Generalized best-first search strategies and the optimality of A*
Journal of the ACM (JACM)
Optimal solutions for multi-unit combinatorial auctions: branch and bound heuristics
Proceedings of the 2nd ACM conference on Electronic commerce
New methods to color the vertices of a graph
Communications of the ACM
Backtrack programming techniques
Communications of the ACM
Approximation algorithms
Algorithm for optimal winner determination in combinatorial auctions
Artificial Intelligence
Computational Optimization and Applications
Machine Learning
Branch-And-Price: Column Generation for Solving Huge Integer Programs
Operations Research
A Computational Study of Search Strategies for Mixed Integer Programming
INFORMS Journal on Computing
BOB: improved winner determination in combinatorial auctions and generalizations
Artificial Intelligence
Finding Cuts in the TSP (A preliminary report)
Finding Cuts in the TSP (A preliminary report)
Integer Programming for Combinatorial Auction Winner Determination
ICMAS '00 Proceedings of the Fourth International Conference on MultiAgent Systems (ICMAS-2000)
Resource allocation in competitive multiagent systems
Resource allocation in competitive multiagent systems
Active-constraint variable ordering for faster feasibility of mixed integer linear programs
Mathematical Programming: Series A and B
Branching on general disjunctions
Mathematical Programming: Series A and B
Operations Research Letters
Optimization of a 532-city symmetric traveling salesman problem by branch and cut
Operations Research Letters
A unified method for handling discrete and continuous uncertainty in Bayesian Stackelberg games
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
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Deciding what question to branch on at each node is a key element of search algorithms. In this paper, we describe a collection of techniques for branching decisions that are motivated from an information-theoretic perspective. The idea is to drive the search to reduce the uncertainty (entropy) in the current subproblem. We present four families of methods for branch question selection in mixed integer programming that use this idea. In the first, a variable to branch on is selected based on lookahead. This method performs comparably to strong branching on MIPLIB, and better than strong branching on hard real-world procurement optimization instances on which CPLEX's default strong branching outperforms CPLEX's default branching strategy. The second family combines this idea with strong branching. The third family does not use lookahead, but instead exploits the tie between indicator variables and the variables they govern. This significantly outperforms the state-of-the-art branching strategies on both combinatorial procurement problems and facility location problems. The fourth family concerns branching using carefully constructed linear inequality constraints over sets of variables.