Reduce-and-Split Cuts: Improving the Performance of Mixed-Integer Gomory Cuts

Reduce-and-Split Cuts: Improving the Performance of Mixed-Integer Gomory Cuts

Mixed integer Gomory cuts have become an integral part of state-of-the-art software for solving mixed integer linear programming problems. Therefore, improvements in the performance of these cutting planes can be of great practical value. In this paper we present a simple and fast heuristic for improving the coefficients on the continuous variables in the mixed integer Gomory cuts. This is moti...

Numerically Safe Gomory Mixed-Integer Cuts

W describe a simple process for generating numerically safe cutting planes using floating-point arithmetic and the mixed-integer rounding procedure. Applying this method to the rows of the simplex tableau permits the generation of Gomory mixed-integer cuts that are guaranteed to be satisfied by all feasible solutions to a mixed-integer programming problem (MIP). We report on tests with the MIPL...

A relax-and-cut framework for Gomory mixed-integer cuts

Gomory mixed-integer cuts (GMICs) are widely used in modern branchand-cut codes for the solution of mixed-integer programs. Typically, GMICs are iteratively generated from the optimal basis of the current linear programming (LP) relaxation, and immediately added to the LP before the next round of cuts is generated. Unfortunately, this approach is prone to instability. In this paper we analyze a...

K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau

On the strength of Gomory mixed-integer cuts as group cuts

Gomory mixed-integer (GMI) cuts generated from optimal simplex tableaus are known to be useful in solving mixed-integer programs. Further, it is well-known that GMI cuts can be derived from facets of Gomory’s master cyclic group polyhedron and its mixed-integer extension studied by Gomory and Johnson. In this paper we examine why cutting planes derived from other facets of master cyclic group p...