Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments

Kazeem Adewale Osuolale

doi:doi:10.11648/j.mma.20210604.12

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Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments

Kazeem Adewale Osuolale

Published in Mathematical Modelling and Applications (Volume 6, Issue 4)

Received: 24 October 2021 Accepted: 9 November 2021 Published: 24 December 2021

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Abstract

Orthogonal Array-based Latin Hypercube Designs (OALHDs) have not only become popular in practice among strategies used in the development of computer experiments but also useful whenever interest is focused on performing some physical experiments. Design construction for computer experiments is a new issue in this part of the world since it is more about experimental planning rather than modelling aspect in which some progress has been made. The Bush Construction Type II method was presented in this paper to construct a strong Orthogonal Array (OA) of strength three, using Galois Fields (GF) of order s which gave rise to the constructed Orthogonal Array-Based Latin Hypercube Designs (OALHD) for computer experiments. Orthogonal Array-based Latin Hypercube Design was used in this paper as a Latin hypercube design constructed based on orthogonal array in order to achieve better space-filling properties that would otherwise not be possessed by a random Latin hypercube design (LHD). Orthogonal Array (N, k) LHD were constructed at parameter values of OA (N, k)=(64, 6) and (125, 7). This study is an improvement on the early paper which adopted the Bush Construction Type I technique and it therefore aimed at proposing a novel approach that employed the maximin criterion in the k-Nearest Neighbour with Euclidean distance for constructing strong orthogonal arrays along with the Orthogonal Array-Based Latin Hypercube Designs (OALHDs). The OA (64, 6) LHD and OA (125, 7) LHD constructed have better space-filling properties and they achieve uniformity in each dimension. This study concludes that the constructed OALHDs can be used whenever interest is focused on performing either a conventional or computer experiment on real life situations. A program implementation for the construction of OALHDs was done using MATLAB 2016 computer package.

Published in	Mathematical Modelling and Applications (Volume 6, Issue 4)
DOI	10.11648/j.mma.20210604.12
Page(s)	92-100
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Computer Experiments, Bush Construction Type II Method, Galois Fields, Latin Hypercube Designs, Orthogonal Array

References

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Kazeem Adewale Osuolale. (2021). Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments. Mathematical Modelling and Applications, 6(4), 92-100. https://doi.org/10.11648/j.mma.20210604.12

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Kazeem Adewale Osuolale. Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments. Math. Model. Appl. 2021, 6(4), 92-100. doi: 10.11648/j.mma.20210604.12

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Kazeem Adewale Osuolale. Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments. Math Model Appl. 2021;6(4):92-100. doi: 10.11648/j.mma.20210604.12

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@article{10.11648/j.mma.20210604.12,
  author = {Kazeem Adewale Osuolale},
  title = {Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments},
  journal = {Mathematical Modelling and Applications},
  volume = {6},
  number = {4},
  pages = {92-100},
  doi = {10.11648/j.mma.20210604.12},
  url = {https://doi.org/10.11648/j.mma.20210604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20210604.12},
  abstract = {Orthogonal Array-based Latin Hypercube Designs (OALHDs) have not only become popular in practice among strategies used in the development of computer experiments but also useful whenever interest is focused on performing some physical experiments. Design construction for computer experiments is a new issue in this part of the world since it is more about experimental planning rather than modelling aspect in which some progress has been made. The Bush Construction Type II method was presented in this paper to construct a strong Orthogonal Array (OA) of strength three, using Galois Fields (GF) of order s which gave rise to the constructed Orthogonal Array-Based Latin Hypercube Designs (OALHD) for computer experiments. Orthogonal Array-based Latin Hypercube Design was used in this paper as a Latin hypercube design constructed based on orthogonal array in order to achieve better space-filling properties that would otherwise not be possessed by a random Latin hypercube design (LHD). Orthogonal Array (N, k) LHD were constructed at parameter values of OA (N, k)=(64, 6) and (125, 7). This study is an improvement on the early paper which adopted the Bush Construction Type I technique and it therefore aimed at proposing a novel approach that employed the maximin criterion in the k-Nearest Neighbour with Euclidean distance for constructing strong orthogonal arrays along with the Orthogonal Array-Based Latin Hypercube Designs (OALHDs). The OA (64, 6) LHD and OA (125, 7) LHD constructed have better space-filling properties and they achieve uniformity in each dimension. This study concludes that the constructed OALHDs can be used whenever interest is focused on performing either a conventional or computer experiment on real life situations. A program implementation for the construction of OALHDs was done using MATLAB 2016 computer package.},
 year = {2021}
}

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TY  - JOUR
T1  - Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments
AU  - Kazeem Adewale Osuolale
Y1  - 2021/12/24
PY  - 2021
N1  - https://doi.org/10.11648/j.mma.20210604.12
DO  - 10.11648/j.mma.20210604.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 92
EP  - 100
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20210604.12
AB  - Orthogonal Array-based Latin Hypercube Designs (OALHDs) have not only become popular in practice among strategies used in the development of computer experiments but also useful whenever interest is focused on performing some physical experiments. Design construction for computer experiments is a new issue in this part of the world since it is more about experimental planning rather than modelling aspect in which some progress has been made. The Bush Construction Type II method was presented in this paper to construct a strong Orthogonal Array (OA) of strength three, using Galois Fields (GF) of order s which gave rise to the constructed Orthogonal Array-Based Latin Hypercube Designs (OALHD) for computer experiments. Orthogonal Array-based Latin Hypercube Design was used in this paper as a Latin hypercube design constructed based on orthogonal array in order to achieve better space-filling properties that would otherwise not be possessed by a random Latin hypercube design (LHD). Orthogonal Array (N, k) LHD were constructed at parameter values of OA (N, k)=(64, 6) and (125, 7). This study is an improvement on the early paper which adopted the Bush Construction Type I technique and it therefore aimed at proposing a novel approach that employed the maximin criterion in the k-Nearest Neighbour with Euclidean distance for constructing strong orthogonal arrays along with the Orthogonal Array-Based Latin Hypercube Designs (OALHDs). The OA (64, 6) LHD and OA (125, 7) LHD constructed have better space-filling properties and they achieve uniformity in each dimension. This study concludes that the constructed OALHDs can be used whenever interest is focused on performing either a conventional or computer experiment on real life situations. A program implementation for the construction of OALHDs was done using MATLAB 2016 computer package.
VL  - 6
IS  - 4
ER  -

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Author Information

Kazeem Adewale Osuolale

Biostatistics Sub-Unit, Grant, Monitoring and Evaluation Unit, Nigerian Institute of Medical Research Yaba, Lagos, Nigeria

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Kazeem Adewale Osuolale. (2021). Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments. Mathematical Modelling and Applications, 6(4), 92-100. https://doi.org/10.11648/j.mma.20210604.12

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Kazeem Adewale Osuolale. Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments. Math. Model. Appl. 2021, 6(4), 92-100. doi: 10.11648/j.mma.20210604.12

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Kazeem Adewale Osuolale. Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments. Math Model Appl. 2021;6(4):92-100. doi: 10.11648/j.mma.20210604.12

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@article{10.11648/j.mma.20210604.12,
  author = {Kazeem Adewale Osuolale},
  title = {Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments},
  journal = {Mathematical Modelling and Applications},
  volume = {6},
  number = {4},
  pages = {92-100},
  doi = {10.11648/j.mma.20210604.12},
  url = {https://doi.org/10.11648/j.mma.20210604.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20210604.12},
  abstract = {Orthogonal Array-based Latin Hypercube Designs (OALHDs) have not only become popular in practice among strategies used in the development of computer experiments but also useful whenever interest is focused on performing some physical experiments. Design construction for computer experiments is a new issue in this part of the world since it is more about experimental planning rather than modelling aspect in which some progress has been made. The Bush Construction Type II method was presented in this paper to construct a strong Orthogonal Array (OA) of strength three, using Galois Fields (GF) of order s which gave rise to the constructed Orthogonal Array-Based Latin Hypercube Designs (OALHD) for computer experiments. Orthogonal Array-based Latin Hypercube Design was used in this paper as a Latin hypercube design constructed based on orthogonal array in order to achieve better space-filling properties that would otherwise not be possessed by a random Latin hypercube design (LHD). Orthogonal Array (N, k) LHD were constructed at parameter values of OA (N, k)=(64, 6) and (125, 7). This study is an improvement on the early paper which adopted the Bush Construction Type I technique and it therefore aimed at proposing a novel approach that employed the maximin criterion in the k-Nearest Neighbour with Euclidean distance for constructing strong orthogonal arrays along with the Orthogonal Array-Based Latin Hypercube Designs (OALHDs). The OA (64, 6) LHD and OA (125, 7) LHD constructed have better space-filling properties and they achieve uniformity in each dimension. This study concludes that the constructed OALHDs can be used whenever interest is focused on performing either a conventional or computer experiment on real life situations. A program implementation for the construction of OALHDs was done using MATLAB 2016 computer package.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Orthogonal Array-Based Latin Hypercube Designs for Computer Experiments
AU  - Kazeem Adewale Osuolale
Y1  - 2021/12/24
PY  - 2021
N1  - https://doi.org/10.11648/j.mma.20210604.12
DO  - 10.11648/j.mma.20210604.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 92
EP  - 100
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20210604.12
AB  - Orthogonal Array-based Latin Hypercube Designs (OALHDs) have not only become popular in practice among strategies used in the development of computer experiments but also useful whenever interest is focused on performing some physical experiments. Design construction for computer experiments is a new issue in this part of the world since it is more about experimental planning rather than modelling aspect in which some progress has been made. The Bush Construction Type II method was presented in this paper to construct a strong Orthogonal Array (OA) of strength three, using Galois Fields (GF) of order s which gave rise to the constructed Orthogonal Array-Based Latin Hypercube Designs (OALHD) for computer experiments. Orthogonal Array-based Latin Hypercube Design was used in this paper as a Latin hypercube design constructed based on orthogonal array in order to achieve better space-filling properties that would otherwise not be possessed by a random Latin hypercube design (LHD). Orthogonal Array (N, k) LHD were constructed at parameter values of OA (N, k)=(64, 6) and (125, 7). This study is an improvement on the early paper which adopted the Bush Construction Type I technique and it therefore aimed at proposing a novel approach that employed the maximin criterion in the k-Nearest Neighbour with Euclidean distance for constructing strong orthogonal arrays along with the Orthogonal Array-Based Latin Hypercube Designs (OALHDs). The OA (64, 6) LHD and OA (125, 7) LHD constructed have better space-filling properties and they achieve uniformity in each dimension. This study concludes that the constructed OALHDs can be used whenever interest is focused on performing either a conventional or computer experiment on real life situations. A program implementation for the construction of OALHDs was done using MATLAB 2016 computer package.
VL  - 6
IS  - 4
ER  -

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