  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.
