A stochastic quasi-Newton method for simulation response optimization

A stochastic quasi-Newton method for simulation response optimization

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Article ID: iaor20084108
Country: Netherlands
Volume: 173
Issue: 1
Start Page Number: 30
End Page Number: 46
Publication Date: Aug 2006
Journal: European Journal of Operational Research
Authors: ,
Keywords: simulation: applications
Abstract:

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 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.

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