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. © 2011 Springer-Verlag.
CITATION STYLE
Delort, C., Spanjaard, O., & Weng, P. (2011). Committee selection with a weight constraint based on a pairwise dominance relation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6992 LNAI, pp. 28–41). https://doi.org/10.1007/978-3-642-24873-3_3
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