Skip to main content
Springer Nature Link
Log in

Optimizing Least-Cost Steiner Tree in Graphs via an Encoding-Free Genetic Algorithm

  • Conference paper
  • First Online:
Advances in Swarm Intelligence (ICSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10385))

Included in the following conference series:

  • 1737 Accesses

Abstract

Most bio-inspired algorithms for solving the Steiner tree problem (STP) require the procedures of encoding and decoding. The frequent operations on both encoding and decoding inevitably result in serious time consumption and extra memory overhead, and then reduced the algorithms’ practicability. If a bio-inspired algorithm is encoding-free, its practicability will be improved. Being motivated by this thinking, this article presents an encoding-free genetic algorithm in solving the STP. To verify our proposed algorithm’s validity and investigate its performance, detailed simulations were carried out. Some insights in this article may also have significance for reference when solving the other problems related to the topological optimization.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Liu, Q., Odaka, T., Kuroiwa, J., et al.: An artificial fish swarm algorithm for the multicast routing problem. IEICE Trans. Commun. E97-B(5), 996–1011 (2014)

    Article  Google Scholar 

  2. Zhou, Z., Jiang, C., Huang, L., et al.: On optimal rectilinear shortest paths and 3-Steiner tree routing in presence of obstacles. J. Softw. 14(9), 1503–1514 (2003). (in Chinese with an English abstract)

    MathSciNet  MATH  Google Scholar 

  3. Li, Z., Shi, H.: A data-aggregation algorithm based on minimum Steiner tree in wireless sensor networks. J. Northwest. Polytech. Univ. 27(4), 558–564 (2009). (in Chinese with an English abstract)

    Google Scholar 

  4. Hwang, F.K., Richards, D.S., Winter, P.: The Steiner Tree Problem, vol. 53. Elsevier, Amsterdam (1992)

    MATH  Google Scholar 

  5. Takahashi, H., Matsuyama, A.: An approximate solution for the Steiner problem in graphs. Math. Jpn. 24(6), 573–577 (1980)

    MathSciNet  MATH  Google Scholar 

  6. Kou, L., Markowsky, G., Berman, L.: A fast algorithm for Steiner trees. Acta Informatica 15, 141–145 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  7. Rayward-Smith, V.J.: The computation of nearly minimal Steiner trees in graphs. Int. J. Math. Educ. Sci. Tech. 14(1), 15–23 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gary, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness (1979)

    Google Scholar 

  9. Plesník, J.: Worst-case relative performances of heuristics for the Steiner problem in graphs. Acta Math. Univ. Comen. LX(2), 269–284 (1991)

    MathSciNet  MATH  Google Scholar 

  10. Fan, Y., Jianjun, Yu., Fang, Z.: Hybrid genetic simulated annealing algorithm based on niching for QoS multicast routing. J. Commun. 29(5), 65–71 (2008). (in Chinese with an English abstract)

    Google Scholar 

  11. Ma, X., Liu, Q.: A particle swarm optimization for Steiner tree problem. In: Proceedings of the 6th International Conference on Natural Computation (ICNC), pp. 2561–2565 (2010)

    Google Scholar 

  12. Zhong, W.L., Huang, J., Zhang, J.: A novel particle swarm optimization for the Steiner tree problem in graphs. In: IEEE World Congress on Evolutionary Computation, pp. 2460–2467 (2008)

    Google Scholar 

  13. Ma, X., Liu, Q.: An artificial fish swarm algorithm for Steiner tree problem. In: IEEE-FUZZ, pp. 59–63 (2009)

    Google Scholar 

  14. Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Tech. J. 36(6), 1389–1401 (1957)

    Article  Google Scholar 

  15. Koza, J.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

Download references

Acknowledgements

This research is supported in part by National Science Foundation of China (No. 61502385, No. 61401354, No. 61503299), Key Basic Research Fund of Shaanxi Province (2016JQ6015), and Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 16JK1554).

Author information

Authors and Affiliations

  1. Faculty of Automation and Information Engineering, Xi’an University of Technology, Xi’an, China

    Qing Liu, Rongjun Tang, Jingyan Kang, Junliang Yao, Wenqing Wang & Yali Wu

  2. Shaanxi Key Laboratory of Complex System Control and Intelligent Information Processing, Xi’an, China

    Qing Liu, Junliang Yao, Wenqing Wang & Yali Wu

Authors
  1. Qing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rongjun Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingyan Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Junliang Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wenqing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yali Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qing Liu .

Editor information

Editors and Affiliations

  1. Peking University, Beijing, China

    Ying Tan

  2. Kyushu University, Fukuoka, Japan

    Hideyuki Takagi

  3. Southern University of Science and Technology, Shenzhen, China

    Yuhui Shi

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Liu, Q., Tang, R., Kang, J., Yao, J., Wang, W., Wu, Y. (2017). Optimizing Least-Cost Steiner Tree in Graphs via an Encoding-Free Genetic Algorithm. In: Tan, Y., Takagi, H., Shi, Y. (eds) Advances in Swarm Intelligence. ICSI 2017. Lecture Notes in Computer Science(), vol 10385. Springer, Cham. https://doi.org/10.1007/978-3-319-61824-1_42

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-61824-1_42

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61823-4

  • Online ISBN: 978-3-319-61824-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics