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Three models for resilient network design and a genetic algorithm to approach them

This paper examines the types of directed networks with one source and onesink. The problem of resilient network design is studied with respect to suchnetworks. The upper and the lower bound of the capacity are given for eachedge in the network, while the cost of each edge is given as the function of edgecapacity. Said problem of network design consists of selecting a subset of edgesin the given network, which induces an optimal subnetwork to be resilient afterdisruptive event. The restoration behaviour of each edge in a networkNafterthe disruptive event is described by using a non-linear function that enables themodelling of three components affecting resilience: the remaining capacity ofthe edge after the disruption, the degree to which capability can be recoveredand the recovery speed. Three different models for designing a resilient net-work are proposed and then formulated as problems of non-linear optimisation.A simple genetic algorithm using stochastic ranking, which can be used to ap-proach all three proposed network design problems, is proposed. One numericalexample is used to illustrate the proposed procedure and the effectiveness ofthe proposed algorithm.

flow networks ; design ; resilience ; genetic algorithm

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