Abstract
In the area of computer simulation, Latin hypercube designs play an important role. In this paper the classes of maximin and Audze-Eglais Latin hypercube designs are considered. Up to now only several two-dimensional designs and a few higher dimensional designs for these classes have been published. Using periodic designs and the Enhanced Stochastic Evolutionary algorithm of Jin et al. (2005), we obtain new results which we compare to existing results. We thus construct a database of approximate maximin and Audze-Eglais Latin hypercube designs for up to ten dimensions and for up to 300 design points.
Highlights
A k-dimensional Latin hypercube design (LHD) of n points, is a set of n points xi = ∈ {0, . . . , n − 1}k such that for each dimension j all xij are distinct
This paper discusses existing and new results in the field of maximin and AudzeEglais Latin hypercube designs. Such designs play an important role in the area of computer simulation
The first heuristic is based on the observation that many optimal LHDs, and two-dimensional LHDs in particular, exhibit a periodic structure
Summary
A few authors consider the construction of maximin LHDs. For example, Morris and Mitchell (1995) used simulated annealing to find approximate maximin LHDs for up to five dimensions and up to 12 design points, and a few larger values, with respect to the 1- and 2-distance measure. The ESE-algorithm of Jin et al (2005) described and periodic designs are used to generate new approximate maximin and Audze-Eglais LHDs. Computational results for up to ten dimensions and for up to 300 design points, as well as a comparison of the new and existing results, are provided in Sect.
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