Automated Response Surface Methodology for Stochastic Optimization Models with Unknown Variance

Response Surface Methodology (RSM) is a tool that was introduced in the early 50's by Box and Wilson (1951). It is a collection of mathematical and statistical techniques useful for the approximation and optimization of stochastic models. Applications of RSM can be found in e.g. chemical, engineering and clinical sciences. In this paper we are interested in finding the best settings for an automated RSM procedure when there is very little information about the stochastic objective function. We will present a framework of the RSM procedures for finding optimal solutions in the presence of noise. We emphasize the use of both stopping rules and restart procedures. Good stopping rules recognize when no further improvement is being made. Restarts are used to escape from non-optimal regions of the domain. We compare different versions of the RSM algorithms on a number of test functions, including a simulation model for cancer screening. The results show that co! nsiderable improvement is possible over the proposed settings in the existing literature.