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

Geng Lin (), Wenxing Zhu and M. Montaz Ali
Additional contact information
Geng Lin: Minjiang University
Wenxing Zhu: Fuzhou University
M. Montaz Ali: University of the Witwatersrand

Journal of Combinatorial Optimization, 2016, vol. 32, issue 2, No 14, 563-593

Abstract: 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.

Keywords: Winner determination problem; Discrete dynamic convexized method; Local search; Adaptive penalty function (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9883-9

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