A tabu search for the design of capacitated rooted survivable planar networks

Alain Hertz () and Thomas Ridremont
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Alain Hertz: Polytechnique and GERAD
Thomas Ridremont: Polytechnique and GERAD

Journal of Heuristics, 2020, vol. 26, issue 6, No 3, 829-850

Abstract: Abstract Consider a rooted directed graph G with a subset of vertices called terminals, where each arc has a positive integer capacity and a non-negative cost. For a given positive integer k, we say that G is k-survivable if every of its subgraphs obtained by removing at most k arcs admits a feasible flow that routes one unit of flow from the root to every terminal. We aim at determining a k-survivable subgraph of G of minimum total cost. We focus on the case where the input graph G is planar and propose a tabu search algorithm whose main procedure takes advantage of planar graph duality properties. In particular, we prove that it is possible to test the k-survivability of a planar graph by solving a series of shortest path problems. Experiments indicate that the proposed tabu search algorithm produces optimal solutions in a very short computing time, when these are known.

Keywords: Capacitated rooted survivable networks; Planar graphs; Tabu search (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10732-020-09453-x

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