A multi-objective imperialist competitive algorithm to solve a new multi-modal tree hub location problem

A hub location problem is a main group of the transportation network, which is utilized as a connecting and switching point for demand between origins and destinations. Recently, a tree hub location problem has been introduced as an incomplete hub network with single assignment, in which hubs are connected by means of a tree. This paper presents a new bi-objective, multi-modal tree hub location problem with different capacity levels. Besides the location and allocation decisions in tree hub network, this model decides on transportation modes and capacity levels such that the total transportation cost and time are minimized. Additionally, a multi-objective imperialist competitive algorithm (MOICA) is proposed to solve the presented model and obtain Pareto-optimal solutions of the given problem. Finally, the performance of this algorithm is compared with a non-dominated sorting genetic algorithm (NSGA-II).