Numerically Safe Gomory Mixed-Integer Cuts

We 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 MIPLIB 3.0 and MIPLIB 2003 test collections as well as with MIP instances derived from the TSPLIB traveling salesman library.