A very fast method for guaranteed generation of one facet for 0-1 knapsack polyhedron

Abstract

The 0-1 knapsack polyhedron as the most basic relaxation of a 0-1 integer program has attracted attention of many researchers over the years. We present a very fast method that is guaranteed to generate one facet for the 0-1 knapsack polyhedron. Unlike lifting of cover inequities, our method does not require an initial minimal cover or a predetermined lifting sequencing, and its worst-case complexity is linear in number of variables. Therefore, with minimal computational burden, it can be used to generate a potentially strong valid inequality based on any 0-1 relaxation of a general (mixed) integer program (M)IP. Such valid inequalities can be added to the (M)IP problem prior to solving, or given their low computational cost, can be generated during solving the (M)IP, checked to see if they separate the incumbent fractional solution, and added to the problem if they do.