Integer and combinatorial optimization
Integer and combinatorial optimization
Computationally Manageable Combinational Auctions
Management Science
Bidding and allocation in combinatorial auctions
Proceedings of the 2nd ACM conference on Electronic commerce
Towards a universal test suite for combinatorial auction algorithms
Proceedings of the 2nd ACM conference on Electronic commerce
Algorithm for optimal winner determination in combinatorial auctions
Artificial Intelligence
Taming the Computational Complexity of Combinatorial Auctions: Optimal and Approximate Approaches
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
An Algorithm for Multi-Unit Combinatorial Auctions
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Learning the Empirical Hardness of Optimization Problems: The Case of Combinatorial Auctions
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
Solving concisely expressed combinatorial auction problems
Eighteenth national conference on Artificial intelligence
Combinatorial Auctions: A Survey
INFORMS Journal on Computing
A portfolio approach to algorithm select
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
CABOB: a fast optimal algorithm for combinatorial auctions
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 2
The Landscape of Electronic Market Design
Management Science
A model and heuristic algorithms for multi-unit nondiscriminatory combinatorial auction
Computers and Operations Research
Solving multiple scenarios in a combinatorial auction
Computers and Operations Research
Matrix Bidding in Combinatorial Auctions
Operations Research
Solving Truckload Procurement Auctions Over an Exponential Number of Bundles
Transportation Science
A Generalized Wedelin Heuristic for Integer Programming
INFORMS Journal on Computing
From high-level model to branch-and-price solution in G12
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
A lagrangian heuristic for winner determination problem in combinatorial auctions
AI'05 Proceedings of the 18th Australian Joint conference on Advances in Artificial Intelligence
A robust multi-unit ascending-price auction with complementarities against strategic manipulation
PRIMA'10 Proceedings of the 13th international conference on Principles and Practice of Multi-Agent Systems
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When combinatorial bidding is permitted in auctions, such as the proposed FCC Auction #31, the resulting full valuations and winner-determination problem can be computationally challenging. We present a branch-and-price algorithm based on a set-packing formulation originally proposed by Dietrich and Forrest (2002, "A column generation approach for combinatorial auctions," in Mathematics of the Internet: E-Auction and Markets. The IMA Volumes in Mathematics and Its Applications, Vol. 127, Springer-Verlag, New York, 15-26). This formulation has a variable for every possible combination of winning bids for each bidder. Our algorithm exploits the structure of the XOR-of-OR bidding language used by the FCC. We also present a new methodology to produce realistic test problems based on the round-by-round results of FCC Auction #4. We generate 2,639 test problems, which involve 99 items and are substantially larger than most of the previously used benchmark problems. Because there are no real-life test problems for combinatorial spectrum auctions with the XOR-of-OR language, we used these test problems to observe the computational behavior of our algorithm. Our algorithm can solve all but one test problem within 10 minutes, appears to be very robust, and for difficult instances compares favorably to the natural formulation solved using a commercial optimization package with default settings. Although spectrum auctions are used as the guiding example to describe the merits of branch and price for combinatorial auctions, our approach applies to auctions of multiple goods in other scenarios similarly.