A matheuristic for the 0–1 generalized quadratic multiple knapsack problem

  • Yassine AdouaniEmail author
  • Bassem Jarboui
  • Malek Masmoudi
Original Paper


In this study, we address the 0–1 generalized quadratic multiple Knapsack problem. We use a linearization technique of the existing mathematical model and we propose a new matheuristic that we called Matheuristic Variable Neighborhood Search combining variable neighborhood search with integer programing to solve the large sized instances. The matheuristic considers a local search technique with an adaptive perturbation mechanism to assign the classes to different knapsacks, and then once the assignment is identified, applies the IP to select the items to allocate to each knapsack. Experimental results obtained on a wide set of benchmark instances clearly show the competitiveness of the proposed approach compared to the best state-of-the-art solving techniques.


Generalized quadratic knapsack problem Linearization Matheuristic Variable neighborhood search Integer programing 


Supplementary material

11590_2019_1503_MOESM1_ESM.pdf (140 kb)
Supplementary material 1 (pdf 140 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yassine Adouani
    • 1
    Email author
  • Bassem Jarboui
    • 2
  • Malek Masmoudi
    • 3
  1. 1.Laboratory of Modeling and Optimization for Decisional, Industrial and Logistic Systems (MODILS), Faculty of Economics and Management Sciences of SfaxUniversity of SfaxSfaxTunisia
  2. 2.Higher Colleges of TechnologyAbu DhabiUnited Arab Emirates
  3. 3.Faculty of Sciences and TechniquesUniversity of Lyon, University Jean Monnet Saint-EtienneSaint-EtienneFrance

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