IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v18y2021i2d10.1007_s10287-021-00387-8.html
   My bibliography  Save this article

Single cut and multicut stochastic dual dynamic programming with cut selection for multistage stochastic linear programs: convergence proof and numerical experiments

Author

Listed:
  • Michelle Bandarra

    (FGV)

  • Vincent Guigues

    (FGV)

Abstract

We introduce a variant of Multicut Decomposition Algorithms, called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates a class of cut selection strategies to choose the most relevant cuts of the approximate recourse functions. This class contains Level 1 (Philpott et al. in J Comput Appl Math 290:196–208, 2015) and Limited Memory Level 1 (Guigues in Eur J Oper Res 258:47–57, 2017) cut selection strategies, initially introduced for respectively Stochastic Dual Dynamic Programming and Dual Dynamic Programming. We prove the almost sure convergence of the method in a finite number of iterations and obtain as a by-product the almost sure convergence in a finite number of iterations of Stochastic Dual Dynamic Programming combined with our class of cut selection strategies. We compare the performance of Multicut Decomposition Algorithms, Stochastic Dual Dynamic Programming, and their variants with cut selection (using Level 1 and Limited Memory Level 1) on several instances of a portfolio problem. On these experiments, in general, Stochastic Dual Dynamic Programming is quicker (i.e., satisfies the stopping criterion quicker) than Multicut Decomposition Algorithms and cut selection allows us to decrease the computational bulk with Limited Memory Level 1 being more efficient (sometimes much more) than Level 1.

Suggested Citation

  • Michelle Bandarra & Vincent Guigues, 2021. "Single cut and multicut stochastic dual dynamic programming with cut selection for multistage stochastic linear programs: convergence proof and numerical experiments," Computational Management Science, Springer, vol. 18(2), pages 125-148, June.
  • Handle: RePEc:spr:comgts:v:18:y:2021:i:2:d:10.1007_s10287-021-00387-8
    DOI: 10.1007/s10287-021-00387-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-021-00387-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10287-021-00387-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Shapiro, Alexander & Tekaya, Wajdi & da Costa, Joari Paulo & Soares, Murilo Pereira, 2013. "Risk neutral and risk averse Stochastic Dual Dynamic Programming method," European Journal of Operational Research, Elsevier, vol. 224(2), pages 375-391.
    2. Nils Löhndorf & David Wozabal & Stefan Minner, 2013. "Optimizing Trading Decisions for Hydro Storage Systems Using Approximate Dual Dynamic Programming," Operations Research, INFORMS, vol. 61(4), pages 810-823, August.
    3. Vincent Guigues, 2014. "SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning," Computational Optimization and Applications, Springer, vol. 57(1), pages 167-203, January.
    4. Guigues, Vincent, 2017. "Dual Dynamic Programing with cut selection: Convergence proof and numerical experiments," European Journal of Operational Research, Elsevier, vol. 258(1), pages 47-57.
    5. Z. L. Chen & W. B. Powell, 1999. "Convergent Cutting-Plane and Partial-Sampling Algorithm for Multistage Stochastic Linear Programs with Recourse," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 497-524, September.
    6. Weini Zhang & Hamed Rahimian & Güzin Bayraksan, 2016. "Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 385-404, August.
    7. Birge, John R. & Louveaux, Francois V., 1988. "A multicut algorithm for two-stage stochastic linear programs," European Journal of Operational Research, Elsevier, vol. 34(3), pages 384-392, March.
    8. John R. Birge, 1985. "Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs," Operations Research, INFORMS, vol. 33(5), pages 989-1007, October.
    9. Philpott, A.B. & de Matos, V.L., 2012. "Dynamic sampling algorithms for multi-stage stochastic programs with risk aversion," European Journal of Operational Research, Elsevier, vol. 218(2), pages 470-483.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guigues, Vincent & Shapiro, Alexander & Cheng, Yi, 2023. "Duality and sensitivity analysis of multistage linear stochastic programs," European Journal of Operational Research, Elsevier, vol. 308(2), pages 752-767.
    2. Lorenzo Reus & Guillermo Alexander Sepúlveda-Hurtado, 2023. "Foreign exchange trading and management with the stochastic dual dynamic programming method," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-38, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. de Queiroz, Anderson Rodrigo, 2016. "Stochastic hydro-thermal scheduling optimization: An overview," Renewable and Sustainable Energy Reviews, Elsevier, vol. 62(C), pages 382-395.
    3. Andre Luiz Diniz & Maria Elvira P. Maceira & Cesar Luis V. Vasconcellos & Debora Dias J. Penna, 2020. "A combined SDDP/Benders decomposition approach with a risk-averse surface concept for reservoir operation in long term power generation planning," Annals of Operations Research, Springer, vol. 292(2), pages 649-681, September.
    4. Zhou, Shaorui & Zhang, Hui & Shi, Ning & Xu, Zhou & Wang, Fan, 2020. "A new convergent hybrid learning algorithm for two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 283(1), pages 33-46.
    5. 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.
    6. Liu, Rui Peng & Shapiro, Alexander, 2020. "Risk neutral reformulation approach to risk averse stochastic programming," European Journal of Operational Research, Elsevier, vol. 286(1), pages 21-31.
    7. Lorenzo Reus & Guillermo Alexander Sepúlveda-Hurtado, 2023. "Foreign exchange trading and management with the stochastic dual dynamic programming method," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-38, December.
    8. Soares, Murilo Pereira & Street, Alexandre & Valladão, Davi Michel, 2017. "On the solution variability reduction of Stochastic Dual Dynamic Programming applied to energy planning," European Journal of Operational Research, Elsevier, vol. 258(2), pages 743-760.
    9. Weini Zhang & Hamed Rahimian & Güzin Bayraksan, 2016. "Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 385-404, August.
    10. D. Ávila & A. Papavasiliou & N. Löhndorf, 2022. "Parallel and distributed computing for stochastic dual dynamic programming," Computational Management Science, Springer, vol. 19(2), pages 199-226, June.
    11. Davi Valladão & Thuener Silva & Marcus Poggi, 2019. "Time-consistent risk-constrained dynamic portfolio optimization with transactional costs and time-dependent returns," Annals of Operations Research, Springer, vol. 282(1), pages 379-405, November.
    12. Martin Šmíd & Václav Kozmík, 2024. "Approximation of multistage stochastic programming problems by smoothed quantization," Review of Managerial Science, Springer, vol. 18(7), pages 2079-2114, July.
    13. Daniel F. Salas & Warren B. Powell, 2018. "Benchmarking a Scalable Approximate Dynamic Programming Algorithm for Stochastic Control of Grid-Level Energy Storage," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 106-123, February.
    14. Vincent Guigues & Renato D. C. Monteiro, 2021. "Stochastic Dynamic Cutting Plane for Multistage Stochastic Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 513-559, May.
    15. Guigues, Vincent & Shapiro, Alexander & Cheng, Yi, 2023. "Duality and sensitivity analysis of multistage linear stochastic programs," European Journal of Operational Research, Elsevier, vol. 308(2), pages 752-767.
    16. Daniel R. Jiang & Warren B. Powell, 2018. "Risk-Averse Approximate Dynamic Programming with Quantile-Based Risk Measures," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 554-579, May.
    17. Escudero, Laureano F. & Monge, Juan F. & Rodríguez-Chía, Antonio M., 2020. "On pricing-based equilibrium for network expansion planning. A multi-period bilevel approach under uncertainty," European Journal of Operational Research, Elsevier, vol. 287(1), pages 262-279.
    18. Lorenzo Reus & Rodolfo Prado, 2022. "Need to Meet Investment Goals? Track Synthetic Indexes with the SDDP Method," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 47-69, June.
    19. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    20. Bushaj, Sabah & Büyüktahtakın, İ. Esra & Haight, Robert G., 2022. "Risk-averse multi-stage stochastic optimization for surveillance and operations planning of a forest insect infestation," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1094-1110.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:comgts:v:18:y:2021:i:2:d:10.1007_s10287-021-00387-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.