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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
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    References listed on IDEAS

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    1. Sven de Vries & Rakesh V. Vohra, 2003. "Combinatorial Auctions: A Survey," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 284-309, August.
    2. 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.
    3. 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.
    4. 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.
    5. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    6. 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.
    7. 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.
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    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.

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