Solving the combinatorial double auction problem

This paper studies the solution of several types of combinatorial (double) auctions. Such auctions have recently been used in business-to-business trading in a centralized marketplace, or in multi-agent coordination systems in artificial intelligence. When the goods are indivisible, solving the winner determination problem (WDP) is an integer programming problem and NP-hard in its general form. We show that a general combinatorial double auction can be reduced to a combinatorial single-sided auction, which is a multi-dimensional knapsack problem. Next, we compare the performance of several solution approaches for this type of problem. We contrast the branch-and-bound method with the intelligent search method proposed separately in three well-referenced papers. We found that theoretically the LP relaxation bounds always dominate the bounds used in the specialized intelligent searches. We also found empirically that the performance of this branch-and-bound method is superior to the specialized search methods that have been proposed for this class of problems.