In many practical optimization problems, the number of function evaluations is severely limited by time or cost. This practical consideration has driven the development of efficient methods for global optimization which require only small numbers of function evaluations. This talk will consider, in particular, the method of Jones {\em et al.} in which the objective is modelled by a linear predictor which interpolates the function at a set of sample points. A corresponding standard error function models the uncertainty in the predictor at points not yet sampled. By optimizing a merit function of the predictor and standard error, the best new sample point is determined. A procedure for generating appropriate test problems for such methods will be described. Extensive testing of the method has allowed its reliability to be properly assessed and techniques for its improvement will be discussed. The optimization of the merit function is, itself, a global optimization problem and the scope for its efficient solution will be examined.
Note that the postscript version is of finer resolution.