Optimal LHS - Journal of Applied Statistics, Vol. 30, No....

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Journal of Applied Statistics, Vol. 30, No. 5, 2003, 585–598 Optimal orthogonal-array-based latin hypercubes STEPHEN LEARY, ATUL BHASKAR & ANDY KEANE, Computational Engineering and Design Centre, University of Southampton, UK  The use of optimal orthogonal array latin hypercube designs is proposed. Orthogonal arrays were proposed for constructing latin hypercube designs by Tang (1993). Such designs generally have better space Flling properties than random latin hypercube designs. Even so, these designs do not necessarily Fll the space particularly well. As a result, we consider orthogonal-array-based latin hypercube designs that try to achieve optimality in some sense. Optimization is performed by adapting strategies found in Morris & Mitchell (1995) and Ye et al. (2000). The strategies here search only orthogonal-array-based latin hypercube designs and, as a result, optimal designs are found in a more e cient fashion. The designs found are in general agreement with existing optimal designs reported elsewhere. 1 Introduction A major application area for designed experiments is to enable the optimization of complex engineering systems. Such systems are generally represented by expensive computer codes (for instance, a Fnite element solution in a structural analysis, or a Navier–Stokes solution in computational ±uid dynamics (C²D)). Due to the expense of the code, direct optimization is quite often infeasible and approximation methods are then considered. The output of these expensive computer codes can be, for instance, approximated using a response surface model, see for example, Myers & Montgomery (1995), or by a kriging model, for example Jones et al . (1998). Correspondence : Andy Keane, Computational Engineering and Design Centre, School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK ISSN 0266-4763 print; 1360-0532 online/03/050585-14 © 2003 Taylor & ²rancis Ltd DOI: 10.1080/0266476032000053691
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586 S. Leary et al. One key question when the available data are to be limited due to the cost of running the model is: at which values of the input variables do we run the code? In the absence of any a priori information on the system of interest, it is commonly recognized that some form of uniformity of the design points throughout the region of interest is favourable. Many experimental design planning methods exist in the literature and an exhaustive list is well beyond the scope of this paper. Here, we restrict ourselves to latin hypercube designs, Frst introduced by McKay et al . (1979). A latin hypercube is an n by m matrix, each column of which is a permutation of1,2,. .., n . Such designs are seen to enjoy good ‘space-Flling’ properties, covering the design space well without replication. However, one must note that amongst various latin hypercube designs, some are better than others, so optimal latin hypercube designs have recently been considered (Park, 1994; Tang, 1994; Morris and Mitchell, 1995; Ye, 1998 and Ye et al ., 2000).
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Optimal LHS - Journal of Applied Statistics, Vol. 30, No....

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