Skip to main content
SpringerLink
Log in

Modelling ACO: Composed Permutation Problems

  • Conference paper
  • First Online:
Ant Algorithms (ANTS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2463))

Included in the following conference series:

Abstract

The behaviour of Ant Colony Optimization (ACO) algorithms is studied on optimization problems that are composed of different types of subproblems. Numerically exact results are derived using a deterministic model for ACO that is based on the average expected behaviour of the artificial ants. These computations are supplemented by test runs with an ACO algorithm on the same problem instances. It is shown that different scaling of the objective function on isomorphic subproblems has a strong influence on the optimization behaviour of ACO. Moreover, it is shown that ACOs behaviour on a subproblem depends heavily on the type of the other subproblems. This is true even when the subproblems are independent in the sense that the value of the objective function is the sum of the qualities of the solutions of the subproblems. We propose two methods for handling scaling problems (pheromone update masking and rescaling of the objective function) that can improve ACOs behaviour. Consequences of our findings for using ACO on real-world problems are pointed out.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. (1992). Optimization, Learning and Natural Algorithms (in Italian). PhD thesis, Dipartimento di Elettronica, Politecnico di Milano, Italy.

    Google Scholar 

  2. Dorigo, M., and Di Caro, G. (1999). The ant colony optimization meta-heuristic. In Corne, D., Dorigo, M., and Glover, F., editors, New Ideas in Optimization, 11–32, McGraw-Hill, London.

    Google Scholar 

  3. Dorigo, M., Maniezzo, V., and Colorni, A. (1996). The Ant System: Optimization by a Colony of Cooperating Agents. IEEE Trans. Systems, Man, and Cybernetics-Part B, 26:29–41.

    Article  Google Scholar 

  4. Gutjahr, W. (2000). A graph-based Ant System and its convergence, Future Generation Computer Systems, 16:873–888.

    Article  Google Scholar 

  5. Gutjahr, W. (2002). ACO algorithms with guaranteed convergence to the optimal solution. Information Processing Letters, 82:145–153.

    Article  MATH  MathSciNet  Google Scholar 

  6. Merkle, D., and Middendorf, M. (2000). An Ant Algorithm with a new Pheromone Evaluation Rule for Total Tardiness Problems. In Cagnoni, S., et al. (Eds.) Real-World Applications of Evolutionary Computing, LNCS 1803, 287–296, Springer.

    Chapter  Google Scholar 

  7. Merkle, D., and Middendorf, M. (2001). A New Approach to Solve Permutation Scheduling Problems with Ant Colony Optimization. In Boers, E. J. W., et al. (Eds.) Applications of Evolutionary Computing, LNCS 2037, 213–222, Springer.

    Chapter  Google Scholar 

  8. Merkle, D., and Middendorf, M. (2001). On the Behaviour of Ant Algorithms: Studies on Simple Problems. In Proceedings of the 4th Metaheuristics International Conference (MIC’2001), Porto, 573–577.

    Google Scholar 

  9. Merkle, D., and Middendorf, M. (2001). Modelling the Dynamics of Ant Colony Optimization. TR 412, Institute AIFB, University of Karlsruhe. To appear in Evolutionary Computation.

    Google Scholar 

  10. Merkle, D., and Middendorf, M. (2002). Studies on the Dynamics of Ant Colony Optimization Algorithms. To appear in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2002), New York, 2002.

    Google Scholar 

  11. Stützle, T. and Dorigo, M. (2000). A short convergence proof for a class of ACO algorithms. TR 2000-35, IRIDIA, Universitè Libre de Bruxelles, Belgium.

    Google Scholar 

  12. Stützle, T. and Dorigo, M. (2001). An Experimental Study of the Simple Ant Colony Optimization Algorithm. In Proc. 2001 WSES Int. Conference on Evolutionary Computalution Computation (EC’01), WSES-Press International, 2001.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Applied Computer Science and Formal Description Methods, University of Karlsruhe, Germany

    Daniel Merkle

  2. Computer Science Group, Catholic University of Eichstätt-Ingolstadt, Germany

    Martin Middendorf

Authors
  1. Daniel Merkle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Middendorf
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IRIDIA, Université de Bruxelles, CP 194/6 Avenue Franklin D. Roosevelt 50, 1050, Brussels, Belgium

    Marco Dorigo , Gianni Di Caro  & Michael Sampels ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Merkle, D., Middendorf, M. (2002). Modelling ACO: Composed Permutation Problems. In: Dorigo, M., Di Caro, G., Sampels, M. (eds) Ant Algorithms. ANTS 2002. Lecture Notes in Computer Science, vol 2463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45724-0_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-45724-0_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44146-5

  • Online ISBN: 978-3-540-45724-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation