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Simulation optimization via kriging: a sequential search using expected improvement with computing budget constraints

Author

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  • Ning Quan
  • Jun Yin
  • Szu Ng
  • Loo Lee

Abstract

Metamodels are commonly used as fast surrogates for the objective function to facilitate the optimization of simulation models. Kriging (or the Gaussian process model) is a very popular metamodel form for deterministic and, recently, stochastic simulations. This article proposes a two-stage sequential framework for the optimization of stochastic simulations with heterogeneous variances under computing budget constraints. The proposed two-stage framework is based on the kriging model and incorporates optimal computing budget allocation techniques and the expected improvement function to drive and improve the estimation of the global optimum. Empirical results indicate that it is effective in obtaining optimal solutions and is more efficient than alternative metamodel-based techniques. The framework is also applied to a complex real ocean liner bunker fuel management problem with promising results.

Suggested Citation

  • Ning Quan & Jun Yin & Szu Ng & Loo Lee, 2013. "Simulation optimization via kriging: a sequential search using expected improvement with computing budget constraints," IISE Transactions, Taylor & Francis Journals, vol. 45(7), pages 763-780.
    • Handle: RePEc:taf:uiiexx:v:45:y:2013:i:7:p:763-780
    DOI: 10.1080/0740817X.2012.706377
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    Citations

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    Cited by:

    1. Ehsan Mehdad & Jack P. C. Kleijnen, 2018. "Efficient global optimisation for black-box simulation via sequential intrinsic Kriging," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(11), pages 1725-1737, November.
    2. Rojas Gonzalez, Sebastian & Jalali, Hamed & Van Nieuwenhuyse, Inneke, 2020. "A multiobjective stochastic simulation optimization algorithm," European Journal of Operational Research, Elsevier, vol. 284(1), pages 212-226.
    3. Giulia Pedrielli & K. Selcuk Candan & Xilun Chen & Logan Mathesen & Alireza Inanalouganji & Jie Xu & Chun-Hung Chen & Loo Hay Lee, 2019. "Generalized Ordinal Learning Framework (GOLF) for Decision Making with Future Simulated Data," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(06), pages 1-35, December.
    4. Fani Boukouvala & M. M. Faruque Hasan & Christodoulos A. Floudas, 2017. "Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption," Journal of Global Optimization, Springer, vol. 67(1), pages 3-42, January.
    5. Mehdad, E. & Kleijnen, Jack P.C., 2014. "Global Optimization for Black-box Simulation via Sequential Intrinsic Kriging," Discussion Paper 2014-063, Tilburg University, Center for Economic Research.
    6. Wate, P. & Iglesias, M. & Coors, V. & Robinson, D., 2020. "Framework for emulation and uncertainty quantification of a stochastic building performance simulator," Applied Energy, Elsevier, vol. 258(C).
    7. Peter L. Salemi & Eunhye Song & Barry L. Nelson & Jeremy Staum, 2019. "Gaussian Markov Random Fields for Discrete Optimization via Simulation: Framework and Algorithms," Operations Research, INFORMS, vol. 67(1), pages 250-266, January.
    8. Jalali, Hamed & Van Nieuwenhuyse, Inneke & Picheny, Victor, 2017. "Comparison of Kriging-based algorithms for simulation optimization with heterogeneous noise," European Journal of Operational Research, Elsevier, vol. 261(1), pages 279-301.
    9. Kamiński, Bogumił, 2015. "A method for the updating of stochastic kriging metamodels," European Journal of Operational Research, Elsevier, vol. 247(3), pages 859-866.
    10. Songhao Wang & Szu Hui Ng & William Benjamin Haskell, 2022. "A Multilevel Simulation Optimization Approach for Quantile Functions," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 569-585, January.
    11. Kleijnen, Jack P.C., 2013. "Simulation-Optimization via Kriging and Bootstrapping : A Survey (Revision of CentER DP 2011-064)," Other publications TiSEM 6ac4e049-ad86-447f-aeec-a, Tilburg University, School of Economics and Management.
    12. Lihua Sun & L. Jeff Hong & Zhaolin Hu, 2014. "Balancing Exploitation and Exploration in Discrete Optimization via Simulation Through a Gaussian Process-Based Search," Operations Research, INFORMS, vol. 62(6), pages 1416-1438, December.
    13. Pooriya Beyhaghi & Ryan Alimo & Thomas Bewley, 2020. "A derivative-free optimization algorithm for the efficient minimization of functions obtained via statistical averaging," Computational Optimization and Applications, Springer, vol. 76(1), pages 1-31, May.
    14. Mehdad, E., 2015. "Kriging metamodels and global opimization in simulation," Other publications TiSEM 5b5c276a-fe68-4ce9-b8a8-1, Tilburg University, School of Economics and Management.
    15. Qun Meng & Songhao Wang & Szu Hui Ng, 2022. "Combined Global and Local Search for Optimization with Gaussian Process Models," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 622-637, January.
    16. Pedrielli, Giulia & Wang, Songhao & Ng, Szu Hui, 2020. "An extended Two-Stage Sequential Optimization approach: Properties and performance," European Journal of Operational Research, Elsevier, vol. 287(3), pages 929-945.
    17. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.

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