An efficient local search algorithm for the winner determination problem

Combinatorial auction, which allows bidders to bid on combinations of items, is an important type of market mechanism. The winner determination problem (WDP) has extensive applications in combinatorial auctions, and attracts more and more attention due to its strong relevance to business. However, this problem is intractable in theory as it has been proven to be NP-hard, and is also a challenging combinatorial optimization problem in practice. This paper is devoted to designing an efficient heuristic algorithm for solving the WDP. This proposed heuristic algorithm dubbed abcWDP is based on an effective yet simple local search framework, and equipped with three novel strategies, i.e., configuration checking, free-bid exploiting, and pseudo-tie mechanism. Extensive computational experiments on a broad range of benchmarks demonstrate that abcWDP performs much better than state-of-the-art algorithms and CPLEX in terms of both revenue and running time. More encouragingly, our abcWDP algorithm as a sequential algorithm even achieves better computational results than the multi-thread implemented algorithm CARA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CA}_\mathrm{RA}$$\end{document}, which confirms its efficiency.