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Generating and improving orthogonal designs by using mixed integer programming

Listed author(s):
  • Vieira Jr., Hélcio
  • Sanchez, Susan
  • Kienitz, Karl Heinz
  • Belderrain, Mischel Carmen Neyra
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    Analysts faced with conducting experiments involving quantitative factors have a variety of potential designs in their portfolio. However, in many experimental settings involving discrete-valued factors (particularly if the factors do not all have the same number of levels), none of these designs are suitable. In this paper, we present a mixed integer programming (MIP) method that is suitable for constructing orthogonal designs, or improving existing orthogonal arrays, for experiments involving quantitative factors with limited numbers of levels of interest. Our formulation makes use of a novel linearization of the correlation calculation. The orthogonal designs we construct do not satisfy the definition of an orthogonal array, so we do not advocate their use for qualitative factors. However, they do allow analysts to study, without sacrificing balance or orthogonality, a greater number of quantitative factors than it is possible to do with orthogonal arrays which have the same number of runs.

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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 215 (2011)
    Issue (Month): 3 (December)
    Pages: 629-638

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    Handle: RePEc:eee:ejores:v:215:y:2011:i:3:p:629-638
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    1. van Dam, E.R. & Rennen, G. & Husslage, B.G.M., 2007. "Bounds for Maximin Latin Hypercube Designs," Discussion Paper 2007-16, Tilburg University, Center for Economic Research.
    2. Kleijnen, Jack P. C., 2005. "An overview of the design and analysis of simulation experiments for sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 164(2), pages 287-300, July.
    3. Appa, G. & Magos, D. & Mourtos, I., 2006. "Searching for Mutually Orthogonal Latin Squares via integer and constraint programming," European Journal of Operational Research, Elsevier, vol. 173(2), pages 519-530, September.
    4. Lejeune, Miguel A., 2003. "Heuristic optimization of experimental designs," European Journal of Operational Research, Elsevier, vol. 147(3), pages 484-498, June.
    5. Edwin Dam & Bart Husslage & Dick Hertog, 2010. "One-dimensional nested maximin designs," Journal of Global Optimization, Springer, vol. 46(2), pages 287-306, February.
    6. van Beers, Wim C.M. & Kleijnen, Jack P.C., 2008. "Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1099-1113, May.
    7. Kuhfeld, Warren F. & Suen, Chung-yi, 2005. "Some new orthogonal arrays," Statistics & Probability Letters, Elsevier, vol. 75(3), pages 169-178, December.
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