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A Simulated Annealing Algorithm with Constant Temperature for Discrete Stochastic Optimization

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Author Info

  • Mahmoud H. Alrefaei

    (Department of Mathematics and Statistics, Jordan University of Science & Technology, Irbid 22110, Jordan)

  • Sigrún Andradóttir

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

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    Abstract

    We present a modification of the simulated annealing algorithm designed for solving discrete stochastic optimization problems. Like the original simulated annealing algorithm, our method has the hill climbing feature, so it can find global optimal solutions to discrete stochastic optimization problems with many local solutions. However, our method differs from the original simulated annealing algorithm in that it uses a constant (rather than decreasing) temperature. We consider two approaches for estimating the optimal solution. The first approach uses the number of visits the algorithm makes to the different states (divided by a normalizer) to estimate the optimal solution. The second approach uses the state that has the best average estimated objective function value as estimate of the optimal solution. We show that both variants of our method are guaranteed to converge almost surely to the set of global optimal solutions, and discuss how our work applies in the discrete deterministic optimization setting. We also show how both variants can be applied for solving discrete optimization problems when the objective function values are estimated using either transient or steady-state simulation. Finally, we include some encouraging numerical results documenting the behavior of the two variants of our algorithm when applied for solving two versions of a particular discrete stochastic optimization problem, and compare their performance with that of other variants of the simulated annealing algorithm designed for solving discrete stochastic optimization problems.

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    File URL: http://dx.doi.org/10.1287/mnsc.45.5.748
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 45 (1999)
    Issue (Month): 5 (May)
    Pages: 748-764

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    Handle: RePEc:inm:ormnsc:v:45:y:1999:i:5:p:748-764

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    Related research

    Keywords: global optimization; discrete parameters; simulated annealing; simulation optimization;

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    Citations

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    Cited by:
    1. Wang, Honggang, 2012. "Retrospective optimization of mixed-integer stochastic systems using dynamic simplex linear interpolation," European Journal of Operational Research, Elsevier, vol. 217(1), pages 141-148.
    2. Shamsuddin Ahmed, 2013. "Performance of derivative free search ANN training algorithm with time series and classification problems," Computational Statistics, Springer, vol. 28(5), pages 1881-1914, October.
    3. João Claro & Jorge Sousa, 2010. "A multiobjective metaheuristic for a mean-risk static stochastic knapsack problem," Computational Optimization and Applications, Springer, vol. 46(3), pages 427-450, July.
    4. Alrefaei, Mahmoud H. & Alawneh, Ameen J., 2005. "Solution quality of random search methods for discrete stochastic optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(2), pages 115-125.
    5. Vaaler, Paul M. & Aguilera, Ruth V. & Flores, Ricardo G., 2007. "New Methods for Ex Post Evaluation of Regional Grouping Schemes in International Business Research: A Simulated Annealing Approach," Working Papers 07-0105, University of Illinois at Urbana-Champaign, College of Business.

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