Exploratory Optimal Latin Hypercube Designs for Computer Simulated Experiments

Abstract

The aim of this paper is to present the construction of the optimal design for computer simulated experiments (CSE) based on three different classes of Latin hypercube design (LHD), random Latin hypercube design (RLHD), symmetric Latin hypercube design (SLHD), and orthogonal array-based Latin hypercube design (OALHD), respectively. We first consider the property of design through various optimality criteria such as φ p criterion, maximin distance criterion, and the mean of correlation coefficient between design columns. After the design properties of each class of design are validated, we compare the prediction accuracy of the surrogate models namely Response surface methodology (RSM) and Kriging model (KRG), conducted by using the optimal design from those three classes of LHD. The results indicate that OALHD has the best design property over all dimensions of problem under consideration. Moreover, OALHD is superior to SLHD and RLHD in terms of prediction accuracy when both of RSM and KRG models are performed. Hence OALHD is recommended as the best design choice for CSE.