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The Inverse 0,1-Knapsack Problem: Theory, Algorithms and Computational Experiments

par Roland, Julien ;Figueira, José J.R.;De Smet, Yves
Référence Discrete Optimization
Publication Publié, 2012

Article révisé par les pairs

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Résumé :

The inverse {0,1}-knapsack problem consists of finding a minimal adjustment of the profit vector such that a given feasible set of items becomes an optimal solution. In this paper, two models are considered. In the first, the adjustment is measured by the Chebyshev norm. A pseudo-polynomial time algorithm is proposed to solve it. In the second, the adjustment is based on the Manhattan norm. This model is reduced to solve a linear integer program. While the first problem is proved to be co-NP-Complete, the second is co-NP-Hard and strong arguments are against its co-NP-Completeness. For both models, a bilevel linear integer programming formulation is also presented. Numerical results from computational experiments to assessing the feasibility of these approaches are reported. © 2013 Elsevier B.V. All rights reserved.