Formulations for designing robust networks. An application to wind power collection

Abstract : We are interested in the design of survivable capacitated rooted Steiner networks. Given a graph G = (V, E), capacity and cost functions on E, a root r, a subset T of V of terminals and an integer k, we search for a minimum cost subset E ⊂ E, covering T and r, such that the network induced by E is k-survivable: after the removal of any k edges, there still exists a feasible flow from r to T. We also consider the possibility of protecting a given number of edges. We propose three different formulations: a cut-set, a flow and a bi-level formulation where the second-level is a min-max problem (with an attacker and a defender). We propose algorithms for each problem formulation and compare their efficiency.
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Cédric Bentz, Marie-Christine Costa, Pierre-Louis Poirion, Thomas Ridremont. Formulations for designing robust networks. An application to wind power collection. Electronic Notes in Discrete Mathematics, Elsevier, 2018, Inernational network optimization conference 2017., 64, pp.365-374. ⟨10.1016/j.endm.2018.02.011⟩. ⟨hal-01465398⟩

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