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Simulation-Based Optimization with Stochastic Approximation Using Common Random Numbers

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Author Info

  • Nathan L. Kleinman

    (Options and Choices, Inc. (OCI), 2232 Dell Range Blvd., Suite 300, Cheyenne, Wyoming 82009)

  • James C. Spall

    (The Johns Hopkins University Applied Physics Laboratory, Johns Hopkins Road, Laurel, Maryland 20723)

  • Daniel Q. Naiman

    (The Johns Hopkins University Department of Mathematical Sciences, Baltimore, Maryland 21218)

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    Abstract

    The method of Common Random Numbers is a technique used to reduce the variance of difference estimates in simulation optimization problems. These differences are commonly used to estimate gradients of objective functions as part of the process of determining optimal values for parameters of a simulated system. Asymptotic results exist which show that using the Common Random Numbers method in the iterative Finite Difference Stochastic Approximation optimization algorithm (FDSA) can increase the optimal rate of convergence of the algorithm from the typical rate of k -1/3 to the faster k -1/2 , where k is the algorithm's iteration number. Simultaneous Perturbation Stochastic Approximation (SPSA) is a newer and often much more efficient optimization algorithm, and we will show that this algorithm, too, converges faster when the Common Random Numbers method is used. We will also provide multivariate asymptotic covariance matrices for both the SPSA and FDSA errors.

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    File URL: http://dx.doi.org/10.1287/mnsc.45.11.1570
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 45 (1999)
    Issue (Month): 11 (November)
    Pages: 1570-1578

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    Handle: RePEc:inm:ormnsc:v:45:y:1999:i:11:p:1570-1578

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    Related research

    Keywords: Common Random Numbers; Simultaneous Perturbation Stochastic Approximation (SPSA); Finite Difference Stochastic Approximation (FDSA); discrete event dynamic systems;

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    Cited by:
    1. Qi, Xiangtong & Song, Dong-Ping, 2012. "Minimizing fuel emissions by optimizing vessel schedules in liner shipping with uncertain port times," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(4), pages 863-880.
    2. Nicolai, R.P. & Koning, A.J., 2006. "A general framework for statistical inference on discrete event systems," Econometric Institute Research Papers EI 2006-45, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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