Sustainable hierarchical multi-modal hub network design problem: bi-objective formulations and solution algorithms

This paper presents a bi-objective model for the design and optimization of a sustainable hierarchical multi-modal hub network. The proposed model focuses on sustainability by considering economic, environmental, and social aspects of the decisions in a hierarchical network. A case of Turkish network for freight transportation is used to validate the proposed model. To solve the small-sized problems, the augmented epsilon constraint method version 2 (AUGMECON2) is applied. It can be inferred from the Pareto-optimal set obtained by AUGMECON2 that the effect of increasing the number of hubs after a threshold is marginal. The current contribution proposes two multi-objective genetic algorithms (NSGA-II and NRGA), which incorporate LP solving and Dijkstra algorithm. The results show the superiority of NRGA compared to NSGA-II in terms of solution time. Also, we present an alternative, more efficient formulation to the problem. Based on the alternative formulation, in addition to AUGMECON2, we use two exact methods, including Torabi and Hassini (TH) method and augmented weighted Tchebycheff procedure (AWTP), to find Pareto-optimal solutions for small, medium, and large-sized problems (including the case study). The performance of the proposed solution methods is measured using some multi-objective indicators. The results show the superiority of AUGMECON2.