Using a Mixed Integer Programming Tool for Solving the 0–1 Quadratic Knapsack Problem

In this paper we will consider the 0–1 quadratic knapsack problem (QKP). Our purpose is to show that using a linear reformulation of this problem and a standard mixed integer programming tool, it is possible to solve the QKP efficiently in terms of computation time and the size of problems considered, in comparison to existing methods. Considering a problem involving n variables, the linearization technique we propose has the advantage of adding only (n – 1) real variables and 2(n – 1) constraints. We present extensive computational results on randomly generated instances and on structured problems coming from applications. For example, the method allows us to solve randomly generated QKP instances exactly with up to 140 variables.