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Solving mixed-integer robust optimization problems with interval uncertainty using Benders decomposition

Author

Listed:
  • Sauleh Siddiqui

    (Johns Hopkins University, Baltimore, MD, USA)

  • Steven A Gabriel

    (Department of Civil Engineering, Applied Mathematics & Statistics, and Scientific Computation Program, University of Maryland, College Park, MD, USA)

  • Shapour Azarm

    (Department of Mechanical Engineering, Applied Mathematics & Statistics, and Scientific Computation Program, University of Maryland, College Park, MD, USA)

Abstract

Uncertainty and integer variables often exist together in economics and engineering design problems. The goal of robust optimization problems is to find an optimal solution that has acceptable sensitivity with respect to uncertain factors. Including integer variables with or without uncertainty can lead to formulations that are computationally expensive to solve. Previous approaches for robust optimization problems under interval uncertainty involve nested optimization or are not applicable to mixed-integer problems where the objective or constraint functions are neither quadratic, nor linear. The overall objective in this paper is to present an efficient robust optimization method that does not contain nested optimization and is applicable to mixed-integer problems with quasiconvex constraints (⩽ type) and convex objective funtion. The proposed method is applied to a variety of numerical examples to test its applicability and numerical evidence is provided for convergence in general as well as some theoretical results for problems with linear constraints.

Suggested Citation

  • Sauleh Siddiqui & Steven A Gabriel & Shapour Azarm, 2015. "Solving mixed-integer robust optimization problems with interval uncertainty using Benders decomposition," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(4), pages 664-673, April.
    • Handle: RePEc:pal:jorsoc:v:66:y:2015:i:4:p:664-673
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    Citations

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    Cited by:

    1. Joe Naoum-Sawaya & Christoph Buchheim, 2016. "Robust Critical Node Selection by Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 162-174, February.
    2. Unai Aldasoro & María Merino & Gloria Pérez, 2019. "Time consistent expected mean-variance in multistage stochastic quadratic optimization: a model and a matheuristic," Annals of Operations Research, Springer, vol. 280(1), pages 151-187, September.
    3. Yokoyama, Ryohei & Nakamura, Ryo & Wakui, Tetsuya, 2017. "Performance comparison of energy supply systems under uncertain energy demands based on a mixed-integer linear model," Energy, Elsevier, vol. 137(C), pages 878-887.
    4. Milford, James & Henrion, Max & Hunter, Chad & Newes, Emily & Hughes, Caroline & Baldwin, Samuel F., 2022. "Energy sector portfolio analysis with uncertainty," Applied Energy, Elsevier, vol. 306(PA).
    5. Lv, Chaoxian & Yu, Hao & Li, Peng & Wang, Chengshan & Xu, Xiandong & Li, Shuquan & Wu, Jianzhong, 2019. "Model predictive control based robust scheduling of community integrated energy system with operational flexibility," Applied Energy, Elsevier, vol. 243(C), pages 250-265.

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