Optimal Latin-hypercube designs for computer experiments

Abstract Latin-hypercube designs (Lhd) were considered by Mckay et al. (1979) as designs for computer experiments. Sacks et al. (1989a) and Shewry and Wynn (1987) proposed optimal designs for computer experiments which minimize the integrated mean squared error (IMSE) and maximize entropy, respectively, based on some spatial prediction models. In this paper, optimal Latin-hypercube designs minimizing IMSE or maximizing entropy are considered. These designs turn out to be well spread over the design region without replicated coordinate values, often symmetric, and nearly optimal among all Latin-hypercube designs. A 2-stage (exchange- and Newton-type) computational algorithm for finding the proposed design is presented. An example is given to illustrate that a small prediction error is obtained from the optimal Lhd than from the usual Lhd's. Several pictures of designs constructed by the algorithm are presented.