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A variant of the classical knapsack problem is considered in which each itemis associated with an integer weight and a qualitative level. We define adominance relation over the feasible subsets of the given item set and showthat this relation defines a preorder. We propose a dynamic programmingalgorithm to compute the entire set of non-dominated rank cardinality vectorsand we state two greedy algorithms, which efficiently compute a singleefficient solution.

The {0,1}-knapsack problem with qualitative levels