Estimation of global minimum value of the optimality criteria for constructing optimal Latin hypercube designs

Abstract

Recent advances in computational power have led to study of physical processes through deterministic computer simulated experiments (CSE). Normally CSEs are time consuming and computationally expensive to run. Hence a selection of design to run CSE is very critical. The space filling designs, like Latin hypercube design (LHD) which aim to spread the design points over the region of interest are commonly used to comprehend the output of CSE. The optimal design for a given problem is obtained using search algorithms with a pre-specified optimality criterion. Searching for the optimal design is a computational
burden especially when the dimension of the problem is large. Further, the search process may be terminated when the local optimum value of a given optimality criterion is obtained and hence the optimal design would not be reached. The aim of this paper is to estimate the global minimum of the most popular criterion namely Phi_p using the extreme value distribution theory. The proposed method has been implemented using various dimensions of LHD. The estimated global minimum values of Phi_p criterion can be used as a monitoring tool of the search path in the sense that how far from the global minimum during the search process. Further, the obtained results can also be used as a crucial guideline to terminate the search process before the computational burden is prohibitive.