Structural alignment of large—size proteins via lagrangian relaxation
Proceedings of the sixth annual international conference on Computational biology
Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Discrete location problems with push-pull objectives
Discrete Applied Mathematics
Greedy, genetic, and greedy genetic algorithms for the quadratic knapsack problem
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
An approximate dynamic programming approach to convex quadratic knapsack problems
Computers and Operations Research
Upper bounds and exact algorithms for p-dispersion problems
Computers and Operations Research
The quadratic multiple knapsack problem and three heuristic approaches to it
Proceedings of the 8th annual conference on Genetic and evolutionary computation
A hub location problem with fully interconnected backbone and access networks
Computers and Operations Research
The quadratic knapsack problem-a survey
Discrete Applied Mathematics
Evolving heuristically difficult instances of combinatorial problems
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
An approximate dynamic programming approach to convex quadratic knapsack problems
Computers and Operations Research
Upper bounds and exact algorithms for p-dispersion problems
Computers and Operations Research
A genetic algorithm for the quadratic multiple knapsack problem
BVAI'07 Proceedings of the 2nd international conference on Advances in brain, vision and artificial intelligence
Reoptimization in Lagrangian methods for the 0-1 quadratic knapsack problem
Computers and Operations Research
A computational study on the quadratic knapsack problem with multiple constraints
Computers and Operations Research
Optimizing query shortcuts in RDF databases
ESWC'11 Proceedings of the 8th extended semantic web conference on The semanic web: research and applications - Volume Part II
On a nonseparable convex maximization problem with continuous knapsack constraints
Operations Research Letters
The submodular knapsack polytope
Discrete Optimization
Comparisons and enhancement strategies for linearizing mixed 0-1 quadratic programs
Discrete Optimization
The quadratic 0-1 knapsack problem with series-parallel support
Operations Research Letters
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
On reduction of duality gap in quadratic knapsack problems
Journal of Global Optimization
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
Generalized quadratic multiple knapsack problem and two solution approaches
Computers and Operations Research
On the admission of dependent flows in powerful sensor networks
IEEE/ACM Transactions on Networking (TON)
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The Quadratic Knapsack Problem (QKP) calls for maximizing a quadratic objective function subject to a knapsack constraint, where all coefficients are assumed to be nonnegative and all variables are binary. The problem has applications in location and hydrology, and generalizes the problem of checking whether a graph contains a clique of a given size. We propose an exact branch-and-bound algorithm for QKP, where upper bounds are computed by considering a Lagrangian relaxation that is solvable through a number of (continuous) knapsack problems. Suboptimal Lagrangian multipliers are derived by using subgradient optimization and provide a convenient reformulation of the problem. We also discuss the relationship between our relaxation and other relaxations presented in the literature. Heuristics, reductions, and branching schemes are finally described. In particular, the processing of each node of the branching tree is quite fast: We do not update the Lagrangian multipliers, and use suitable data structures to compute an upper bound in linear expected time in the number of variables. We report exact solution of instances with up to 400 binary variables, i.e., significantly larger than those solvable by the previous approaches. The key point of this improvement is that the upper bounds we obtain are typically within 1% of the optimum, but can still be derived effectively. We also show that our algorithm is capable of solving reasonable-size Max Clique instances from the literature.