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A Branch and Bound Method for Stochastic Global Optimization


  • V.I. Norkin
  • G.C. Pflug
  • A. Ruszczynski


A stochastic version of the branch and bound method is proposed for solving stochastic global optimization problems. The method, instead of deterministic bounds, uses stochastic upper and lower estimates of the optimal value of subproblems, to guide the partitioning process. Almost sure convergence of the method is proved and random accuracy estimates derived. Methods for constructing random bounds for stochastic global optimization problems are discussed. The theoretical considerations are illustrated with an example of a facility location problem.

Suggested Citation

  • V.I. Norkin & G.C. Pflug & A. Ruszczynski, 1996. "A Branch and Bound Method for Stochastic Global Optimization," Working Papers wp96065, International Institute for Applied Systems Analysis.
  • Handle: RePEc:wop:iasawp:wp96065

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    References listed on IDEAS

    1. labbe, M. & Peeters, D. & Thisse, J.F., 1992. "Location on Networks," Papers 9216, Universite Libre de Bruxelles - C.E.M.E..
      • LABBE, Martine & PEETERS, Dominique & THISSE, Jacques-François, 1993. "Location on Networks," CORE Discussion Papers 1993040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. V.I. Norkin & Y.M. Ermoliev & A. Ruszczynski, 1994. "On Optimal Allocation of Indivisibles Under Uncertainty," Working Papers wp94021, International Institute for Applied Systems Analysis.
    3. John R. Birge, 1985. "Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs," Operations Research, INFORMS, vol. 33(5), pages 989-1007, October.
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    Cited by:

    1. Didier Rullière & Alaeddine Faleh & Frédéric Planchet & Wassim Youssef, 2013. "Exploring or reducing noise? A global optimization algorithm in the presence of noise," Post-Print hal-00759677, HAL.
    2. Y.M. Ermoliev & V.I. Norkin, 1998. "Monte Carlo Optimization and Path Dependent Nonstationary Laws of Large Numbers," Working Papers ir98009, International Institute for Applied Systems Analysis.
    3. repec:hal:wpaper:hal-00759677 is not listed on IDEAS
    4. Johannes Royset, 2013. "On sample size control in sample average approximations for solving smooth stochastic programs," Computational Optimization and Applications, Springer, vol. 55(2), pages 265-309, June.
    5. Contreras, Ivan & Cordeau, Jean-François & Laporte, Gilbert, 2011. "Stochastic uncapacitated hub location," European Journal of Operational Research, Elsevier, vol. 212(3), pages 518-528, August.
    6. Lee, Der-Horng & Dong, Meng & Bian, Wen, 2010. "The design of sustainable logistics network under uncertainty," International Journal of Production Economics, Elsevier, vol. 128(1), pages 159-166, November.

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