Normalization in R2-Based Hypervolume and Hypervolume Contribution Approximation

In this paper, we examine the effect of normalization in R2-based hypervolume and hypervolume contribution approximation. The fact is that the region with different scales on objective space brings approximation bias. The basic idea of normalization is to perform a coordinate transformation to make the shape of the approximated region more regular, and then transform it to obtain the final value according to the property of hypervolume and hypervolume contribution. The performance of normalization is evaluated on different datasets by comparing it with the original R2-based method. We use two different metrics to evaluate hypervolume and hypervolume contribution separately, and the results indicate that normalization does exactly improve the approximation accuracy and outperforms the original R2-based method.