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Stopping Rules for the Stochastic Nested Partitions Method

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Abstract

We have recently developed a global optimization methodology for solving combinatorial problems with either deterministic or stochastic performance functions. This method, the Nested Partitions (NP) method has been shown to generate a Markov chain and with probability one to converge to a global optimum. In this paper, we study the rate of convergence of the method through the use of Markov Chain Monte Carlo (MCMC) methods, and use this to derive stopping rules that can be applied during simulation-based optimization. A numerical example serves to illustrate the feasibility of our approach.

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Authors and Affiliations

  1. IE Department, University of Wisconsin, 1513 University Avenue, Madison, WI, 53706

    Leyuan Shi

  2. IMSE Department, Iowa State University, 205 Engineering Annex, Ames, IA, 50011

    Sigurdur O´lafsson

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  1. Leyuan Shi
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  2. Sigurdur O´lafsson
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Shi, L., O´lafsson, S. Stopping Rules for the Stochastic Nested Partitions Method. Methodology and Computing in Applied Probability 2, 37–58 (2000). https://doi.org/10.1023/A:1010055101140

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