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2009•INFORMS journal on computingOpen access

Numerically Safe Gomory Mixed-Integer Cuts

William J. Cook, Sanjeeb Dash, Ricardo Fukasawa, Marcos Goycoolea

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Travelling salesman problem, Rounding, Integer programming, Cutting-plane method, Integer (computer science), Mathematics, Simplex, Combinatorics

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