Orthogonal-maximin Latin Hypercube Designs

A randomly generated Latin hypercube design (LHD) can be quite structured: the variables may be highly correlated or the design may not have good space-filling properties. There are procedures for finding good LHDs by minimizing the pairwise correlations or by maximizing the inter-site distances. In this article we show that these two criteria need not be in close agreement. We propose a multi-objective optimization approach to find good LHDs by combining correlation and distance performance measures. We also propose a new exchange algorithm for efficiently generating such designs. Several examples are presented to show that the new algorithm is fast, and that the optimal designs are good in terms of both the correlation and distance criteria.