Expected improvement in efficient global optimization through bootstrapped kriging

Jack P.C. Kleijnen, W.C.M. van Beers, I. van Nieuwenhuyse

Research output: Contribution to journalArticleScientificpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)59-73
JournalJournal of Global Optimization
Volume54
Issue number1
Publication statusPublished - 2012

Fingerprint

Kriging
Global optimization
Global Optimization
Design of experiments
Estimator
Bootstrapping
Global Optimum
Spatial Correlation
Test function
Experimental design
Gaussian Process
Predictors
Simulation Model
Output
Modeling
Demonstrate
Simulation

Cite this

@article{df994fa15ce84e7caed2611d1235c3fa,
title = "Expected improvement in efficient global optimization through bootstrapped kriging",
abstract = "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.",
author = "Kleijnen, {Jack P.C.} and {van Beers}, W.C.M. and {van Nieuwenhuyse}, I.",
note = "Appeared earlier as CentER DP 2011-015",
year = "2012",
language = "English",
volume = "54",
pages = "59--73",
journal = "Journal of Global Optimization",
issn = "0925-5001",
publisher = "Springer Netherlands",
number = "1",

}

Expected improvement in efficient global optimization through bootstrapped kriging. / Kleijnen, Jack P.C.; van Beers, W.C.M.; van Nieuwenhuyse, I.

In: Journal of Global Optimization, Vol. 54, No. 1, 2012, p. 59-73.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Expected improvement in efficient global optimization through bootstrapped kriging

AU - Kleijnen, Jack P.C.

AU - van Beers, W.C.M.

AU - van Nieuwenhuyse, I.

N1 - Appeared earlier as CentER DP 2011-015

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

M3 - Article

VL - 54

SP - 59

EP - 73

JO - Journal of Global Optimization

JF - Journal of Global Optimization

SN - 0925-5001

IS - 1

ER -