Lagrangean methods for 0-1 quadratic problems
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
An exact algorithm for the 0–1 collapsing knapsack problem
Discrete Applied Mathematics - Special volume: viewpoints on optimization
Solving quadratic (0,1)-problems by semidefinite programs and cutting planes
Mathematical Programming: Series A and B
Implementing Quicksort programs
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Exact Solution of the Quadratic Knapsack Problem
INFORMS Journal on Computing
Using a Mixed Integer Programming Tool for Solving the 0-1 Quadratic Knapsack Problem
INFORMS Journal on Computing
Lagrangean heuristics combined with reoptimization for the 0-1 bidimensional knapsack problem
Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02
The quadratic knapsack problem-a survey
Discrete Applied Mathematics
Sensitivity analysis of the knapsack sharing problem: Perturbation of the weight of an item
Computers and Operations Research
Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction
INFORMS Journal on Computing
Journal of Computer and System Sciences
An effective GRASP and tabu search for the 0-1 quadratic knapsack problem
Computers and Operations Research
A simplified binary artificial fish swarm algorithm for 0-1 quadratic knapsack problems
Journal of Computational and Applied Mathematics
Hi-index | 0.02 |
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. Thus, taking this huge number of resolutions into account, we propose to embed reoptimization techniques for improving the efficiency of the preprocessing phase of the 0-1 quadratic knapsack resolution. Namely, reoptimization is introduced to accelerate each independent sequence of 0-1 linear knapsack problems induced by the Lagrangian relaxation as well as the Lagrangian decomposition. Numerous numerical experiments validate the relevance of our approach.