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Heuristic Methods for Solving Euclidean Non-uniform Steiner Tree Problems
Ian Frommer*1, Bruce Golden2, and Guruprasad Pundoor2
1Department of Mathematics, University of Maryland, College Park, MD 20742
2R.H. Smith School of Business, University of Maryland, College Park, MD 20742
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.
*Corresponding author. Email:orbit@glue.umd.edu
LNCS 3103, p. 392 f.
lncs@springer.de
© Springer-Verlag Berlin Heidelberg 2004