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Integer set reduction for stochastic mixed-integer programming

Author

Listed:
  • Saravanan Venkatachalam

    (Wayne State University)

  • Lewis Ntaimo

    (Texas A & M University)

Abstract

Two-stage stochastic mixed-integer programs (SMIPs) with general integer variables in the second-stage are generally difficult to solve. This paper develops the theory of integer set reduction for characterizing a subset of the convex hull of feasible integer points of the second-stage subproblem which can be used for solving the SMIP with pure integer recourse. The basic idea is to use the smallest possible subset of the subproblem feasible integer set to generate a valid inequality like Fenchel decomposition cuts with a goal of reducing computation time. An algorithm for obtaining such a subset based on the solution of the subproblem linear programming relaxation is devised and incorporated into a decomposition method for SMIP. To demonstrate the performance of the new integer set reduction methodology, a computational study based on randomly generated knapsack test instances was performed. The results of the study show that integer set reduction aids in speeding up cut generation, leading to better bounds in solving SMIPs with pure integer recourse than using a direct solver.

Suggested Citation

  • Saravanan Venkatachalam & Lewis Ntaimo, 2023. "Integer set reduction for stochastic mixed-integer programming," Computational Optimization and Applications, Springer, vol. 85(1), pages 181-211, May.
    • Handle: RePEc:spr:coopap:v:85:y:2023:i:1:d:10.1007_s10589-023-00457-4
    DOI: 10.1007/s10589-023-00457-4
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    References listed on IDEAS

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    1. E. Andrew Boyd, 1994. "Fenchel Cutting Planes for Integer Programs," Operations Research, INFORMS, vol. 42(1), pages 53-64, February.
    2. Lewis Ntaimo, 2010. "Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse," Operations Research, INFORMS, vol. 58(1), pages 229-243, February.
    3. Rüdiger Schultz, 1993. "Continuity Properties of Expectation Functions in Stochastic Integer Programming," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 578-589, August.
    4. M T Ramos & J Sáez, 2005. "Solving capacitated facility location problems by Fenchel cutting planes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 297-306, March.
    5. Lewis Ntaimo, 2013. "Fenchel decomposition for stochastic mixed-integer programming," Journal of Global Optimization, Springer, vol. 55(1), pages 141-163, January.
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