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Application-driven Sequential Designs for Simulation Experiments : Kriging Metamodeling

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  • Kleijnen, J.P.C.

    (Tilburg University, School of Economics and Management)

  • van Beers, W.C.M.

    (Tilburg University, School of Economics and Management)

Abstract

This paper proposes a novel method to select an experimental design for interpolation in simulation. Although the paper focuses on Kriging in deterministic simulation, the method also applies to other types of metamodels (besides Kriging), and to stochastic simulation. The paper focuses on simulations that require much computer time, so it is important to select a design with a small number of observations. The proposed method is therefore sequential. The novelty of the method is that it accounts for the specific input/output function of the particular simulation model at hand; that is, the method is application-driven or customized. This customization is achieved through cross-validation and jackknifing. The new method is tested through two academic applications, which demonstrate that the method indeed gives better results than either sequential designs based on an approximate Kriging prediction variance formula or designs with prefixed sample sizes.
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Suggested Citation

  • Kleijnen, J.P.C. & van Beers, W.C.M., 2003. "Application-driven Sequential Designs for Simulation Experiments : Kriging Metamodeling," Other publications TiSEM 1af5ac49-a5f3-4b8a-901c-b, Tilburg University, School of Economics and Management.
  • Handle: RePEc:tiu:tiutis:1af5ac49-a5f3-4b8a-901c-b094a45ea518
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    References listed on IDEAS

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    1. W C M van Beers & J P C Kleijnen, 2003. "Kriging for interpolation in random simulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 255-262, March.
    2. Kleijnen, Jack P. C. & Sargent, Robert G., 2000. "A methodology for fitting and validating metamodels in simulation," European Journal of Operational Research, Elsevier, vol. 120(1), pages 14-29, January.
    3. Sungmin Park & John W. Fowler & Gerald T. Mackulak & J. Bert Keats & W. Matthew Carlyle, 2002. "D-Optimal Sequential Experiments for Generating a Simulation-Based Cycle Time-Throughput Curve," Operations Research, INFORMS, vol. 50(6), pages 981-990, December.
    4. B. J. A. Mertens, 2001. "Downdating: Interdisciplinary Research Between Statistics and Computing," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(3), pages 358-366, November.
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    Citations

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    Cited by:

    1. Xiao, Ning-Cong & Zuo, Ming J. & Zhou, Chengning, 2018. "A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 330-338.
    2. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-09, Tilburg University, Center for Economic Research.
    3. Xin, Fukang & Wang, Pan & Wang, Qirui & Li, Lei & Cheng, Lei & Lei, Huajin & Ma, Fangyun, 2024. "Parallel adaptive ensemble of metamodels combined with hypersphere sampling for rare failure events," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    4. 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.
    5. Kleijnen, J.P.C., 2006. "White Noise Assumptions Revisited : Regression Models and Statistical Designs for Simulation Practice," Discussion Paper 2006-50, Tilburg University, Center for Economic Research.
    6. Edwin Dam & Bart Husslage & Dick Hertog, 2010. "One-dimensional nested maximin designs," Journal of Global Optimization, Springer, vol. 46(2), pages 287-306, February.
    7. Maroussa Zagoraiou & Alessandro Baldi Antognini, 2009. "Optimal designs for parameter estimation of the Ornstein–Uhlenbeck process," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(5), pages 583-600, September.
    8. Gaofeng Jia & Alexandros A. Taflanidis & Norberto C. Nadal-Caraballo & Jeffrey A. Melby & Andrew B. Kennedy & Jane M. Smith, 2016. "Surrogate modeling for peak or time-dependent storm surge prediction over an extended coastal region using an existing database of synthetic storms," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(2), pages 909-938, March.
    9. Scott L. Rosen & Christopher P. Saunders & Samar K Guharay, 2015. "A Structured Approach for Rapidly Mapping Multilevel System Measures via Simulation Metamodeling," Systems Engineering, John Wiley & Sons, vol. 18(1), pages 87-101, January.
    10. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    11. Kleijnen, J.P.C. & van Beers, W.C.M. & van Nieuwenhuyse, I., 2008. "Constrained Optimization in Simulation : A Novel Approach," Discussion Paper 2008-95, Tilburg University, Center for Economic Research.
    12. Daniel J Klein & Michael Baym & Philip Eckhoff, 2014. "The Separatrix Algorithm for Synthesis and Analysis of Stochastic Simulations with Applications in Disease Modeling," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-10, July.
    13. Stinstra, Erwin & den Hertog, Dick, 2008. "Robust optimization using computer experiments," European Journal of Operational Research, Elsevier, vol. 191(3), pages 816-837, December.
    14. Jize Zhang & Alexandros A. Taflanidis & Norberto C. Nadal-Caraballo & Jeffrey A. Melby & Fatimata Diop, 2018. "Advances in surrogate modeling for storm surge prediction: storm selection and addressing characteristics related to climate change," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(3), pages 1225-1253, December.
    15. M I Reis dos Santos & P M Reis dos Santos, 2011. "Construction and validation of distribution-based regression simulation metamodels," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1376-1384, July.
    16. Gaofeng Jia & Alexandros Taflanidis & Norberto Nadal-Caraballo & Jeffrey Melby & Andrew Kennedy & Jane Smith, 2016. "Surrogate modeling for peak or time-dependent storm surge prediction over an extended coastal region using an existing database of synthetic storms," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(2), pages 909-938, March.
    17. Stinstra, E., 2006. "The meta-model approach for simulation-based design optimization," Other publications TiSEM 713f828a-4716-4a19-af00-e, Tilburg University, School of Economics and Management.
    18. Stinstra, E. & den Hertog, D., 2005. "Robust Optimization Using Computer Experiments," Other publications TiSEM 69d6e378-c9f9-44e8-9602-f, Tilburg University, School of Economics and Management.
    19. Song, Kunling & Zhang, Yugang & Shen, Linjie & Zhao, Qingyan & Song, Bifeng, 2021. "A failure boundary exploration and exploitation framework combining adaptive Kriging model and sample space partitioning strategy for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    20. P. Pedone & G. Vicario & D. Romano, 2009. "Kriging‐based sequential inspection plans for coordinate measuring machines," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(2), pages 133-149, March.
    21. Gan, Guojun & Lin, X. Sheldon, 2015. "Valuation of large variable annuity portfolios under nested simulation: A functional data approach," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 138-150.
    22. Jack P. C. Kleijnen & Susan M. Sanchez & Thomas W. Lucas & Thomas M. Cioppa, 2005. "State-of-the-Art Review: A User’s Guide to the Brave New World of Designing Simulation Experiments," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 263-289, August.
    23. Siem, A.Y.D. & den Hertog, D., 2007. "Kriging Models That Are Robust With Respect to Simulation Errors," Other publications TiSEM fe73dc8b-20d6-4f50-95eb-f, Tilburg University, School of Economics and Management.
    24. Kleijnen, J.P.C., 2007. "Screening Experiments for Simulation : A Review," Discussion Paper 2007-21, Tilburg University, Center for Economic Research.
    25. Mlakar, Miha & Petelin, Dejan & Tušar, Tea & Filipič, Bogdan, 2015. "GP-DEMO: Differential Evolution for Multiobjective Optimization based on Gaussian Process models," European Journal of Operational Research, Elsevier, vol. 243(2), pages 347-361.

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