IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v108y2001i2d10.1023_a1026490318131.html
   My bibliography  Save this article

Online Surrogate Problem Methodology for Stochastic Discrete Resource Allocation Problems

Author

Listed:
  • K. Gokbayrak
  • C. G. Cassandras

Abstract

We consider stochastic discrete optimization problems where the decision variables are nonnegative integers. We propose and analyze an online control scheme which transforms the problem into a surrogate continuous optimization problem and proceeds to solve the latter using standard gradient-based approaches, while simultaneously updating both the actual and surrogate system states. It is shown that the solution of the original problem is recovered as an element of the discrete state neighborhood of the optimal surrogate state. For the special case of separable cost functions, we show that this methodology becomes particularly efficient. Finally, convergence of the proposed algorithm is established under standard technical conditions; numerical results are included in the paper to illustrate the fast convergence of this approach.

Suggested Citation

  • K. Gokbayrak & C. G. Cassandras, 2001. "Online Surrogate Problem Methodology for Stochastic Discrete Resource Allocation Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 349-376, February.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:2:d:10.1023_a:1026490318131
    DOI: 10.1023/A:1026490318131
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1026490318131
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1026490318131?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. Leyuan Shi & Sigurdur Ólafsson, 2000. "Nested Partitions Method for Global Optimization," Operations Research, INFORMS, vol. 48(3), pages 390-407, 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. K. Gokbayrak & C.G. Cassandras, 2002. "Generalized Surrogate Problem Methodology for Online Stochastic Discrete Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 97-132, July.

    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. Chang, Kuo-Hao & Kuo, Po-Yi, 2018. "An efficient simulation optimization method for the generalized redundancy allocation problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1094-1101.
    2. Lee, Loo Hay & Chew, Ek Peng & Manikam, Puvaneswari, 2006. "A general framework on the simulation-based optimization under fixed computing budget," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1828-1841, November.
    3. David R. Morrison & Jason J. Sauppe & Wenda Zhang & Sheldon H. Jacobson & Edward C. Sewell, 2017. "Cyclic best first search: Using contours to guide branch‐and‐bound algorithms," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 64-82, February.
    4. Tahir Ekin & Stephen Walker & Paul Damien, 2023. "Augmented simulation methods for discrete stochastic optimization with recourse," Annals of Operations Research, Springer, vol. 320(2), pages 771-793, January.
    5. Lingxuan Liu & Leyuan Shi, 2019. "Simulation Optimization on Complex Job Shop Scheduling with Non-Identical Job Sizes," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(05), pages 1-26, October.
    6. Choi, Hyunhong & Koo, Yoonmo, 2018. "Using Contingent Valuation and Numerical Methods to Determine Optimal Locations for Environmental Facilities: Public Arboretums in South Korea," Ecological Economics, Elsevier, vol. 149(C), pages 184-201.
    7. Gino Lim & Laleh Kardar & Wenhua Cao, 2014. "A hybrid framework for optimizing beam angles in radiation therapy planning," Annals of Operations Research, Springer, vol. 217(1), pages 357-383, June.
    8. Michael Macgregor Perry, 2021. "Fisheries Management in Congested Waters: A Game-Theoretic Assessment of the East China Sea," Papers 2110.13966, arXiv.org, revised Feb 2022.
    9. Jeffrey D. Camm & James J. Cochran & David J. Curry & Sriram Kannan, 2006. "Conjoint Optimization: An Exact Branch-and-Bound Algorithm for the Share-of-Choice Problem," Management Science, INFORMS, vol. 52(3), pages 435-447, March.
    10. Zhenyuan Liu & Lei Xiao & Jing Tian, 2016. "An activity-list-based nested partitions algorithm for resource-constrained project scheduling," International Journal of Production Research, Taylor & Francis Journals, vol. 54(16), pages 4744-4758, August.
    11. Weiwei Chen & Jie Song & Leyuan Shi & Liang Pi & Peter Sun, 2013. "Data mining-based dispatching system for solving the local pickup and delivery problem," Annals of Operations Research, Springer, vol. 203(1), pages 351-370, March.
    12. K. Gokbayrak & C.G. Cassandras, 2002. "Generalized Surrogate Problem Methodology for Online Stochastic Discrete Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 97-132, July.
    13. Lihua Sun & L. Jeff Hong & Zhaolin Hu, 2014. "Balancing Exploitation and Exploration in Discrete Optimization via Simulation Through a Gaussian Process-Based Search," Operations Research, INFORMS, vol. 62(6), pages 1416-1438, December.
    14. Pieter-Tjerk de Boer & Dirk Kroese & Shie Mannor & Reuven Rubinstein, 2005. "A Tutorial on the Cross-Entropy Method," Annals of Operations Research, Springer, vol. 134(1), pages 19-67, February.
    15. Pedrielli, Giulia & Wang, Songhao & Ng, Szu Hui, 2020. "An extended Two-Stage Sequential Optimization approach: Properties and performance," European Journal of Operational Research, Elsevier, vol. 287(3), pages 929-945.
    16. J Kim & J Yang & S Ólafsson, 2009. "An optimization approach to partitional data clustering," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(8), pages 1069-1084, August.
    17. Xiao-Ming Yang & Xin-Jia Jiang, 2020. "Yard Crane Scheduling in the Ground Trolley-Based Automated Container Terminal," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(02), pages 1-28, March.
    18. Alexandre Belloni & Robert Freund & Matthew Selove & Duncan Simester, 2008. "Optimizing Product Line Designs: Efficient Methods and Comparisons," Management Science, INFORMS, vol. 54(9), pages 1544-1552, September.
    19. Leyuan Shi & Sigurdur O´lafsson, 2000. "Nested Partitions Method for Stochastic Optimization," Methodology and Computing in Applied Probability, Springer, vol. 2(3), pages 271-291, September.
    20. Michael C. Fu, 2002. "Feature Article: Optimization for simulation: Theory vs. Practice," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 192-215, August.

    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:joptap:v:108:y:2001:i:2:d:10.1023_a:1026490318131. 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.