Construction of nested orthogonal latin hypercube designs

Yang, Jinyu; Liu, Min Qian; Lin, Dennis K.J.

doi:10.5705/ss.2012.139

Cited by 29 publications

(38 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, q d − 1}. Let b = (q d − 1)/(d(q − 1)) , where c denotes the largest integer less than or equal to c. As shown in Steinberg and Lin (2006) and Pang, Liu, and Lin (2009), the corresponding columns of the first m = bd nonzero elements of Algorithm 1 (Construction of symmetric LHDs).…”

Section: Resultsmentioning

confidence: 99%

Construction of orthogonal symmetric Latin hypercube designs

et al. 2018

Self Cite

View full text Add to dashboard Cite

Latin hypercube designs (LHDs) have found wide application in computer experiments. It is known that orthogonal LHDs guarantee the orthogonality between all linear effects, and symmetric LHDs ensure the orthogonality between linear and second-order effects. In this paper, we propose a construction method for orthogonal symmetric LHDs. Most resulting LHDs can accommodate the maximum number of factors, thus can study many more factors than existing ones. Moveover, several methods for constructing nearly orthogonal symmetric LHDs are also provided. All the constructed orthogonal and nearly orthogonal LHDs could be utilized to generate more nearly orthogonal symmetric LHDs. A detailed comparison with existing designs shows that the resulting designs have more flexible and economical run sizes and have many desirable design properties.

show abstract

Section: Resultsmentioning

confidence: 99%

Construction of orthogonal symmetric Latin hypercube designs

et al. 2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…Comparing the proposed methods with the approach in Lin, Mukerjee, and Tang (2009), all orthogonal Latin hypercubes by the latter can be produced by the former with r = 1. Corollaries 1 and 2 highlight an important contribution of the proposed methods as they provide many new orthogonal Latin hypercubes of rs 2 runs where s is odd and r ̸ = s 2 c −2 for any positive integer c. (Orthogonal Latin hypercubes with odd s and r = s 2 c −2 were given by Pang, Liu, and Lin (2009).) Such run sizes of orthogonal Latin hypercubes cannot be found by existing methods.…”

Section: Corollary 2 For a Generalization Methods That Applies Columnmentioning

confidence: 99%

A general construction for space-filling Latin hypercubes

Lin¹,

Kang²

2017

STAT SINICA

View full text Add to dashboard Cite

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.

show abstract

“…Pang et al [2009] propose a general construction method for OLH in which Steinberg and Lin's [2006] approach is a special case (p = 2). Pang et al [2009] show that an OLH may be constructed for n = p d , where p is a prime number and d is a power of 2. Additionally, the number of factors that may be addressed is also a function of d.…”

Section: Previous Approaches To Creating Olhs and Nolhsmentioning

confidence: 99%

“…Steinberg and Lin [2006] recognize that "the primary limitation to our method is the severe sample size constraint" (p. 287). Likewise, Pang et al [2009] acknowledge that "the primary limitation to the [our] method is the sample size constraint" (p. 1726). Our work overcomes these constraints.…”

Section: Previous Approaches To Creating Olhs and Nolhsmentioning

confidence: 99%

“…To mitigate this problem, many researchers [Iman and Conover 1982;Florian 1992;Owen 1994;Ye 1998;Steinberg and Lin 2006;Cioppa and Lucas 2007;Joseph and Hung 2008;Pang et al 2009;Moon et al 2011] have developed algorithms to reduce or eliminate correlations among input variables in LHs. An LH with zero correlation between any of its input variables is an orthogonal Latin hypercube (OLH).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Constructing nearly orthogonal latin hypercubes for any nonsaturated run-variable combination

Hernández

Lucas

Carlyle

2012

ACM Trans. Model. Comput. Simul.

View full text Add to dashboard Cite

States Naval Postgraduate SchoolWe present a new method for constructing nearly orthogonal Latin hypercubes that greatly expands their availability to experimenters. Latin hypercube designs have proven useful for exploring complex, highdimensional computational models, but can be plagued with unacceptable correlations among input variables. To improve upon their effectiveness, many researchers have developed algorithms that generate orthogonal and nearly orthogonal Latin hypercubes. Unfortunately, these methodologies can have strict limitations on the feasible number of experimental runs and variables. To overcome these restrictions, we develop a mixed integer programming algorithm that generates Latin hypercubes with little or no correlation among their columns for most any determinate run-variable combination-including fully saturated designs. Moreover, many designs can be constructed for a specified number of runs and factors-thereby providing experimenters with a choice of several designs. In addition, our algorithm can be used to quickly adapt to changing experimental conditions by augmenting existing designs by adding new variables or generating new designs to accommodate a change in runs.

show abstract

Construction of nested orthogonal latin hypercube designs

Cited by 29 publications

References 0 publications

Construction of orthogonal symmetric Latin hypercube designs

Construction of orthogonal symmetric Latin hypercube designs

A general construction for space-filling Latin hypercubes

Constructing nearly orthogonal latin hypercubes for any nonsaturated run-variable combination

Contact Info

Product

Resources

About