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In the last few years, the p-hub maximal covering problem has been applied in a variety of applications, including the design of air transportation networks, distribution systems for perishable products, postal delivery networks, and tourism routing. In hub-based systems, disruptions at hubs or unavailability of routes significantly affect service levels and result in excessive costs; to tackle these problems; selecting (single or multiple) backup hubs for unavailable hubs and rerouting the related flows are often proposed. This study develops two bi-objective reliable single allocation p-hub maximal covering problems considering two objectives: maximizing expected covered flows and minimizing congestion. After formulating the initial non-linear models, their linearized models are presented; after proving the NP-Completeness of the developed models, the non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve them. In order to show the superior performance of the proposed NSGA-II, a well-known evolutionary algorithm, the multi-objective particle swarm optimization (MOPSO) and the epsilon constraint methods are utilized and the results are analyzed and compared. The parameters of the proposed algorithms are calibrated using the Taguchi approach. Also, a case study and some parametric analyses are done.

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