A matrix-T approach to the sequential design of optimization experiments

Santiago, Eduardo

doi:10.1080/0740817x.2010.504687

Cited by 5 publications

(6 citation statements)

References 22 publications

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“…91-106] (also discussing a number of EI variations). Classic EI assumes deterministic simulation aimed at finding the unconstrained global minimum of the objective function, using the Kriging predictor y and its classic estimated predictor variance s 2 (x) defined in (4) and (5). This EI uses the following steps.…”

Section: Classic Eimentioning

confidence: 99%

“…In this subsection we estimate the coverage rates of 90% CIs; i.e., do these intervals indeed have a 90% probability of covering the true value? Note that the classic method and our method use the same point predictor but different estimated variances; see (4), (5), and (10).…”

Section: Coverage Rates In a Kriging Modelmentioning

confidence: 99%

“…For the latter noise we refer to [2], [23], and [32]. • Application to large-scale industrial problems, such as the so-called MOPTA08 problem with 124 inputs and 68 inequality constraints for the outputs; see [24] • Comparison of EGO with other approaches; see [5].…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

See 2 more Smart Citations

Expected improvement in efficient global optimization through bootstrapped kriging

2011

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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. Keywords Simulation • Optimization • Kriging • Bootstrap 1 Introduction Simulation is often used to estimate the global optimum of the real system being simulated (like many researchers in this area do, we use the terms "optimum" and "optimization" even

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Section: Classic Eimentioning

confidence: 99%

Section: Coverage Rates In a Kriging Modelmentioning

confidence: 99%

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Expected improvement in efficient global optimization through bootstrapped kriging

2011

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“…Most of the procedures that use metamodels consist of sequential iterations between parameter estimation (rebuilding the model) and optimization of the model at the given iteration. These methods are mainly discussed in the context of sequential design of optimization experiments …”

Section: Introductionmentioning

confidence: 99%

A Bayesian Approach to Sequential Optimization based on Computer Experiments

Tajbakhsh

Rosenberger

2014

Quality & Reliability Eng

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Computer experiments are used frequently for the study and improvement of a process under study. Optimizing such process based on a computer model is costly, so an approximation of the computer model, or metamodel, is used. Efficient global optimization (EGO) is a sequential optimization method for computer experiments based on a Gaussian process model approximation to the computer model response. A long-standing problem in EGO is that it does not consider the uncertainty in the parameter estimates of the Gaussian process. Treating these estimates as if they are the true parameters leads to an improper assessment of the precision of the approximation, a precision that is crucial to assess not only in optimization but in metamodeling in general. One way to account for these uncertainties is to use bootstrapping, studied by previous authors. Alternatively, some other authors have mentioned how a Bayesian approach may be the best way to incorporate the parameter uncertainty in the optimization, but no fully Bayesian approach for EGO has been implemented in practice. In this paper, we present a fully Bayesian implementation of the EGO method. The proposed Bayesian EGO algorithm is validated through simulation of noisy nonlinear functions and compared with the standard EGO method and the bootstrapped EGO. We also apply the Bayesian EGO algorithm to the optimization of a stochastic computer model. It is shown how a Bayesian approach to EGO allows one to optimize any function of the posterior predictive density.

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“…• Application to large-scale industrial problems, such as the so-called MOPTA08 problem with 124 inputs and 68 inequality constraints for the outputs; see [24] • Comparison of EGO with other approaches; see [5]. random LHS implies sampling error, we repeat the whole experiment 30 times (so the number of "macroreplicates" is 30).…”

Section: Hartmann-6 Functionmentioning

confidence: 99%