Abstract
We address a variant of the classical Steiner tree problem defined over undirected graphs. The objective is to determine the Steiner tree rooted at a source node with minimum cost and such that the number of edges is less than or equal to a given threshold. The link constrained Steiner tree problem (\(\mathcal {LCSTP}\)) belongs to the NP-hard class. We formulate a Lagrangian relaxation for the \(\mathcal {LCSTP}\) in order to determine valid bounds on the optimal solution. To solve the Lagrangian dual, we develop a dual ascent heuristic based on updating one multiplier at time. The proposed heuristic relies on the execution of some sub-gradient iterations whenever the multiplier update procedure is unable to generate a significant increase of the Lagrangian dual objective. We calculate an upper bound on the \(\mathcal {LCSTP}\) by adjusting the infeasibility of the solution obtained at each iteration. The solution strategy is tested on instances inspired by the scientific literature.
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Di Puglia Pugliese, L., Gaudioso, M., Guerriero, F., Miglionico, G. (2016). An Algorithm to Find the Link Constrained Steiner Tree in Undirected Graphs. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_63
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DOI: https://doi.org/10.1007/978-3-319-42432-3_63
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