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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

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File URL: http://hdl.handle.net/10.1007/s10898-011-9741-y
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Article provided by Springer in its journal Journal of Global Optimization.

Volume (Year): 54 (2012)
Issue (Month): 1 (September)
Pages: 59-73

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Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:59-73
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  1. den Hertog, D. & Kleijnen, J.P.C. & Siem, A.Y.D., 2004. "The Correct Kriging Variance Estimated by Bootstrapping," Discussion Paper 2004-46, Tilburg University, Center for Economic Research.
  2. 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.
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