A new criterion for Latin hypercube optimization

In this contribution, a new approach for optimizing LH designs based on the estimation and evaluation of pdfs is presented. The proposed algorithm minimizes the mean absolute error between the estimated pdf of the LH design,evaluated solely on its data points, and the uniform distribution. To validate the functionality of the new approach, it is compared to other state-of-the-art methods to create space-filling designs. The methods are compared using the KL divergence of the resulting datasets and the uniform distribution, as well as the
resulting computation times for various dimensions and number of data points. Overall, the KL divergence performance of the new approach is outstanding, but expensive in terms of the computational demand. An additional benefit of the proposed approach is that it allows higher flexibility for DoE desgins. For example, it can be extended to approach any arbitrary point distribution, not just uniform, and may be suitable for the integration of constrains.