A Multi-objective Imperialist Competitive Algorithm for a Capacitated Single-allocation Hub Location Problem

In this paper, we present a novel multi-objective mathematical model for capacitated single allocation hub location problem. There are the vehicle capacity constraint and capacity restrictions amount of the incoming flow to the hub while the balancing requirements of incoming quantities of flow to the each hub is considered. Moreover, there is a set of available capacities for each potential hub, among which one can be chosen. The multiple objectives are to minimize total cost of the networks regarding minimizing maximum travel time between nodes. Due to NP-Hard property of our problem, this model is solved by a multi-objective imperialist competitive algorithm (MOICA) and finally, to prove its efficiency, the related results are compared with the results obtained by the well-known multi-objective evolutionary algorithm, called NSGA-II. The associated results confirm the efficiency and the effectiveness of our proposed MOICA to provide good solutions, especially for medium and large-sized problems.