TY - JOUR

T1 - A stochastic quasi-Newton method for simulation response optimization

AU - Kao, Chiang

AU - Chen, Shih Pin

PY - 2006/8/16

Y1 - 2006/8/16

N2 - 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.

AB - 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.

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U2 - 10.1016/j.ejor.2004.12.011

DO - 10.1016/j.ejor.2004.12.011

M3 - Article

AN - SCOPUS:33646120566

VL - 173

SP - 30

EP - 46

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -