Solving mixed integer programming problems using automatic reformulation
Operations Research
Discrete optimization
Optimization
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Solving airline crew scheduling problems by branch-and-cut
Management Science
Computational Optimization and Applications
Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
On the Separation of Maximally Violated mod-k Cuts
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
An Exponential Lower Bound on the Length of Some Classes of Branch-and-Cut Proofs
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Polyhedral Study of the Cardinality Constrained Knapsack Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
General Mixed Integer Programming: Computational Issues for Branch-and-Cut Algorithms
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Branch-and-Cut Algorithms for Combinatorial Optimization and Their Implementation in ABACUS
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Cutting planes in integer and mixed integer programming
Discrete Applied Mathematics
An augment-and-branch-and-cut framework for mixed 0-1 programming
Combinatorial optimization - Eureka, you shrink!
Exponential Lower Bounds on the Lengths of Some Classes of Branch-and-Cut Proofs
Mathematics of Operations Research
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
On the MIR Closure of Polyhedra
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Can pure cutting plane algorithms work?
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Two-Step MIR Inequalities for Mixed Integer Programs
INFORMS Journal on Computing
On counting lattice points and Chvátal-Gomory cutting planes
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Lift-and-project cuts for mixed integer convex programs
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Lifted Tableaux Inequalities for 0--1 Mixed-Integer Programs: A Computational Study
INFORMS Journal on Computing
Mixed-integer cuts from cyclic groups
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
On applying cutting planes in DLL-Based algorithms for pseudo-boolean optimization
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A relax-and-cut framework for gomory's mixed-integer cuts
CPAIOR'10 Proceedings of the 7th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Combining Lift-and-Project and Reduce-and-Split
INFORMS Journal on Computing
INFORMS Journal on Computing
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We investigate the use of Gonory's mixed integer cuts within a branch-and-cut framework. It has been argued in the literature that ''a marriage of classical cutting planes and tree search is out of the question as far as the solution of large-scale combinatorial optimization problems is concerned'' [16] because the cuts generated at one node of the search tree need not be valid at other nodes. We show that it is possible, by using a simple lifting procedure, to make Gomory cuts generated at a node of the enumeration tree globally valid in the case of mixed 0-1 programs. The procedure essentially amounts to treating the variables fixed at 0 or 1 as if they were free. We also show why this lifting procedure is not valid for general (other than 0-1) mixed integer programs. Other issues addressed in the paper are of a computational nature, such as strategies for generating the cutting planes, deciding between branching and cutting, etc. The result is a robust mixed integer program solver.