IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v283y2020i1p33-46.html
   My bibliography  Save this article

A new convergent hybrid learning algorithm for two-stage stochastic programs

Author

Listed:
  • Zhou, Shaorui
  • Zhang, Hui
  • Shi, Ning
  • Xu, Zhou
  • Wang, Fan

Abstract

This study proposes a new hybrid learning algorithm to approximate the expected recourse function for two-stage stochastic programs. The proposed algorithm, which is called projected stochastic hybrid learning algorithm, is a hybrid of piecewise linear approximation and stochastic subgradient methods. Piecewise linear approximations are updated adaptively by using stochastic subgradient and sample information on the objective function itself. In order to achieve a global optimum, a projection step that implements the stochastic subgradient method is performed to jump out from a local optimum. For general two-stage stochastic programs, we prove the convergence of the algorithm. Furthermore, the algorithm can drop the projection steps for two-stage stochastic programs with network recourse. Therefore, the pure piecewise linear approximation method is convergent when the initial piecewise linear functions are properly constructed. Computational results indicate that the algorithm exhibits rapid convergence.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:283:y:2020:i:1:p:33-46
    DOI: 10.1016/j.ejor.2019.11.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719309038
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Restrepo, María I. & Gendron, Bernard & Rousseau, Louis-Martin, 2017. "A two-stage stochastic programming approach for multi-activity tour scheduling," European Journal of Operational Research, Elsevier, vol. 262(2), pages 620-635.
    2. Raymond K. Cheung & Chuen-Yih Chen, 1998. "A Two-Stage Stochastic Network Model and Solution Methods for the Dynamic Empty Container Allocation Problem," Transportation Science, INFORMS, vol. 32(2), pages 142-162, May.
    3. Dong-Ping Song & Jing-Xin Dong, 2008. "Empty Container Management in Cyclic Shipping Routes," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 10(4), pages 335-361, December.
    4. Raymond K.-M. Cheung & Warren B. Powell, 2000. "Shape -- A Stochastic Hybrid Approximation Procedure for Two-Stage Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 73-79, February.
    5. 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.
    6. Moreno, Alfredo & Alem, Douglas & Ferreira, Deisemara & Clark, Alistair, 2018. "An effective two-stage stochastic multi-trip location-transportation model with social concerns in relief supply chains," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1050-1071.
    7. 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.
    8. Raymond K. Cheung & Warren B. Powell, 1996. "An Algorithm for Multistage Dynamic Networks with Random Arc Capacities, with an Application to Dynamic Fleet Management," Operations Research, INFORMS, vol. 44(6), pages 951-963, December.
    9. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, I: Single Period Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 21-39, February.
    10. 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.
    11. Jean-François Cordeau & François Soumis & Jacques Desrosiers, 2000. "A Benders Decomposition Approach for the Locomotive and Car Assignment Problem," Transportation Science, INFORMS, vol. 34(2), pages 133-149, May.
    12. Warren Powell & Andrzej Ruszczyński & Huseyin Topaloglu, 2004. "Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 814-836, November.
    13. Shapiro, Alexander, 2011. "Analysis of stochastic dual dynamic programming method," European Journal of Operational Research, Elsevier, vol. 209(1), pages 63-72, February.
    14. Belgacem Bouzaiene-Ayari & Clark Cheng & Sourav Das & Ricardo Fiorillo & Warren B. Powell, 2016. "From Single Commodity to Multiattribute Models for Locomotive Optimization: A Comparison of Optimal Integer Programming and Approximate Dynamic Programming," Transportation Science, INFORMS, vol. 50(2), pages 366-389, May.
    15. 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.
    16. Kibaek Kim & Sanjay Mehrotra, 2015. "A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management," Operations Research, INFORMS, vol. 63(6), pages 1431-1451, December.
    17. Long, Yin & Lee, Loo Hay & Chew, Ek Peng, 2012. "The sample average approximation method for empty container repositioning with uncertainties," European Journal of Operational Research, Elsevier, vol. 222(1), pages 65-75.
    18. 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.
    19. Alem, Douglas & Clark, Alistair & Moreno, Alfredo, 2016. "Stochastic network models for logistics planning in disaster relief," European Journal of Operational Research, Elsevier, vol. 255(1), pages 187-206.
    20. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, II: Multiperiod Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 40-54, February.
    21. P. Girardeau & V. Leclere & A. B. Philpott, 2015. "On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 130-145, February.
    Full references (including those not matched with items on IDEAS)

    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:eee:ejores:v:283:y:2020:i:1:p:33-46. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Haili He). General contact details of provider: http://www.elsevier.com/locate/eor .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.