Response surface methodology with stochastic constraints for expensive simulation

This paper 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 stochastic and deterministic constraints. This extension is obtained through the generalization of the estimated steepest descent—used in classic RSM—using ideas from interior point methods, especially affine scaling. The new search direction is scale independent, which is important for practitioners since it avoids some numerical complications and problems commonly encountered. Furthermore, this paper derives a heuristic that uses this search direction iteratively. The heuristic is intended for problems in which each simulation run is expensive and the computer budget is limited, so that the search needs to reach a neighborhood of the true optimum quickly. Moreover, although the heuristic is meant for stochastic problems, it can be easily simplified for deterministic ones. Numerical illustrations give encouraging results. (Simulation, interior point methods, stochastic optimization, bootstrap) ∗Corresponding author