A Graph Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions

Abstract

Combinatorial auctions are increasingly being used to allocate bundles of items among interested bidders. However, as the number of bundles increases, it takes exponentially longer to solve for the winners in the auction. In such situations, regular solvers such as IBM CPLEX or AMPL fail to produce the optimal solution either completely due to computational limitations or in reasonable time. We propose an Ant Colony-based algorithm (TrACA) that produces optimal or near-optimal results within specified time. Experiments are performed on 90 instances to show and compare the performance of TrACA to the current state-of-the-art memetic algorithm (MA). Results indicate that in a given run-time, the median of results from TrACA statistically significantly outperforms MA results in 85% of the cases. Further, the best value from TrACA is at least as good as MA values in 100% of the cases. Additionally, to better understand the why deterministic algorithms fail or take too long for approximating winners in such auctions, we analyze empirical hardness of tested instances and use a standard supervised learning method to build a predictive model of TrACA run-times. Using the predictive model, we highlight factors that make winner determination in combinatorial auctions computationally hard to estimate and show why TrACA is better suited to handle such hard instances.

Keywords: ant colony, wdp, combinatorial auctions, heuristics, evolutionary

JEL Classification: C63, C61