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A hybrid metaheuristic for the Knapsack Problem with Forfeits

  • Optimization
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Abstract

In this paper, we present a novel hybrid metaheuristic for the Knapsack Problem with Forfeits (KPF). KPF is a recently introduced generalization of the Knapsack Problem. In this variant, a penalty cost incurs whenever both items composing a so-called forfeit pair belong to the solution. Our proposed algorithm, called GA–CG Forfeits, combines the strengths of the Genetic and Carousel Greedy paradigms. In this work, we define the algorithm and compare it with two previously proposed heuristics on a set of benchmark instances. In these tests, GA–CG Forfeits provided significantly better solutions than the other two algorithms on all instances.

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Data availability

The datasets generated during the current study are available from the corresponding author (Andrea Raiconi) on reasonable request.

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Acknowledgements

C. D’Ambrosio has been supported by the Italian Ministry of University and Research (MUR) and European Union with the program PON “Ricerca e Innovazione” 2014–2020, Azione 1.2 “Mobilità dei Ricercatori” (AIM “Attraction and International Mobility”-LINEA 1), POC R&I 2014–2020.

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Authors and Affiliations

  1. University of Molise, Campobasso, 86100, Italy

    Giovanni Capobianco

  2. University of Salerno, Fisciano, 84084, Italy

    Ciriaco D’Ambrosio, Andrea Raiconi & Gaetano Vitale

  3. IRCCS Neuromed, Pozzilli, 86077, Italy

    Luigi Pavone & Fabio Sebastiano

Authors
  1. Giovanni Capobianco
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  2. Ciriaco D’Ambrosio
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  3. Luigi Pavone
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  4. Andrea Raiconi
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  5. Gaetano Vitale
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  6. Fabio Sebastiano
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Contributions

Giovanni Capobianco, Ciriaco D’Ambrosio, Luigi Pavone, Andrea Raiconi, Gaetano Vitale, and Fabio Sebastiano contributed to conceptualization, methodology, software, and writing—original draft preparation and revision.

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Correspondence to Andrea Raiconi.

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Capobianco, G., D’Ambrosio, C., Pavone, L. et al. A hybrid metaheuristic for the Knapsack Problem with Forfeits. Soft Comput 26, 749–762 (2022). https://doi.org/10.1007/s00500-021-06331-x

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