Response surface methodology with stochastic constraints for expensive simulation

Abstract

This article investigates simulation-based optimization problems with a stochastic objective function, stochastic output constraints, and deterministic input constraints. More specifically, it generalizes classic response surface methodology (RSM) to account for these constraints. This Generalized RSM—abbreviated to GRSM—generalizes the estimated steepest descent—used in classic RSM—applying ideas from interior point methods, especially affine scaling. This new search direction is scale independent, which is important for practitioners because it avoids some numerical complications and problems commonly encountered. Furthermore, the article derives a heuristic that uses this search direction iteratively. This heuristic is intended for problems in which simulation runs are expensive, so that the search needs to reach a neighbourhood of the true optimum quickly. The new heuristic is compared with OptQuest, which is the most popular heuristic available with several simulation software packages. Numerical illustrations give encouraging results.