IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v208y2011i2p109-118.html
   My bibliography  Save this article

A comparison of global and semi-local approximation in T-stage stochastic optimization

Author

Listed:
  • Cervellera, C.
  • Macciò, D.

Abstract

The paper presents a comparison between two different flavors of nonlinear models to be used for the approximate solution of T-stage stochastic optimization (TSO) problems, a typical paradigm of Markovian decision processes. Specifically, the well-known class of neural networks is compared with a semi-local approach based on kernel functions, characterized by less demanding computational requirements. To this purpose, two alternative methods for the numerical solution of TSO are considered, one corresponding to the classic approximate dynamic programming (ADP) and the other based on a direct optimization of the optimal control functions, introduced here for the first time. Advantages and drawbacks in the TSO context of the two classes of approximators are analyzed, in terms of computational burden and approximation capabilities. Then, their performances are evaluated through simulations in two important high-dimensional TSO test cases, namely inventory forecasting and water reservoirs management.

Suggested Citation

  • Cervellera, C. & Macciò, D., 2011. "A comparison of global and semi-local approximation in T-stage stochastic optimization," European Journal of Operational Research, Elsevier, vol. 208(2), pages 109-118, January.
    • Handle: RePEc:eee:ejores:v:208:y:2011:i:2:p:109-118
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00538-2
    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. Sharon A. Johnson & Jery R. Stedinger & Christine A. Shoemaker & Ying Li & José Alberto Tejada-Guibert, 1993. "Numerical Solution of Continuous-State Dynamic Programs Using Linear and Spline Interpolation," Operations Research, INFORMS, vol. 41(3), pages 484-500, June.
    2. Victoria C. P. Chen & David Ruppert & Christine A. Shoemaker, 1999. "Applying Experimental Design and Regression Splines to High-Dimensional Continuous-State Stochastic Dynamic Programming," Operations Research, INFORMS, vol. 47(1), pages 38-53, February.
    3. Archibald, T. W. & Buchanan, C. S. & Thomas, L. C. & McKinnon, K. I. M., 2001. "Controlling multi-reservoir systems," European Journal of Operational Research, Elsevier, vol. 129(3), pages 619-626, March.
    4. R. Zoppoli & M. Sanguineti & T. Parisini, 2002. "Approximating Networks and Extended Ritz Method for the Solution of Functional Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 403-440, February.
    5. Cervellera, Cristiano & Chen, Victoria C.P. & Wen, Aihong, 2006. "Optimization of a large-scale water reservoir network by stochastic dynamic programming with efficient state space discretization," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1139-1151, June.
    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. Zéphyr, Luckny & Lang, Pascal & Lamond, Bernard F. & Côté, Pascal, 2017. "Approximate stochastic dynamic programming for hydroelectric production planning," European Journal of Operational Research, Elsevier, vol. 262(2), pages 586-601.
    2. Guo, Xianping & Zhang, Wenzhao, 2014. "Convergence of controlled models and finite-state approximation for discounted continuous-time Markov decision processes with constraints," European Journal of Operational Research, Elsevier, vol. 238(2), pages 486-496.

    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. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2013. "Dynamic Programming and Value-Function Approximation in Sequential Decision Problems: Error Analysis and Numerical Results," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 380-416, February.
    2. Zehua Yang & Victoria C. P. Chen & Michael E. Chang & Melanie L. Sattler & Aihong Wen, 2009. "A Decision-Making Framework for Ozone Pollution Control," Operations Research, INFORMS, vol. 57(2), pages 484-498, April.
    3. M. Baglietto & C. Cervellera & M. Sanguineti & R. Zoppoli, 2010. "Management of water resource systems in the presence of uncertainties by nonlinear approximation techniques and deterministic sampling," Computational Optimization and Applications, Springer, vol. 47(2), pages 349-376, October.
    4. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2014. "Approximate dynamic programming for stochastic N-stage optimization with application to optimal consumption under uncertainty," Computational Optimization and Applications, Springer, vol. 58(1), pages 31-85, May.
    5. Cervellera, Cristiano, 2023. "Optimized ensemble value function approximation for dynamic programming," European Journal of Operational Research, Elsevier, vol. 309(2), pages 719-730.
    6. Huiyuan Fan & Prashant K. Tarun & Victoria C. P. Chen & Dachuan T. Shih & Jay M. Rosenberger & Seoung Bum Kim & Robert A. Horton, 2018. "Data-driven optimization for Dallas Fort Worth International Airport deicing activities," Annals of Operations Research, Springer, vol. 263(1), pages 361-384, April.
    7. Cervellera, Cristiano & Chen, Victoria C.P. & Wen, Aihong, 2006. "Optimization of a large-scale water reservoir network by stochastic dynamic programming with efficient state space discretization," European Journal of Operational Research, Elsevier, vol. 171(3), pages 1139-1151, June.
    8. T.W. Archibald & K.I.M. McKinnon & L.C. Thomas, 2006. "Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(3), pages 217-225, April.
    9. Zéphyr, Luckny & Lang, Pascal & Lamond, Bernard F. & Côté, Pascal, 2017. "Approximate stochastic dynamic programming for hydroelectric production planning," European Journal of Operational Research, Elsevier, vol. 262(2), pages 586-601.
    10. Somayeh Moazeni & Warren B. Powell & Boris Defourny & Belgacem Bouzaiene-Ayari, 2017. "Parallel Nonstationary Direct Policy Search for Risk-Averse Stochastic Optimization," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 332-349, May.
    11. Chen, Ruoran & Deng, Tianhu & Huang, Simin & Qin, Ruwen, 2015. "Optimal crude oil procurement under fluctuating price in an oil refinery," European Journal of Operational Research, Elsevier, vol. 245(2), pages 438-445.
    12. Diego Klabjan & Daniel Adelman, 2007. "An Infinite-Dimensional Linear Programming Algorithm for Deterministic Semi-Markov Decision Processes on Borel Spaces," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 528-550, August.
    13. Chen, Victoria C. P., 1999. "Application of orthogonal arrays and MARS to inventory forecasting stochastic dynamic programs," Computational Statistics & Data Analysis, Elsevier, vol. 30(3), pages 317-341, May.
    14. Ariyajunya, Bancha & Chen, Ying & Chen, Victoria C.P. & Kim, Seoung Bum & Rosenberger, Jay, 2021. "Addressing state space multicollinearity in solving an ozone pollution dynamic control problem," European Journal of Operational Research, Elsevier, vol. 289(2), pages 683-695.
    15. Cristiano Cervellera & Danilo Macciò & Marco Muselli, 2010. "Functional Optimization Through Semilocal Approximate Minimization," Operations Research, INFORMS, vol. 58(5), pages 1491-1504, October.
    16. Dachuan Shih & Seoung Kim & Victoria Chen & Jay Rosenberger & Venkata Pilla, 2014. "Efficient computer experiment-based optimization through variable selection," Annals of Operations Research, Springer, vol. 216(1), pages 287-305, May.
    17. A. Alessandri & C. Cervellera & M. Sanguineti, 2007. "Functional Optimal Estimation Problems and Their Solution by Nonlinear Approximation Schemes," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 445-466, September.
    18. Tetsuo Iida & Paul H. Zipkin, 2006. "Approximate Solutions of a Dynamic Forecast-Inventory Model," Manufacturing & Service Operations Management, INFORMS, vol. 8(4), pages 407-425, October.
    19. Ying Chen & Krystel K. Castillo-Villar & Bing Dong, 2021. "Stochastic control of a micro-grid using battery energy storage in solar-powered buildings," Annals of Operations Research, Springer, vol. 303(1), pages 197-216, August.
    20. Per Krusell & Anthony A. Smith & Jr., 1998. "Income and Wealth Heterogeneity in the Macroeconomy," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 867-896, October.

    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:208:y:2011:i:2:p:109-118. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.