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.
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.
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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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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