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Solution quality of random search methods for discrete stochastic optimization

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  • Alrefaei, Mahmoud H.
  • Alawneh, Ameen J.

Abstract

In this paper, we propose a framework for selecting a high quality global optimal solution for discrete stochastic optimization problems with a predetermined confidence level using general random search methods. This procedure is based on performing the random search algorithm several replications to get estimate of the error gap between the estimated optimal value and the actual optimal value. A confidence set that contains the optimal solution is then constructed and methods of the indifference zone approach are used to select the optimal solution with high probability. The proposed procedure is applied on a simulated annealing algorithm for solving a particular discrete stochastic optimization problem involving queuing models. The numerical results indicate that the proposed technique indeed locate a high quality optimal solution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:68:y:2005:i:2:p:115-125
    DOI: 10.1016/j.matcom.2004.10.004
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    References listed on IDEAS

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    1. David S. Johnson & Cecilia R. Aragon & Lyle A. McGeoch & Catherine Schevon, 1989. "Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning," Operations Research, INFORMS, vol. 37(6), pages 865-892, December.
    2. Barry L. Nelson & Julie Swann & David Goldsman & Wheyming Song, 2001. "Simple Procedures for Selecting the Best Simulated System When the Number of Alternatives is Large," Operations Research, INFORMS, vol. 49(6), pages 950-963, December.
    3. 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.
    4. 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.
    5. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
    6. Alkhamis, Talal M. & Ahmed, Mohamed A. & Tuan, Vu Kim, 1999. "Simulated annealing for discrete optimization with estimation," European Journal of Operational Research, Elsevier, vol. 116(3), pages 530-544, August.
    7. Alrefaei, Mahmoud H. & Andradottir, Sigrun, 2001. "A modification of the stochastic ruler method for discrete stochastic optimization," European Journal of Operational Research, Elsevier, vol. 133(1), pages 160-182, August.
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    Cited by:

    1. Tsai, Shing Chih, 2011. "Selecting the best simulated system with weighted control-variate estimators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 705-717.

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