Strengthening lattice-free cuts using non-negativity

In recent years there has been growing interest in generating valid inequalities for mixedinteger programs using sets with 2 or more constraints. In particular, Andersen et al. (2007) and Borozan and Cornu´ejols (2007) study sets defined by equations that contain exactly one integer variable per row. The integer variables are not restricted in sign. Cutting planes based on this approach have already been computationally studied by Espinoza [15] for general mixed-integer problems and there is ongoing computational research in this area. In this paper, we extend the model studied in the earlier papers and require the integer variables to be non-negative. We extend the results in Andersen et al. (2007) and Borozan and Cornu´ejols (2007) to our case and show that cuts generated by their approach can be strengthened by using the non-negativity of the integer variables. In particular, it is possible to obtain cuts which have negative coefficients for some variables.

• Type: Journal
• Year: 2011
• Where: DISOPT
• Authors: Ricardo Fukasawa, Oktay Günlük
• Keywords: Computer Networks, DISOPT 2011, Integer Problems, Integer Variables, Valid Inequalities