Abstract
The object under study is a combinatorial optimization problem motivated by the topological network design of communication systems, meeting reliability constraints. Specifically, we introduce the Generalized Steiner Problem with Node-Connectivity Constraints and Hostile Reliability, or GSPNCHR for short. Since the GSPNCHR belongs to the class of \(\mathcal {NP}\)-Hard problems, approximative algorithms are adequate for medium and large-sized networks. As a consequence, we develop a GRASP/VND methodology. The VND includes three local searches, that replace special elementary paths or trees, preserving feasibility. Our goal is to find a minimum-cost solution, meeting a reliability threshold, where both nodes and links may fail with given probabilities. We adapted TSPLIB benchmark in order to highlight the effectiveness of our proposal. The results suggest that our heuristic is cost-effective, providing highly-reliable networks.
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Acknowledgements
This work is partially supported by Project ANII FCE_1_2019_1_156693 Teoría y Construcción de Redes de Máxima Confiabilidad, MATHAMSUD 19-MATH-03 Rare events analysis in multi-component systems with dependent components and STIC-AMSUD ACCON Algorithms for the capacity crunch problem in optical networks.
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Laborde, S., Robledo, F., Romero, P., Viera, O. (2021). A GRASP/VND Heuristic for the Generalized Steiner Problem with Node-Connectivity Constraints and Hostile Reliability. In: Mladenovic, N., Sleptchenko, A., Sifaleras, A., Omar, M. (eds) Variable Neighborhood Search. ICVNS 2021. Lecture Notes in Computer Science(), vol 12559. Springer, Cham. https://doi.org/10.1007/978-3-030-69625-2_4
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