Abstract
This paper is devoted to a knapsack problem with a cardinality constraint when dropping the assumption of additive representability [10]. More precisely, we assume that we only have a classification of the items into ordered classes. We aim at generating the set of preferred subsets of items, according to a pairwise dominance relation between subsets that naturally extends the ordering relation over classes [4,16]. We first show that the problem reduces to a multiobjective knapsack problem with cardinality constraint. We then propose two polynomial algorithms to solve it, one based on a multiobjective dynamic programming scheme and the other on a multiobjective branch and bound procedure. We conclude by providing numerical tests to compare both approaches.
This research has been supported by the project ANR-09-BLAN-0361 GUaranteed Efficiency for PAReto optimal solutions Determination (GUEPARD).
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Delort, C., Spanjaard, O., Weng, P. (2011). Committee Selection with a Weight Constraint Based on a Pairwise Dominance Relation. In: Brafman, R.I., Roberts, F.S., Tsoukià s, A. (eds) Algorithmic Decision Theory. ADT 2011. Lecture Notes in Computer Science(), vol 6992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24873-3_3
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DOI: https://doi.org/10.1007/978-3-642-24873-3_3
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