A study on algorithms for optimization of Latin hypercubes

A crucial component in the statistical simulation of a computationally expensive model is a good design of experiments. In this paper we compare the efficiency of the columnwise–pairwise (CP) and genetic algorithms for the optimization of Latin hypercubes (LH) for the purpose of sampling in statistical investigations. The performed experiments indicate, among other results, that CP methods are most efficient for small and medium size LH, while an adopted genetic algorithm performs better for large LH. Two optimality criteria suggested in the literature are evaluated with respect to statistical properties and efficiency. The obtained results lead us to favor a criterion based on the physical analogy of minimization of forces between charged particles suggested in Audze and Eglais (1977. Problems Dyn. Strength 35, 104–107) over a ‘maximin distance’ criterion from Johnson et al. (1990. J. Statist. Plann. Inference 26, 131–148).