Theory of linear and integer programming
Theory of linear and integer programming
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Logic cuts for processing networks with fixed charges
Computers and Operations Research
Characterization and Theoretical Comparison of Branch-and-Bound Algorithms for Permutation Problems
Journal of the ACM (JACM)
The Power of Dominance Relations in Branch-and-Bound Algorithms
Journal of the ACM (JACM)
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Efficient conflict driven learning in a boolean satisfiability solver
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
Test Sets and Inequalities for Integer Programs
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
MIP: Theory and Practice - Closing the Gap
Proceedings of the 19th IFIP TC7 Conference on System Modelling and Optimization: Methods, Theory and Applications
Where are the hard knapsack problems?
Computers and Operations Research
Optimizing over the first Chvátal closure
Mathematical Programming: Series A and B
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Matheuristics: Hybridizing Metaheuristics and Mathematical Programming
Matheuristics: Hybridizing Metaheuristics and Mathematical Programming
A complexity analysis of space-bounded learning algorithms for the constraint satisfaction problem
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Operations Research Letters
Conflict analysis in mixed integer programming
Discrete Optimization
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The concept of dominance among nodes of a branch-and-bound tree, although known for a long time, is typically not exploited by general-purpose mixed-integer linear programming (MILP) codes. The starting point of our work was the general-purpose dominance procedure proposed in the 1980s by Fischetti and Toth, where the dominance test at a given node of the branch-and-bound tree consists of the (possibly heuristic) solution of a restricted MILP only involving the fixed variables. Both theoretical and practical issues concerning this procedure are analyzed, and important improvements are proposed. In particular, we use the dominance test not only to fathom the current node of the tree, but also to derive variable configurations called “nogoods” and, more generally, “improving moves.” These latter configurations, which we rename “pruning moves” so as to stress their use in a node-fathoming context, are used during the enumeration to fathom large sets of dominated solutions in a computationally effective way. Computational results on a testbed of MILP instances whose structure is amenable to dominance are reported, showing that the proposed method can lead to a considerable speedup when embedded in a commercial MILP solver.