Optimization by simulation metamodelling methods

We consider how simulation metamodels can be used to optimize the performance of a system that depends on a number of factors. We focus on the situation where the number of simulation runs that can be made is limited, and where a large number of factors must be included in the metamodel. Bayesian methods are particularly useful in this situation and can handle problems for which classical stochastic optimization can fail. We describe the basic Bayesian methodology, and then an extension to this that fits a quadratic response surface which, for function minimization, is guaranteed to be positive definite. An example is presented to illustrate the methods proposed in this paper.