Kriging metamodel with modified nugget-effect: The heteroscedastic variance case

Yin, Jun; Ng, Szu Hui; Ng, Kien Ming

doi:10.1016/j.cie.2011.05.008

Cited by 79 publications

(61 citation statements)

References 20 publications

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“…. τ 2 n ) [11,42]. In our framework, the observation noise is homoscedastic, but a generalized model is used for the EQI criterion computation (see 3.5).…”

Section: Kriging With Noisy Observationsmentioning

confidence: 99%

A benchmark of kriging-based infill criteria for noisy optimization

Picheny

Wagner

Ginsbourger³

2013

Struct Multidisc Optim

279

178

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Responses of many real-world problems can only be evaluated perturbed by noise. In order to make an efficient optimization of these problems possible, intelligent optimization strategies successfully coping with noisy evaluations are required. In this article, a comprehensive review of existing kriging-based methods for the optimization of noisy functions is provided. In summary, ten methods for choosing the sequential samples are described using a unified formalism. They are compared on analytical benchmark problems, whereby the usual assumption of homoscedastic Gaussian noise made in the underlying models is meet. Different problem configurations (noise level, maximum number of observations, initial number of observations) and setups (covariance functions, budget, initial sample size) are considered. It is found that the choices of the initial sample size and the covariance function are not critical. The choice of the method, however, can result in significant differences in the performance. In particular, the three most intuitive criteria are found as poor alternatives. Although no criterion is found consistently more efficient than the others, two specialized methods appear more robust on average.

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“…. τ 2 n ) [11,42]. In our framework, the observation noise is homoscedastic, but a generalized model is used for the EQI criterion computation (see 3.5).…”

Section: Kriging With Noisy Observationsmentioning

confidence: 99%

A benchmark of kriging-based infill criteria for noisy optimization

Picheny

Wagner

Ginsbourger³

2013

Struct Multidisc Optim

279

178

View full text Add to dashboard Cite

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“…In recent years, a number of Kriging-based optimization algorithms have been proposed that can handle heterogeneous noise, based on stochastic Kriging models (see Ankenman, Nelson, and Staum, 2010;Cressie, 1993 , andYin et al, 2011 ). To the best of our knowledge, the performance of these algorithms has not yet been compared.…”

Section: Introductionmentioning

confidence: 99%

“…In practice, however, the noise is heterogeneous ( Kim & Nelson, 2006;Kleijnen & Van Beers, 2005;Yin, Ng, & Ng, 2011 ). In recent years, a number of Kriging-based optimization algorithms have been proposed that can handle heterogeneous noise, based on stochastic Kriging models (see Ankenman, Nelson, and Staum, 2010;Cressie, 1993 , andYin et al, 2011 ).…”

Section: Introductionmentioning

confidence: 99%

Comparison of Kriging-Based Methods for Simulation Optimization with Heterogeneous Noise

2015

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a b s t r a c tIn this article we investigate the unconstrained optimization (minimization) of the performance of a system that is modeled through a discrete-event simulation. In recent years, several algorithms have been proposed which extend the traditional Kriging-based simulation optimization algorithms (assuming deterministic outputs) to problems with noise. Our objective in this paper is to compare the relative performance of a number of these algorithms on a set of well-known analytical test functions, assuming different patterns of heterogeneous noise. We also apply the algorithms to a popular inventory test problem. The conclusions and insights obtained may serve as a useful guideline for researchers aiming to apply Kriging-based algorithms to solve engineering and/or business problems, and may be useful in the development of future algorithms.

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“…Our methodology is similar to the one that is used to incorporate internal noise in Kriging and is published under different names; see Opsomer et al (1999); Ankenman et al (2010); Yin et al (2011).…”

Section: Stochastic Simulation and Ik: Sikmentioning

confidence: 99%

“…We tried to use the MATLAB code developed by Ankenman et al (2010) and Yin et al (2011) to experiment with these Kriging variants (OK for deterministic simulation and SK for random simulation), but their MATLAB code crashed in experiments with d > 1. So we use the R package mlegp to implement OK and SK; see Dancik (2013) for more details.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Stochastic Intrinsic Kriging for Simulation Metamodelling

Mehdad

Kleijnen

2014

SSRN Journal

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We derive intrinsic Kriging, using Matherons intrinsic random functions which eliminate the trend in classic Kriging. We formulate this intrinsic Kriging as a metamodel in deterministic and random simulation models. For random simulation we derive an experimental design that also specifies the number of replications that varies with the input combinations. We compare intrinsic Kriging and classic Kriging in several numerical experiments with deterministic and random simulations. These experiments suggest that intrinsic Kriging gives more accurate metamodel, in most experiments.

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Kriging metamodel with modified nugget-effect: The heteroscedastic variance case

Cited by 79 publications

References 20 publications

A benchmark of kriging-based infill criteria for noisy optimization

A benchmark of kriging-based infill criteria for noisy optimization

Comparison of Kriging-Based Methods for Simulation Optimization with Heterogeneous Noise

Stochastic Intrinsic Kriging for Simulation Metamodelling

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