Committee Selection with a Weight Constraint Based on a Pairwise Dominance Relation

Charles Delort 1 Olivier Spanjaard 1 Paul Weng 1
1 DECISION
LIP6 - Laboratoire d'Informatique de Paris 6
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.
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Charles Delort, Olivier Spanjaard, Paul Weng. Committee Selection with a Weight Constraint Based on a Pairwise Dominance Relation. 2nd International Conference on Algorithmic Decision Theory (ADT'11), Oct 2011, Piscataway, NJ, United States. Springer, 2nd International Conference on Algorithmic Decision Theory (ADT'11), 6992, pp.28-41, Lecture Notes in Artificial Intelligence. 〈10.1007/978-3-642-24873-3_3〉. 〈hal-01285704〉

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