Response Surface Methodology's Steepest Ascent and Step Size Revisited

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages32
Volume2002-64
Publication statusPublished - 2002

Publication series

NameCentER Discussion Paper
Volume2002-64

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Mathematical programming
Statistical methods
Experiments
Polynomials

Keywords

  • response surface methodology

Cite this

Kleijnen, J. P. C., den Hertog, D., & Angun, M. E. (2002). Response Surface Methodology's Steepest Ascent and Step Size Revisited. (CentER Discussion Paper; Vol. 2002-64). Tilburg: Operations research.
Kleijnen, J.P.C. ; den Hertog, D. ; Angun, M.E. / Response Surface Methodology's Steepest Ascent and Step Size Revisited. Tilburg : Operations research, 2002. (CentER Discussion Paper).
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Kleijnen, JPC, den Hertog, D & Angun, ME 2002 'Response Surface Methodology's Steepest Ascent and Step Size Revisited' CentER Discussion Paper, vol. 2002-64, Operations research, Tilburg.

Response Surface Methodology's Steepest Ascent and Step Size Revisited. / Kleijnen, J.P.C.; den Hertog, D.; Angun, M.E.

Tilburg : Operations research, 2002. (CentER Discussion Paper; Vol. 2002-64).

Research output: Working paperDiscussion paperOther research output

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Kleijnen JPC, den Hertog D, Angun ME. Response Surface Methodology's Steepest Ascent and Step Size Revisited. Tilburg: Operations research. 2002. (CentER Discussion Paper).