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

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