Skip to main content

Ant Colony Optimization for Multiple Knapsack Problem and Model Bias

  • Conference paper
Numerical Analysis and Its Applications (NAA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3401))

Included in the following conference series:

Abstract

The Ant Colony Optimization (ACO) algorithms are being applied successfully to a wide range of problems. ACO algorithms could be good alternatives to existing algorithms for hard combinatorial optimization problems (COPs). In this paper we investigate the influence of model bias in model-based search as ACO. We present the effect of two different pheromone models for ACO algorithm to tackle the Multiple Knapsack Problem (MKP). The MKP is a subset problem and can be seen as a general model for any kind of binary problems with positive coefficients. The results show the importance of the pheromone model to quality of the solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dorigo, M., Di Caro, G.: The Ant Colony Optimization metaheuristic. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Idea in Optimization, pp. 11–32. McGraw-Hill, New York (1999)

    Google Scholar 

  2. Dorigo, M., Di Caro, G., Gambardella, L.M.: Ant Algorithms for Distributed Discrete Optimization. J. of Artificial Life 5, 137–172 (1999)

    Article  Google Scholar 

  3. Ferreira, C.E., Martin, A., Weismantel, R.: Solving Multiple Knapsack Problems by Cutting Planes. SIAM Journal on Optimization 6(3), 858–877 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dorigo, M., Gambardella, L.M.: Ant Colony System: A cooperative Learning Approach to the Traveling Salesman Problem. IEEE Transaction on Evolutionary Computation 1, 53–66 (1999)

    Article  Google Scholar 

  5. Gambardella, M.L., Taillard, E.D., Dorigo, M.: Ant Colonies for the QAP. J. of Oper. Res. Soc. 50, 167–176 (1999)

    MATH  Google Scholar 

  6. Kochenberger, G., McCarl, G., Wymann, F.: A Heuristic for General Integer Programming. J. of Decision Sciences 5, 34–44 (1974)

    Google Scholar 

  7. Leguizamon, G., Michalevich, Z.: A New Version of Ant System for Subset Problems. In: Proceedings of Int. Conf. on Evolutionary Computations, Washington (1999)

    Google Scholar 

  8. Marchetti-Spaccamela, A., Vercellis, C.: Stochastic on-line Knapsack Problems. J. of Mathematical Programming 68(1), 73–104 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Osman, I.H., Kelley, J.P.: Metaheuristic: An Overview. In: Osman, I.H., Kelley, J.P. (eds.) Metaheuristic: Theory and Applications. Kluwer Academic Publishers, Dordrecht (1996)

    Google Scholar 

  10. Schaffer, A.A., Yannakakis, M.: Simple Local Search Problems that are Hard to Solve. Society for Industrial Applied Mathematics Journal on Computing 20, 56–87 (1991)

    MathSciNet  Google Scholar 

  11. Wolpert, D., Macready, W.: No Free Lunch Theorems for Optimization. IEEE Transactions on Evolutionary Computation, 67–82 (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fidanova, S. (2005). Ant Colony Optimization for Multiple Knapsack Problem and Model Bias. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-31852-1_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24937-5

  • Online ISBN: 978-3-540-31852-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics