Using a Lagrangian heuristic for a combinatorial auction problem

In this paper, a combinatorial auction problem is modeled as a NP-complete set packing problem and a Lagrangian relaxation based heuristic algorithm is proposed. Extensive experiments are conducted using benchmark CATS test sets and more complex test sets. The algorithm provides optimal solutions for most test sets and is always 1%from the optimal solutions for all CATS test sets. Comparisons with CPLEX 8.0 are also provided, which show that the algorithm provides good solutions

[1]  Yoav Shoham,et al.  Taming the Computational Complexity of Combinatorial Auctions: Optimal and Approximate Approaches , 1999, IJCAI.

[2]  Arne Andersson,et al.  Integer programming for combinatorial auction winner determination , 2000, Proceedings Fourth International Conference on MultiAgent Systems.

[3]  David Levine,et al.  CABOB: A Fast Optimal Algorithm for Combinatorial Auctions , 2001, IJCAI.

[4]  Craig Boutilier,et al.  Solving Combinatorial Auctions Using Stochastic Local Search , 2000, AAAI/IAAI.

[5]  Sven de Vries,et al.  Combinatorial Auctions: A Survey , 2003, INFORMS J. Comput..

[6]  David Levine,et al.  CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions , 2005, Manag. Sci..

[7]  Matteo Fischetti,et al.  A Heuristic Method for the Set Covering Problem , 1999, Oper. Res..

[8]  Andrew Lim,et al.  Using a Lagrangian Heuristic for a Combinatorial Auction Problem , 2006, Int. J. Artif. Intell. Tools.

[9]  Marshall L. Fisher,et al.  The Lagrangian Relaxation Method for Solving Integer Programming Problems , 2004, Manag. Sci..

[10]  Yoav Shoham,et al.  Towards a universal test suite for combinatorial auction algorithms , 2000, EC '00.

[11]  Hoong Chuin Lau,et al.  An intelligent brokering system to support multi-agent Web-based 4/sup th/-party logistics , 2002, 14th IEEE International Conference on Tools with Artificial Intelligence, 2002. (ICTAI 2002). Proceedings..

[12]  Tuomas Sandholm,et al.  Algorithm for optimal winner determination in combinatorial auctions , 2002, Artif. Intell..