New computational results with an exact knapsack separation procedure for structured Binary Integer Programming problems

Abstract

In this paper we report new computational results with an approach based on the generation of general cutting planes for several classes of Binary Integer Programming (BIP) Problems such as Generalized Assignment, Multi-Dimensional Knapsack, Capacitated P-median and Capacitated Network Location. These problems are characterized by a formulation including a great number of knapsack constraints, which, in general make these problems very hard to solve. The state of the art on these problems requires to use approaches based on Lagrangean Relaxation or decomposition approaches like Dantzig-Wolfe and Column Generation techniques. In this paper we present an approach based on the generation of general cutting planes of the polytope associated with each knapsack constraints. Computational experience on a wide set of benchamrk instances is carried out.