Skip to main content

Artificial Immune System to Find a Set of k-Spanning Trees with Low Costs and Distinct Topologies

  • Conference paper
Artificial Immune Systems (ICARIS 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4628))

Included in the following conference series:

Abstract

This work proposes an Artificial Immune System to find a set of k spanning trees with low costs and distinct topologies. The attainment of this set of solutions is necessary when the problem has restrictions or when the interest is to present good alternative solutions for posterior decision making. Solving this problem means to explore an enormous space of solutions that grows as the number of graph nodes increases; it becomes impractible using exact or comparative methods. However, it is known that bio-inspired algorithms have a high capacity of exploration and exploitation of the search space. Moreover, inherent characteristics of AIS become the search mechanism more efficient allowing the resolution of this problem in a feasible computational time.

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 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. Ahuja, R.K., Magnati, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms and Applications, 1st edn. Prentice-Hall, United States (1993)

    Google Scholar 

  2. Ali, M., Ramamurthy, B., Deogun, J.S.: Routing and Wavelenght Assignment with Power Considerations in Optical Networks. Computer Networks 32, 539–555 (2000)

    Article  Google Scholar 

  3. Almeida, T.A., Yamakami, A.: Evolutionary Computation Applied to Solve the Minimum Spanning Tree Problem with Fuzzy Parameters. Master Thesis, School of Electrical and Computing Engineering, State University of Campinas (in Portuguese) (2006)

    Google Scholar 

  4. Coello Coello, C.A., Cortés, N.C.: Solving Multiobjective Optimization Problems Using an Artificial Immune System. Genetic Programming and Evolvable Machines 6, 163–190 (2005)

    Article  Google Scholar 

  5. Dasgupta, D.: Artificial Immune Systems and Their Applications, 1st edn. Springer, Nova York (1998)

    Google Scholar 

  6. De Castro, L.N., Von Zuben, F.J.: Immune Engineering: Development and Application of Computational Tools Inspired in Artificial Immune Systems. PhD Thesis, State University of Campinas, School of Electrical and Computing Engineering (in Portuguese) (2001)

    Google Scholar 

  7. Keko, H., Skok, M., Skrlec, D.: Artificial Immune Systems in Solving Routing Problems. Computer as Tool. In: EUROCON 2003. Computer as Tool, The IEEE Region, vol. 8(1), pp. 62–66 (2003)

    Google Scholar 

  8. Lederberg, J.: Ontogeny of the Clonal Selection Theory of Antibody Formation. Annals of the New York Ac. of Sc. 546, 175–182 (1988)

    Article  Google Scholar 

  9. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, 3rd edn. Springer, Heidelberg (1996)

    MATH  Google Scholar 

  10. Minty, G.J.: A Simple Algorithm for Listing All the Trees of a Graph. IEEE Transactions on Circuit Theory CT-12, 120 (1965)

    Google Scholar 

  11. Murty, K.G.: An Algorithm for Ranking All the Assignments in Order of Increasing Cost. Operations Research 16, 682–687 (1986)

    Article  Google Scholar 

  12. Okada, S.: Interactions Among Paths in Fuzzy Shortest Path Problems. In: Proceedings of the 9th International Fuzzy Systems Associations World Congress, pp. 41–46 (2001)

    Google Scholar 

  13. Raidl, R.G., Julstrom, B.A.: Edge-Sets: An Effective Evolutionary Coding of Spanning Trees. Research Report, Vienna University of Technology, Institute of Computer Graphics and Algorithms (2001)

    Google Scholar 

  14. Sörensen, K., Janssens, G.K.: An Algorithm to Generate All Spanning Trees of a Graph in Order of Increasing Cost. Operacional Research 25, 219–229 (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Leandro Nunes de Castro Fernando José Von Zuben Helder Knidel

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Berbert, P.C., Freitas Filho, L.J.R., Almeida, T.A., Carvalho, M.B., Yamakami, A. (2007). Artificial Immune System to Find a Set of k-Spanning Trees with Low Costs and Distinct Topologies. In: de Castro, L.N., Von Zuben, F.J., Knidel, H. (eds) Artificial Immune Systems. ICARIS 2007. Lecture Notes in Computer Science, vol 4628. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73922-7_34

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73922-7_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73921-0

  • Online ISBN: 978-3-540-73922-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics