Generalized best-first search strategies and the optimality of A*
Journal of the ACM (JACM)
Integer and combinatorial optimization
Integer and combinatorial optimization
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
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)
Conflict analysis in mixed integer programming
Discrete Optimization
On the Complexity of Selecting Disjunctions in Integer Programming
SIAM Journal on Optimization
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Deciding what question to branch on at each node is a key element of search algorithms. We introduce the information-theoretic paradigm for branching question selection. The idea is to drive the search to reduce uncertainty (entropy) in the current subproblem. We present four families of methods that fall within this paradigm. 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 other variables they govern. This significantly outperforms the state-of-the-art branching strategies. The fourth family is about branching using carefully constructed linear inequality constraints over sets of variables.