The binary knapsack problem with qualitative levels

Luca E. Schäfer, Tobias Dietz, Maria Barbati, José Rui Figueira, Salvatore Greco, Stefan Ruzika

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    A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this relation defines a preorder. We propose a dynamic programming algorithm to compute the entire set of non-dominated rank cardinality vectors and we state two greedy algorithms, which efficiently compute a single efficient solution.
    Original languageEnglish
    Article number0
    Pages (from-to)508-514
    Number of pages7
    JournalEuropean Journal of Operational Research
    Issue number2
    Early online date25 Jul 2020
    Publication statusPublished - 1 Mar 2021


    • Computing science
    • Knapsack problem
    • Non-dominance
    • Qualitative levels
    • Dynamic programming


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