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Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes

Author

Listed:
  • Jing Zhang

    (College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410072, China)

  • Jin Xu

    (College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410072, China)

  • Kai Jia

    (College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410072, China)

  • Yimin Yin

    (College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410072, China)

  • Zhengming Wang

    (College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410072, China)

Abstract

Sliced Latin hypercube designs (SLHDs) are widely used in computer experiments with both quantitative and qualitative factors and in batches. Optimal SLHDs achieve better space-filling property on the whole experimental region. However, most existing methods for constructing optimal SLHDs have restriction on the run sizes. In this paper, we propose a new method for constructing SLHDs with arbitrary run sizes, and a new combined space-filling measurement describing the space-filling property for both the whole design and its slices. Furthermore, we develop general algorithms to search for the optimal SLHD with arbitrary run sizes under the proposed measurement. Examples are presented to illustrate that effectiveness of the proposed methods.

Suggested Citation

  • Jing Zhang & Jin Xu & Kai Jia & Yimin Yin & Zhengming Wang, 2019. "Optimal Sliced Latin Hypercube Designs with Slices of Arbitrary Run Sizes," Mathematics, MDPI, vol. 7(9), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:854-:d:267711
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    References listed on IDEAS

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    1. Edwin R. van Dam & Gijs Rennen & Bart Husslage, 2009. "Bounds for Maximin Latin Hypercube Designs," Operations Research, INFORMS, vol. 57(3), pages 595-608, June.
    2. Peter Z. G. Qian, 2012. "Sliced Latin Hypercube Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 393-399, March.
    3. Edwin R. van Dam & Bart Husslage & Dick den Hertog & Hans Melissen, 2007. "Maximin Latin Hypercube Designs in Two Dimensions," Operations Research, INFORMS, vol. 55(1), pages 158-169, February.
    4. Xiangshun Kong & Mingyao Ai & Kwok Leung Tsui, 2018. "Flexible sliced designs for computer experiments," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(3), pages 631-646, June.
    5. Hao Chen & Hengzhen Huang & Dennis K. J. Lin & Min‐Qian Liu, 2016. "Uniform sliced Latin hypercube designs," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(5), pages 574-584, September.
    6. Grosso, A. & Jamali, A.R.M.J.U. & Locatelli, M., 2009. "Finding maximin latin hypercube designs by Iterated Local Search heuristics," European Journal of Operational Research, Elsevier, vol. 197(2), pages 541-547, September.
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    Cited by:

    1. Yang You & Guang Jin & Zhengqiang Pan & Rui Guo, 2021. "MP-CE Method for Space-Filling Design in Constrained Space with Multiple Types of Factors," Mathematics, MDPI, vol. 9(24), pages 1-13, December.

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