HV-Net: Hypervolume Approximation Based on DeepSets

In this letter, we propose HV-Net, a new method for hypervolume approximation in evolutionary multiobjective 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 nondominated solution set. The input of HV-Net is a nondominated 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 techniques for hypervolume approximation.