Multivariate versus univariate Kriging metamodels for multi-response simulation models

Kleijnen, J.P.C.; Mehdad, Ehsan

doi:10.1016/j.ejor.2014.02.001

Cited by 53 publications

(29 citation statements)

References 26 publications

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“…A number of recent applications using computer simulators are also mentioned by Levy and Steinberg . For applications in Operations Research, the reader is referred to Kleijnen and Mehdad …”

Section: Objective and Research Methodologymentioning

confidence: 99%

“…This problem can be addressed using the indirect definition of the covariance function by treating the Gaussian process as the output of stable linear filters . An alternative is to use the linear model of coregionalization, such as it is defined by Kleijnen and Mehdad . Moreover, when dealing with multiple response variables, the definition of the covariance function is extremely complicated, and the computational cost increases significantly, because the covariance matrix is of the order Nq × Nq , and its inversion takes time of the order O ( N 3 q 3 ).…”

Section: Gaussian Process Modelmentioning

confidence: 99%

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Gaussian Process Model – An Exploratory Study in the Response Surface Methodology

Costa

Lourenço

2015

Quality & Reliability Eng

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This paper explores the benefits of Gaussian process model as an alternative modeling technique for problems developed in the Response Surface Methodology framework. Three case studies with different type and number of responses were investigated, and the compromise solutions obtained with three modeling techniques were evaluated. Results provide evidences of the Gaussian process model usefulness for stochastic responses, namely, when responses are correlated.

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Section: Objective and Research Methodologymentioning

confidence: 99%

Section: Gaussian Process Modelmentioning

confidence: 99%

Gaussian Process Model – An Exploratory Study in the Response Surface Methodology

Costa

Lourenço

2015

Quality & Reliability Eng

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“…Here, the cross-correlation between the real process and the computer model is considered in the covariance matrix of the full dataset d (see Equation (A1)) and is considered as a "separable models" form described in Kleijnen and Mehdad (2014). Given the observed d (assumed to be normally distributed given θ , β, σ 2 , φ), the marginal of θ , p(θ |d), describes the uncertainty surrounding the calibration parameter and is important for determining the estimation of θ (e.g., in the setting of θ for future computer runs).…”

Section: Calibrationmentioning

confidence: 99%

Calibration, Validation, and Prediction in Random Simulation Models

Yuan

2015

ACM Trans. Model. Comput. Simul.

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Model calibration and validation are important processes in the development of stochastic computer models of real complex systems. This article introduces an integrated approach for model calibration, validation, and prediction based on Gaussian process metamodels and a Bayesian approach. Within this integrated approach, a sequential approach is further proposed for stochastic computer model calibration. Several design criteria for this sequential stage are proposed and studied, including an entropy-based criterion and one based on minimizing prediction error. To further use the data resources to improve the performance of both calibration and prediction, an adaptive procedure that combines these criteria is introduced to balance the resource allocation between the calibration and prediction. The accuracy and efficiency of the proposed sequential calibration approach and the integrated approach are illustrated with several numerical examples. ACM Reference Format:Jun Yuan and Szu Hui Ng. 2015. Calibration, validation, and prediction in random simulation models: Gaussian process metamodels and a bayesian integrated solution. ACM Trans. Model.

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“…The optimization problem is multi-modal because EI = 0 at each sample location that has already been simulated. Various methods for estimating the global optimum on this problem are mentioned in Kleijnen (2015), (p. 268). In this context, it should be noted that we operate under the assumption that the components are so computationally expensive that the internal computational complexity of BEGO is negligible in comparison.…”

Section: Numerical Test Problemsmentioning

confidence: 99%

Adaptive efficient global optimization of systems with independent components

Rehman

Langelaar

2017

Struct Multidisc Optim

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We present a novel approach for efficient optimization of systems consisting of expensive to simulate components and relatively inexpensive system-level simulations. We consider the types of problem in which the components of the system problem are independent in the sense that they do not exchange coupling variables, however, design variables can be shared across components. Component metamodels are constructed using Kriging. The metamodels are adaptively sampled based on a system level infill sampling criterion using Efficient Global Optimization. The effectiveness of the technique is demonstrated by applying it on numerical examples and an engineering case study. Results show steady and fast converge to the global deterministic optimum of the problems.

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Multivariate versus univariate Kriging metamodels for multi-response simulation models

Cited by 53 publications

References 26 publications

Gaussian Process Model – An Exploratory Study in the Response Surface Methodology

Gaussian Process Model – An Exploratory Study in the Response Surface Methodology

Calibration, Validation, and Prediction in Random Simulation Models

Adaptive efficient global optimization of systems with independent components

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