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

Authors:

Alejandro S. Hernandez,

Thomas W. Lucas,

Matthew CarlyleAuthors Info & Claims

ACM Transactions on Modeling and Computer Simulation (TOMACS), Volume 22, Issue 4

Article No.: 20, Pages 1 - 17

https://doi.org/10.1145/2379810.2379813

Published: 21 November 2012 Publication History

Abstract

We 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, high-dimensional 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.

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Parker JLucas TCarlyle W(2024)Sequentially extending space-filling experimental designs by optimally permuting and stacking columns of the design matrixEuropean Journal of Operational Research10.1016/j.ejor.2024.06.020319:2(600-610)Online publication date: Dec-2024
https://doi.org/10.1016/j.ejor.2024.06.020
Brackett‐Rozinsky NLemire D(2024)Batched ranged random integer generationSoftware: Practice and Experience10.1002/spe.336955:1(155-169)Online publication date: 25-Aug-2024
https://doi.org/10.1002/spe.3369
Lucas TParker J(2023)The Variability in Design-Quality Measures for Multiple Types of Spacefilling Designs Created by Leading Software PackagesProceedings of the Winter Simulation Conference10.5555/3643142.3643185(516-527)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3643142.3643185
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Index Terms

Constructing nearly orthogonal latin hypercubes for any nonsaturated run-variable combination
1. Mathematics of computing
  1. Probability and statistics
    1. Statistical paradigms
      1. Statistical graphics

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Published In

cover image ACM Transactions on Modeling and Computer Simulation

ACM Transactions on Modeling and Computer Simulation Volume 22, Issue 4

November 2012

135 pages

ISSN:1049-3301

EISSN:1558-1195

DOI:10.1145/2379810

Issue’s Table of Contents

Copyright © 2012 ACM.

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Publication History

Published: 21 November 2012

Accepted: 01 July 2012

Revised: 01 February 2012

Received: 01 August 2011

Published in TOMACS Volume 22, Issue 4

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Cited By

Parker JLucas TCarlyle W(2024)Sequentially extending space-filling experimental designs by optimally permuting and stacking columns of the design matrixEuropean Journal of Operational Research10.1016/j.ejor.2024.06.020319:2(600-610)Online publication date: Dec-2024
https://doi.org/10.1016/j.ejor.2024.06.020
Brackett‐Rozinsky NLemire D(2024)Batched ranged random integer generationSoftware: Practice and Experience10.1002/spe.336955:1(155-169)Online publication date: 25-Aug-2024
https://doi.org/10.1002/spe.3369
Lucas TParker J(2023)The Variability in Design-Quality Measures for Multiple Types of Spacefilling Designs Created by Leading Software PackagesProceedings of the Winter Simulation Conference10.5555/3643142.3643185(516-527)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3643142.3643185
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Lucas TParker J(2023)The Variability in Design-Quality Measures for Multiple Types of Space-Filling Designs Created by Leading Software Packages2023 Winter Simulation Conference (WSC)10.1109/WSC60868.2023.10407287(516-527)Online publication date: 10-Dec-2023
https://doi.org/10.1109/WSC60868.2023.10407287
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