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Multivariate versus univariate Kriging metamodels for multi-response simulation models

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  • Kleijnen, Jack P.C.
  • Mehdad, Ehsan

Abstract

To analyze the input/output behavior of simulation models with multiple responses, we may apply either univariate or multivariate Kriging (Gaussian process) metamodels. In multivariate Kriging we face a major problem: the covariance matrix of all responses should remain positive-definite; we therefore use the recently proposed “nonseparable dependence” model. To evaluate the performance of univariate and multivariate Kriging, we perform several Monte Carlo experiments that simulate Gaussian processes. These Monte Carlo results suggest that the simpler univariate Kriging gives smaller mean square error.

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  • Kleijnen, Jack P.C. & Mehdad, Ehsan, 2014. "Multivariate versus univariate Kriging metamodels for multi-response simulation models," European Journal of Operational Research, Elsevier, vol. 236(2), pages 573-582.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:2:p:573-582
    DOI: 10.1016/j.ejor.2014.02.001
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    1. D den Hertog & J P C Kleijnen & A Y D Siem, 2006. "The correct Kriging variance estimated by bootstrapping," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(4), pages 400-409, April.
    2. Roustant, Olivier & Ginsbourger, David & Deville, Yves, 2012. "DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i01).
    3. Kleijnen, J.P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2008. "Constrained Optimization in Simulation : A Novel Approach," Other publications TiSEM e49ba0fc-853c-4a13-b564-d, Tilburg University, School of Economics and Management.
    4. Hernandez, Andres F. & Grover, Martha A., 2013. "Error estimation properties of Gaussian process models in stochastic simulations," European Journal of Operational Research, Elsevier, vol. 228(1), pages 131-140.
    5. Kleijnen, Jack P.C. & Beers, Wim van & Nieuwenhuyse, Inneke van, 2010. "Constrained optimization in expensive simulation: Novel approach," European Journal of Operational Research, Elsevier, vol. 202(1), pages 164-174, April.
    6. Gneiting, Tilmann & Kleiber, William & Schlather, Martin, 2010. "Matérn Cross-Covariance Functions for Multivariate Random Fields," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1167-1177.
    7. J P C Kleijnen & M T Smits, 2003. "Performance metrics in supply chain management," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(5), pages 507-514, May.
    8. Kleijnen, Jack P.C. & Mehdad, E., 2013. "Conditional simulation for efficient global optimization," Other publications TiSEM 52e4860d-9887-4a63-b19a-7, Tilburg University, School of Economics and Management.
    9. Kleijnen, J.P.C. & Smits, M.T., 2003. "Performance metrics in supply chain management," Other publications TiSEM 80777aed-0c9f-4ded-b0bb-f, Tilburg University, School of Economics and Management.
    10. Higdon, Dave & Gattiker, James & Williams, Brian & Rightley, Maria, 2008. "Computer Model Calibration Using High-Dimensional Output," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 570-583, June.
    11. Jack P.C. Kleijnen, 2015. "Design and Analysis of Simulation Experiments," International Series in Operations Research and Management Science, Springer, edition 2, number 978-3-319-18087-8, December.
    12. van Ham, G. & Rotmans, J. & Kleijnen, J.P.C., 1992. "Techniques for sensitivity analysis of simulation models : A case study of the CO2 greenhouse effect," Other publications TiSEM 71317a03-3399-4554-83cb-4, Tilburg University, School of Economics and Management.
    13. Xi Chen & Bruce E. Ankenman & Barry L. Nelson, 2013. "Enhancing Stochastic Kriging Metamodels with Gradient Estimators," Operations Research, INFORMS, vol. 61(2), pages 512-528, April.
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    8. Rahat, Alma A.M. & Wang, Chunlin & Everson, Richard M. & Fieldsend, Jonathan E., 2018. "Data-driven multi-objective optimisation of coal-fired boiler combustion systems," Applied Energy, Elsevier, vol. 229(C), pages 446-458.
    9. Kleijnen, Jack & van Nieuwenhuyse, I. & van Beers, W.C.M., 2022. "Constrained Optimization in Simulation : Efficient Global Optimization and Karush-Kuhn-Tucker Conditions," Other publications TiSEM 903e51c8-bed3-4e97-990f-c, Tilburg University, School of Economics and Management.

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