### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Operations research |

Number of pages | 32 |

Volume | 2002-64 |

Publication status | Published - 2002 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2002-64 |

### Fingerprint

### Keywords

- response surface methodology

### Cite this

*Response Surface Methodology's Steepest Ascent and Step Size Revisited*. (CentER Discussion Paper; Vol. 2002-64). Tilburg: Operations research.

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

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Response Surface Methodology's Steepest Ascent and Step Size Revisited

AU - Kleijnen, J.P.C.

AU - den Hertog, D.

AU - Angun, M.E.

N1 - Pagination: 32

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - response surface methodology

M3 - Discussion paper

VL - 2002-64

T3 - CentER Discussion Paper

BT - Response Surface Methodology's Steepest Ascent and Step Size Revisited

PB - Operations research

CY - Tilburg

ER -