A stochastic quasi-Newton method for simulation response optimization

Simulation response optimization has wide applications for management of systems that are so complicated that the performance can only be evaluated by using simulation. This paper modifies the quasi-Newton method used in deterministic optimization to suit the stochastic environment in simulation response optimization. The basic idea is to use the estimated subgradient calculated from different replications and a metric matrix updated from the Broyden–Fletcher–Goldfarb–Shanno (BFGS) formula to yield a quasi-Newton search direction. To avoid misjudging the minimal point, in both the line search and the quasi-Newton iterations, due to the stochastic nature, a t-test instead of a simple comparison of the mean responses is performed. It is proved that the resulting stochastic quasi-Newton algorithm is able to generate a sequence that converges to the optimal point, under certain conditions. Empirical results from a four-station queueing problem and an (s, S) inventory problem indicate that this method is able to find the optimal solutions in a statistical sense. Moreover, this method is robust with respect to the number of replications conducted at each trial point.