Multiobjective 0/1 Knapsack Problem using Adaptive ε-Dominance

  • Crina Groşan
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 34)


The multiobjective 0/1 knapsack problem is a generalization of the well known 0/1 knapsack problem in which multiple knapsacks are considered. A new evolutionary algorithm for solving multiobjective 0/1 knapsack problem is proposed in this paper. This algorithm used a ε-dominance relation for direct comparison of two solutions. This algorithm try to improve another algorithm which also uses an ε domination relation between solutions. In this new algorithm the value of ε is adaptive (can be changed) depending on the solutions quality improvement. Several numerical experiments are performed using the best recent algorithms proposed for this problem. Experimental results clearly show that the proposed algorithm outperforms the existing evolutionary approaches for this problem.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Balas, E., Zemel, E. An algorithms for large zero-one knapsack problems, in Operations Research, Vol 28, pp. 1130–1154, 1980.MATHMathSciNetGoogle Scholar
  2. 2.
    Chvatal, V. Hard knapsack problems, Operations Research, Vol 28, pp. 1402–1411, 1980.MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Corne, D.W., Knowles, J.D. The Pareto-Envelope based Selection Algorithm for Multiobjective Optimization, in Proceedings of the Sixth International Conference on Parallel Problem Solving from Nature, Springer-Verlag, Berlin, 2000, pp. 839–848.Google Scholar
  4. 4.
    Deb, K., Agrawal, S., Pratap, A., Meyarivan, T. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA II, in M. S. et al. Eds, Parallel Problem Solving From Nature – PPSN VI, Springer-Verlag, Berlin, 2000, pp. 849–858.Google Scholar
  5. 5.
    Grosan, C. Improving the performance of evolutionary algorithms for the multiobjective 0/1 knapsack problem using ε -dominance, In Proceedings of Congress on Evolutionary Computation (CEC), Portland, 2004.Google Scholar
  6. 6.
    Ingargiola, G. P., Korsh, J. F. A reduction algorithm for zero-one single knapsack problems, in Management Science Vol. 20, pp. 460–463, 1975.Google Scholar
  7. 7.
    Jaszkiewicz, A. On the performance of Multiple Objective Local Search on the 0/1 Knapsack problem – A Comparative Experiment, IEEE Transaction on Evolutionary Computation, Vol 6, pp. 402–412, 2002.CrossRefGoogle Scholar
  8. 8.
    Ko, I. Using AI techniques and learning to solve multi-level knapsack problems. PhD thesis, University of Colorado at Boulder, Boulder, CO, 1993.Google Scholar
  9. 9.
    Laumans, M., Thiele, L., Deb, K., and Zitzler, E. Combining convergence and diversity in evolutionary multi-objective optimization. Evolutionary Computation 10(3), 2002.Google Scholar
  10. 10.
    Loots, W. Smith, T.H.C. A parallel algorithm for the zero-one knapsack problem, International Journal Parallel Program, Vol. 21, pp. 313–348, 1992.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Martello, S., Toth, P. Knapsack problems: Algorithms and computer implementation, Willey and Sons, Chichester, 1990.Google Scholar
  12. 12.
    Martello, S., Toth, P. An upper bound for the zero-one knapsack problem and a branch and bound algorithm. European Journal of Operational Research, Vol. 1, pp. 169–175, 1977.MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Penn, M., Hasson, D., Avriel, M. Solving the 0/1 proportional Knapsack problem by sampling, J. Optim. Theory Appl pp. 261–272, 1994.Google Scholar
  14. 14.
    Sahni, S. Approximate algorithms for the 0/1 knapsack problem, Journal of ACM, Vol. 22, pp. 115–124, 1975.MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Vasquez, M., Hao, J.K. A hybrid approach for the 0/1 multidimensional knapsack problem, in Proceedings of the 13th International Joint Conference on Artificial Intelligence pp. 328–333, 2001.Google Scholar
  16. 16.
    Zitzler, E., Thiele, L. Multiobjective optimization using evolutionary algorithms-a comparative case study. In Fifth International Conference on Parallel Problem Solving from Nature, A. E. Eiben, T. Back, M. Schoenauer and H. P. Schwefel Eds., Springer, Berlin, Germany, 1998, pp. 292–301.Google Scholar
  17. 17.
    Zitzler, E., Thiele, L. Multiobjective Evolutionary Algorithms: A comparative case study and the Strength Pareto Approach, IEEE Transaction on Evolutionary Computation, Vol 3, pp. 257–271, 1999.CrossRefGoogle Scholar
  18. 18.
    Zitzler, E. Evolutionary algorithms for multiobjective optimization: Methods and Applications, Ph. D. thesis, Swiss Federal Institute of Technology (ETH) Zurich, Switzerland.Google Scholar
  19. 19.
    Zitzler, E., Laumanns, M., Thiele, L. SPEA 2: Improving the Strength Pareto Evolutionary Algorithm, TIK Report 103, Computer Engineering and Networks Laboratory (TIK), Department of Electrical Engineering Swiss federal Institute of Technology (ETH) Zurich, 2001.Google Scholar
  20. 20. zitzler/testdata.htmlGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Crina Groşan
    • 1
  1. 1.Department of Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania

Personalised recommendations