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Expected improvement in efficient global optimization through bootstrapped kriging


  • Jack Kleijnen


  • Wim Beers


  • Inneke Nieuwenhuyse



This article uses a sequentialized experimental design to select simulation input combinations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code). This design and analysis adapt the classic “expected improvement” (EI) in “efficient global optimization” (EGO) through the introduction of an improved estimator of the Kriging predictor variance; this estimator uses parametric bootstrapping. Classic EI and bootstrapped EI are compared through various test functions, including the six-hump camel-back and several Hartmann functions. These empirical results demonstrate that in some applications bootstrapped EI finds the global optimum faster than classic EI does; in general, however, the classic EI may be considered to be a robust global optimizer. Copyright The Author(s) 2012

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:59-73
    DOI: 10.1007/s10898-011-9741-y

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    References listed on IDEAS

    1. Markus Abt, 1999. "Estimating the Prediction Mean Squared Error in Gaussian Stochastic Processes with Exponential Correlation Structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 563-578.
    2. D den Hertog & J P C Kleijnen & A Y D Siem, 2006. "The correct Kriging variance estimated by bootstrapping," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 400-409, April.
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    Cited by:

    1. Kleijnen, Jack P.C. & Mehdad, E., 2013. "Conditional simulation for efficient global optimization," Other publications TiSEM 52e4860d-9887-4a63-b19a-7, Tilburg University, School of Economics and Management.
    2. Mehdad, E. & Kleijnen, Jack P.C., 2014. "Classic Kriging versus Kriging with Bootstrapping or Conditional Simulation : Classic Kriging's Robust Confidence Intervals and Optimization (Revised version of CentER DP 2013-038)," Discussion Paper 2014-076, Tilburg University, Center for Economic Research.
    3. Kleijnen, Jack P.C., 2013. "Simulation-Optimization via Kriging and Bootstrapping : A Survey (Revision of CentER DP 2011-064)," Discussion Paper 2013-064, Tilburg University, Center for Economic Research.
    4. Morales-Enciso, Sergio & Branke, Juergen, 2015. "Tracking global optima in dynamic environments with efficient global optimization," European Journal of Operational Research, Elsevier, vol. 242(3), pages 744-755.
    5. Jalali, Hamed & Van Nieuwenhuyse, Inneke & Picheny, Victor, 2017. "Comparison of Kriging-based algorithms for simulation optimization with heterogeneous noise," European Journal of Operational Research, Elsevier, vol. 261(1), pages 279-301.
    6. repec:spr:annopr:v:240:y:2016:i:1:d:10.1007_s10479-015-2019-x is not listed on IDEAS

    More about this item


    Simulation; Optimization; Kriging; Bootstrap;


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