## A Taxonomy of Global Optimization Methods Based on Response Surfaces (2001)

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Venue: | Journal of Global Optimization |

Citations: | 121 - 1 self |

### BibTeX

@ARTICLE{Jones01ataxonomy,

author = {Donald R. Jones},

title = {A Taxonomy of Global Optimization Methods Based on Response Surfaces},

journal = {Journal of Global Optimization},

year = {2001},

volume = {21},

pages = {345--383}

}

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### Abstract

Abstract. This paper presents a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have non-obvious failure modes. Understanding these failure modes is essential for the development of practical algorithms that fulfill the intuitive promise of the response surface approach. Key words: global optimization, response surface, kriging, splines 1.

### Citations

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(Show Context)
Citation Context ...ify which input variables are the most important (highest contribution to the variance of the output) and ‘main effect plots’ can be created to visualize input-output relationships (see Booker, 1998; =-=Jones et al., 1998-=-). Using the surfaces as fast surrogates also makes it possible to quickly compute tradeoff curves between competing objectives. Multidisciplinary problems can be handled by linking response surfaces ... |

216 |
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(Show Context)
Citation Context ... �y and �R, we may write this as � y − 1�µ − y∗ � ′ � R r − �µ r ′ �−1 � y − 1�µ 1 y∗ � − �µ . (16) 2�σ 2sGLOBAL OPTIMIZATION BASED ON RESPONSE SURFACES 359 Now, from the partitioned inverse formula (=-=Theil, 1971-=-, p. 18), we have the following explicit expression for �R −1 : � R−1 + R−1r � 1 − r ′ R−1r �−1 � � ′ −1 −1 ′ −1 −1 r R −R r 1 − r R r − � 1 − r ′ R−1r � � −1 � � ′ −1 ′ −1 −1 . r R 1 − r R r Substitu... |

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(Show Context)
Citation Context ...eighborhood of the tentative solution to force the gradient of the surface to agree with the gradient of the true function (kriging can also be directly adapted to utilize derivative information; see =-=Koehler and Owen, 1996-=-). This idea is explored in Figure 7. We begin with the situation just described, where the minimum of the spline occurs at a sampled point. Since this means we have tentatively converged, we continue... |

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(Show Context)
Citation Context ... design and optimization. The intuitive promise of the response surface approach is illustrated in Figure 1. On the left of the figure we show the contours of the two-dimensional Branin test function =-=Dixon and Szego, 1978-=-. On the right, we show the contours of a ‘kriging’ response surface fit to 21 points (shown as spheres). The kriging predictor is so accurate that some people do not even notice the difference betwee... |

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