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

Abstract

This paper examines the types of directed networks with one source and one sink. The problem of resilient network design is studied with respect to such networks. The upper and the lower bound of the capacity are given for each edge in the network, while the cost of each edge is given as the function of edge capacity. Said problem of network design consists of selecting a subset of edges in the given network, which induces an optimal subnetwork to be resilient after disruptive event. The restoration behaviour of each edge in a network N after the disruptive event is described by using a non-linear function that enables the modelling of three components affecting resilience: the remaining capacity of the edge after the disruption, the degree to which capability can be recovered and the recovery speed. Three different models for designing a resilient network are proposed and then formulated as problems of non-linear optimisation. A simple genetic algorithm using stochastic ranking, which can be used to approach all three proposed network design problems, is proposed. One numerical example is used to illustrate the proposed procedure and the effectiveness of the proposed algorithm.