Abstract
This paper deals with a new heuristic for the Steiner tree problem (STP) in graphs which aims for the efficient construction of approximate solutions in very large graphs. The algorithm is based on a partitioning approach in which instances are divided into several subinstances that are small enough to be solved to optimality. A heuristic solution of the complete instance can then be constructed through the combination of the subinstances’ solutions. To this end, a new STP-specific partitioning scheme based on the concept of Voronoi diagrams is introduced. This partitioning scheme is then combined with state-of-the-art exact and heuristic methods for the STP. The implemented algorithms are also embedded into a memetic algorithm, which incorporates reduction tests, an algorithm for solution recombination and a variable neighborhood descent that uses best-performing neighborhood structures from the literature. All implemented algorithms are evaluated using previously existing benchmark instances and by using a set of new very large-scale real-world instances. The results show that our approach yields good quality solutions within relatively short time.
This work is supported by the Austrian Science Fund (FWF) under grants I892-N23 and P26755-N26.
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Leitner, M., Ljubić, I., Luipersbeck, M., Resch, M. (2014). A Partition-Based Heuristic for the Steiner Tree Problem in Large Graphs. In: Blesa, M.J., Blum, C., Voß, S. (eds) Hybrid Metaheuristics. HM 2014. Lecture Notes in Computer Science, vol 8457. Springer, Cham. https://doi.org/10.1007/978-3-319-07644-7_5
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DOI: https://doi.org/10.1007/978-3-319-07644-7_5
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