest) HVC.