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SICOpt: Solution Approach for Nonlinear Integer Stochastic Programming Problems

Author

Listed:
  • P. Beraldi

    (University of Calabria)

  • D. Conforti

    (University of Calabria)

  • A. Violi

    (Supercomputing Center for Computational Engineering)

Abstract

We propose a novel solution approach for the class of two-stage nonlinear integer stochastic programming models. These problems are characterized by large scale dimensions, as the number of constraints and variables depend on the number of realizations (scenarios) used to capture the underlying distributions of the random data. In addition, the integrality constraints on the decision variables make the solution process even much more difficult preventing the application of general purpose solvers. The proposed solution approach integrates the branch-and-bound framework with the interior point method. The main advantage of this choice is the effective exploitation of the specific structure exhibited by the different subproblems at each node of the search tree. A specifically designed warm start procedure and an early branching technique improve the overall efficiency. Our contribution is well founded from a theoretical point of view and is characterized by good computational efficiency, without any loss in terms of effectiveness. Some preliminary numerical results, obtained by solving a challenging real-life problem, prove the robustness and the efficiency of the proposed approach.

Suggested Citation

  • P. Beraldi & D. Conforti & A. Violi, 2009. "SICOpt: Solution Approach for Nonlinear Integer Stochastic Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 17-36, October.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:1:d:10.1007_s10957-009-9555-y
    DOI: 10.1007/s10957-009-9555-y
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    References listed on IDEAS

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    1. John R. Birge & Liqun Qi, 1988. "Computing Block-Angular Karmarkar Projections with Applications to Stochastic Programming," Management Science, INFORMS, vol. 34(12), pages 1472-1479, December.
    2. Irvin J. Lustig & John M. Mulvey & Tamra J. Carpenter, 1991. "Formulating Two-Stage Stochastic Programs for Interior Point Methods," Operations Research, INFORMS, vol. 39(5), pages 757-770, October.
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