Kriging for interpolation in random simulation

Beers, W.C.M. van; Kleijnen, J.P.C.

doi:10.1057/palgrave.jors.2601492

Cited by 209 publications

(94 citation statements)

References 8 publications

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“…In random simulation, however, the observed output is only one of the many possible values. For random simulations, [25] replaces w(d i ) in (9) by the average observed output…”

Section: Kriging: New Resultsmentioning

confidence: 99%

“…Nevertheless, [25] gives examples in which the Kriging predictions based on (18) are much better than the regression predictions (regression metamodels may be useful for other goals such as understanding, screening, and validation). (Reference [22] includes a computer program in C-called PErK-which allows random output, but I do not know any applications.…”

Section: Kriging: New Resultsmentioning

confidence: 99%

“…Only in 2003, Van Beers and I started applying Kriging to random simulation models; see [25]. Although Kriging in random simulation is still rare, I strongly believe that the track record Kriging achieved in deterministic simulation holds promise for Kriging in random simulation!…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Kriging Metamodeling in Simulation: A Review

2007

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This article reviews Kriging (also called spatial correlation modeling). It presents the basic Kriging assumptions and formulas-contrasting Kriging and classic linear regression metamodels. Furthermore, it extends Kriging to random simulation, and discusses bootstrapping to estimate the variance of the Kriging predictor. Besides classic one-shot statistical designs such as Latin Hypercube Sampling, it reviews sequentialized and customized designs. It ends with topics for future research.

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“…In random simulation, however, the observed output is only one of the many possible values. For random simulations, [25] replaces w(d i ) in (9) by the average observed output…”

Section: Kriging: New Resultsmentioning

confidence: 99%

Section: Kriging: New Resultsmentioning

confidence: 99%

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Kriging Metamodeling in Simulation: A Review

2007

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“…Therefore we do not require our Kriging predictor to equal the observed average outputs, whereas we did in previous publications (Van Beers and Kleijnen, 2003;Kleijnen et al, 2010).…”

Section: Monotonicity-preserving Bootstrapped Krigingmentioning

confidence: 99%

Monotonicity-preserving bootstrapped Kriging metamodels for expensive simulations

Kleijnen

Beers

2013

Journal of the Operational Research Society

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Monotonicity-preserving bootstrapped kriging metamodels for expensive simulationsKleijnen, J.P.C.; van Beers, W.C.M. General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.-Users may download and print one copy of any publication from the public portal for the purpose of private study or research -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright, please contact us providing details, and we will remove access to the work immediately and investigate your claim. Kriging metamodels (also called Gaussian process or spatial correlation models) approximate the Input/ Output functions implied by the underlying simulation models. Such metamodels serve sensitivity analysis, especially for computationally expensive simulations. In practice, simulation analysts often know that this Input/Output function is monotonic. To obtain a Kriging metamodel that preserves this characteristic, this article uses distribution-free bootstrapping assuming each input combination is simulated several times to obtain more reliable averaged outputs. Nevertheless, these averages still show sampling variation, so the Kriging metamodel does not need to be an exact interpolator; bootstrapping gives a noninterpolating Kriging metamodel. Bootstrapping may use standard Kriging software. The method is illustrated through the popular M/M/1 model with either the mean or the 90% quantile as output; these outputs are monotonic functions of the traffic rate. The empirical results demonstrate that monotonicity-preserving bootstrapped Kriging gives higher probability of covering the true outputs, without lengthening the confidence interval.

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“…Clearly, a Simulation-Optimization (SO) becomes necessary to find more interest and popularity than other optimization methods, in order to the complexity of many real world optimization problems in way of mathematical formulation analyzing (Dellino et al, 2014). The main goals of simulation can be defined as two, first what-if study of model or sensitivity analysis, and second is optimization and validation of model (van Beers & Kleijnen, 2003). The essential benefit of simulation is its ability to cover complex processes, either deterministic or random while eliminating mathematical sophistication (Figueira & Almada-Lobo, 2014).…”

Section: Introductionmentioning

confidence: 99%

Recent developments in metamodel based robust black-box simulation optimization: An overview

Parnianifard¹,

Azfanizam²,

Ariffin³

et al. 2019

10.5267/j.dsl

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In the real world of engineering problems, in order to reduce optimization costs in physical processes, running simulation experiments in the format of computer codes have been conducted. It is desired to improve the validity of simulation-optimization results by attending the source of variability in the model's output(s). Uncertainty can increase complexity and computational costs in Designing and Analyzing of Computer Experiments (DACE). In this state-of the art review paper, a systematic qualitative and quantitative review is implemented among Metamodel Based Robust Simulation Optimization (MBRSO) for black-box and expensive simulation models under uncertainty. This context is focused on the management of uncertainty, particularly based on the Taguchi worldview on robust design and robust optimization methods in the class of dual response methodology when simulation optimization can be handled by surrogates. At the end, while both trends and gaps in the research field are highlighted, some suggestions for future research are directed.

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Kriging for interpolation in random simulation

Cited by 209 publications

References 8 publications

Kriging Metamodeling in Simulation: A Review

Kriging Metamodeling in Simulation: A Review

Monotonicity-preserving bootstrapped Kriging metamodels for expensive simulations

Recent developments in metamodel based robust black-box simulation optimization: An overview

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