Exact solution method to solve large scale integer quadratic multidimensional knapsack problems

In this paper we develop a branch–and–bound algorithm for solving a particular integer quadratic multi–knapsack problem. The problem we study is defined as the maximization of a concave separable quadratic objective function over a convex set of linear constraints and bounded integer variables. Our exact solution method is based on the computation of an upper bound and also includes pre–procedure techniques in order to reduce the problem size before starting the branch–and–bound process. We lead a numerical comparison between our method and three other existing algorithms. The approach we propose outperforms other procedures for large–scaled instances (up to 2000 variables and constraints).