Abstract
A Lagrangean relaxation of the quadratic knapsack problem is studied. It is shown, among other properties, that the best value of the Lagrangean multiplier, and hence the best bound for the original problem, can be determined in at most n−1 applications of a maximum flow algorithm to a network with n+2 vertices and n+m arcs, where n and m denote the numbers of variables and of quadratic terms. A branch-and-bound algorithm using this result is presented and computational experience is reported on.
Paper presented at the NETFLOW 83 International Workshop, Pisa, Italy, 28–31 March 1983.
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© 1989 Springer-Verlag
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Chaillou, P., Hansen, P., Mahieu, Y. (1989). Best network flow bounds for the quadratic knapsack problem. In: Simeone, B. (eds) Combinatorial Optimization. Lecture Notes in Mathematics, vol 1403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083467
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DOI: https://doi.org/10.1007/BFb0083467
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