A recursive procedure to generate all cuts for 0-1 mixed integer programs
Mathematical Programming: Series A and B
Mixed-Integer Cuts from Cyclic Groups
Mathematical Programming: Series A and B
Inequalities from Two Rows of a Simplex Tableau
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
On the facets of mixed integer programs with two integer variables and two constraints
Mathematical Programming: Series A and B
Minimal Valid Inequalities for Integer Constraints
Mathematics of Operations Research
An Analysis of Mixed Integer Linear Sets Based on Lattice Point Free Convex Sets
Mathematics of Operations Research
Computing with multi-row gomory cuts
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Lifting integer variables in minimal inequalities corresponding to lattice-free triangles
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Mixed-integer sets from two rows of two adjacent simplex bases
Mathematical Programming: Series A and B - Series B - Special Issue: Combinatorial Optimization and Integer Programming
Minimal Inequalities for an Infinite Relaxation of Integer Programs
SIAM Journal on Discrete Mathematics
A Geometric Perspective on Lifting
Operations Research
Operations Research Letters
On degenerate multi-row Gomory cuts
Operations Research Letters
A probabilistic analysis of the strength of the split and triangle closures
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Experiments with Two-Row Cuts from Degenerate Tableaux
INFORMS Journal on Computing
Approximating the Split Closure
INFORMS Journal on Computing
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Following the flurry of recent theoretical work on cutting planes from two row mixed integer group relaxations of an LP tableau, we report on some computational tests to evaluate the effectiveness of two row cuts based on lattice-free (type 2) triangles having more than one integer point on one side. A heuristic procedure to generate such triangles is presented, and then the coefficients of the integer variables are tightened by lifting. As a first step in testing the effectiveness of the triangle cuts, we make comparisons between the gap closed using Gomory mixed integer cuts for one round and the gap closed in one round using all the triangles generated by our heuristic. Our tests are carried out on different classes of randomly generated instances designed to represent different models in the literature by varying the number of integer non-basic variables, bounds and non-negativity constraints.