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One-dimensional nested maximin designs

Author

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  • Edwin Dam

    ()

  • Bart Husslage

    ()

  • Dick Hertog

    ()

Abstract

The design of computer experiments is an important step in black box evaluation and optimization processes.When dealing with multiple black box functions the need often arises to construct designs for all black boxes jointly, instead of individually.These so-called nested designs are used to deal with linking parameters and sequential evaluations.In this paper we discuss one-dimensional nested maximin designs.We show how to nest two designs optimally and develop a heuristic to nest three and four designs.Furthermore, it is proven that the loss in space-fillingness, with respect to traditional maximin designs, is at most 14:64 percent and 19:21 percent, when nesting two and three designs, respectively.
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Suggested Citation

  • Edwin Dam & Bart Husslage & Dick Hertog, 2010. "One-dimensional nested maximin designs," Journal of Global Optimization, Springer, vol. 46(2), pages 287-306, February.
  • Handle: RePEc:spr:jglopt:v:46:y:2010:i:2:p:287-306
    DOI: 10.1007/s10898-009-9426-y
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    File URL: http://hdl.handle.net/10.1007/s10898-009-9426-y
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    References listed on IDEAS

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    1. 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.
    2. Husslage, B.G.M. & van Dam, E.R. & den Hertog, D. & Stehouwer, H.P. & Stinstra, E., 2003. "Collaborative metamodelling : Coordinating simulation-based product design," Other publications TiSEM 0196e58f-78a8-4653-a48b-8, Tilburg University, School of Economics and Management.
    3. Castillo, Ignacio & Kampas, Frank J. & Pintér, János D., 2008. "Solving circle packing problems by global optimization: Numerical results and industrial applications," European Journal of Operational Research, Elsevier, vol. 191(3), pages 786-802, December.
    4. 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.
    5. van Dam, E.R. & Husslage, B.G.M. & den Hertog, D. & Melissen, H., 2005. "Maximin Latin Hypercube Designs in Two Dimensions," Discussion Paper 2005-8, Tilburg University, Center for Economic Research.
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    Cited by:

    1. 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.
    2. Victor Gergel & Vladimir Grishagin & Alexander Gergel, 2016. "Adaptive nested optimization scheme for multidimensional global search," Journal of Global Optimization, Springer, vol. 66(1), pages 35-51, September.
    3. 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.
    4. Vieira Jr., Hélcio & Sanchez, Susan & Kienitz, Karl Heinz & Belderrain, Mischel Carmen Neyra, 2011. "Generating and improving orthogonal designs by using mixed integer programming," European Journal of Operational Research, Elsevier, vol. 215(3), pages 629-638, December.
    5. János Pintér & Zoltán Horváth, 2013. "Integrated experimental design and nonlinear optimization to handle computationally expensive models under resource constraints," Journal of Global Optimization, Springer, vol. 57(1), pages 191-215, September.
    6. repec:eee:apmaco:v:318:y:2018:i:c:p:270-280 is not listed on IDEAS

    More about this item

    Keywords

    Computer simulation; Global optimization; Linking parameter; Maximin design; Mixed integer linear programming; Packing problem; Space-filling; Training and test set;

    JEL classification:

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

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