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A Unified Framework for Multistage Mixed Integer Linear Optimization

In: Bilevel Optimization

Author

Listed:
  • Suresh Bolusani

    (Lehigh University)

  • Stefano Coniglio

    (University of Southampton)

  • Ted K. Ralphs

    (Lehigh University)

  • Sahar Tahernejad

    (Lindo Systems, Inc.)

Abstract

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, the nature of the value function of the second-stage problem, highlighting its connection to dual functions and the theory of duality for mixed integer linear optimization problems, and summarize different reformulations. We then present two main solution techniques, one based on a Benders-like decomposition to approximate either the risk function or the value function, and the other one based on cutting plane generation.

Suggested Citation

  • Suresh Bolusani & Stefano Coniglio & Ted K. Ralphs & Sahar Tahernejad, 2020. "A Unified Framework for Multistage Mixed Integer Linear Optimization," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 513-560, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-52119-6_18
    DOI: 10.1007/978-3-030-52119-6_18
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    Citations

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    Cited by:

    1. Stefano Coniglio & Mathias Sirvent & Martin Weibelzahl, 2021. "Airport capacity extension, fleet investment, and optimal aircraft scheduling in a multilevel market model: quantifying the costs of imperfect markets," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 367-408, June.
    2. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    3. Bjørndal, Endre & Bjørndal, Mette Helene & Coniglio, Stefano & Körner, Marc-Fabian & Leinauer, Christina & Weibelzahl, Martin, 2023. "Energy storage operation and electricity market design: On the market power of monopolistic storage operators," European Journal of Operational Research, Elsevier, vol. 307(2), pages 887-909.
    4. Coniglio, Stefano & Furini, Fabio & San Segundo, Pablo, 2021. "A new combinatorial branch-and-bound algorithm for the Knapsack Problem with Conflicts," European Journal of Operational Research, Elsevier, vol. 289(2), pages 435-455.
    5. Stefano Coniglio & Stefano Gualandi, 2022. "Optimizing over the Closure of Rank Inequalities with a Small Right-Hand Side for the Maximum Stable Set Problem via Bilevel Programming," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1006-1023, March.
    6. Christiansen, Jeffrey & Ernst, Andreas T. & Rieger, Janosch, 2024. "A robust optimization approach for a two-player force-design game," European Journal of Operational Research, Elsevier, vol. 318(2), pages 656-669.

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