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Variable Neighborhood Search with Dynamic Exploration for the Set Union Knapsack Problem

In: Combinatorial Optimization and Applications

Author

Listed:
  • Igor Machado Coelho

    (Universidade do Estado do Rio de Janeiro
    Instituto de Computação, Universidade Federal Fluminense)

  • Saïd Hanafi

    (Université Polytechnique de Hauts de France, CNRS UMR 8201)

  • Raca Todosijevic

    (Université Polytechnique de Hauts de France, CNRS UMR 8201)

  • Mustapha Ratli

    (Université Polytechnique de Hauts de France, CNRS UMR 8201)

  • Bernard Gendron

    (CIRRELT, Université de Montréal)

Abstract

In the set-union knapsack problem (SUKP), we are given a set of elements, each with a positive weight, and a set of items, each with a positive profit and a corresponding set of associated elements. An item is included in the knapsack only if all its associated elements are included. The SUKP is to select the items to be included in the knapsack such that the total profit of the selected items is maximized and the capacity of the knapsack is not exceeded. We propose a variable neighborhood search to solve the SUKP and show, on a set of benchmark instances from the literature, that this method is competitive with the state-of-the-art heuristics for the problem. In addition, we focus on simplicity of the proposed algorithm while providing competitive results, thus showing that less may yield more.

Suggested Citation

  • Igor Machado Coelho & Saïd Hanafi & Raca Todosijevic & Mustapha Ratli & Bernard Gendron, 2024. "Variable Neighborhood Search with Dynamic Exploration for the Set Union Knapsack Problem," International Series in Operations Research & Management Science, in: Teodor Gabriel Crainic & Michel Gendreau & Antonio Frangioni (ed.), Combinatorial Optimization and Applications, pages 17-35, Springer.
    • Handle: RePEc:spr:isochp:978-3-031-57603-4_2
    DOI: 10.1007/978-3-031-57603-4_2
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