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Robust Optimization Using Computer Experiments

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  • Stinstra, E.
  • den Hertog, D.

    (Tilburg University, Center For Economic Research)

Abstract

During metamodel-based optimization three types of implicit errors are typically made. The first error is the simulation-model error, which is defined by the difference between reality and the computer model. The second error is the metamodel error, which is defined by the difference between the computer model and the metamodel. The third is the implementation error. This paper presents new ideas on how to cope with these errors during optimization, in such a way that the final solution is robust with respect to these errors. We apply the robust counterpart theory of Ben-Tal and Nemirovsky to the most frequently used metamodels: linear regression and Kriging models. The methods proposed are applied to the design of two parts of the TV tube. The simulation-model errors receive little attention in the literature, while in practice these errors may have a significant impact due to propagation of such errors.
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Suggested Citation

  • Stinstra, E. & den Hertog, D., 2005. "Robust Optimization Using Computer Experiments," Discussion Paper 2005-90, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:69d6e378-c9f9-44e8-9602-f44e2ddac178
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    References listed on IDEAS

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    1. J P C Kleijnen & W C M van Beers, 2004. "Application-driven sequential designs for simulation experiments: Kriging metamodelling," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 876-883, August.
    2. Dick Den Hertog & Etienne De Klerk & Kees Roos, 2002. "On convex quadratic approximation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(3), pages 376-385, August.
    3. 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.
    4. Sturm, J.F., 2002. "Implementation of Interior Point Methods for Mixed Semidefinite and Second Order Cone Optimization Problems," Other publications TiSEM b25faf5d-0142-4e14-b598-a, Tilburg University, School of Economics and Management.
    5. den Hertog, Dick & Stehouwer, Peter, 2002. "Optimizing color picture tubes by high-cost nonlinear programming," European Journal of Operational Research, Elsevier, vol. 140(2), pages 197-211, July.
    6. Sturm, J.F., 2002. "Implementation of Interior Point Methods for Mixed Semidefinite and Second Order Cone Optimization Problems," Discussion Paper 2002-73, Tilburg University, Center for Economic Research.
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    Citations

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    Cited by:

    1. Ouyang, Linhan & Ma, Yizhong & Wang, Jianjun & Tu, Yiliu, 2017. "A new loss function for multi-response optimization with model parameter uncertainty and implementation errors," European Journal of Operational Research, Elsevier, vol. 258(2), pages 552-563.
    2. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    3. Ben-Tal, A. & den Hertog, D., 2011. "Immunizing Conic Quadratic Optimization Problems Against Implementation Errors," Discussion Paper 2011-060, Tilburg University, Center for Economic Research.
    4. Fajemisin, Adejuyigbe O. & Maragno, Donato & den Hertog, Dick, 2024. "Optimization with constraint learning: A framework and survey," European Journal of Operational Research, Elsevier, vol. 314(1), pages 1-14.
    5. Dellino, G. & Kleijnen, Jack P.C. & Meloni, C., 2009. "Robust Optimization in Simulation : Taguchi and Krige Combined," Other publications TiSEM d919b893-db2b-4d97-a392-4, Tilburg University, School of Economics and Management.
    6. Harris, Richard D.F. & Stoja, Evarist & Tan, Linzhi, 2017. "The dynamic Black–Litterman approach to asset allocation," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1085-1096.
    7. Huang, Dashan & Zhu, Shushang & Fabozzi, Frank J. & Fukushima, Masao, 2010. "Portfolio selection under distributional uncertainty: A relative robust CVaR approach," European Journal of Operational Research, Elsevier, vol. 203(1), pages 185-194, May.
    8. Gabriella Dellino & Jack P. C. Kleijnen & Carlo Meloni, 2012. "Robust Optimization in Simulation: Taguchi and Krige Combined," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 471-484, August.
    9. Siem, A.Y.D., 2008. "Property preservation and quality measures in meta-models," Other publications TiSEM 259d3ed2-1a23-48fe-8af8-2, Tilburg University, School of Economics and Management.
    10. Koubaa, Rayhane & Bacha, Seddik & Smaoui, Mariem & krichen, Lotfi, 2020. "Robust optimization based energy management of a fuel cell/ultra-capacitor hybrid electric vehicle under uncertainty," Energy, Elsevier, vol. 200(C).
    11. Han Men & Robert M. Freund & Ngoc C. Nguyen & Joel Saa-Seoane & Jaime Peraire, 2014. "Fabrication-Adaptive Optimization with an Application to Photonic Crystal Design," Operations Research, INFORMS, vol. 62(2), pages 418-434, April.
    12. Siem, A.Y.D. & den Hertog, D., 2007. "Kriging Models That Are Robust With Respect to Simulation Errors," Discussion Paper 2007-68, Tilburg University, Center for Economic Research.
    13. Dimitris Bertsimas & Omid Nohadani & Kwong Meng Teo, 2010. "Robust Optimization for Unconstrained Simulation-Based Problems," Operations Research, INFORMS, vol. 58(1), pages 161-178, February.
    14. Ben-Tal, A. & den Hertog, D., 2011. "Immunizing Conic Quadratic Optimization Problems Against Implementation Errors," Other publications TiSEM 9f3fba48-8501-4ec8-9241-5, Tilburg University, School of Economics and Management.
    15. He, Zhen & Zhu, Peng-Fei & Park, Sung-Hyun, 2012. "A robust desirability function method for multi-response surface optimization considering model uncertainty," European Journal of Operational Research, Elsevier, vol. 221(1), pages 241-247.

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    More about this item

    Keywords

    computer simulation; robust counterpart; simulation-model error; implementation error; metamodel error;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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