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Response surface methodology's steepest ascent and step size revisited

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  • 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.
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  • 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
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    1. 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.
    2. 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.
    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. 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.
    5. 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.
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    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. Kleijnen, J.P.C., 2006. "Generalized Response Surface Methodology : A New Metaheuristic," Discussion Paper 2006-77, Tilburg University, Center for Economic Research.
    3. 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.
    4. Pourmohammadi, Pardis & Saif, Ahmed, 2023. "Robust metamodel-based simulation-optimization approaches for designing hybrid renewable energy systems," Applied Energy, Elsevier, vol. 341(C).
    5. 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.
    6. 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.
    7. 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.
    8. 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.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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