IDEAS home Printed from https://ideas.repec.org/p/tiu/tiucen/7f9f17ee-db7f-4041-a686-d41f32a78539.html
   My bibliography  Save this paper

Response Surface Methodology

Author

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

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
    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. 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. Kleijnen, Jack P.C., 2014. "Response Surface Methodology," Other publications TiSEM 7f9f17ee-db7f-4041-a686-d, Tilburg University, School of Economics and Management.
    7. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    8. 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.
    9. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    10. 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.
    11. 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.
    12. Editors, 2014. "International Journal of Systems Science," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 1-1, December.
    13. 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.
    14. Yanikoglu, I. & den Hertog, D. & Kleijnen, Jack P.C., 2013. "Adjustable Robust Parameter Design with Unknown Distributions," Discussion Paper 2013-022, Tilburg University, Center for Economic Research.
    15. 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.
    Full references (including those not matched with items on IDEAS)

    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. Kleijnen, Jack P.C., 2017. "Regression and Kriging metamodels with their experimental designs in simulation: A review," European Journal of Operational Research, Elsevier, vol. 256(1), pages 1-16.
    2. 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.
    3. Kleijnen, J.P.C., 2015. "Regression and Kriging Metamodels with Their Experimental Designs in Simulation : Review," Other publications TiSEM c592e895-1656-43c3-8c7e-f, Tilburg University, School of Economics and Management.
    4. 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.
    5. Qi Zhang & Jiaqiao Hu, 2019. "Simulation Optimization Using Multi-Time-Scale Adaptive Random Search," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(06), pages 1-34, December.
    6. Shen-Tsu Wang, 2016. "Integrating grey sequencing with the genetic algorithm--immune algorithm to optimise touch panel cover glass polishing process parameter design," International Journal of Production Research, Taylor & Francis Journals, vol. 54(16), pages 4882-4893, August.
    7. Yek, Peter Nai Yuh & Cheng, Yoke Wang & Liew, Rock Keey & Wan Mahari, Wan Adibah & Ong, Hwai Chyuan & Chen, Wei-Hsin & Peng, Wanxi & Park, Young-Kwon & Sonne, Christian & Kong, Sieng Huat & Tabatabaei, 2021. "Progress in the torrefaction technology for upgrading oil palm wastes to energy-dense biochar: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 151(C).
    8. Qin, Caiyan & Kim, Joong Bae & Lee, Bong Jae, 2019. "Performance analysis of a direct-absorption parabolic-trough solar collector using plasmonic nanofluids," Renewable Energy, Elsevier, vol. 143(C), pages 24-33.
    9. Kaushik, Lav Kumar & Muthukumar, P., 2020. "Thermal and economic performance assessments of waste cooking oil /kerosene blend operated pressure cook-stove with porous radiant burner," Energy, Elsevier, vol. 206(C).
    10. Yaman, Hayri & Yesilyurt, Murat Kadir & Uslu, Samet, 2022. "Simultaneous optimization of multiple engine parameters of a 1-heptanol / gasoline fuel blends operated a port-fuel injection spark-ignition engine using response surface methodology approach," Energy, Elsevier, vol. 238(PC).
    11. Visva Bharati Barua & Mariya Munir, 2021. "A Review on Synchronous Microalgal Lipid Enhancement and Wastewater Treatment," Energies, MDPI, vol. 14(22), pages 1-20, November.
    12. Chang, Kuo-Hao & Kuo, Po-Yi, 2018. "An efficient simulation optimization method for the generalized redundancy allocation problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1094-1101.
    13. Ramos, Ana & Monteiro, Eliseu & Rouboa, Abel, 2019. "Numerical approaches and comprehensive models for gasification process: A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 110(C), pages 188-206.
    14. D. M. D. Rasika & Janak K. Vidanarachchi & Selma F. Luiz & Denise Rosane Perdomo Azeredo & Adriano G. Cruz & Chaminda Senaka Ranadheera, 2021. "Probiotic Delivery through Non-Dairy Plant-Based Food Matrices," Agriculture, MDPI, vol. 11(7), pages 1-23, June.
    15. M'Arimi, M.M. & Mecha, C.A. & Kiprop, A.K. & Ramkat, R., 2020. "Recent trends in applications of advanced oxidation processes (AOPs) in bioenergy production: Review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 121(C).
    16. Muhammad, Gul & Potchamyou Ngatcha, Ange Douglas & Lv, Yongkun & Xiong, Wenlong & El-Badry, Yaser A. & Asmatulu, Eylem & Xu, Jingliang & Alam, Md Asraful, 2022. "Enhanced biodiesel production from wet microalgae biomass optimized via response surface methodology and artificial neural network," Renewable Energy, Elsevier, vol. 184(C), pages 753-764.
    17. Renzi, Massimiliano & Bietresato, Marco & Mazzetto, Fabrizio, 2016. "An experimental evaluation of the performance of a SI internal combustion engine for agricultural purposes fuelled with different bioethanol blends," Energy, Elsevier, vol. 115(P1), pages 1069-1080.
    18. Chamberlin Stéphane Azebaze Mboving & Zbigniew Hanzelka & Andrzej Firlit, 2022. "Analysis of the Factors Having an Influence on the LC Passive Harmonic Filter Work Efficiency," Energies, MDPI, vol. 15(5), pages 1-51, March.
    19. Lu Chen & Qincheng Chen & Pinhua Rao & Lili Yan & Alghashm Shakib & Guoqing Shen, 2018. "Formulating and Optimizing a Novel Biochar-Based Fertilizer for Simultaneous Slow-Release of Nitrogen and Immobilization of Cadmium," Sustainability, MDPI, vol. 10(8), pages 1-14, August.
    20. Biranchi Panda & K. Shankhwar & Akhil Garg & M. M. Savalani, 2019. "Evaluation of genetic programming-based models for simulating bead dimensions in wire and arc additive manufacturing," Journal of Intelligent Manufacturing, Springer, vol. 30(2), pages 809-820, February.

    More about this item

    Keywords

    simulation; optimization; regression; robustness; risk;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:7f9f17ee-db7f-4041-a686-d41f32a78539. 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.