Greedy, genetic, and greedy genetic algorithms for the quadratic knapsack problem
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
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Proceedings of the 8th annual conference on Genetic and evolutionary computation
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Discrete Applied Mathematics
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Proceedings of the 11th Annual conference on Genetic and evolutionary computation
An Artificial Bee Colony Algorithm for the Quadratic Knapsack Problem
ICONIP '09 Proceedings of the 16th International Conference on Neural Information Processing: Part II
Reoptimization in Lagrangian methods for the 0-1 quadratic knapsack problem
Computers and Operations Research
Naive and heuristic permutation-coded genetic algorithms for the quadratic knapsack problem
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
A simplified binary artificial fish swarm algorithm for 0-1 quadratic knapsack problems
Journal of Computational and Applied Mathematics
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In this paper we will consider the 0-1 quadratic knapsack problem (QKP). Our purpose is to show that using a linear reformulation of this problem and a standard mixed integer programming tool, it is possible to solve the QKP efficiently in terms of computation time and the size of problems considered, in comparison to existing methods. Considering a problem involvingn variables, the linearization technique we propose has the advantage of adding only ( n - 1) real variables and 2( n - 1) constraints. We present extensive computational results on randomly generated instances and on structured problems coming from applications. For example, the method allows us to solve randomly generated QKP instances exactly with up to 140 variables.