An Artificial Bee Colony Algorithm for the 0–1 Multidimensional Knapsack Problem

  • Shyam Sundar
  • Alok Singh
  • André Rossi
Part of the Communications in Computer and Information Science book series (CCIS, volume 94)

Abstract

In this paper, we present an artificial bee colony (ABC) algorithm for the 0-1 Multidimensional Knapsack Problem (MKP_01). The objective of MKP_01 is to find a subset of a given set of n objects in such a way that the total profit of the objects included in the subset is maximized, while a set of knapsack constraints remains satisfied. The ABC algorithm is a new metaheuristic technique based on the intelligent foraging behavior of honey bee swarms. Heuristic-based repair operators and local search are incorporated into our ABC algorithm. Computational results demonstrate that our ABC algorithm not only produces better results but converges very rapidly in comparison with other swarm-based approaches.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chu, P.C., Beasley, J.E.: A Genetic Algorithm for the Multidimentional Knapsack Problem. Journal of Heuristic 4, 63–86 (1998)MATHCrossRefGoogle Scholar
  2. 2.
    Kong, M., Tian, P., Kao, Y.: A New Ant Colony Optimization Algorithm for the Multidimensional Knapsack Problem. Computers and Operations Research 35, 2672–2683 (2008)MATHMathSciNetGoogle Scholar
  3. 3.
    Alaya, I., Solnon, C., Ghéira, K.: Ant Algorithm for the Multi-Dimensional Knapsack Problem. In: International Conference on Bio-Inspired Optimization Methods and Their Applications (BIOMA 2004), pp. 63–72 (2004)Google Scholar
  4. 4.
    Fidanova, S.: Evolutionary Algorithm for Multidimensional Knapsack Problem. In: PPSN VII Workshop (2002)Google Scholar
  5. 5.
    Leguizamon, G., Michalewicz, Z.: A New Version of Ant System for Subset Problem. In: Congress on Evolutionary Computation, pp. 1459–1464 (1999)Google Scholar
  6. 6.
    Karaboga, D.: An Idea Based on Honey Bee Swarm for Numerical Optimization. Technical Report TR06, Computer Engineering Department, Erciyes University, Turkey (2005)Google Scholar
  7. 7.
    Basturk, B., Karaboga, D.: An Artificial Bee Colony (ABC) Algorithm for Numeric Function Optimization. In: Proceedings of the IEEE Swarm Intelligence Symposium, Indianapolis, USA, May 12-14 (2006)Google Scholar
  8. 8.
    Basturk, B., Karaboga, D.: A Powerful and Efficient Algorithm for Numeric Function Optimization: Artificial Bee Colony (ABC) algorithm. Journal of Global Optimization 39, 459–471 (2007)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Basturk, B., Karaboga, D.: Artificial Bee Colony (ABC) Optimization Algorithm for Solving Constrained Optimization Problems. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds.) IFSA 2007. LNCS (LNAI), vol. 4529, pp. 789–798. Springer, Heidelberg (2007)Google Scholar
  10. 10.
    Karaboga, D., Basturk, B.: On the Performance of Artificial Bee Colony (ABC) Algorithm. Applied Soft Computing 8, 687–697 (2008)CrossRefGoogle Scholar
  11. 11.
    Singh, A.: An Artificial Bee Colony (ABC) Algorithm for the Leaf-Constrained Minimum Spanning Tree Problem. Applied Soft Computing 9, 625–631 (2009)CrossRefGoogle Scholar
  12. 12.
    Pirkul, H.: A Heuristic Solution Procedure for the Multiconstraint Zero–One Knapsack Problem. Naval Research Logistics 34, 61–72 (1987)CrossRefGoogle Scholar
  13. 13.
    Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley, Chichester (1990)MATHGoogle Scholar
  14. 14.
    Singh, A., Gupta, A.K.: Two Heuristics for the One-Dimensional Bin-Packing Problem. OR Spectrum 29, 765–781 (2007)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Shyam Sundar
    • 1
  • Alok Singh
    • 1
  • André Rossi
    • 2
  1. 1.Department of Computer and Information SciencesUniversity of HyderabadHyderabadIndia
  2. 2.Lab-STICC, Université de Bretagne-SudLorient CedexFrance

Personalised recommendations