Optimal Latin hypercube designs (LHDs), including maximin distance LHDs, maximum projection LHDs and orthogonal LHDs, are widely used in computer experiments. It is challenging to construct such designs with flexible sizes, especially for large ones, for two main reasons. One reason is that theoretical results, such as algebraic constructions ensuring the maximin distance property or orthogonality, are only available for certain design sizes. For design sizes where theoretical results are unavailable, search algorithms can generate designs. However, their numerical performance is not guaranteed to be optimal. Another reason is that when design sizes increase, the number of permutations grows exponentially. Constructing optimal LHDs is a discrete optimization process, and enumeration is nearly impossible for large or moderate design sizes. Various search algorithms and algebraic constructions have been proposed to identify optimal LHDs, each having its own pros and cons. We develop the R package LHD which implements various search algorithms and algebraic constructions. We embedded different optimality criteria into each of the search algorithms, and they are capable of constructing different types of optimal LHDs even though they were originally invented to construct maximin distance LHDs only. Another input argument that controls maximum CPU time is added to each of the search algorithms to let users flexibly allocate their computational resources. We demonstrate functionalities of the package by using various examples, and we provide guidance for experimenters on finding suitable optimal designs. The LHD package is easy to use for practitioners and possibly serves as a benchmark for future developments in LHD.
Wang et al. (Mon,) studied this question.