A Fedorov Exchange Algorithm for D-optimal Design

Optimal design algorithms are particularly useful for creating designs in difficult situations, such as when experimental conditions enforce inconvenient block sizes. Several packages are now available for computer-aided design of experiments on personal computers (PCs) either in the form of Fortran source code or as easy-to-use commercial packages. Most of these packages could not find a good design for say a 23x 32 X 14 experiment in blocks of size 10. This kind of requirement is not unusual where there are say 14 species of timber or types of cheese, and the block size is dictated by the number of experimental runs which can be carried out in one day or from one batch of material. Our algorithm allows blocking, including the use of unequal block sizes. Another important application is in augmenting an experiment which has already been carried out. Our algorithm allows some of the candidate points, those in the experiment which has been carried out, to be forced into the design. Let X be an N x k matrix containing N possible or candidate design points. We want to find a subset of n out of the N points which maximizes the determinant D = IXnXn I

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