IDEAS home Printed from https://ideas.repec.org/p/tiu/tiutis/b4eb1336-e9d8-441a-ac87-0d8696680d09.html
   My bibliography  Save this paper

Maximin Latin hypercube designs in two dimensions

Author

Listed:
  • van Dam, E.R.

    (Tilburg University, School of Economics and Management)

  • den Hertog, D.

    (Tilburg University, School of Economics and Management)

  • Husslage, B.G.M.

    (Tilburg University, School of Economics and Management)

  • Melissen, H.

Abstract

The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n nonattacking rooks on an n × n chessboard such that the minimal distance between pairs of rooks is maximized. Maximin Latin hypercube designs are important for the approximation and optimization of black-box functions. In this paper, general formulas are derived for maximin Latin hypercube designs for general n , when the distance measure is l (infinity) or l 1 . Furthermore, for the distance measure l 2 , we obtain maximin Latin hypercube designs for n (le) 70 and approximate maximin Latin hypercube designs for other values of n . All these maximin Latin hypercube designs can be downloaded from the website http://www.spacefillingdesigns.nl. We show that the reduction in the maximin distance caused by imposing the Latin hypercube design structure is small. This justifies the use of maximin Latin hypercube designs instead of unrestricted designs.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • van Dam, E.R. & den Hertog, D. & Husslage, B.G.M. & Melissen, H., 2007. "Maximin Latin hypercube designs in two dimensions," Other publications TiSEM b4eb1336-e9d8-441a-ac87-0, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:b4eb1336-e9d8-441a-ac87-0d8696680d09
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/803551/Maximinl.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Artan Dimnaku & Rex Kincaid & Michael Trosset, 2005. "Approximate Solutions of Continuous Dispersion Problems," Annals of Operations Research, Springer, vol. 136(1), pages 65-80, April.
    2. den Hertog, Dick & Stehouwer, Peter, 2002. "Optimizing color picture tubes by high-cost nonlinear programming," European Journal of Operational Research, Elsevier, vol. 140(2), pages 197-211, July.
    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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. 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.
    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. Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2005. "Nested Maximin Latin Hypercube Designs in Two Dimensions," Discussion Paper 2005-79, Tilburg University, Center for Economic Research.
    6. B. Addis & M. Locatelli & F. Schoen, 2008. "Disk Packing in a Square: A New Global Optimization Approach," INFORMS Journal on Computing, INFORMS, vol. 20(4), pages 516-524, November.
    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. 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.
    10. Stinstra, E., 2006. "The meta-model approach for simulation-based design optimization," Other publications TiSEM 713f828a-4716-4a19-af00-e, Tilburg University, School of Economics and Management.
    11. Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2005. "Nested Maximin Latin Hypercube Designs in Two Dimensions," Other publications TiSEM 3e013144-3e4c-460c-96bc-1, Tilburg University, School of Economics and Management.
    12. 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.
    13. 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.
    14. Brekelmans, Ruud & Driessen, Lonneke & Hamers, Herbert & den Hertog, Dick, 2005. "Constrained optimization involving expensive function evaluations: A sequential approach," European Journal of Operational Research, Elsevier, vol. 160(1), pages 121-138, January.
    15. Ivo Couckuyt & Dirk Deschrijver & Tom Dhaene, 2014. "Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization," Journal of Global Optimization, Springer, vol. 60(3), pages 575-594, November.
    16. Yanikoglu, I. & den Hertog, D., 2011. "Safe Approximations of Chance Constraints Using Historical Data," Other publications TiSEM ab77f6f2-248a-42f1-bde1-0, Tilburg University, School of Economics and Management.
    17. 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.
    18. Yanikoglu, I. & den Hertog, D., 2011. "Safe Approximations of Chance Constraints Using Historical Data," Discussion Paper 2011-137, Tilburg University, Center for Economic Research.
    19. Rennen, G., 2008. "Subset Selection from Large Datasets for Kriging Modeling," Discussion Paper 2008-26, Tilburg University, Center for Economic Research.
    20. 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.

    More about this item

    JEL classification:

    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General

    Statistics

    Access and download statistics

    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:tiu:tiutis:b4eb1336-e9d8-441a-ac87-0d8696680d09. 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: Richard Broekman (email available below). General contact details of provider: https://www.tilburguniversity.edu/about/schools/economics-and-management/ .

    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.