IDEAS home Printed from https://ideas.repec.org/p/tiu/tiucen/69d6e378-c9f9-44e8-9602-f44e2ddac178.html
   My bibliography  Save this paper

Robust Optimization Using Computer Experiments

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

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
    as

    Download full text from publisher

    File URL: https://repository.tilburguniversity.edu/bitstreams/e95f88b9-89ac-4a3c-8dac-9b9ec04f9391/download
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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. 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.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Richard D F Harris & Evarist Stoja & Linzhi Tan, 2016. "The dynamic Black-Litterman approach to asset allocation," Bank of England working papers 596, Bank of England.
    3. 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.
    4. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Edwin Dam & Bart Husslage & Dick Hertog, 2010. "One-dimensional nested maximin designs," Journal of Global Optimization, Springer, vol. 46(2), pages 287-306, February.
    4. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    5. 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.
    6. 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.
    7. Anand, C. & Sotirov, R. & Terlaky, T. & Zheng, Z., 2007. "Magnetic resonance tissue density estimation using optimal SSFP pulse-sequence design," Other publications TiSEM 371b5075-1085-4bf5-bd55-4, Tilburg University, School of Economics and Management.
    8. R. Andreani & G. Haeser & A. Ramos & D. O. Santos & L. D. Secchin & A. Serranoni, 2025. "Strong global convergence properties of algorithms for nonlinear symmetric cone programming," Computational Optimization and Applications, Springer, vol. 91(2), pages 397-421, June.
    9. Appino, Riccardo Remo & González Ordiano, Jorge Ángel & Mikut, Ralf & Faulwasser, Timm & Hagenmeyer, Veit, 2018. "On the use of probabilistic forecasts in scheduling of renewable energy sources coupled to storages," Applied Energy, Elsevier, vol. 210(C), pages 1207-1218.
    10. Xinfu Liu & Zuojun Shen, 2016. "Rapid Smooth Entry Trajectory Planning for High Lift/Drag Hypersonic Glide Vehicles," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 917-943, March.
    11. Zohrizadeh, Fariba & Josz, Cedric & Jin, Ming & Madani, Ramtin & Lavaei, Javad & Sojoudi, Somayeh, 2020. "A survey on conic relaxations of optimal power flow problem," European Journal of Operational Research, Elsevier, vol. 287(2), pages 391-409.
    12. Zhao, Shuaidong & Zhang, Kuilin, 2020. "A distributionally robust stochastic optimization-based model predictive control with distributionally robust chance constraints for cooperative adaptive cruise control under uncertain traffic conditi," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 144-178.
    13. Rennen, G. & Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2009. "Nested Maximin Latin Hypercube Designs," Discussion Paper 2009-06, Tilburg University, Center for Economic Research.
    14. Brekelmans, Ruud & Driessen, Lonneke & Hamers, Herbert & den Hertog, Dick, 2005. "Constrained optimization involving expensive function evaluations: A sequential approach," European Journal of Operational Research, Elsevier, vol. 160(1), pages 121-138, January.
    15. Zhang, Wei & (Ato) Xu, Wangtu, 2017. "Simulation-based robust optimization for the schedule of single-direction bus transit route: The design of experiment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 203-230.
    16. Yanikoglu, I. & den Hertog, D., 2011. "Safe Approximations of Chance Constraints Using Historical Data," Other publications TiSEM ab77f6f2-248a-42f1-bde1-0, Tilburg University, School of Economics and Management.
    17. Mehdad, E. & Kleijnen, Jack P.C., 2014. "Classic Kriging versus Kriging with Bootstrapping or Conditional Simulation : Classic Kriging's Robust Confidence Intervals and Optimization (Revised version of CentER DP 2013-038)," Other publications TiSEM 4915047b-afe4-4fc7-8a1c-4, Tilburg University, School of Economics and Management.
    18. 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.
    19. 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.
    20. Dellino, G. & Lino, P. & Meloni, C. & Rizzo, A., 2009. "Kriging metamodel management in the design optimization of a CNG injection system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2345-2360.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tiu:tiucen:69d6e378-c9f9-44e8-9602-f44e2ddac178. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Richard Broekman (email available below). General contact details of provider: http://center.uvt.nl .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.