A hybrid of clustering and meta-heuristic algorithms to solve a p-mobile hub location–allocation problem with the depreciation cost of hub facilities

Hubs act as intermediate points for the transfer of materials in the transportation system. In this study, a novel p-mobile hub location–allocation problem is developed. Hub facilities can be transferred to other hubs for the next period. Implementation of mobile hubs can reduce the costs of opening and closing the hubs, particularly in an environment with rapidly changing demands. On the other hand, the movement of facilities reduces lifespan and adds relevant costs. The depreciation cost and lifespan of hub facilities must be considered and the number of movements of the hub’s facilities must be assumed to be limited. Three objective functions are considered to minimize costs, noise pollutions, and the harassment caused by the establishment of a hub for people, a new objective that locates hubs in less populated areas. A multi-objective mixed-integer non-linear programming (MINLP) model is developed. To solve the proposed model, four meta-heuristic algorithms, namely multi-objective particle swarm optimization (MOPSO), a non-dominated sorting genetic algorithm (NSGA-II), a hybrid of k-medoids as a famous clustering algorithm and NSGA-II (KNSGA-II), and a hybrid of K-medoids and MOPSO (KMOPSO) are implemented. The results indicate that KNSGA-II is superior to other algorithms. Also, a case study in Iran is implemented and the related results are analyzed.