IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v74y2019i1d10.1007_s10589-019-00104-x.html
   My bibliography  Save this article

On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems

Author

Listed:
  • Wim Ackooij

    (EDF R&D. OSIRIS 7)

  • Welington Oliveira

    (MINES ParisTech, PSL - Research University, CMA - Centre de Mathématiques Appliquées)

  • Yongjia Song

    (Clemson University)

Abstract

We consider well-known decomposition techniques for multistage stochastic programming and a new scheme based on normal solutions for stabilizing iterates during the solution process. The given algorithms combine ideas from finite perturbation of convex programs and level bundle methods to regularize the so-called forward step of these decomposition methods. Numerical experiments on a hydrothermal scheduling problem indicate that our algorithms are competitive with the state-of-the-art approaches such as multistage regularized decomposition, nested decomposition and stochastic dual dynamic programming.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:1:d:10.1007_s10589-019-00104-x
    DOI: 10.1007/s10589-019-00104-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-019-00104-x
    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/s10589-019-00104-x?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. Homem-de-Mello, Tito & Pagnoncelli, Bernardo K., 2016. "Risk aversion in multistage stochastic programming: A modeling and algorithmic perspective," European Journal of Operational Research, Elsevier, vol. 249(1), pages 188-199.
    2. Wolf, Christian & Fábián, Csaba I. & Koberstein, Achim & Suhl, Leena, 2014. "Applying oracles of on-demand accuracy in two-stage stochastic programming – A computational study," European Journal of Operational Research, Elsevier, vol. 239(2), pages 437-448.
    3. 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.
    4. Wim Ackooij & Welington Oliveira, 2014. "Level bundle methods for constrained convex optimization with various oracles," Computational Optimization and Applications, Springer, vol. 57(3), pages 555-597, April.
    5. Wim Ackooij & Nicolas Lebbe & Jérôme Malick, 2017. "Regularized decomposition of large scale block-structured robust optimization problems," Computational Management Science, Springer, vol. 14(3), pages 393-421, July.
    6. 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.
    7. 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.
    8. K. Linowsky & A. B. Philpott, 2005. "On the Convergence of Sampling-Based Decomposition Algorithms for Multistage Stochastic Programs," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 349-366, May.
    9. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    10. David P. Morton, 1998. "Stopping Rules for a Class of Sampling-Based Stochastic Programming Algorithms," Operations Research, INFORMS, vol. 46(5), pages 710-718, October.
    11. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
    12. Lemaréchal, C. & Nemirovskii, A. & Nesterov, Y., 1995. "New variants of bundle methods," LIDAM Reprints CORE 1166, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. W. Ackooij & A. Frangioni & W. Oliveira, 2016. "Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support," Computational Optimization and Applications, Springer, vol. 65(3), pages 637-669, December.
    14. John R. Birge, 1985. "Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs," Operations Research, INFORMS, vol. 33(5), pages 989-1007, October.
    15. Georg Ch Pflug & Werner Römisch, 2007. "Modeling, Measuring and Managing Risk," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6478, January.
    16. 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.
    17. Wolf, Christian & Koberstein, Achim, 2013. "Dynamic sequencing and cut consolidation for the parallel hybrid-cut nested L-shaped method," European Journal of Operational Research, Elsevier, vol. 230(1), pages 143-156.
    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. Arnab Bhattacharya & Jeffrey P. Kharoufeh & Bo Zeng, 2023. "A Nonconvex Regularization Scheme for the Stochastic Dual Dynamic Programming Algorithm," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1161-1178, September.
    2. Murwan Siddig & Yongjia Song, 2022. "Adaptive partition-based SDDP algorithms for multistage stochastic linear programming with fixed recourse," Computational Optimization and Applications, Springer, vol. 81(1), pages 201-250, January.
    3. 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.
    4. 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.

    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. Murwan Siddig & Yongjia Song, 2022. "Adaptive partition-based SDDP algorithms for multistage stochastic linear programming with fixed recourse," Computational Optimization and Applications, Springer, vol. 81(1), pages 201-250, January.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. Saif Benjaafar & Daniel Jiang & Xiang Li & Xiaobo Li, 2022. "Dynamic Inventory Repositioning in On-Demand Rental Networks," Management Science, INFORMS, vol. 68(11), pages 7861-7878, November.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Blanchot, Xavier & Clautiaux, François & Detienne, Boris & Froger, Aurélien & Ruiz, Manuel, 2023. "The Benders by batch algorithm: Design and stabilization of an enhanced algorithm to solve multicut Benders reformulation of two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 309(1), pages 202-216.
    16. 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.
    17. Arnab Bhattacharya & Jeffrey P. Kharoufeh & Bo Zeng, 2023. "A Nonconvex Regularization Scheme for the Stochastic Dual Dynamic Programming Algorithm," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1161-1178, September.
    18. 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.
    19. Babak Saleck Pay & Yongjia Song, 2020. "Partition-based decomposition algorithms for two-stage Stochastic integer programs with continuous recourse," Annals of Operations Research, Springer, vol. 284(2), pages 583-604, January.
    20. Vitor L. de Matos & David P. Morton & Erlon C. Finardi, 2017. "Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling," Annals of Operations Research, Springer, vol. 253(2), pages 713-731, June.

    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:coopap:v:74:y:2019:i:1:d:10.1007_s10589-019-00104-x. 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.