Exploring CP-IP based techniques for the bid evaluation in combinatorial auctions

Combinatorial auctions are now an important e-commerce application where bidders can bid on combination of items. The problem of selecting the best bids that cover all items, i.e., the winner determination problem (WDP), is NP-hard. The time constrained variant of this problem, considered in this paper, is the bid evaluation problem where temporal windows and precedence constraints are associated to each task in the bid. Many approaches have been proposed for the winner determination problem, coming mainly from the Integer Programming (IP) community and recently from the multi-agent community, while the bid evaluation problem received less attention. Surprisingly, the Constraint Programming (CP) community has almost never considered neither of the problems, while we believe that CP solvers or hybrid CP-IP solvers can provide an important contribution to the field. In particular, as soon as temporal side constraints are introduced in the problem. In this paper, we propose different algorithms based on CP, IP and CP-IP. We show that even the simplest pure CP based approach outperforms existing approaches. Since none of the algorithms developed in this paper dominates all the others, they are good candidates for algorithm portfolio design. Therefore, we identified a set of instance-dependent structural features that allow to select the best class of algorithms to apply. An interesting result achieved is that we found a correspondence between the standard deviation of the clustering coefficient and the performances of IP or CP based algorithms. We believe this is the first step toward an automatic algorithm portfolio selection.