STHV-Net: Hypervolume Approximation based on Set Transformer

In this paper, we propose STHV-Net to approximate the hypervolume indicator based on Set Transformer. Set Transformer is an advanced model to process set-form data which concentrates on the interaction of set elements. STHV-Net receives a non-dominated positive solution set of any size and outputs an approximate hyper-volume value of this solution set. The output value is independent of the order of the elements in the input set. The performance of STHV-Net is compared with three existing approximation methods (Monte Carlo, R2 indicator, HV-Net) using two evaluation criteria: approximation errors and computing time. Our experimental results show that STHV-Net is superior to the Monte Carlo method and the R2 indicator method with respect to these two criteria. Compared with HV-Net, our method can obtain lower approximation errors at the cost of a slightly longer computing time. We provide six representative models with different parameter sizes for users who have different preferences about the tradeoff between approximation error and computing time.