Connectedness and Local Search for Bicriteria Knapsack Problems

  • Arnaud Liefooghe
  • Luís Paquete
  • Marco Simões
  • José R. Figueira
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6622)


This article reports an experimental study on a given structural property of connectedness of optimal solutions for two variants of the bicriteria knapsack problem. A local search algorithm that explores this property is then proposed and its performance is compared against exact algorithms in terms of running time and number of optimal solutions found. The experimental results indicate that this simple local search algorithm is able to find a representative set of optimal solutions in most of the cases, and in much less time than exact approaches.


Local Search Feasible Solution Knapsack Problem Neighborhood Structure Local Search Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beier, R., Vöcking, B.: Probabilistic analysis of knapsack core algorithms. In: Proc. of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pp. 468–477 (2004)Google Scholar
  2. 2.
    Ehrgott, M.: Multicriteria optimization. Lecture Notes in Economics and Mathematical Systems, vol. 491. Springer, Heidelberg (2000)zbMATHGoogle Scholar
  3. 3.
    Ehrgott, M., Klamroth, K.: Connectedness of efficient solutions in multiple criteria combinatorial optimization. European Journal of Operational Research 97(1), 159–166 (1997)CrossRefzbMATHGoogle Scholar
  4. 4.
    Goldberg, D.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Boston (1989)zbMATHGoogle Scholar
  5. 5.
    Gorski, J., Klamroth, K., Ruzika, S.: Connectedness of efficient solutions in multiple objective combinatorial optimization. Tech. Rep. 102/2006, University of Kaiserslautern, Department of Mathematics (2006)Google Scholar
  6. 6.
    Gorski, J., Paquete, L.: On a particular case of the multi-criteria unconstrained optimization problem. Electronic Notes on Discrete Mathematics 36, 135–142 (2010)CrossRefzbMATHGoogle Scholar
  7. 7.
    Kung, H., Luccio, F., Preparata, F.: On finding the maxima of a set of vectors. Journal of ACM 22(4), 469–476 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Nemhauser, G., Ullman, Z.: Discrete dynamic programming and capital allocation. Management Science 15(9), 494–505 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Paquete, L., Schiavinotto, T., Stützle, T.: On local optima in multiobjective combinatorial optimization problems. Annals of Operations Research 156(1), 83–97 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Paquete, L., Stützle, T.: Clusters of non-dominated solutions in multiobjective combinatorial optimization: An experimental analysis. In: Multiobjective Programming and Goal Programming. Lecture Notes in Economics and Mathematical Systems, vol. 618, pp. 69–77. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    da Silva, C.G., Clímaco, J., Figueira, J.R.: Geometrical configuration of the Pareto fronteir of the bi-criteria 0-1-knapsack problem. Tech. Rep. 16/2004, INESC, Coimbra, Portugal (2004)Google Scholar
  12. 12.
    Verel, S., Liefooghe, A., Jourdan, L., Dhaenens, C.: Analyzing the effect of objective correlation on the efficient set of MNK-landscapes. In: Proc. of the 5th Conference on Learning and Intelligent OptimizatioN (LION 5). LNCS. Springer, Heidelberg (2011) (to appear) Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Arnaud Liefooghe
    • 1
  • Luís Paquete
    • 2
  • Marco Simões
    • 2
  • José R. Figueira
    • 3
  1. 1.LIFL – CNRS – INRIA Lille-Nord EuropeUniversité Lille 1France
  2. 2.CISUC, Department of Informatics EngineeringUniversity of CoimbraPortugal
  3. 3.INPL, École des Mines de Nancy, Laboratoire LORIAFrance

Personalised recommendations