A Cooperative Learning Approach for the Quadratic Knapsack Problem

  • Eduardo Lalla-Ruiz
  • Eduardo Segredo
  • Stefan Voß
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11353)


The Quadratic Knapsack Problem (QKP) is a well-known optimization problem aimed to maximize a quadratic objective function subject to linear capacity constraints. It has several applications in different fields such as telecommunications, graph theory, logistics, hydrology and data allocation, among others. In this paper, we propose the application of a novel population-based metaheuristic referred to as Multi-leader Migrating Birds Optimization (MMBO), which exploits the concepts of cooperation and communication along the search leading to a collective learning, to solve a wide range of well-known QKP instances.


  1. 1.
    Billionnet, A., Soutif, É.: An exact method based on lagrangian decomposition for the 0–1 quadratic knapsack problem. Eur. J. Oper. Res. 157(3), 565–575 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Caprara, A., Pisinger, D., Toth, P.: Exact solution of the quadratic knapsack problem. INFORMS J. Comput. 11(2), 125–137 (1999)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cunha, J.O., Simonetti, L., Lucena, A.: Lagrangian heuristics for the quadratic knapsack problem. Comput. Optim. Appl. 63, 97–120 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Fomeni, F., Letchford, A.: A dynamic programming heuristic for the quadratic knapsack problem. INFORMS J. Comput. 26(1), 173–182 (2013)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Gallo, G., Hammer, P.L., Simeone, B.: Quadratic knapsack problems. In: Padberg, M.W. (ed.) Combinatorial Optimization, pp. 132–149. Springer, Berlin (1980). Scholar
  6. 6.
    Lalla-Ruiz, E., de Armas, J., Expósito-Izquierdo, C., Melián-Batista, B., Moreno-Vega, J.M.: Multi-leader migrating birds optimisation: a novel nature-inspired metaheuristic for combinatorial problems. Int. J. Bio-Inspired Comput. 10, 89–98 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Eduardo Lalla-Ruiz
    • 1
    • 4
  • Eduardo Segredo
    • 2
    • 3
  • Stefan Voß
    • 1
  1. 1.Institute of Information SystemsUniversity of HamburgHamburgGermany
  2. 2.School of ComputingEdinburgh Napier UniversityEdinburghUK
  3. 3.Dpto. de Ingeniería Informática y de SistemasUniversidad de La LagunaSan Cristóbal de La LagunaSpain
  4. 4.Department of Industrial Engineering and Business Information SystemsUniversity of TwenteEnschedeThe Netherlands

Personalised recommendations