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Evolutionary Intelligence

, Volume 4, Issue 1, pp 51–65 | Cite as

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

  • Pablo RabanalEmail author
  • Ismael Rodríguez
  • Fernando Rubio
Special Issue

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.

Keywords

River formation dynamics Steiner tree problem Heuristic algorithms NP-hard problems 

Notes

Acknowledgments

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

References

  1. 1.
    Bern M, Plassmann P (1989) The Steiner tree problem with edge lengths 1 and 2. Inform Proc Lett 32:171–176zbMATHCrossRefMathSciNetGoogle Scholar
  2. 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 4–11Google Scholar
  3. 3.
    Chiong R (ed) (2009) Nature-inspired algorithms for optimisation. Volume 193 of studies in computational intelligence. Springer, BerlinGoogle Scholar
  4. 4.
    Clementi AEF (1999) Improved non-approximability results for minimum vertex cover with density constraints. Theor Comput Sci 225:113–128zbMATHCrossRefMathSciNetGoogle Scholar
  5. 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., OrlandoGoogle Scholar
  6. 6.
    Dorigo M (2004) Ant colony optimization. MIT Press, New YorkzbMATHCrossRefGoogle Scholar
  7. 7.
    Eiben AE, Smith JE (2003) Introduction to evolutionary computing. Springer, BerlinzbMATHGoogle Scholar
  8. 8.
    Fleischer M (1995) Simulated annealing: past, present, and future. In: Proceedings of the 27th conference on winter simulation, pp 155–161Google Scholar
  9. 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 1276–1280Google Scholar
  10. 10.
    Hwang F, Richards D, Winter P (1992) The steiner tree problem. North-HollandGoogle Scholar
  11. 11.
    Ivanov A, Tuzhelin A (1994) Minimal networks: the steiner problem and its generalizations. CRC Press, ClevelandzbMATHGoogle Scholar
  12. 12.
    De Jong KA (2006) Evolutionary computation: a unified approach. MIT Press, New YorkzbMATHGoogle Scholar
  13. 13.
    Kahng AB, Robins G (1995) On optimal interconnections for VLSI. Kluwer Publishers, BostonzbMATHGoogle Scholar
  14. 14.
    Karp RM (1972) Reducibility among combinatorial problems. In: Miller RE, Thatcher JW (eds) Complexity of computer computations. Plenum Press, New York, pp 85–103Google Scholar
  15. 15.
    Kirkpatrick S, Gelatt CD Jr., Vecchi MP (1983) Optimization by simulated annealing. Sci Agric 220(4598):671MathSciNetGoogle Scholar
  16. 16.
    Koch T (2009) Steinlib testdata library. Technical report, Konrad-Zuse-Zentrum für Informationstechnik Berlin. http://steinlib.zib.de/steinlib.php
  17. 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, BerlinGoogle Scholar
  18. 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 42–51Google Scholar
  19. 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 331–336Google Scholar
  20. 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 163–177Google Scholar
  21. 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 60–71Google Scholar
  22. 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 333–368Google Scholar
  23. 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 292–306Google Scholar
  24. 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, CalgaryGoogle Scholar
  25. 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 770–779Google Scholar
  26. 26.
    Takahashi H, Matsuyama A (1980) An approximate solution for the Steiner problem in graphs. Math Japonica 24:6MathSciNetGoogle Scholar
  27. 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 114–149Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Pablo Rabanal
    • 1
    Email author
  • Ismael Rodríguez
    • 1
  • Fernando Rubio
    • 1
  1. 1.Dept. Sistemas Informáticos y Computación. Facultad de InformáticaUniversidad Complutense de MadridMadridSpain

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