INFORMS Journal on Computing
Algorithms to separate {0, 1/2}-chvátal-gomory cuts
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Disjunctive cuts for non-convex mixed integer quadratically constrained programs
IPCO'08 Proceedings of the 13th 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
DRL*: A hierarchy of strong block-decomposable linear relaxations for 0-1 MIPs
Discrete Applied Mathematics
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
On the Chvátal-Gomory closure of a compact convex set
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Improving cutting plane generation with 0-1 inequalities by bi-criteria separation
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
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
The chvátal-gomory closure of an ellipsoid is a polyhedron
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Computational experience with general cutting planes for the Set Covering problem
Operations Research Letters
How to select a small set of diverse solutions to mixed integer programming problems
Operations Research Letters
Using symmetry to optimize over the sherali-adams relaxation
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Lifted and Local Reachability Cuts for the Vehicle Routing Problem with Time Windows
Computers and Operations Research
Improved bounds for large scale capacitated arc routing problem
Computers and Operations Research
Approximating the Split Closure
INFORMS Journal on Computing
Computers and Operations Research
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How difficult is, in practice, to optimize exactly over the first Chvátal closure of a generic ILP? Which fraction of the integrality gap can be closed this way, e.g., for some hard problems in the MIPLIB library? Can the first-closure optimization be useful as a research (off-line) tool to guess the structure of some relevant classes of inequalities, when a specific combinatorial problem is addressed? In this paper we give answers to the above questions, based on an extensive computational analysis. Our approach is to model the rank-1 Chvátal-Gomory separation problem, which is known to be NP-hard, through a MIP model, which is then solved through a general-purpose MIP solver. As far as we know, this approach was never implemented and evaluated computationally by previous authors, though it gives a very useful separation tool for general ILP problems. We report the optimal value over the first Chvátal closure for a set of ILP problems from MIPLIB 3.0 and 2003. We also report, for the first time, the optimal solution of a very hard instance from MIPLIB 2003, namely nsrand-ipx, obtained by using our cut separation procedure to preprocess the original ILP model. Finally, we describe a new class of ATSP facets found with the help of our separation procedure.