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Discrete Optimization via Simulation

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Handbook of Simulation Optimization

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 216))

Abstract

This chapter describes tools and techniques that are useful for optimization via simulation—maximizing or minimizing the expected value of a performance measure of a stochastic simulation—when the decision variables are discrete. Ranking and selection, globally and locally convergent random search and ordinal optimization are covered, along with a collection of “enhancements” that may be applied to many different discrete optimization via simulation algorithms. We also provide strategies for using commercial solvers.

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Notes

  1. 1.

    One can also define convergence of \(\hat{g}(\mathbf{x}_{m}^{{\ast}})\), the estimated optimal value, but we do not do so here. See for instance Andradóttir [1].

  2. 2.

    Clearly any minimization problem on g(x) can be formulated as a maximization problem. If an estimator \(\hat{g}(\mathbf{x})\) of g(x) could be negative, then MRAS/SMRAS maximizes s(g(x)) instead, where s is a non-negative, strictly increasing function.

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Acknowledgements

This work was supported in part by the National Science Foundation 1099 under Grant CMMI-1233376, and by the Hong Kong Research Grants Council under Project 613011, 613012 and N_HKUST626/10.

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Authors and Affiliations

  1. City University of Hong Kong, Kowloon Tong, Hong Kong

    L. Jeff Hong

  2. Northwestern University, Evanston, IL, USA

    Barry L. Nelson

  3. George Mason University, Fairfax, VA, USA

    Jie Xu

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  1. L. Jeff Hong
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Correspondence to Jie Xu .

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  1. University of Maryland, College Park, Maryland, USA

    Michael C Fu

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Hong, L.J., Nelson, B.L., Xu, J. (2015). Discrete Optimization via Simulation. In: Fu, M. (eds) Handbook of Simulation Optimization. International Series in Operations Research & Management Science, vol 216. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1384-8_2

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