In this paper we address the hub location problem in which capacity restrictions are introduced into the objective function as a penalty cost to represent their congestion effects on respective hubs. The goal of hub location problems is to locate an optimal set of hubs while minimizing sum of the transportation and opening costs under various constraints such as number of hubs, delay time and capacities of hubs. Moreover, we propose a more realistic variant of the problem where the capacities of hubs are not only a limitation in selecting the hubs. In practice, capacities of hubs are predicted by a strategic plan, but these predictions generally fail to meet the expectations due to changes in the flow in future and competitive nature of air transportation. A particle swarm optimization (PSO) is proposed to handle the complex nature of this problem and shorten the computing times. The performance of the proposed PSO is analyzed comparatively on the Australia Post (AP) data sets. The numerical results show that the proposed method can find the optimal solutions in less computation time in comparison with the earlier multiple allocation hub location models. (C) 2018 Elsevier Ltd. All rights reserved.