Space-filling Latin hypercube designs for computer experiments

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. (J. Stat. Plan. Interference 134(1):268-687, 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. All these designs can be downloaded from the website http://www.spacefillingdesigns.nl.

Optimal Latin hypercube designs for the Kullback–Leibler criterion

“…A method to estimate the criterion based on the distance to nearest neighbors (Kosachenko and Leonenko 1987) could decrease the running time. The computational time could be also reduced by selecting the design into a subclass of LHD such as symmetric LHD (Ye et al 2000) or periodic designs (Husslage et al 2006).…”

“…Another algorithm (genetic algorithm, simulated annealing algorithm) might be more appropriate for this criterion. Grosso et al (2009) and Husslage et al (2006) obtained much better maximin LHDs by using iterated local search heuristics.…”

Surrogate‐based methods for black‐box optimization

“…From the above discussion, we summarize the two most important requirements for a good experimental design (Husslage et al., ; Stinstra et al., ) are as follows: Space‐fill: The design points should be uniformly spread over the entire design space. …”

“…Moreover, the space‐fill measure in this case, that is, , is quite simple. For that reason, distance designs are the most well studied among all experimental designs (Stinstra et al., ; Forrester et al., ; Husslage et al., ).…”

An efficient optimum Latin hypercube sampling technique based on sequencing optimisation using simulated annealing

“…Such a numerical scheme is called optimum Latin hypercube sampling (OLHS). Nowadays, there have been various numerical algorithms proposed for OLHS using several space filing objective functions (Jin, Chen, and Sudjianto 2005;Liefvendahl and Stocki 2006;Conley 2007;Grosso, Jamali, and Locatelli 2009;Viana, Venter, and Balabanov 2010;Georgiou and Stylianou 2011;Husslage, Rennen, van Dam, and den Hertog 2011;Zhu, Liu, Long, and Peng 2011;Loeppky, Moore, and Williams 2012;Talke and Borkowski 2012;Yin and Liu 2013). The well-known and most used methods used as an OLHS benchmark are genetic algorithm (GA) (Liefvendahl and Stocki 2006) and enhanced stochastic evolutionary algorithm (ESEA) (Jin et al 2005).…”