Exploring local search in winner determination problem

• Authors: Raj Jog Singh;Anup Kumar Sen
• Venue: Information Technology and Management
• Year: 2008

In Combinatorial Auctions, multiple goods (items) are available for auction simultaneously, and bidders bid for combinations of goods called bundles. In the single unit combinatorial auction problem, there is only single unit of each item present and the items are considered to be indivisible. This forms the supply side constraint resulting in a need by the seller to decide on which bundles to allocate for maximizing the revenue. Determining these winning bundles is an NP-complete problem and is known by the name of Winner Determination Problem (WDP) in literature. Combinatorial auction mechanism has a wide range of practical applications such as allocation of railroads, auction of adjacent pieces of real estate, auction of airport landing slots, distributed job shop scheduling etc. The optimal heuristic search algorithms like CASS and CABOB proposed for solving the WDP take a lot of CPU time for solving large problem instances. Though these algorithms give optimal solutions, they would be useful only in scenarios where time is not at all a constraint, and the bidding is a one time affair. This poses a limitation in conducting combinatorial auctions with multiple rounds of bidding and hence hinders the widespread use of combinatorial auctions on the patterns of traditional English auction and internet auctions. Thus faster solution of WDP holds the key to widespread use and popularity of combinatorial auctions. This paper attempts to address the above issue, and proposes a simple local search technique LSWDP (Local Search for Winner Determination Problem) that runs very fast and provides solutions quite close to optimal for a number of applications. It also outputs optimal solutions in many instances taking only a fraction of the CPU time taken by CASS. In addition LSWDP was found to outperform the anytime algorithm CASS given a time cutoff. This paper also presents an enhancement called LSCN (Local Search using Complimentary Neighborhood) that provides still better solutions in terms of close to optimal behavior and achieves a much better strike rate in hitting optimal solutions. LSCN runs slower than LSWDP but still takes only a fraction of the CPU time taken by CASS thus encouraging the use of local search for combinatorial auctions. Finally, an extension to multi-partition search has been proposed and analyzed.