IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v159y2004i1p121-131.html
   My bibliography  Save this article

Response surface methodology's steepest ascent and step size revisited

Author

Listed:
  • Kleijnen, Jack P. C.
  • den Hertog, Dick
  • Angun, Ebru

Abstract

Response Surface Methodology (RSM) searches for the input combination maximizing the output of a real system or its simulation.RSM is a heuristic that locally fits first-order polynomials, and estimates the corresponding steepest ascent (SA) paths.However, SA is scale-dependent; and its step size is selected intuitively.To tackle these two problems, this paper derives novel techniques combining mathematical statistics and mathematical programming.Technique 1 called 'adapted' SA (ASA) accounts for the covariances between the components of the estimated local gradient.ASA is scale-independent.The step-size problem is solved tentatively.Technique 2 does follow the SA direction, but with a step size inspired by ASA.Mathematical properties of the two techniques are derived and interpreted; numerical examples illustrate these properties.The search directions of the two techniques are explored in Monte Carlo experiments.These experiments show that - in general - ASA gives a better search direction than SA.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Kleijnen, Jack P. C. & den Hertog, Dick & Angun, Ebru, 2004. "Response surface methodology's steepest ascent and step size revisited," European Journal of Operational Research, Elsevier, vol. 159(1), pages 121-131, November.
  • Handle: RePEc:eee:ejores:v:159:y:2004:i:1:p:121-131
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(03)00414-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Joan M. Donohue & Ernest C. Houck & Raymond H. Myers, 1995. "Simulation Designs for the Estimation of Quadratic Response Surface Gradients in the Presence of Model Misspecification," Management Science, INFORMS, vol. 41(2), pages 244-262, February.
    2. Joan M. Donohue & Ernest C. Houck & Raymond H. Myers, 1993. "Simulation Designs and Correlation Induction for Reducing Second-Order Bias in First-Order Response Surfaces," Operations Research, INFORMS, vol. 41(5), pages 880-902, October.
    3. Driessen, L. & Brekelmans, R.C.M. & Hamers, H.J.M. & den Hertog, D., 2001. "On D-Optimality Based Trust Regions for Black-Box Optimization Problems," Discussion Paper 2001-69, Tilburg University, Center for Economic Research.
    4. Neddermeijer, H.G. & van Oortmarssen, G.J. & Piersma, N. & Dekker, R., 2000. "A framework for response surface methodology for simulation optimization," Econometric Institute Research Papers EI 2000-14/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Safizadeh, M. Hossein, 2002. "Minimizing the bias and variance of the gradient estimate in RSM simulation studies," European Journal of Operational Research, Elsevier, vol. 136(1), pages 121-135, January.
    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. 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. Soonhui Lee & Tito Homem-de-Mello & Anton Kleywegt, 2012. "Newsvendor-type models with decision-dependent uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 189-221, October.
    3. Pourmohammadi, Pardis & Saif, Ahmed, 2023. "Robust metamodel-based simulation-optimization approaches for designing hybrid renewable energy systems," Applied Energy, Elsevier, vol. 341(C).
    4. Kleijnen, Jack P.C. & den Hertog, Dick & Angun, Ebru, 2006. "Response surface methodology's steepest ascent and step size revisited: Correction," European Journal of Operational Research, Elsevier, vol. 170(2), pages 664-666, April.
    5. Angun, M.E. & Gürkan, G. & den Hertog, D. & Kleijnen, J.P.C., 2002. "Response surface methodology revisited," Other publications TiSEM 32c35a04-3de9-4dee-a242-6, Tilburg University, School of Economics and Management.
    6. Angun, M.E., 2004. "Black box simulation optimization : Generalized response surface methodology," Other publications TiSEM 2548e953-54ce-44e2-8c5b-7, Tilburg University, School of Economics and Management.
    7. Kleijnen, J.P.C., 2006. "Generalized Response Surface Methodology : A New Metaheuristic," Discussion Paper 2006-77, Tilburg University, Center for Economic Research.
    8. Kleijnen, Jack P.C. & Beers, Wim van & Nieuwenhuyse, Inneke van, 2010. "Constrained optimization in expensive simulation: Novel approach," European Journal of Operational Research, Elsevier, vol. 202(1), pages 164-174, April.

    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. Angun, M.E., 2004. "Black box simulation optimization : Generalized response surface methodology," Other publications TiSEM 2548e953-54ce-44e2-8c5b-7, Tilburg University, School of Economics and Management.
    2. Angun, M.E. & Gürkan, G. & den Hertog, D. & Kleijnen, J.P.C., 2002. "Response surface methodology revisited," Other publications TiSEM 32c35a04-3de9-4dee-a242-6, Tilburg University, School of Economics and Management.
    3. Safizadeh, M. Hossein, 2002. "Minimizing the bias and variance of the gradient estimate in RSM simulation studies," European Journal of Operational Research, Elsevier, vol. 136(1), pages 121-135, January.
    4. Batmaz, Inci & Tunali, Semra, 2003. "Small response surface designs for metamodel estimation," European Journal of Operational Research, Elsevier, vol. 145(2), pages 455-470, March.
    5. Angun, M.E. & Kleijnen, Jack P.C., 2012. "An asymptotic test of optimality conditions in multiresponse simulation optimization," Other publications TiSEM a69dfa59-b0e1-45bd-8cd6-a, Tilburg University, School of Economics and Management.
    6. 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.
    7. R. C. M. Brekelmans & L. T. Driessen & H. J. M. Hamers & D. den. Hertog, 2005. "Gradient Estimation Schemes for Noisy Functions," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 529-551, September.
    8. 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.
    9. Kleijnen, J.P.C. & Sanchez, S.M. & Lucas, T.W. & Cioppa, T.M., 2003. "A User's Guide to the Brave New World of Designing Simulation Experiments," Discussion Paper 2003-1, Tilburg University, Center for Economic Research.
    10. 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.
    11. D. Huang & T. Allen & W. Notz & N. Zeng, 2006. "Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models," Journal of Global Optimization, Springer, vol. 34(3), pages 441-466, March.
    12. 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.
    13. Kleijnen, J.P.C., 2004. "Design and Analysis of Monte Carlo Experiments," Discussion Paper 2004-17, Tilburg University, Center for Economic Research.
    14. Ebru Angün & Jack Kleijnen, 2012. "An Asymptotic Test of Optimality Conditions in Multiresponse Simulation Optimization," INFORMS Journal on Computing, INFORMS, vol. 24(1), pages 53-65, February.
    15. Gomes, J.H.F. & Paiva, A.P. & Costa, S.C. & Balestrassi, P.P. & Paiva, E.J., 2013. "Weighted Multivariate Mean Square Error for processes optimization: A case study on flux-cored arc welding for stainless steel claddings," European Journal of Operational Research, Elsevier, vol. 226(3), pages 522-535.
    16. Andrei A. Prudius & Sigrún Andradóttir, 2012. "Averaging frameworks for simulation optimization with applications to simulated annealing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(6), pages 411-429, September.
    17. M Laguna & J Molina & F Pérez & R Caballero & A G Hernández-Díaz, 2010. "The challenge of optimizing expensive black boxes: a scatter search/rough set theory approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 53-67, January.
    18. Bettonvil, B.W.M. & Del Castillo, E. & Kleijnen, Jack P.C., 2005. "Statistical Testing of Optimality Conditions in Multiresponse Simulation-Based Optimization (Replaced by Discussion Paper 2007-45)," Discussion Paper 2005-81, Tilburg University, Center for Economic Research.
    19. Arsham H., 1998. "Techniques for Monte Carlo Optimizing," Monte Carlo Methods and Applications, De Gruyter, vol. 4(3), pages 181-230, December.
    20. Kleijnen, Jack P. C., 2005. "An overview of the design and analysis of simulation experiments for sensitivity analysis," European Journal of Operational Research, Elsevier, vol. 164(2), pages 287-300, July.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: 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:eee:ejores:v:159:y:2004:i:1:p:121-131. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.