Skip to main content
SpringerLink
Log in

Studying the application of ant colony optimization and river formation dynamics to the steiner tree problem

  • Special Issue
  • Published:
Evolutionary Intelligence Aims and scope Submit manuscript

Abstract

River formation dynamics (RFD) (Rabanal et al. in Using river formation dynamics to design heuristic algorithms. In: Unconventional computation, UC’07, LNCS 4618. Springer, pp 163–177, 2007; Rabanal et al. in Applying river formation dynamics to solve NP-complete problems. In: Chiong R (ed) Nature-inspired algorithms for optimisation, volume 193 of Studies in Computational Intelligence. Springer, pp 333–368, 2009) is a heuristic optimization algorithm based on copying how water forms rivers by eroding the ground and depositing sediments. We apply this method to solve the Steiner tree problem (STP), a well-known NP-hard problem having applications to areas like telecommunications routing or VLSI design among many others. We show that the gradient orientation of RFD makes it especially suitable for solving this problem, and we report the results of several experiments where RFD, as well as an implementation of Ant Colony Optimization (ACO) (Dorigo in ant colony optimization. MIT Press, New York, 2004), are applied to some benchmark graphs from the SteinLib Testdata Library (Koch in Steinlib testdata library. Technical report, Konrad-Zuse-Zentrum für Informationstechnik Berlin, 2009). We also study the capability of RFD and ACO to deal with a scenario where the graph is modified after a solution is found, and next a solution for the new graph has to be found - either by running the algorithm from scratch or by adapting the structures previously formed by the algorithms to construct their previous solution.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Notes

  1. Usually, this implies either to repeat a node or to kill the ant. In both cases, the last movements of the ant were useless.

References

  1. Bern M, Plassmann P (1989) The Steiner tree problem with edge lengths 1 and 2. Inform Proc Lett 32:171–176

    Article  MATH  MathSciNet  Google Scholar 

  2. Caldwell A, Kahng A, Mantik S, Markov I, Zelikovsky A (1998) On wirelength estimations for row-based placement. In: International symposium on physical design. ACM Press, New York, pp 4–11

  3. Chiong R (ed) (2009) Nature-inspired algorithms for optimisation. Volume 193 of studies in computational intelligence. Springer, Berlin

    Google Scholar 

  4. Clementi AEF (1999) Improved non-approximability results for minimum vertex cover with density constraints. Theor Comput Sci 225:113–128

    Article  MATH  MathSciNet  Google Scholar 

  5. Das S, Gosavi SV, Hsu WH, Vaze SA (2002) An ant colony approach for the steiner tree problem. In: GECCO’02: proceedings of the genetic and evolutionary computation conference, page 135. Morgan Kaufmann Publishers Inc., Orlando

  6. Dorigo M (2004) Ant colony optimization. MIT Press, New York

    Book  MATH  Google Scholar 

  7. Eiben AE, Smith JE (2003) Introduction to evolutionary computing. Springer, Berlin

    MATH  Google Scholar 

  8. Fleischer M (1995) Simulated annealing: past, present, and future. In: Proceedings of the 27th conference on winter simulation, pp 155–161

  9. Hu Y, Jing T, Hong X, Feng Z, Hu X, Yan G (2004) An efficient rectilinear Steiner minimum tree algorithm based on ant colony optimization. In: IEEE ICCCAS. IEEE Computer Society Press, Los Alamitos, pp 1276–1280

  10. Hwang F, Richards D, Winter P (1992) The steiner tree problem. North-Holland

  11. Ivanov A, Tuzhelin A (1994) Minimal networks: the steiner problem and its generalizations. CRC Press, Cleveland

    MATH  Google Scholar 

  12. De Jong KA (2006) Evolutionary computation: a unified approach. MIT Press, New York

    MATH  Google Scholar 

  13. Kahng AB, Robins G (1995) On optimal interconnections for VLSI. Kluwer Publishers, Boston

    MATH  Google Scholar 

  14. Karp RM (1972) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW (eds) Complexity of computer computations. Plenum Press, New York, pp 85–103

    Google Scholar 

  15. Kirkpatrick S, Gelatt CD Jr., Vecchi MP (1983) Optimization by simulated annealing. Sci Agric 220(4598):671

    MathSciNet  Google Scholar 

  16. Koch T (2009) Steinlib testdata library. Technical report, Konrad-Zuse-Zentrum für Informationstechnik Berlin. http://steinlib.zib.de/steinlib.php

  17. Korte B, Prömel HJ, Steger S et al (1990) Steiner trees in VLSI-layouts. In: Korte B (ed) Paths, flows and VLSI-layout. Springer, Berlin

    Google Scholar 

  18. Luyet L, Varone S, Zufferey N (2007) An ant algorithm for the steiner tree problem in graphs. In: EvoWorkshops 2007 on EvoCoMnet, EvoFIN, EvoIASP, EvoINTERACTION, EvoMUSART, EvoSTOC and EvoTransLog. Springer, Berlin, pp 42–51

  19. Prossegger M, Bouchachia A (2008) Ant colony optimization for Steiner tree problems. In: 5th international conference on soft computing as transdisciplinary science and technology. ACM Press, New York, pp 331–336

  20. Rabanal P, Rodríguez I, Rubio F (2007) Using river formation dynamics to design heuristic algorithms. In: Unconventional computation, UC’07, LNCS 4618. Springer, pp 163–177

  21. Rabanal P, Rodríguez I, Rubio F (2008) Finding minimum spanning/distances trees by using river formation dynamics. In: Ant colony optimization and Swarm intelligence, ANTS’08, LNCS 5217. Springer, pp 60–71

  22. Rabanal P, Rodríguez I, Rubio F (2009) Applying river formation dynamics to solve NP-complete problems. In: Chiong R (ed) Nature-inspired algorithms for optimisation, volume 193 of studies in computational intelligence. Springer, pp 333–368

  23. Rabanal P, Rodríguez I, Rubio F (2009) A formal approach to heuristically test restorable systems. In: 6th international colloquium on theoretical aspects of computing—ICTAC 2009, LNCS 5684. Springer, pp 292–306

  24. Rabanal P, Rodríguez I, Rubio F (2010) Applying river formation dynamics to the steiner tree problem. In: International conference on cognitive informatics (ICCI’10). IEEE Computer Society Press, Calgary

  25. Robins G, Zelikovsky A (2000) Improved Steiner tree approximation in graphs. In: Eleventh annual ACM-SIAM symposium on discrete algorithms. Society for Industrial and Applied Mathematics, pp 770–779

  26. Takahashi H, Matsuyama A (1980) An approximate solution for the Steiner problem in graphs. Math Japonica 24:6

    MathSciNet  Google Scholar 

  27. Weise T, Chiong R (2009) Evolutionary approaches and their applications to distributed systems. In: Intelligent systems for automated learning and adaptation: emerging trends and applications, chap 6. pp 114–149

Download references

Acknowledgments

Research partially supported by projects TIN2009-14312-C02-01, and UCM-BSCH GR58/08—group number 910606.

Author information

Authors and Affiliations

  1. Dept. Sistemas Informáticos y Computación. Facultad de Informática, Universidad Complutense de Madrid, C/Profesor José García Santesmases, s/n, 28040, Madrid, Spain

    Pablo Rabanal, Ismael Rodríguez & Fernando Rubio

Authors
  1. Pablo Rabanal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ismael Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fernando Rubio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pablo Rabanal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rabanal, P., Rodríguez, I. & Rubio, F. Studying the application of ant colony optimization and river formation dynamics to the steiner tree problem. Evol. Intel. 4, 51–65 (2011). https://doi.org/10.1007/s12065-011-0049-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12065-011-0049-0

Keywords

Search

Navigation