Skip to main content

A Hybridised GA for the Steiner Minimal Tree Problem

  • Conference paper
  • First Online:
Artificial Intelligence and Cognitive Science (AICS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2464))

Included in the following conference series:

  • 562 Accesses

Abstract

In this paper the application of a Genetic Algorithm (GA) (including operators such as mutation, slicing, gluing and crossover) to solve the Steiner Tree Problem is described. Extra heuristics have also been considered in order to improve the quality of the results as well as the computational time. The results obtained with our algorithm fall close to the optimal solution, and compare positively with those obtained by other authors [7].

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. S.L. Martins, C.C. Ribeiro, and M.C. Souza: A parallel GRASP for the Steiner problem in graphs. In A. Ferreira and J. Rolim, editors, Proceedings of IRREGULAR’ 98-5th International Symposium on Solving Irregularly Structured Problems in Parallel, Lecture Notes in Computer Science, Springer-Verlag, 1457 (1998) pp. 285–297.

    Chapter  Google Scholar 

  2. E.N. Gilbert, H.O. Pollack: Steiner Minimal Trees. SIAM J.Appl.Math. Vol 16, No.1, 1986, pp.1–29.

    Article  Google Scholar 

  3. B.A. Julstrom: A Genetic Algorithm for Rectilinear Steiner Problem. Fhith International Conference on Genetic Algorithms, 1993, pages 474–480.

    Google Scholar 

  4. J. Hesser, R. Manner and O. Stucky: Optimization of Steiner Trees Using Genetic Algorithms. Thrid International Conference on Genetic Algorithms, George Mason University, 1989, pages 231–237.

    Google Scholar 

  5. F.C. Harris Jr: Parallel Computation of Steiner Minimal Trees. PhD thesis, Clemson, University Clemson, SC 29634, May 1994.

    Google Scholar 

  6. F.C. Harris Jr: A stochastic optimization algorithm for Steiner minimal trees. Congr.Number., 105:54–64, 1994

    Google Scholar 

  7. J. Jones, F.C. Harris Jr: A Genetic Algorithm for the Steiner Minimal Tree Problem, Proc. ISCA’s Int. Conf. on Intelligent Systems (IS’ 96) Reno, NV, June 19–21, 1996.

    Google Scholar 

  8. J.L. Fernández-Villacañas, S. Amin: Simulated Jumping in Genetic Algorithms for a set of test functions. Proceedings of the IASTED International Conference on Intelligent Information Systems, Grand Bahama Island, December, 1997.

    Google Scholar 

  9. M. Brazil, D.H. Lee, J.H. Rubinstein, D.A. Thomas, J.F. Weng and N.C. Wormald: Network Optimisation of Underground Mine Design. AusIMM Proceedings Volume 305, No 1, 2000.

    Google Scholar 

  10. H. Esbensen: Computing Near-Optimal Solutions to the Steiner Problem in a Graph Using a Genetic Algorithm. Networks 26 (1995), 173–185

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Panadero, R., Fernández-Villacañas, J.L. (2002). A Hybridised GA for the Steiner Minimal Tree Problem. In: O’Neill, M., Sutcliffe, R.F.E., Ryan, C., Eaton, M., Griffith, N.J.L. (eds) Artificial Intelligence and Cognitive Science. AICS 2002. Lecture Notes in Computer Science(), vol 2464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45750-X_32

Download citation

  • DOI: https://doi.org/10.1007/3-540-45750-X_32

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44184-7

  • Online ISBN: 978-3-540-45750-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics