Reoptimization in Lagrangian methods for the 0–1 quadratic knapsack problem

Publication year: 2012
Source: Computers & Operations Research, Volume 39, Issue 1, January 2012, Pages 12-18

Lucas, Létocart , Anass, Nagih , Gérard, Plateau

The 0–1 quadratic knapsack problem consists of maximizing a quadratic objective function subject to a linear capacity constraint. To exactly solve large instances of this problem with a tree search algorithm (e.g., a branch and bound method), the knowledge of good lower and upper bounds is crucial for pruning the tree but also for fixing as many variables as possible in a preprocessing phase. The upper bounds used in the best known exact approaches are based on Lagrangian relaxation and decomposition. It appears that the computation of these Lagrangian dual bounds involves the resolution of numerous 0–1 linear knapsack subproblems….