A branch-and-bound algorithm to solve large scale integer quadratic multidimensional knapsack problem

The separable quadratic multi-knapsack problem (QMKP) consists in maximizing a concave separable quadratic integer (non pure binary) function subject to m linear capacity constrainsts. In this paper we develop a branch-and-bound algorithm to solve (QMKP) to optimality. This method is based on the computation of a tight upper bound for (QMKP) wich is derived from a linearization and a surrogate relaxation. Our branch-and-bound also incorporates pre-processing procedures. The computational performance of our branch-andèbound is copared to that of three exact methods: a branch-and-bound algorithm developed by Djerdjour et al. (1988), a 0-1 linearization ethod originally applied to the separable quadratic knapsack problem with a single constraint that we extend to the case of m constraints, a standard branch-and-bound algorithm (Cplex 9.0 quadratic optimization). Our branch-and-bound clearly outperforms other methods for large instances (up to 2000 variables and constraints)