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Simulation-Optimization via Kriging and Bootstrapping: A Survey (Revision of CentER DP 2011-064)


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  • Kleijnen, Jack P.C.

    (Tilburg University, Center for Economic Research)


Abstract: This article surveys optimization of simulated systems. The simulation may be either deterministic or random. The survey reflects the author’s extensive experience with simulation-optimization through Kriging (or Gaussian process) metamodels. The analysis of these metamodels may use parametric bootstrapping for deterministic simulation or distribution-free bootstrapping (or resampling) for random simulation. The survey covers: (1) Simulation-optimization through "efficient global optimization" (EGO) using "expected improvement" (EI); this EI uses the Kriging predictor variance, which can be estimated through parametric bootstrapping accounting for estimation of the Kriging parameters. (2) Optimization with constraints for multiple random simulation outputs and deterministic inputs through mathematical programming applied to Kriging metamodels validated through distribution-free bootstrapping. (3) Taguchian robust optimization for uncertain environments, using mathematical programming— applied to Kriging metamodels— and distribution- free bootstrapping to estimate the variability of the Kriging metamodels and the resulting robust solution. (4) Bootstrapping for improving convexity or preserving monotonicity of the Kriging metamodel.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2013-064.

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Date of creation: 2013
Date of revision:
Handle: RePEc:dgr:kubcen:2013064

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Keywords: simulation; optimization; stochastic process; non-linear programming; risk;

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  1. Mehdad, E. & Kleijnen, Jack P.C., 2013. "Bootstrapping and Conditional Simulation in Kriging: Better Confidence Intervals and Optimization," Discussion Paper 2013-038, Tilburg University, Center for Economic Research.
  2. Dellino, G. & Kleijnen, Jack P.C. & Meloni, C., 2010. "Robust optimization in simulation: Taguchi and Response Surface Methodology," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3792109, Tilburg University.
  3. Christian Dehlendorff & Murat Kulahci & Klaus Kaae Andersen, 2011. "Designing simulation experiments with controllable and uncontrollable factors for applications in healthcare," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(1), pages 31-49, 01.
  4. Kleijnen, Jack P.C. & Beers, Wim van & Nieuwenhuyse, Inneke van, 2010. "Constrained optimization in expensive simulation: Novel approach," European Journal of Operational Research, Elsevier, vol. 202(1), pages 164-174, April.
  5. Kleijnen, Jack P.C. & Beers, W.C.M. van & Nieuwenhuyse, I. van, 2010. "Constrained optimization in simulation: A novel approach," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3583585, Tilburg University.
  6. Yanikoglu, I. & Hertog, D. den & Kleijnen, Jack P.C., 2013. "Adjustable Robust Parameter Design with Unknown Distributions," Discussion Paper 2013-022, Tilburg University, Center for Economic Research.
  7. Jack Kleijnen & Wim Beers & Inneke Nieuwenhuyse, 2012. "Expected improvement in efficient global optimization through bootstrapped kriging," Journal of Global Optimization, Springer, vol. 54(1), pages 59-73, September.
  8. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
  9. Kleijnen, Jack P.C. & Mehdad, E. & Beers, W.C.M. van, 2012. "Convex and monotonic bootstrapped kriging," Open Access publications from Tilburg University urn:nbn:nl:ui:12-5662135, Tilburg University.
  10. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages S243-S256, December.
  11. Kleijnen, J.P.C., 2008. "Review of the book [Design and Analysis of Simulation Experiments]," Open Access publications from Tilburg University urn:nbn:nl:ui:12-4379049, Tilburg University.
  12. Kleijnen, Jack P.C. & Deflandre, David, 2006. "Validation of regression metamodels in simulation: Bootstrap approach," European Journal of Operational Research, Elsevier, vol. 170(1), pages 120-131, April.
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