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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. 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.
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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. 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.

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

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