IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v32y2016i2d10.1007_s10878-015-9883-9.html
   My bibliography  Save this article

An effective discrete dynamic convexized method for solving the winner determination problem

Author

Listed:
  • Geng Lin

    (Minjiang University)

  • Wenxing Zhu

    (Fuzhou University)

  • M. Montaz Ali

    (University of the Witwatersrand)

Abstract

The winner determination problem (WDP) arises in combinatorial auctions. It is known to be NP-hard. In this paper, we propose a discrete dynamic convexized method for solving this problem. We first propose an adaptive penalty function to convert the WDP into an equivalent unconstrained integer programming problem. Based on the structure of the WDP, we construct an unconstrained auxiliary function, which is maximized iteratively using a local search and is updated whenever a better maximizer is found. By increasing the value of a parameter in the auxiliary function, the maximization of the auxiliary function can escape from previously converged local maximizers. To evaluate the performance of the dynamic convexized method, extensive experiments were carried out on realistic test sets from the literature. Computational results and comparisons show that the proposed algorithm improved the best known solutions on a number of benchmark instances.

Suggested Citation

  • Geng Lin & Wenxing Zhu & M. Montaz Ali, 2016. "An effective discrete dynamic convexized method for solving the winner determination problem," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 563-593, August.
  • Handle: RePEc:spr:jcomop:v:32:y:2016:i:2:d:10.1007_s10878-015-9883-9
    DOI: 10.1007/s10878-015-9883-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-015-9883-9
    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/s10878-015-9883-9?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. Lü, Zhipeng & Hao, Jin-Kao, 2010. "A memetic algorithm for graph coloring," European Journal of Operational Research, Elsevier, vol. 203(1), pages 241-250, May.
    2. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    3. Sven de Vries & Rakesh V. Vohra, 2003. "Combinatorial Auctions: A Survey," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 284-309, August.
    4. M. Ali & W. Zhu, 2013. "A penalty function-based differential evolution algorithm for constrained global optimization," Computational Optimization and Applications, Springer, vol. 54(3), pages 707-739, April.
    5. Wenxing Zhu & Geng Lin & M. M. Ali, 2013. "Max- k -Cut by the Discrete Dynamic Convexized Method," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 27-40, February.
    6. Abrache, Jawad & Crainic, Teodor Gabriel & Gendreau, Michel, 2005. "Models for bundle trading in financial markets," European Journal of Operational Research, Elsevier, vol. 160(1), pages 88-105, January.
    7. Geng Lin & Wenxing Zhu, 2012. "A discrete dynamic convexized method for the max-cut problem," Annals of Operations Research, Springer, vol. 196(1), pages 371-390, July.
    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. Abhishek Ray & Mario Ventresca & Karthik Kannan, 2021. "A Graph-Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions," Information Systems Research, INFORMS, vol. 32(4), pages 1099-1114, 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. Jawad Abrache & Teodor Crainic & Michel Gendreau & Monia Rekik, 2007. "Combinatorial auctions," Annals of Operations Research, Springer, vol. 153(1), pages 131-164, September.
    2. Fuda Ma & Jin-Kao Hao, 2017. "A multiple search operator heuristic for the max-k-cut problem," Annals of Operations Research, Springer, vol. 248(1), pages 365-403, January.
    3. Mishra, Debasis & Parkes, David C., 2007. "Ascending price Vickrey auctions for general valuations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 335-366, January.
    4. Lamprirni Zarpala & Dimitris Voliotis, 2022. "A core-selecting auction for portfolio's packages," Papers 2206.11516, arXiv.org, revised Feb 2024.
    5. Robert W. Day & Peter Cramton, 2012. "Quadratic Core-Selecting Payment Rules for Combinatorial Auctions," Operations Research, INFORMS, vol. 60(3), pages 588-603, June.
    6. Bourbeau, Benoit & Gabriel Crainic, Teodor & Gendreau, Michel & Robert, Jacques, 2005. "Design for optimized multi-lateral multi-commodity markets," European Journal of Operational Research, Elsevier, vol. 163(2), pages 503-529, June.
    7. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
    8. Oktay Günlük & Lászlo Ladányi & Sven de Vries, 2005. "A Branch-and-Price Algorithm and New Test Problems for Spectrum Auctions," Management Science, INFORMS, vol. 51(3), pages 391-406, March.
    9. Vangerven, Bart & Goossens, Dries R. & Spieksma, Frits C.R., 2017. "Winner determination in geometrical combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 258(1), pages 254-263.
    10. A Drexl & K Jørnsten, 2007. "Reflections about pseudo-dual prices in combinatorial auctions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1652-1659, December.
    11. Zhang, Bo & Yao, Tao & Friesz, Terry L. & Sun, Yuqi, 2015. "A tractable two-stage robust winner determination model for truckload service procurement via combinatorial auctions," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 16-31.
    12. Ervasti, Valtteri & Leskelä, Riikka-Leena, 2010. "Allocative efficiency in simulated multiple-unit combinatorial auctions with quantity support," European Journal of Operational Research, Elsevier, vol. 203(1), pages 251-260, May.
    13. Richard Li-Yang Chen & Shervin AhmadBeygi & Amy Cohn & Damian R. Beil & Amitabh Sinha, 2009. "Solving Truckload Procurement Auctions Over an Exponential Number of Bundles," Transportation Science, INFORMS, vol. 43(4), pages 493-510, November.
    14. Song, Jiongjiong & Regan, Amelia, 2005. "Approximation algorithms for the bid construction problem in combinatorial auctions for the procurement of freight transportation contracts," Transportation Research Part B: Methodological, Elsevier, vol. 39(10), pages 914-933, December.
    15. Jing Yu & Lining Xing & Xu Tan, 0. "The new treatment mode research of hepatitis B based on ant colony algorithm," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.
    16. Fernanda Nakano Kazama & Aluizio Fausto Ribeiro Araujo & Paulo Barros Correia & Elaine Guerrero-Peña, 2021. "Constraint-guided evolutionary algorithm for solving the winner determination problem," Journal of Heuristics, Springer, vol. 27(6), pages 1111-1150, December.
    17. Park, Sunju & Rothkopf, Michael H., 2005. "Auctions with bidder-determined allowable combinations," European Journal of Operational Research, Elsevier, vol. 161(2), pages 399-415, March.
    18. Vohra, Rakesh V., 2015. "Combinatorial Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    19. Goossens, D.R. & Müller, R.J. & Spieksma, F.C.R., 2007. "Matrix bids in combinatorial auctions: expressiveness and micro-economic properties," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    20. Jérémie Gallien & Lawrence M. Wein, 2005. "A Smart Market for Industrial Procurement with Capacity Constraints," Management Science, INFORMS, vol. 51(1), pages 76-91, January.

    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:jcomop:v:32:y:2016:i:2:d:10.1007_s10878-015-9883-9. 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.