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

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. den Hertog, D. & Kleijnen, J.P.C. & Siem, A.Y.D., 2004. "The Correct Kriging Variance Estimated by Bootstrapping," Other publications TiSEM 00a66547-3e9a-4ccf-8c7b-8, Tilburg University, School of Economics and Management.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. 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.
    4. 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.
    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.
    7. 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.
    8. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    9. 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.
    10. 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.
    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. 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.
    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. 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.
    13. 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.
    14. 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.
    15. 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. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    4. 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.
    5. 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.
    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. Edwin Dam & Bart Husslage & Dick Hertog, 2010. "One-dimensional nested maximin designs," Journal of Global Optimization, Springer, vol. 46(2), pages 287-306, February.
    8. Agnieszka Kurdyś-Kujawska & Agnieszka Sompolska-Rzechuła & Joanna Pawłowska-Tyszko & Michał Soliwoda, 2021. "Crop Insurance, Land Productivity and the Environment: A Way forward to a Better Understanding," Agriculture, MDPI, vol. 11(11), pages 1-17, November.
    9. van der Laan, G. & Talman, A.J.J. & Yang, Z.F., 2005. "Computing Integral Solutions of Complementarity Problems," Discussion Paper 2005-5, Tilburg University, Center for Economic Research.
    10. Wenfeng Chi & Yuanyuan Zhao & Wenhui Kuang & Tao Pan & Tu Ba & Jinshen Zhao & Liang Jin & Sisi Wang, 2021. "Impact of Cropland Evolution on Soil Wind Erosion in Inner Mongolia of China," Land, MDPI, vol. 10(6), pages 1-16, June.
    11. Yulin Zhao, 2012. "Positive Solutions for ( k , n − k ) Conjugate Multipoint Boundary Value Problems in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-18, August.
    12. Nick Middleton & Utchang Kang, 2017. "Sand and Dust Storms: Impact Mitigation," Sustainability, MDPI, vol. 9(6), pages 1-22, June.
    13. Tarantino, Emanuele & Pavanini, Nicola & Mayordomo, Sergio, 2020. "The Impact of Alternative Forms of Bank Consolidation on Credit Supply and Financial Stability," CEPR Discussion Papers 15069, C.E.P.R. Discussion Papers.
    14. Truong Duong & Nguyen Tan, 2012. "On the existence of solutions to generalized quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 52(4), pages 711-728, April.
    15. Misbah Haque & Imran Ali, 2016. "Uncertain Environment and Organizational Performance: The Mediating Role of Organizational Innovation," Asian Social Science, Canadian Center of Science and Education, vol. 12(9), pages 124-124, September.
    16. repec:spo:wpmain:info:hdl:2441/2082 is not listed on IDEAS
    17. , & ,, 2015. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society, vol. 10(2), May.
    18. Navid Bayati & Mehdi Savaghebi, 2021. "Protection Systems for DC Shipboard Microgrids," Energies, MDPI, vol. 14(17), pages 1-20, August.
    19. Velloso, Helvia & Vézina, François & Bustillo, Inés, 2006. "The Canadian retirement income system," Documentos de Proyectos 3682, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    20. Jesus M. Carro & Alejandra Traferri, 2014. "State Dependence And Heterogeneity In Health Using A Bias‐Corrected Fixed‐Effects Estimator," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(2), pages 181-207, March.
    21. Nobuyoshi Yamori & Ayami Kobayashi, 2007. "Wealth Effect Of Public Fund Injections To Ailing Banks: Do Deferred Tax Assets And Auditing Firms Matter?," The Japanese Economic Review, Japanese Economic Association, vol. 58(4), pages 466-483, December.

    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.