R2-based Hypervolume Contribution Approximation

In this paper, a new hypervolume contribution approximation method is proposed which is formulated as an R2 indicator. The basic idea of the proposed method is to use different line segments only in the hypervolume contribution region for the hypervolume contribution approximation. Compared with a traditional method which is based on the R2 indicator to approximate the hypervolume, the new method can directly approximate the hypervolume contribution and will utilize all the direction vectors only in the hypervolume contribution region. The new method, the traditional method and the Monte Carlo sampling method are compared through numerical experiments. Our experimental results show the superiority of the new method over the other two methods, where the new method achieves the best performance for comparing hypervolume contributions of different solutions and identifying the solution with the smallest hypervolume contribution.

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