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A Simulated Annealing Algorithm with Constant Temperature for Discrete Stochastic Optimization

Author

Listed:
  • 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)

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.

Suggested Citation

  • Mahmoud H. Alrefaei & Sigrún Andradóttir, 1999. "A Simulated Annealing Algorithm with Constant Temperature for Discrete Stochastic Optimization," Management Science, INFORMS, vol. 45(5), pages 748-764, May.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:5:p:748-764
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    File URL: http://dx.doi.org/10.1287/mnsc.45.5.748
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    Cited by:

    1. Katsumi Morikawa & Katsuhiko Takahashi & Daisuke Hirotani, 0. "Performance evaluation of candidate appointment schedules using clearing functions," Journal of Intelligent Manufacturing, Springer, vol. 0, pages 1-10.
    2. 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.
    3. Ahmed, Mohamed A. & Alkhamis, Talal M., 2009. "Simulation optimization for an emergency department healthcare unit in Kuwait," European Journal of Operational Research, Elsevier, vol. 198(3), pages 936-942, November.
    4. Alkhamis, Talal M. & Ahmed, Mohamed A., 2006. "A modified Hooke and Jeeves algorithm with likelihood ratio performance extrapolation for simulation optimization," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1802-1815, November.
    5. 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.
    6. Hemmelmayr, Vera & Doerner, Karl F. & Hartl, Richard F. & Savelsbergh, Martin W.P., 2010. "Vendor managed inventory for environments with stochastic product usage," European Journal of Operational Research, Elsevier, vol. 202(3), pages 686-695, May.
    7. 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.
    8. Pichitlamken, Juta & Nelson, Barry L. & Hong, L. Jeff, 2006. "A sequential procedure for neighborhood selection-of-the-best in optimization via simulation," European Journal of Operational Research, Elsevier, vol. 173(1), pages 283-298, August.
    9. 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.
    10. Rosen, Scott L. & Harmonosky, Catherine M. & Traband, Mark T., 2007. "A simulation optimization method that considers uncertainty and multiple performance measures," European Journal of Operational Research, Elsevier, vol. 181(1), pages 315-330, August.
    11. Alrefaei, Mahmoud H. & Alawneh, Ameen J., 2004. "Selecting the best stochastic system for large scale problems in DEDS," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 237-245.
    12. repec:spr:annopr:v:240:y:2016:i:1:d:10.1007_s10479-015-2019-x is not listed on IDEAS
    13. Lysa Porth & Milton Boyd & Jeffrey Pai, 2016. "Reducing Risk Through Pooling and Selective Reinsurance Using Simulated Annealing: An Example from Crop Insurance," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 41(2), pages 163-191, September.
    14. Angun, M.E., 2004. "Black box simulation optimization : Generalized response surface methodology," Other publications TiSEM 2548e953-54ce-44e2-8c5b-7, Tilburg University, School of Economics and Management.
    15. repec:spr:joinma:v:29:y:2018:i:3:d:10.1007_s10845-015-1134-5 is not listed on IDEAS
    16. 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.

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