An exact method based on Lagrangian decomposition for the 0–1 quadratic knapsack problem - Billionnet, Alain; Soutif, Éric (European journal of operational research, 2004)
The 0–1 quadratic knapsack problem (QKP) consists in maximizing a quadratic pseudo-Boolean function with positive coefficients subject to a linear capacity constraint. In this paper we present an exact method to solve this problem. This method makes use of the computation of an upper bound for (QKP) which is derived from Lagrangian decomposition. It allows us to find the optimum of instances with up to 150 variables whatever their density, and with up to 300 variables for medium and low density.