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Heuristic Methods for Solving Euclidean Non-uniform Steiner Tree Problems

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Genetic and Evolutionary Computation – GECCO 2004 (GECCO 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3103))

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Abstract

In this paper, we consider a variation of the Euclidean Steiner Tree Problem in which the space underlying the set of nodes has a specified non-uniform cost structure. This problem is significant in many practical situations, such as laying cable networks, where the cost for laying a cable can be highly dependent on the location and the nature of the area through which it is to be laid. We empirically test the performance of a genetic-algorithm-based procedure on a variety of test cases of this problem. We also consider the impact on solutions of charging an additional fee per Steiner node. This can be important when Steiner nodes represent junctions that require the installation of additional hardware. In addition, we present novel ways of visualizing the performance and robustness of the genetic algorithm.

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References

  1. Coulston, C.: Constructing exact octagonal Steiner minimal trees. In: Proceedings of the 13th ACM Great Lakes Symposium on VLSI 2003, Washington, DC, USA, pp. 1–6. ACM, New York (2003)

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  2. Coulston, C., Smith, M., Werger, K.: Ants and evolution: The non-uniform Steiner minimal tree problem. In: Artificial Neural Networks in Engineering 2002, St. Louis, Missouri, USA, ASME, pp. 213–218 (2002)

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Ian Frommer

  2. R.H. Smith School of Business, University of Maryland, College Park, MD, 20742, USA

    Bruce Golden & Guruprasad Pundoor

Authors
  1. Ian Frommer
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  2. Bruce Golden
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  3. Guruprasad Pundoor
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Editor information

Editors and Affiliations

  1. Indian Institute of Technology Kanpur, Department of Mechanical Engineering, Kanpur Genetic Algorithms Laboratory (KanGAL), Kanpur, 208016, Uttar Pradesh, India

    Kalyanmoy Deb

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© 2004 Springer-Verlag Berlin Heidelberg

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Frommer, I., Golden, B., Pundoor, G. (2004). Heuristic Methods for Solving Euclidean Non-uniform Steiner Tree Problems. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24855-2_39

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  • DOI: https://doi.org/10.1007/978-3-540-24855-2_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22343-6

  • Online ISBN: 978-3-540-24855-2

  • eBook Packages: Springer Book Archive

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