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Adaptive Partition-Based Level Decomposition Methods for Solving Two-Stage Stochastic Programs with Fixed Recourse

Author

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  • Wim van Ackooij

    (Électricité de France Research & Development, OSIRIS, 91120 Palaiseau, France)

  • Welington de Oliveira

    (Department of Applied Mathematics, Universidade do Estado do Rio de Janeiro, Rio de Janeiro 20550, Brazil)

  • Yongjia Song

    (Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, Virginia 23284)

Abstract

We present a computational study of several strategies to solve two-stage stochastic linear programs by integrating the adaptive partition-based approach with level decomposition. A partition-based formulation is a relaxation of the original stochastic program, obtained by aggregating variables and constraints according to a scenario partition. Partition refinements are guided by the optimal second-stage dual vectors computed at certain first-stage solutions. The proposed approaches rely on the level decomposition with on-demand accuracy to dynamically adjust partitions until an optimal solution is found. Numerical experiments on a large set of test problems including instances with up to one hundred thousand scenarios show the effectiveness of the proposed approaches.

Suggested Citation

  • Wim van Ackooij & Welington de Oliveira & Yongjia Song, 2018. "Adaptive Partition-Based Level Decomposition Methods for Solving Two-Stage Stochastic Programs with Fixed Recourse," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 57-70, February.
    • Handle: RePEc:inm:orijoc:v:30:y:2018:i:1:p:57-70
    DOI: 10.1287/ijoc.2017.0765
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    References listed on IDEAS

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    Cited by:

    1. Wim Ackooij & Welington Oliveira & Yongjia Song, 2019. "On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems," Computational Optimization and Applications, Springer, vol. 74(1), pages 1-42, September.
    2. Teodor Gabriel Crainic & Mike Hewitt & Francesca Maggioni & Walter Rei, 2021. "Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design," Transportation Science, INFORMS, vol. 55(2), pages 414-435, March.
    3. Jiménez, Diego & Angulo, Alejandro & Street, Alexandre & Mancilla-David, Fernando, 2023. "A closed-loop data-driven optimization framework for the unit commitment problem: A Q-learning approach under real-time operation," Applied Energy, Elsevier, vol. 330(PB).
    4. Mínguez, R. & van Ackooij, W. & García-Bertrand, R., 2021. "Constraint generation for risk averse two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 288(1), pages 194-206.
    5. W. Ackooij & X. Warin, 2020. "On conditional cuts for stochastic dual dynamic programming," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 173-199, June.
    6. Young Woong Park, 2021. "Optimization for L 1 -Norm Error Fitting via Data Aggregation," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 120-142, January.

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