Ensemble R2-based Hypervolume Contribution Approximation

The hypervolume-based multi-objective evolutionary algorithms (HV-MOEAs) have proven to be highly effective in solving multi-objective optimization problems. However, the computation time of the hypervolume calculation increases significantly as the number of objectives increases. To address this issue, an R2-based hypervolume contribution approximation (R2-HVC) method was proposed. Nevertheless, the original R2-HVC generates a large number of vectors and computes the HVC only once. In this study, we propose an ensemble method based on the R2-HVC method. By using a small number of vectors for repetitive computation and majority voting, the ensemble method can reduce the probability of making incorrect choices. Experimental results show that the proposed method can improve the approximation accuracy while maintaining a similar computation time to the original R2-HVC method.