Traditionally, in hub covering problems, it is assumed that the covering radius is an exogenous parameter which cannot be controlled by the decision maker. In many real-world cases, with a negligible increase in covering radius, considerable savings in hub establishment costs are possible. On the contrary, changes in problem parameters during the planning horizon cause the results of theoretical models to be impractical in real-world situations. This article proposes a mixed integer model for a multi-period single-allocation hub set covering problem in which the covering radius is a decision variable. The proposed model is validated through a real world case study. Also, due to the NP-Hardness of the problem a modified genetic algorithm (GA) is proposed for solving that. The proposed GA benefits from a dynamic stopping criteria and immigration operator. The performance of the proposed GA is compared with the original GA and imperialist competitive algorithm (ICA). Computational results corroborated efficiency of the proposed algorithm in achieving high-quality solutions in a reasonable time.