Abstract
A generalization of the Ring Star Problem, called Two-Node-connected Star Problem (2NCSP), is here addressed. We are given an undirected graph, pendant-costs and core-costs. The goal is to find the minimum-cost spanning graph, where the core is a two-node-connected component, and the remaining nodes are pendant to this component.
First, we show that the 2NCSP belongs to the \(\mathcal {NP}\)-Hard class. Therefore, a GRASP heuristic is developed, enriched with a Variable Neighborhood Descent (VND). The neighborhood structures include exact integer linear programming models to find best paths as well as a shaking operation in order not to get stuck in a local minima.
We contrast our GRASP/VND methodology with prior works from RSP using TSPLIB, in order to highlight the effectiveness of our heuristic. Our solution outperforms several instances considered in a previous reference related to the RSP. A discussion of the results and trends for future work is provided.
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Recoba, R., Robledo, F., Romero, P., Viera, O. (2016). A GRASP/VND Heuristic for a Generalized Ring Star Problem. In: Blesa, M., et al. Hybrid Metaheuristics. HM 2016. Lecture Notes in Computer Science(), vol 9668. Springer, Cham. https://doi.org/10.1007/978-3-319-39636-1_8
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DOI: https://doi.org/10.1007/978-3-319-39636-1_8
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