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Response Surface Methodology

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  • Kleijnen, Jack P.C.

    (Tilburg University, Center For Economic Research)

Abstract

This chapter first summarizes Response Surface Methodology (RSM), which started with Box and Wilson’s 1951 article on RSM for real, non-simulated systems. RSM is a stepwise heuristic that uses first-order polynomials to approximate the response surface locally. An estimated polynomial metamodel gives an estimated local gradient, which RSM uses in steepest ascent (or descent) to decide on the next local experiment. When RSM approaches the optimum, the latest first-order polynomial is replaced by a second-order polynomial. The fitted second-order polynomial enables the estimation of the optimum. This chapter then focuses on simulated systems, which may violate the assumptions of constant variance and independence. A variant of RSM that provably converges to the true optimum under specific conditions is summarized, and an adapted steepest ascent that is scale-independent is presented. Next, the chapter generalizes RSM to multiple random responses, selecting one response as the goal variable and the other responses as the constrained variables. This generalized RSM is combined with mathematical programming to estimate a better search direction than the steepest ascent direction. To test whether the estimated solution is indeed optimal, bootstrapping may be used. Finally, the chapter discusses robust optimization of the decision variables, while accounting for uncertainties in the environmental variables.
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Suggested Citation

  • Kleijnen, Jack P.C., 2014. "Response Surface Methodology," Discussion Paper 2014-013, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:7f9f17ee-db7f-4041-a686-d41f32a78539
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    References listed on IDEAS

    as
    1. Kuo-Hao Chang & L. Jeff Hong & Hong Wan, 2013. "Stochastic Trust-Region Response-Surface Method (STRONG)---A New Response-Surface Framework for Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 230-243, May.
    2. Bettonvil, Bert & del Castillo, Enrique & Kleijnen, Jack P.C., 2009. "Statistical testing of optimality conditions in multiresponse simulation-based optimization," European Journal of Operational Research, Elsevier, vol. 199(2), pages 448-458, December.
    3. Jack P. C. Kleijnen, 2015. "Response Surface Methodology," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 81-104, Springer.
    4. van den Bogaard, W. & Kleijnen, J.P.C., 1977. "Minimizing waiting times using priority classes : A case study in response surface methodology," Other publications TiSEM 2bb41f9c-6254-441b-ba32-0, Tilburg University, School of Economics and Management.
    5. Dellino, Gabriella & Kleijnen, Jack P.C. & Meloni, Carlo, 2010. "Robust optimization in simulation: Taguchi and Response Surface Methodology," International Journal of Production Economics, Elsevier, vol. 125(1), pages 52-59, May.
    6. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    7. Shi, Wen & Kleijnen, Jack P.C. & Liu, Zhixue, 2014. "Factor screening for simulation with multiple responses: Sequential bifurcation," European Journal of Operational Research, Elsevier, vol. 237(1), pages 136-147.
    8. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    9. M Chih, 2013. "A more accurate second-order polynomial metamodel using a pseudo-random number assignment strategy," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 64(2), pages 198-207, February.
    10. Kuo-Hao Chang & Ming-Kai Li & Hong Wan, 2014. "Combining STRONG with screening designs for large-scale simulation optimization," IISE Transactions, Taylor & Francis Journals, vol. 46(4), pages 357-373.
    11. Editors, 2014. "International Journal of Systems Science," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 1-1, December.
    12. 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.
    13. Yanikoglu, I. & den Hertog, D. & Kleijnen, Jack P.C., 2013. "Adjustable Robust Parameter Design with Unknown Distributions," Other publications TiSEM 47fec228-1ffe-4803-8e97-5, Tilburg University, School of Economics and Management.
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    Keywords

    simulation; optimization; regression; robustness; risk;
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