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Efficient Global Optimization of Expensive Black-Box Functions   总被引:39,自引:0,他引:39  
In many engineering optimization problems, the number of function evaluations is severely limited by time or cost. These problems pose a special challenge to the field of global optimization, since existing methods often require more function evaluations than can be comfortably afforded. One way to address this challenge is to fit response surfaces to data collected by evaluating the objective and constraint functions at a few points. These surfaces can then be used for visualization, tradeoff analysis, and optimization. In this paper, we introduce the reader to a response surface methodology that is especially good at modeling the nonlinear, multimodal functions that often occur in engineering. We then show how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule. The key to using response surfaces for global optimization lies in balancing the need to exploit the approximating surface (by sampling where it is minimized) with the need to improve the approximation (by sampling where prediction error may be high). Striking this balance requires solving certain auxiliary problems which have previously been considered intractable, but we show how these computational obstacles can be overcome.  相似文献
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Summary  In hierarchical cluster analysis dendrogram graphs are used to visualize how clusters are formed. Because each observation is displayed dendrograms are impractical when the data set is large. For non-hierarchical cluster algorithms (e.g. Kmeans) a graph like the dendrogram does not exist. This paper discusses a graph named “clustergram” to examine how cluster members are assigned to clusters as the number of clusters increases. The clustergram can also give insight into algorithms. For example, it can easily be seen that the “single linkage” algorithm tends to form clusters that consist of just one observation. It is also useful in distinguishing between random and deterministic implementations of the Kmeans algorithm. A data set related to asbestos claims and the Thailand Landmine Data are used throughout to illustrate the clustergram.  相似文献
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