Automatic integer programming reformulation using variable neighborhood search.

Abstract

Chvatal-Gomory cuts are well-known cutting planes for Integer Programming problems. As shown in previous works, the inclusion of these cuts allows to significantly reducing the integrality gap. This work presents a Local Search heuristic approach based on Variable Neighborhood Search to discover violated Chv`atal-Gomory inequalities. Since this problem is known to be NP-hard, this approach was designed to generate violated inequalities in restricted amounts of time. Constraints are grouped in several sets, considering the amount of common variables. These sets are processed in parallel in order to obtain the best multipliers and produce violated cuts. We report some preliminary results obtained for MIPLIB 3.0 and 2003 instance sets, comparing our approach with an integer programming based separation method. Our algorithm was able to separate many violated inequalities, reducing the duality gap. Furthermore, it uses an extended numerical precision implementation, since it is not specifically bound to simplex based solvers.