A general construction for space-filling Latin hypercubes

Abstract

We propose a general method for constructing Latin hypercubes of flexible run sizes for computer experiments. The method makes use of arrays with a special structure and Latin hypercubes. By using different such arrays and Latin hypercubes, the proposed method produces various types of Latin hypercubes including orthogonal and nearly orthogonal Latin hypercubes, sliced Latin hypercubes, and Latin hypercubes in marginally coupled designs. In addition, the proposed algebraic design construction is particularly efficient as it does not need any optimization search but still produces Latin hypercubes whose space-filling properties are comparable with those generated by the common and latest methods in the literature.

A Construction Method for Maximin L1-Distance Latin Hypercube Designs

“…To better illustrate the performance of these three methods, we define the Moreover, Lin and Kang (2016)'s method can also be used for generating maximin LHDs under the φ r criterion. Their numerical results have showed that the designs constructed by Lin and Kang (2016)'s method have larger φ r values (so worse) than the designs constructed by the R package SLHD; while our designs have smaller φ r value than designs constructed by the R package SLHD, so our designs perform better than the designs obtained by Lin and Kang (2016)'s method. As an example, using N = 404, we obtain an LHD(100, 50).…”

“…As an example, using N = 404, we obtain an LHD(100, 50). By deleting the last two columns and the last two rows, and rearranging the levels for each column, we obtain an LHD(98, 48) with a φ r value of 0.1096, which is better than any of the LHD(98, 48)'s constructed by Lin and Kang (2016)'s method (whose smallest φ r value is 0.1164). The φ r values are evaluated on standardized designs with n levels scaled to [0.5/n, 1 − 0.5/n].…”

“…Moreover, they showed that maximin L 1 -equidistant designs are uniform projection designs, and provided a method to construct uniform projection designs based on good lattice point sets when the number of rows is an odd prime. Lin and Kang (2016) proposed a general method for constructing Latin hypercubes of flexible run sizes for computer experiments, the method made use of arrays with a special structure and Latin hypercube designs. They showed that their method can be utilized for generating maximin Latin hypercube designs with flexible run sizes under the φ r criterion.…”

Design selection for strong orthogonal arrays

“…Criteria based on orthogonality, distance and discrepancy can all be used for this purpose. Some related recent work includes Georgiou & Efthimiou (), Liu & Liu (), Lin & Kang (), and Xiao & Xu ().…”

A class of space‐filling designs with low‐dimensional stratification and column orthogonality

“…An intuitive approach for constructing space‐filling designs is to employ an algorithmic search or a construction method based on a distance or discrepancy criterion; see Johnson, Moore & Ylvisaker (1990) and Fang, Li & Sudijanto (2006) for early work, and Moon, Dean & Santner (2011), Lin & Kang (2016), Wang, Xiao & Xu (2018), and Sun, Wang & Xu (2019) for more recent developments. Inspired by ‐nets from quasi‐Monte Carlo methods (Niederreiter, 1992), He & Tang (2013) introduced and studied strong orthogonal arrays (SOAs).…”