In the last few years, the p-hub maximal covering problem (pHMCP) has been applied in a variety of applications, including design of air traortation 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 model are presented; after proving the NP-Completeness of the developed models, a non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve it. In order to show the superior performance of the proposed NSGA-II, a well-known evolutionary algorithm, the multi-objective particle swarm optimization (MOPSO), is 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.
