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

Iterative combinatorial auctions are known to resolve bidder preference elicitation problems. However, winner determination is a known key bottleneck that has prevented widespread adoption of such auctions, and adding a time-bound to winner determination further complicates the mechanism. As a result, heuristic-based methods have enjoyed an increase in applicability. We add to the growing body of work in heuristic-based winner determination by proposing an ant colony metaheuristic–based anytime algorithm that produces optimal or near-optimal winner determination results within specified time. Our proposed algorithm resolves the speed versus accuracy problem and displays superior performance compared with 20 past state-of-the-art heuristics and two exact algorithms, for 94 open test auction instances that display a wide variety in bid-bundle composition. Furthermore, we contribute to the literature in two predominant ways: first, we represent the winner determination problem as one of finding the maximum weighted path on a directed cyclic graph; second, we improve upon existing ant colony heuristic–based exploration methods by implementing randomized pheromone updating and randomized graph pruning. Finally, to aid auction designers, we implement the anytime property of the algorithm, which allows auctioneers to stop the algorithm and return a valid solution to the winner determination problem even if it is interrupted before computation ends.

A Tabu Search Method for the Multi-objective Winner Determination Problem of Combinatorial Auctions

We are interested by the problem of combinatorial auctions in which multiple items are sold and bidders submit bids on packages. First, we present a multi-objective formulation for a combinatorial auctions problem extending the existing single-objective models. Indeed, the bids may concern several specifications of the item, involving not only its price, but also its quality, delivery conditions, delivery deadlines, the risk of not being paid after a bid has been accepted and so on. The seller expresses his preferences upon the suggested items and the buyers are in competition with all the specified attributes done by the seller. Second, we develop and implement a metaheuristic algorithm based on a tabu search method.

An Exact Method for the Multi-objective Winner Determination Problem of Combinatorial Auctions

We are interested by the problem of combinatorial auctions in which multiple items are sold and bidders submit bids on packages. First, we present a multi-objective formulation for a combinatorial auctions problem extending the existing single-objective models. Indeed, the bids may concern several specifications of the item, involving not only its price, but also its quality, delivery conditions, delivery deadlines, the risk of not being paid after a bid has been accepted and so on. The seller expresses his preferences upon the suggested items and the buyers are in competition with all the specified attributes done by the seller. Second, we develop and implement an exact algorithm based on a multi-objective branch-and-bound method.

The Cross-Entropy Method for the Winner Determination Problem in Combinatorial Auctions

The combinatorial auction is one of the important methods used for multi-item auctions, and the solution to the winner determination problem (WDP) is the key factor in the widespread application of combinatorial auctions. This paper explores the use of the cross-entropy method to solve the WDP, which is an NP problem. The performance of the proposed approach is evaluated on the basis of two well-known benchmark test cases. The experimental results show that, compared with the genetic algorithm and the particle swarm optimization algorithm, the cross-entropy（CE）method has the advantages of a higher success rate and a shorter time for solving the WDP. Therefore, the CE method provides a high-quality solution for the effective solution of the problem of determining winning bids in combined auctions.

Quantity-Contingent Auctions and Allocation of Airport Slots

In this paper, we define and investigate quantity-contingent auctions. Such auctions can be used when there exist multiple units of a single product and the value of a set of units depends on the total quantity sold. For example, a road network or airport will become congested as the number of users increase so that a permit for use becomes more valuable as the total number allocated decreases. A quantity-contingent auction determines both the number of items sold and an allocation of items to bidders. Because such auctions could be used by bidders to gain excessive market power, we impose constraints limiting market power. We focus on auctions that allocate airport arrival and departure slots. We propose a continuous model and an integer programming model for the associated winner determination problem. Using these models, we perform computational experiments that lend insights into the properties of the quantity-contingent auction.

A Comparative Study of Two Models for Handling Transportation Cost in Combinatorial Auctions

Although combinatorial auctions have been extensively studied, the factor of transportation cost has not been considered in most studies. Without considering transportation cost, the profits of the seller cannot be determined accurately. The goals of this article are to propose models, develop a solution methodology for the winner determination problem (WDP) in combinatorial auctions and study the effects of transportation cost on the seller's profits. Two models are proposed: one model considers transportation cost in WDP whereas the other one does not take transportation cost into account in WDP but calculates the transportation cost based on the solution obtained. The author formulates the WDPs for these two models and proposes a solution method. The author then analyzes and compares the two models to illustrate the advantage of taking transportation cost into account in combinatorial auctions. Finally, the author studies the influence of transportation cost on combinatorial auctions by examples and demonstrate effectiveness of our approach.