On the knapsack closure of 0-1 Integer Linear Programs

Many inequalities for Mixed-Integer Linear Programs (MILPs) or pure Integer Linear Programs (ILPs) are derived from the Gomory corner relaxation, where all the nonbinding constraints at an optimal LP vertex are relaxed. Computational results show that the corner relaxation gives a good approximation of the integer hull for problems with general-integer variables, but the approximation is less satisfactory for problems with 0-1 variables only. A possible explanation is that, for 0-1 ILPs, even the non-binding variable bound constraints xj 0 or xj 1 play an important role, hence their relaxation produces weaker bounds. In this note we address a relaxation for 0-1 ILPs that explicitly takes all variable bound constraints into account. More specifically, we introduce the concept of knapsack closure as a tightening of the classical Chv

• Type: Journal
• Year: 2010
• Where: ENDM
• Authors: Matteo Fischetti, Andrea Lodi
• Keywords: 0-1 Ilps, Corner Relaxation, ENDM 2010, Software Engineering, Variable Bound Constraints