| Author(s): |
Tito Homem-de-Mello, Department of Industrial, Welding and Systems Engineering, Ohio State University |
Title: |
Variable-sample methods and simulated annealing for discrete stochastic optimization – (revised version) |
| Date of Acceptance: |
31.01.2000 |
| Submission Date: |
21.01.2000 |
| Series Title: |
Stochastic Programming E-Print Series
(SPEPS)
|
| Editors: |
Julie L. Higle; Werner Römisch; Surrajeet Sen |
| Complete Preprint: |
pdf
(urn:nbn:de:kobv:11-10046200)
|
| Keywords (eng): |
Stochastic optimization, Monte Carlo methods, simulated annealing, Markov chains, sample-path bounds |
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| Abstract (eng): |
| In this paper we study a modifcation of the well-known simulated annealing method, adapting it to discrete stochastic optimization problems. Our algorithm is based on a variable-sample Monte Carlo technique, in which the objective function is replaced, at each iteration, by a sample average approximation. The idea is to obtain independent estimates of the objective function, to avoid getting "trapped" in a single sample-path. We first provide general results under which variable-sample methods yield consistent estimators as well as bounds on the estimation error. Then, we concentrate on the simulated annealing algorithm, and derive a proper schedule of sample sizes that guarantees convergence of the overall algorithm w.p.1. Because the convergence analysis is done sample-path wise (by means of the law of the iterated logarithm), we are able to obtain our results in a exible setting, which includes the possibility of using different neighborhood structures and different sampling distributions along the algorithm, without making strong assumptions on the underlying distributions. |
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