Using a Lagrangian Heuristic for a Combinatorial Auction Problem - GUO, Yunsong (Institutional Knowledge at Singapore Management University, 2006)
Combinatorial auctions allow bidders to bid for items leading to more efficient allocations, but determining winners in auctions is $\mathcal{NP}$-complete. In this work, a simple yet effective Lagrangian relaxation based heuristic algorithm is presented. Extensive computational experiments using standard benchmark data (CATS) as well as newly generated more realistic test sets were conducted which showed the heuristic was able to provide optimal solutions for most test cases and is within 1% from the optimums for the rest within very short times. Experiements comparing CPLEX 8.0, the fastest current algorithm, showed the heuristic was able to provide equally godd or better solutions often requring less than 1% of the time required by CPLEX 8.0.