IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v84y2021i5d10.1007_s00184-020-00788-w.html
   My bibliography  Save this article

Maximin distance designs based on densest packings

Author

Listed:
  • Liuqing Yang

    (Nankai University)

  • Yongdao Zhou

    (Nankai University)

  • Min-Qian Liu

    (Nankai University)

Abstract

Computer experiments play a crucial role when physical experiments are expensive or difficult to be carried out. As a kind of designs for computer experiments, maximin distance designs have been widely studied. Many existing methods for obtaining maximin distance designs are based on stochastic algorithms, and these methods will be infeasible when the run size or number of factors is large. In this paper, we propose some deterministic construction methods for maximin $$L_2$$ L 2 -distance designs in two to five dimensions based on densest packings. The resulting designs have large $$L_2$$ L 2 -distances and are mirror-symmetric. Some of them have the same $$L_2$$ L 2 -distances as the existing optimal maximin distance designs, and some of the others are completely new. Especially, the resulting 2-dimensional designs possess a good projection property.

Suggested Citation

  • Liuqing Yang & Yongdao Zhou & Min-Qian Liu, 2021. "Maximin distance designs based on densest packings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 615-634, July.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:5:d:10.1007_s00184-020-00788-w
    DOI: 10.1007/s00184-020-00788-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-020-00788-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-020-00788-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Qian Xiao & Hongquan Xu, 2017. "Construction of maximin distance Latin squares and related Latin hypercube designs," Biometrika, Biometrika Trust, vol. 104(2), pages 455-464.
    2. Yu Tang & Hongquan Xu, 2014. "Permuting regular fractional factorial designs for screening quantitative factors," Biometrika, Biometrika Trust, vol. 101(2), pages 333-350.
    3. Xu He, 2017. "Rotated Sphere Packing Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1612-1622, October.
    4. Husslage, B.G.M. & Rennen, G. & van Dam, E.R. & den Hertog, D., 2011. "Space-filling Latin hypercube designs for computer experiments," Other publications TiSEM 694f73df-a373-46a7-aa4d-1, Tilburg University, School of Economics and Management.
    5. 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.
    6. 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.
    7. Husslage, B.G.M., 2006. "Maximin designs for computer experiments," Other publications TiSEM 216147a0-9c82-48d5-8913-6, Tilburg University, School of Economics and Management.
    8. 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.
    9. Yongdao Zhou & Hongquan Xu, 2015. "Space-filling properties of good lattice point sets," Biometrika, Biometrika Trust, vol. 102(4), pages 959-966.
    10. van Dam, E.R. & Rennen, G. & Husslage, B.G.M., 2007. "Bounds for Maximin Latin Hypercube Designs," Other publications TiSEM da0c15be-f18e-474e-b557-f, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gao, Yanping & Yi, Siyu & Zhou, Yongdao, 2022. "Maximin L1-distance Range-fixed Level-augmented designs," Statistics & Probability Letters, Elsevier, vol. 186(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tonghui Pang & Yan Wang & Jian-Feng Yang, 2022. "Asymptotically optimal maximin distance Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 405-418, May.
    2. Rennen, G. & Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2009. "Nested Maximin Latin Hypercube Designs," Discussion Paper 2009-06, Tilburg University, Center for Economic Research.
    3. 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.
    4. Edwin Dam & Bart Husslage & Dick Hertog, 2010. "One-dimensional nested maximin designs," Journal of Global Optimization, Springer, vol. 46(2), pages 287-306, February.
    5. HARCSA Imre Milán & KOVÁCS Sándor & NÁBRÁDI András, 2020. "Economic Analysis Of Subcontract Distilleries By Simulation Modeling Method," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(1), pages 50-63, July.
    6. Husslage, B.G.M. & Rennen, G. & van Dam, E.R. & den Hertog, D., 2008. "Space-Filling Latin Hypercube Designs For Computer Experiments (Revision of CentER DP 2006-18)," Discussion Paper 2008-104, Tilburg University, Center for Economic Research.
    7. 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.
    8. van Dam, E.R. & Rennen, G. & Husslage, B.G.M., 2007. "Bounds for Maximin Latin Hypercube Designs," Other publications TiSEM da0c15be-f18e-474e-b557-f, Tilburg University, School of Economics and Management.
    9. Crombecq, K. & Laermans, E. & Dhaene, T., 2011. "Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling," European Journal of Operational Research, Elsevier, vol. 214(3), pages 683-696, November.
    10. Husslage, B.G.M. & Rennen, G. & van Dam, E.R. & den Hertog, D., 2008. "Space-Filling Latin Hypercube Designs For Computer Experiments (Revision of CentER DP 2006-18)," Other publications TiSEM 1b5d18c7-b66f-4a9f-838c-b, Tilburg University, School of Economics and Management.
    11. Xiangjing Lai & Jin-Kao Hao & Renbin Xiao & Fred Glover, 2023. "Perturbation-Based Thresholding Search for Packing Equal Circles and Spheres," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 725-746, July.
    12. Rennen, G., 2008. "Subset Selection from Large Datasets for Kriging Modeling," Discussion Paper 2008-26, Tilburg University, Center for Economic Research.
    13. Mu, Weiyan & Xiong, Shifeng, 2018. "A class of space-filling designs and their projection properties," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 129-134.
    14. Siem, A.Y.D. & den Hertog, D., 2007. "Kriging Models That Are Robust With Respect to Simulation Errors," Other publications TiSEM fe73dc8b-20d6-4f50-95eb-f, Tilburg University, School of Economics and Management.
    15. Wang, Chunyan & Lin, Dennis K.J., 2024. "Strong orthogonal Latin hypercubes for computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).
    16. Rennen, G., 2008. "Subset Selection from Large Datasets for Kriging Modeling," Other publications TiSEM 9dfe6396-1933-45c0-b4e3-5, Tilburg University, School of Economics and Management.
    17. Rennen, G. & Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2009. "Nested Maximin Latin Hypercube Designs," Other publications TiSEM 1c504ec0-f357-42d2-9c92-9, Tilburg University, School of Economics and Management.
    18. Su, Zheren & Wang, Yaping & Zhou, Yingchun, 2020. "On maximin distance and nearly orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 166(C).
    19. van Dam, E.R., 2008. "Two-dimensional maximin Latin hypercube designs," Other publications TiSEM 61788dd1-b1b5-4c81-9151-8, Tilburg University, School of Economics and Management.
    20. Siem, A.Y.D. & den Hertog, D., 2007. "Kriging Models That Are Robust With Respect to Simulation Errors," Discussion Paper 2007-68, Tilburg University, Center for Economic Research.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:84:y:2021:i:5:d:10.1007_s00184-020-00788-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.