Branch and Bound Heuristics for Multi-Unit Combinatorial Auctions

Title: Branch and Bound Heuristics for Multi-Unit Combinatorial Auctions

Abstract: This research investigates the use of Branch-and-Bound techniques for finding optimal solutions in multi-unit combinatorial auctions. It discusses different methods for efficiently bounding from above the value of the best allocation and suggests the best ordering criterion that provides the best approximation ratio. The results provide theoretical insights into the effectiveness of these techniques and suggest a criterion that can be used to determine the best bids to try first.

Main Research Question: How can Branch-and-Bound techniques be used to find optimal solutions for multi-unit combinatorial auctions?

Methodology: The study uses a Branch-and-Bound approach, which involves bounding from above the value of the best allocation and using an ordering criterion to determine which bids to try first. The authors consider different methods for bounding and suggest a criterion that provides the best approximation ratio.

Results: The results show that Branch-and-Bound techniques can be used to find optimal solutions for multi-unit combinatorial auctions. The study characterizes the best approximation ratio and the ordering criterion that provides it.

Implications: The findings suggest that the suggested ordering criterion can be used to determine the best bids to try first, which can lead to more efficient search processes and better allocation of resources. This can be particularly useful in situations where the number of bids and items are large, making the problem computationally challenging.

Conclusion: In conclusion, the study demonstrates that Branch-and-Bound techniques can be effectively used to find optimal solutions for multi-unit combinatorial auctions. The suggested ordering criterion can be used to determine the best bids to try first, which can lead to more efficient search processes and better allocation of resources.

Link to Article: https://arxiv.org/abs/0202032v1 Authors: arXiv ID: 0202032v1